Tests

Does sending players to the offensive glass leave a team open in transition?

No, in the NBA it costs almost nothing. For every 5 points of offensive rebound rate a team adds, opponents score +0.002 points per possession after its misses (90% interval −0.007 to +0.011); the cost would have to reach +0.086 to cancel the extra rebounds. Net, each 5 points of offensive rebound rate gains +6.6 points per 100 misses (5.6 to 7.5).

664,302 missed field goals in 180 team-seasons of play-by-play, 2020-21 to 2025-26. Each team's offensive rebound rate is compared with what opponents score on the possessions after its misses, within each season; the same team compared with itself from year to year gives the same answer. The net counts the possession the opponent gets afterwards. Intervals: 90%, resampling franchises. Blind to: how many players actually crash (offensive rebound rate is an outcome, not a count), and the controls for big men and team quality are partial.

Should a coach sit a starter who picks up two early fouls?

Usually not. After a second foul in the first quarter a starter loses 3.9 game minutes against his normal (90% interval 3.8 to 4.0), and leaving him in keeps 8.5 more minutes while raising his foul-out risk from 3.5% to 10.2%. Priced in wins, leaving him in is worth +0.33 points of win probability per decision (+0.28 to +0.38), about 0.22 wins per team per season.

124,505 foul-trouble events at four trouble points (second foul in the first quarter through fifth foul in the fourth). Each starter is compared with himself in his other starts that season, at the same second of the game with fewer fouls. A simple model of when fouls arrive gives the minutes kept and the foul-out risk; the win value multiplies those minutes by the rating gap between the starter and the teammates who replace him. Intervals: 90%, resampling players; the decision-model intervals cover sampling only. Blind to: matchups, what the coach knows, and minutes coaches give back later (scaled to those, the win value is about half).

How surprising is it that LeBron never had a single 27-point, 7-rebound, 7-assist game?

Only mildly. A model built from his own 1,622 games expects 1.65 games at exactly 27/7/7 (90% interval 1.29 to 2.05), so getting none happens about 19% of the time. Across all 1,191 players with 400+ games, 25.5% never posted their own rounded career line (23.4% to 27.5%).

Regular-season games with minutes above zero, players with 400+ games and nearly complete box scores, so this covers the modern box-score era. The model (a Gaussian copula) keeps each player's own spread of points, rebounds and assists and joins them with his own correlations between them; treating the three as independent predicts too few exact lines. Lines are rounded career averages. Intervals: 90%, resampling games.

Did EPM, a leading public player rating, change its model?

Yes. Its 2025-26 values were re-issued between 7 Oct 2026 and 20 Oct 2026; for players with 500+ minutes the order barely moved (rank correlation 0.914, 90% interval 0.896 to 0.928), but the spread is 14% wider (10% to 17%). Singular's comparisons with EPM still stand, because they scored the values EPM published at the time.

Our saved copy of the table from 7 Oct 2026 against a fresh pull on 20 Oct 2026, matched player by player. Intervals: 90%, resampling players. The old season table rests on one archived copy, and past-season tables are now behind a subscription.

Is an isolation-heavy offense easier to shut down in the playoffs?

No sign of it. For the same player in the same season, isolation and pick-and-roll plays lose 0.019 points per possession less from the regular season to the playoffs than his other plays (90% interval +0.006 to +0.032). Teams that lean on those plays do no worse in playoff series than their regular-season ratings predict (−0.89 points per 100 possessions per 10 points of share, −2.33 to +0.56); the test rules out a penalty larger than about 13 points of series win probability.

NBA.com Synergy play types, 2015-16 to 2025-26: 695 player-seasons compare each player's isolation and pick-and-roll-handler plays with his other plays, adjusted for the better defenses teams meet in the playoffs. The series test was declared before any outcome was computed: 919 games in 165 series, with a play-by-play stand-in for style that extends it back to 1996-97. Intervals: 90%, resampling players (play types) and team-seasons (series). Blind to: Synergy credits a pick-and-roll to the handler only when he finishes it, so a trap that forces a pass shows up elsewhere; only good teams reach the playoffs.

Does Stop%, the share of possessions a defender ends, measure good defense?

It measures something stable, but it adds nothing to existing defensive ratings. It carries over from season to season at r = 0.88, yet it tracks defensive RAPM (a lineup-based defense rating) less well than the box-score rating DBPM (0.33 against 0.50). Added to DBPM, it changes next-season prediction error by −0.01% (90% interval −0.06% to +0.05%).

Player-seasons from 2003-04 to 2025-26; the correlations use 6,013 player-seasons with 1,000+ minutes. The out-of-sample test fits on 2003-13 and predicts next season's defensive RAPM in 2014-24. Intervals: 90%, resampling players. Blind to: shot deterrence, positional defense and switching, which box scores do not see.

Does preseason tell you anything about how a player's season will go?

Yes: a little for returning players, a lot for rookies. Tested on seasons the model never saw, preseason box scores add 0.023 to the share of variation explained (R²) in a second- or third-year player's season rating (90% interval 0.012 to 0.036), and 0.137 for rookies over draft slot and age (0.089 to 0.181). Among the top tenth of preseason-flagged risers, 71% beat their forecast, against 52% of all returning players.

Player-seasons with 60+ preseason minutes and 500+ regular-season minutes, preseasons 2005-06 to 2025-26. Each season is forecast by a model fit only on earlier seasons (walk-forward), with and without the preseason box score; the season rating is BPM (Box Plus/Minus). Intervals: 90%, resampling players. Blind to: stars resting in preseason, opponent quality and effort, and players whose bad preseason cost them their role (the minutes filter drops them).

Are high-level college shooters failing to make it in the NBA?

Not as a group. Shooters from the 2018-23 draft classes played 330 more NBA minutes in their first three seasons than other picks, both measured against what their draft slot predicts (90% interval −23 to +669). The gap did not shrink in recent classes (+198, −316 to +693), though the players the posts name are a real cluster of misses: 5 of 8 played less than their slot predicts.

Drafted players with a final college season in Jeremias Engelmann's public pre-draft data, classes 2010-25. A shooter made 38%+ of his threes on 5+ attempts per 40 minutes. Expected minutes come from a draft-slot curve; players who never played count as zero. Intervals: 90%, resampling players. Blind to: minutes measure opportunity, not quality; the 2024 and 2025 classes have one or two seasons.

Do unstable rotations hold young players back?

We found no sign of it. Rotation habits belong to the coach (with the same coach, stability carries over at r = 0.54, 90% interval 0.46 to 0.62), but for players 23 or under, one standard deviation more stability goes with −0.155 BPM of development (−0.260 to −0.059), the opposite of the claim. Donovan's six Chicago teams sat about average (−0.020 against the season mean, −0.049 to +0.007).

390 team-seasons from lineup stints, 2013-14 to 2025-26. The measure compares each rotation player's minute-by-minute on-court pattern across every pair of games: 1 means the same minutes every night, 0 means they look random. Counting coach's-decision benchings changes almost nothing. Stable seasons do go with better results beyond the roster (+0.68 points per 100 per standard deviation, +0.42 to +0.96), but nothing shows the coach causes it. Intervals: 90%, cluster bootstrap. This is observational: injured rosters make rotations unstable, and good young players earn fixed roles.

When a player's scoring role shrinks, do his rebounding and defense grow?

Mostly no, in either direction. When roster changes move a player's usage by 5 points, his defensive rebounds change by +0.08 per 36 minutes (90% interval −0.01 to +0.18) and his steals by 0.00 (−0.03 to +0.03). Fouls are the exception: they move against usage, −0.12 per 36 (−0.17 to −0.06), about equally whether usage rises or falls.

7,390 season-to-season pairs, 1998-99 to 2025-26. Usage moves for reasons outside the player's control: the scoring talent added to or lost from his roster. Rising and falling halves are tested separately. Intervals: 90%, resampling players, with a correction for testing six stats. A one-night version (teammates absent) agrees, and adds a small lineup-defense cost on those nights.

Has the league become friendlier to traditional centers?

Not over the last five seasons as a whole. At fixed box-score prices, lineups with a traditional center (6-10 or taller, few threes) gained +0.24 points per 100 possessions in 2021-26 against 2014-21 (90% interval −0.43 to +0.95), and their pay premium at equal production fell by 2.6 points of the salary cap (1.5 to 3.7). The 2025-26 season alone is the exception (interval +2.7 to +5.1); the 2026-27 season will test whether it lasts.

Lineup stints, 2008-09 to 2025-26. Each lineup's results are compared with what its players' box scores predict at fixed prices, and the traditional-center share is tested by season; the declared contrast is 2021-26 against 2014-21. Pay: salary as a share of the cap at equal past production. Intervals: 90%, resampling team-seasons. Blind to: listed heights changed measurement standard around 2019.

Does moving the ball fast (short touches, many passes) make for a better offense?

No. These habits are real team traits: touch length carries over from season to season at r = 0.63 (90% interval 0.55 to 0.69). But across 390 team-seasons, one standard deviation more passes per 100 possessions goes with −0.43 points of offensive rating (−0.75 to −0.23), with pace and last season's offense held fixed; pace itself shows nothing (+0.03, −0.26 to +0.33).

NBA.com team tracking (touches, passes, drives), 2013-14 to 2025-26, with possessions and offensive rating from box scores. Intervals: 90%, resampling franchises. The likely reason runs the other way: teams with a star creator hold the ball and score well. Six traits were tested, so one chance result is possible.

After a drive and kick-out, what should the player who catches it do?

Shoot, by a small margin, or make one patient pass. In 2015-16 tracking data, with the situation at the catch held fixed, the catch-and-shoot three beats any pass by +0.08 points per kick-out (90% interval 0.00 to +0.16, just touching zero), down from a raw gap of +0.20. A pass after one to two seconds scores about as well as the shot, or better (by +0.11, interval −0.01 to +0.24), and holding the ball longer is the worst choice (the shot beats it by +0.18, +0.03 to +0.34).

Raw SportVU tracking (player and ball positions 25 times a second) for 631 games of 2015-16. The detector was tuned on 150 games, frozen, then checked against the NBA's own drive counts (player-by-player r = 0.97). The adjusted values come from a model that sees all ten players and the ball at the catch, combined with a model of who chooses what. Intervals: 90%, resampling games. Blind to: help rotations and defender intent after the catch; points on one possession are mostly noise.

How many NBA minutes until a player's early numbers explain most of his career peak?

Many more than 1,143 on our data. Scored on players no rating weight had seen, Singular's forecast explains 36% of the variation in career peak at 1,143 minutes (90% interval 25% to 42%). It reaches half only at about 3,680 minutes (2,414 to 4,701).

1,416 players who debuted 1997-98 to 2016-17 and reached age 29. Every rating behind a test player's forecast was fitted only on seasons before his checkpoint, and the peak is scored on a scale fitted before the test players arrived. Intervals: 90%, resampling players; in 24% of resamples the forecast never reaches 0.5 by 5,000 minutes.

What did SiPM's fitted weights learn about offense and defense?

Defense leans on lineup data (lineups carry 81% of the defensive projection, 73 to 88) and offense on the box score (40%, 35 to 46): the direction DARKO's published blend takes.

Does a team built from players' prior-season SiPM ratings, at the minutes they actually played, have the net rating the ratings imply?

Adding up each player's SiPM from the season before, weighted by the minutes he went on to play, tracks the team's actual net rating closely: r = 0.81 over 540 held-out team-seasons, with a slope near 1 (0.98). The test is given the real minutes, so it checks the per-possession ratings, not a minutes forecast. Updated 2026-10-15: was r = 0.80 between minutes-weighted team SiPM and actual team net rating; slope 0.98 (r 0.79 to 0.82; slope 0.93 to 1.04 (90%, bootstrap of whole seasons)) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 540 team-seasons, regular-season stints

Does the sum of five players' SiPM forecast a lineup's net rating, and how much noise sits around it?

Across 14,274 held-out lineups with 50+ possessions each way, the sum of the five players' prior-season SiPM correlates with the lineup's net rating at r = 0.29. Average results rise steadily from about -6 to +10 per 100 across the ten forecast groups, while single lineups spread over about 36 points per 100 in every group.

Sample: 14,274 lineup-seasons, median 170 possessions

Does that result hold on other dates?

Level, not ahead. On every game day of 2025-26 (135 dates) SiPM is level with DARKO (+0.148, 90% -0.197 to +0.386 after the 2026-10-07 rerun), and level in the weekly replays of 2025-26, 2024-25 and 2023-24; also level with EPM, xRAPM and the public average.

Sample: 135 dates

Frozen on January 6, 2026, did SiPM predict the rest of 2025-26's lineups as well as the public metrics?

Level with EPM: SiPM +0.077 (two-way 90% -0.067 to +0.220) after the 2026-10-07 rerun. Not ahead.

Sample: 689 games

Frozen on January 6, 2026, did SiPM predict the rest of 2025-26's lineups as well as the public metrics?

Ahead of DARKO at a 90% interval (+0.186, two-way +0.049 to +0.322) but level at the stricter 97.5% bar (-0.015 to +0.390), after the 2026-10-07 rerun.

Sample: 689 games

Does SiPM (Singular Plus-Minus: RAPM v3 + a box model + an age curve) beat a fair baseline, the plain RAPM-and-BPM average given the same machinery?

Yes, narrowly: SiPM (rerun 2 since 2026-10-09) removes +0.025 percentage points more next-season lineup error than the fair bar (90% +0.016 to +0.034), ahead in 16 of 18 held-out seasons.

Sample: 18 held-out seasons

Does our lineup-based rating (RAPM) reproduce the best public version?

Yes. Our pooled 10-season RAPM ranks players like Engelmann's public 10-year RAPM: rank correlation 0.95 (882 players).

Sample: 882 players

How much of a player's next three seasons can public data know?

About 38% of future RAPM, tested forward in time; about 65% is predictable at all. So public data reaches about half of the knowable (57%, 48%, 50% by era since 1998, with missing futures dropped; 61% if they are filled at −2, a basis choice still open).

What does each public data layer add, era by era?

The full box score adds +11 to +15 points of future-RAPM R-squared and lineup data +5 to +6, in every era since 1998, intervals above zero.

Does SiPM's lineup-level edge show up when ranking individual players?

A tie: SiPM minus the plain RAPM-BPM average is +0.0071 in rank correlation (-0.0035 to +0.0179), below the smallest gap the test could detect (0.0164). Two seasons ahead +0.0128 (+0.0012 to +0.0251). Status changed 2026-10-15: next season is still a tie, but two seasons ahead SiPM now beats the plain average (+0.0128, +0.0012 to +0.0251, an interval that excludes zero), so the evidence is split. Updated 2026-10-15: was Spearman gap vs plain average: +0.0060 (-0.0048 to +0.0161) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 6,320 player-seasons, 1,295 players

What does each public data layer add, era by era?

Nine play-by-play measures add nothing; public tracking adds nothing measurable either.

At the top of SiPM's board, are non-creating bigs over-forecast relative to other players there?

When SiPM ranks a non-creating big in the season's top 30, his next-season impact comes in -0.36 points per 100 below the other top-30 players (-0.72 to -0.04) on current production (re-run 2026-10-10). It was -0.52 (-0.95 to -0.14) before the 2026-10-09 SiPM reruns (age term, one height standard, rim deterrence), which closed about a third of the gap. The rest of the cause is not found.

Sample: top 30: 540 rows, 82 NCB rows, 40 players

At the top of SiPM's board, are primary creators under-forecast?

Top-30 primary creators (usage and creation share in the top third) beat their SiPM forecast by +0.27 points per 100 against other top-30 players (+0.04 to +0.49); top 60 +0.17 (-0.00 to +0.34), which now touches zero. Updated 2026-10-15: was +0.28 (+0.03 to +0.52) and top 60 +0.19 (+0.01 to +0.37) before the 2026-10-09 SiPM reruns.

Sample: top 30: 540 rows, 316 creator rows

Are SiPM's walk-forward forecasts of non-creating bigs biased on next season's on-court impact?

Not supported overall. Across all non-creating-big seasons (6-9+, creation share below median) the next-season residual is -0.12 points per 100 against other players (-0.24 to +0.01).

Sample: 4,209 player-seasons, 920 players; player bootstrap 2,000

Is the NCB residual worse after a trade, a summer opening, a starter promotion or a usage/minutes jump?

Not supported. Team change +0.04 (-0.20 to +0.28), summer usage opening +0.01 (-0.23 to +0.25), starter promotion +0.18, usage +3 -0.18, minutes +6 -0.16: no difference in differences excludes zero. Updated 2026-10-15: numbers from the 2026-10-10 re-run (team change was +0.06).

Sample: 4,209 player-seasons, 920 players; player bootstrap 2,000

Do low minutes per game, or the role part of SiPM's forecast, account for the LR02 gap?

Not under the declared rule. top 60: explains -9% of the gap; slope for these bigs −0.04 (90% −0.25 to +0.16); top 30 explains 34%. Role part: top 60: explains -8% of the gap; slope for these bigs −0.07 (90% −0.23 to +0.07); top 30 explains 14%.

Sample: 1080 top-60 rows, 229 non-creating-big rows

Does rebound rate account for the LR02 gap?

Not under the declared rule. top 60: explains 52% of the gap; slope for these bigs −0.17 (90% −0.42 to +0.06); top 30 explains 1%. Across all rows, heavy rebounders outside the group are under-forecast (slope +0.09, +0.02 to +0.14): a lead that rebounds are worth different amounts by type.

Sample: 1080 top-60 rows, 229 non-creating-big rows

Does the luck/gravity increment of the lineup rating account for the LR02 gap?

Not under the declared rule. top 60: explains 1% of the gap; slope for these bigs −0.01 (90% −0.20 to +0.16); top 30 explains 3%.

Sample: 1080 top-60 rows, 229 non-creating-big rows

Is SiPM systematically wrong about high-usage players?

Not detectably. Held out over 18 seasons, high-usage players' lineups beat SiPM's forecast by +0.06 per 100 more than everyone else's (−0.07 to +0.20); with the forecast level held fixed, −0.01 (−0.14 to +0.13). SiPM's box-plus-lineup blend removes the lineup-only bias of SD02. Updated 2026-10-15: was +0.10 per 100 (high-usage minus rest) (90% player bootstrap −0.04 to +0.24) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 4,311 player-seasons, 947 players; high-usage = top 10% usage in t (469 rows)

Do lineup-based impact forecasts under-rate high-usage players' next-season on-court impact?

Held out, a forecast built only from our lineup rating (the analogue of EPM or xRAPM) left high-usage players' next-season lineups +0.29 per 100 better than forecast relative to everyone else (+0.15 to +0.43), mostly on offense (+0.25). A box-only forecast also under-forecast them (+0.21). Updated 2026-10-15: was +0.30 per 100 (high-usage minus rest, lineup-only forecast) (90% player bootstrap +0.17 to +0.44) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 4,311 player-seasons, 947 players; high-usage = top 10% usage in t (469 rows)

For high-usage players whose box and lineup ratings disagree (box higher), which one predicts next season better?

The reverse. For high-usage players whose box rating most exceeds their lineup rating, next-season lineups fell short of SiPM by −0.24 per 100 relative to other high-usage players (−0.52 to +0.03), not distinguishable from zero, and short of a box-only forecast by −0.74 (−1.03 to −0.45). The lineups were closer. Updated 2026-10-15: was SiPM residual −0.32 per 100; box-only −0.97 (90% player bootstrap −0.58 to −0.03; −1.26 to −0.64) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 162 box-over-lineup high-usage rows vs 307 other high-usage rows

Does one postseason say much about a player beyond his regular season?

Not much: one postseason's lift over his regular season is about 4% player and the rest noise, and B15's lineup test gained 0.037% of the error. But a small riser trait is detectable over careers (RI01); the earlier line 'no separate playoff skill is large enough to detect' was withdrawn.

Do some players reliably rise or fall in the playoffs?

Not across years: it holds within one playoff run (split-half 0.33) but does not repeat the next year (r 0.04, -0.01 to 0.09). Usage translation repeats weakly (r 0.17).

Sample: 1,606 rows

Is Durant's drop an isolated case?

Eight public top-100 players drop 30+ places on January 6 (Aaron Gordon, Durant, Amen Thompson, Tari Eason, Aaron Nesmith, Ja Morant, Josh Giddey, Julius Randle), and 23 do in the 2026-27 projection.

Sample: 485-player common set

Within each height bucket, what separates the best players?

Scoring leads in every bucket. Only vision's share differs: smaller for guards than wings (−0.13, 90% −0.22 to −0.01; permutation p 0.008).

Why does SiPM rank Durant about 105th when public models have him about 14th?

In 2024-25 Phoenix teammates shot +2.0 points per 100 above their usual rates with Durant on; SiPM treats that as luck and its chain carried 75% into this season. His Jan 6 lineup rating is 1.03 vs 4.21 on a plain three-season average, the biggest gap of 485 players. Without the luck adjustment he ranks 38th; without the over-35 age term as well, 12th.

Has SiPM forecast a Durant decline each preseason that his lineup results did not show?

Partly, and not lately. His lineups beat the SiPM forecast in Brooklyn (2021-22 +3.04, 2022-23 +1.18 per 100). From 2023-24 they landed on it (−0.34, +0.11, −0.03) while the forecast fell from 5.0 to 2.2. Pooled 2023-24 to 2025-26: −0.50 (−2.25 to +1.69).

Sample: Residual RAPM for every player 2008-09 to 2025-26; Durant 200 game resamples per season

Do one-season drops in defensive lineup rating by players aged 21-25 persist?

About half persists. Players aged 21-25 whose one-season defensive RAPM fell 2+ points below their two prior seasons got back 0.56 of the drop next season (+0.49 to +0.63, 167 drops); 'half or more' is not determined. Older players and rises behave the same way: plain regression to the mean.

Sample: 455 drops of 2+ points, 167 at ages 21-25; 5563 rows in the all-rows regression

After a young player's one-season defensive drop, does SiPM's walk-forward defensive forecast miss in a consistent direction?

No. In the season after a 2+ point drop, young players' lineups defended −0.04 per 100 relative to SiPM's forecast compared with other young players (−0.25 to +0.18). SiPM already expects about half to come back. Updated 2026-10-15: was Defensive miss after drops minus other young rows −0.05 per 100 (90% player bootstrap −0.26 to +0.17) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 100 drops, 1289 rows

Does scaling SiPM's defensive part by k < 1 lower its error on next season's lineups?

No. Production (k = 1) is best. Keeping 90% of the defensive part changes the held-out score by −0.0019 (−0.0038 to −0.0001); keeping 75% by −0.0114 (−0.0160 to −0.0072). A k picked walk-forward also loses (−0.0022).

Sample: 18 target seasons; dpm_v3 T2 harness reproduced exactly (0.6419) before any variant was read

Does SiPM's luck adjustment earn its place?

Dropping the luck adjustment costs clear held-out accuracy (-0.0106, -0.0141 to -0.0069; ahead in only 3 of 18 seasons), even though it would put Durant at 40th. Durant's 2024-25 bonus did not repeat. Updated 2026-10-15: was No-luck-adjustment minus current held-out score: -0.0112 (-0.0147 to -0.0074) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 18 held-out seasons

Should SiPM's luck adjustment spare the part of teammate shooting that a player causes?

Adopted into production SiPM on 2026-10-06, on top of C12. Sparing the part of teammates' shooting a player causes scores level with C12 alone held out (-0.0001, -0.0005 to +0.0002) and level on the lineup rating's own next-season test (+0.0003, -0.0006 to +0.0011). It barely moves Durant (106th to 104th of 485 on January 6; 81st to 83rd in the 2026-27 projection). Updated 2026-10-15: was Held-out score minus current: -0.0001 (-0.0004 to +0.0003) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 18 held-out seasons; 500 paired game resamples

Does fading a luck correction faster improve SiPM?

Carrying one season's luck at about 0.33 instead of 0.75 moves flagged players most toward the public ranks (Durant 106 to 90) but passes the held-out rule by a hair (-0.0011, -0.0022 to +0.00003). It is an engineering choice, not a gravity finding.

Sample: 18 held-out seasons

Does crediting defenders' effect on opponents' three-point residuals in the luck adjustment change held-out accuracy?

Letting each defender's estimated effect enter the expected rate of the threes he defends raises SiPM's held-out score: production G plus defenders minus G +0.0017 (+0.0008 to +0.0027); full joint J +0.0016 (+0.0007 to +0.0026). The offensive joint estimate alone is level (+0.0003). Ratings move little (2025-26 rank correlation 0.9994).

Sample: 18 held-out seasons; 500 paired game resamples

Do defenders' estimated effects on opponents' three-point residuals predict next season's residuals?

Adding the five defenders to the joint gravity model improves next-season prediction of three-point residuals (+0.0040, +0.0019 to +0.0062), but the defensive part does not follow players who change teams.

Sample: Walk-forward three-season windows

Do opponents' three-point residuals while a player is on defense persist for players who change teams, beyond shuffle and noise nulls?

Untested. The luck adjustment also scores opponents' threes and free throws at their expected rates, so a defender who contests well loses that credit. G spares measured gravity on offense only.

Is the opponents' shooting luck that SiPM removes from a player's defense persistent?

Mostly not. Opponents' three-point and free-throw luck with a player on court repeats year to year with r = 0.11 (0.08 to 0.15). Edwards's 2021-22 to 2024-25 mean of −1.36 per 100 is therefore worth about a tenth of that as skill. Added after seeing results.

Sample: 2,279 player pairs

Should a coach's minutes decisions inform a low-minute player's rating?

A prior from minutes, starts and bench depth scores +0.0016 against the old SiPM held out (-0.0026 to +0.0053), level, and pulls flagged low-minute bigs toward the public view (Paul Reed 45th to 104th on Jan 6). Adopted on 2026-10-05.

Sample: 18 held-out seasons

Should the age curve depend on how good a player is?

Alone it is level on accuracy (-0.0002, -0.0008 to +0.0004) and lifts Curry, Durant, Harden and LeBron, but failed one face-validity guard. Adopted together with the minutes prior (C12).

Sample: 18 held-out seasons

Should SiPM's single age curve depend on how explosive a player's game is?

None of three candidates passes the declared rule on the current SiPM (C12 plus G). The reliance term is level on next-season lineups (-0.00005 percentage points of error, 90% -0.00172 to +0.00168) but worse in the player-level test; decline signals are now level (+0.00022, -0.00014 to +0.00054). SiPM unchanged. Updated 2026-10-15: was Reliance term vs current SiPM, lineup test: +0.00029 percentage points of error removed (-0.00028 to +0.00101) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 18 seasons

Does carrying each player's lineup correction into the next season, and scoring shots at the shooter's own rate (RAPM v3), improve the rating?

Yes against 3-season xRAPM: +0.041 percentage points of next-season error removed (90%: +0.033 to +0.050), ahead in 16 of 18 held-out seasons. Since 2026-10-06 the luck adjustment spares measured gravity (variant G), +0.0003 over the luck-only version. Updated 2026-10-15: was +0.036 percentage points of next-season error removed (+0.028 to +0.045) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Which public-data rating best predicts next season's lineups?

Three-season RAPM with a box-score prior (xRAPM) removes the most error: 0.590% of a no-player baseline, against 0.520% for 3-season RAPM and 0.503% for BPM (28 seasons, each predicted forward).

Sample: 28 seasons

Do some players beat (or miss) their forecasts year after year?

Partly. Baseline efficiency misses do not repeat from season to season. SiPM's lineup misses repeat slightly, mostly among stars (Curry and Kawhi most under-forecast). A correction built on each player's past misses does not improve held-out forecasts. Durant: no decline-that-never-came lately (DD05). Updated 2026-10-15: was SiPM lag-1 r of player misses 0.052; stars 0.19 (0.020 to 0.083; 0.08 to 0.29 (stars)) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 6,525 baseline rows / 1,288 players

Do SiPM's lineup forecast errors repeat for the same player?

Slightly: lag-1 r 0.050 (0.018 to 0.080), above the permutation null; stars 0.17 (0.06 to 0.27) with a mean miss of +0.33 per 100 (0.10 to 0.52). Curry and Kawhi are the most persistently under-forecast, but no single player's mean is beyond 2 standard errors. Updated 2026-10-15: was Lag-1 r 0.052; player share 3.8% (null 95th pct 1.9%); stars lag-1 r 0.19 (0.020 to 0.083; 0.08 to 0.29 (stars)) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: Residual RAPM; permutation null

Does the gap between SiPM's box part and lineup part predict its next miss?

Players whose box part exceeds their lineup part keep falling short of SiPM; the reverse keep beating it. Each SD of the gap moves the next miss by -0.10 points per 100 (-0.14 to -0.06). Held out (added after the declared results), the gap alone cuts error by 0.41%.

Sample: 4,311 player-seasons, 947 players

If injury seasons are removed, do the same players stay persistently under- or over-forecast?

Mostly not. The named under-forecast players (Curry, Leonard, Hill, Embiid) beat the forecast in injury seasons too, and removing the injury effect makes their misses larger. On clean seasons alone the stable player share is 2.8% (shuffle null 95th percentile 3.3%, p 0.082); player means correlate 0.821 with the all-season means.

Sample: 4,311 player-seasons, 947 players

Do traits, draft, gravity, injury history and the box-lineup gap together explain the persistent part?

Mixed. All tested inputs together cut the stable player share (from 3.2% to 2.1%), but do not improve held-out error: MSE gain -0.0178 (-0.0384 to 0.0004), now not distinguishable from zero.

Sample: 3,618 scored player-seasons

Does the box score over- or under-translate into lineup impact for particular box profiles?

The declared block (gap plus gap x five traits) does not help held out: gain -0.0018 (-0.0153 to 0.0096).

Sample: 3,618 scored player-seasons

Are players whose box value comes from assists, steals and rebounds rather than points over-forecast?

Not supported. A non-scoring box index (mean z of assists, steals and defensive rebounds, minus z of points) has slope +0.034 on the next miss (-0.009 to +0.080), the wrong sign if anything. Rondo fits the profile; Marion and Calderon only moderately.

Sample: 4,311 player-seasons, 947 players

Do players whose teammates shoot above their norms keep beating SiPM?

Not supported. The teammate three-point residual while he is on offense (3-season mean) has an in-sample slope of -0.052 (-0.089 to -0.013), the wrong sign, and does not help held out (gain -0.0011).

Sample: 3,618 scored player-seasons

Does a player-level correction improve forecasts?

It does not. SiPM, all players: 0.41% of error removed (-0.06 to 0.89%). The star-only variant (added after results) now finds no stable star component in earlier seasons and makes no correction (0.00%).

Sample: 3,618 SiPM rows

Do an opponent adjustment or strictly walk-forward priors change SiPM?

No. Opponent adjustment −0.001 (−0.002 to +0.001); strictly walk-forward priors 0.000 (−0.001 to +0.001).

Can a minutes model beat "same minutes as last season"?

Yes: error 5.5 vs 6.1 minutes a game; against a fitted line on last season's minutes −0.25 (−0.29 to −0.21, earlier run). The 2026-27 projection's top three: Gilgeous-Alexander, Jokić, Wembanyama.

Does the year-to-year reliability of SiPM's lineup part differ for non-creating bigs?

Not the cause. Non-creating bigs' one-season RAPM does repeat less (0.31 vs 0.42; difference −0.19 to −0.04), but their forecast misses do not grow with the lineup part of the forecast (top 60: explains -3% of the gap; slope for these bigs −0.03 (90% −0.35 to +0.20); top 30 explains 21%).

Sample: 1080 top-60 rows, 229 non-creating-big rows

Does a player's playoff-minus-regular-season box production repeat across his postseasons?

Yes, but small. The playoff lift in Game Score per 75 has a between-player spread of 0.55 (0.38 to 0.67); the regular-season spread is 3.83. One postseason is about 4% signal.

Sample: 3782 player-postseasons, 1061 players; 1924 consecutive pairs

Does the lineup-based playoff lift repeat?

Mixed: net lift repeats weakly (r +0.079, +0.034 to +0.121), but neither offense (+0.026) nor defense (-0.013) repeats alone.

Sample: 2696 player-postseasons

Does the sum of prior-season SiPM defensive ratings under-predict points allowed by lineups with primary creators?

Yes, about 0.3-0.5 per 100 per handler: 1 handler +0.51 (+0.21 to +0.82), 2+ +0.80 (+0.44 to +1.16) beyond the rating sum, against lineups with none. Held out, adding handler counts does not improve prediction. Updated 2026-10-15: was 1 handler +0.48, 2+ handlers +0.75 points allowed per 100 beyond the rating sum (vs 0 handlers) (90% team-season bootstrap +0.18 to +0.78; +0.38 to +1.11) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 1,190,442 defensive stints, 4,201,860 possessions, 540 team-seasons

Fitted on our game logs, do per-stat half-lives follow the order Kostya (How DARKO Forgets) reports?

Yes. Next-game half-lives: starting 2.3 days, minutes 7.9, usage 62, 3PA per 36 68, FT% 301, rim % 445, 3P% 1225. Rank correlation with Kostya's eight: 0.95.

Sample: 736,297 player-games 1996-97 to 2025-26; as-of games 2001-02 on

Does the best half-life change when the target moves from the next game to the rest of the season to next season?

Yes. Starting: 2.3 days for the next game, 66 for the rest of the season, 189 for next season. Shooting percentages barely change with the horizon.

Sample: 736,297 player-games

Out of sample, does giving each stat its own half-life beat one shared half-life?

Yes, walk-forward 2006-07 to 2025-26: +2.5% lower squared error on the next game, +3.0% on the rest of the season (22 stats). The project's in-season layer is already per-stat; refitting it adds +0.29%.

Sample: 22 stats

For next-season box-score inputs, do per-stat half-lives refit on the next-season target beat the current inputs and fixed season windows?

Yes: +2.1% lower error over 14 box stats (held out 2013-14 to 2024-25), +5.9% vs the 1/0.75/0.5 season window, +1.6% vs production FT% and 3P%.

Sample: fit on season ends 2001-02 to 2012-13, test 2013-14 to 2024-25 (5,060 rows for points)

Does rebuilding SiPM's box component with the next-season per-stat half-lives improve dpm_v3's T2 test?

Yes: +0.0035 points of lineup error removed (12 of 18 seasons); +0.0042 with FT% and 3P% too. Adopted into production SiPM on 2026-10-07 (variant NP, with the injury clock; SP08).

Sample: Held-out targets 2008-09 to 2025-26 (18 seasons)

Is the SiPM gain from the horizon or from per-stat memory?

Not distinguishable from zero: +0.0012 (-0.0001 to +0.0026); -0.0001 on targets from 2014-15. Per-stat beats shared by +0.0023.

Sample: Held-out targets 2008-09 to 2025-26

On the first games after long absences, does darko_lite's Kalman filter beat its decay layer by more than usual?

Yes: after 250+ days out, the Kalman filter's next-10-game error is 11% below the decay layer's, against 0.4% on other games. The decay layer pulls a returning player toward the league average.

Sample: 917 games, 14 box stats

Does a decay layer with a player-level prior after long absences improve post-return forecasts and SiPM?

Mixed. Replacing the league prior with the player's own level after a return helps after 41+ games out (-5.6% reducible error) but hurts after shorter absences (+0.6%) and nudges the SiPM box rating the wrong way. Not adopted; the clock rule (LY09) does better.

Sample: Test window 1,399 returns by 462 players (104 after 41+ games out, 26 after 82+)

Does a team's preseason net rating improve the project's preseason SiPM forecast of its regular-season net rating, out of sample?

Walk-forward over 480 team-seasons (2010-11..2025-26), adding shrunk preseason net to the feasible SiPM roster forecast cuts squared error by 0.98 (R-squared 0.485 to 0.527); better in 12 of 16 seasons.

Sample: 480 team-seasons; NBA.com preseason logs. Era check: LC-AGE-2005 (2006): Per 100 possessions and centred per season; not otherwise relevant; LC-LOCKOUT-2011 (2011): 2 preseason games: kept, shrinkage gives them little weight; ST-T03 (2012): Per 100 possessions and centred per season; not otherwise relevant; LC-B2B-2015 (2015): Regular-season schedule only: not relevant to preseason games; LC-CAP-2016 (2016): Per 100 possessions and centred per season; not otherwise relevant; ST-T15 (2016): Per 100 possessions and centred per season; not otherwise relevant; LC-TO-2017 (2017): Per 100 possessions and centred per season; not otherwise relevant; LC-REST-2017 (2017): Starters sit more: F3 weights games by regulars' minutes share; LC-SCHED-2017 (2017): Preseason shortened (earlier start): reliability shrinkage + F3 x post-2017 interaction; LC-CBA-2017 (2017): Per 100 possessions and centred per season; not otherwise relevant; ST-T10 (2017): Load management: same as LC-REST-2017; LC-1819-RULES (2018): Per 100 possessions and centred per season; not otherwise relevant; LC-BUBBLE-2019 (2019): Preseason of 2019-20 played normally (Oct. 2019): kept; LC-RESTLABEL-2019 (2019): Data labels only: not used; LC-72G-2020 (2020): Short preseason (Dec. start): kept, shrinkage; LC-TAKE-2022 (2022): Per 100 possessions and centred per season; not otherwise relevant; ST-T11F (2022): Per 100 possessions and centred per season; not otherwise relevant; LC-CUP-2023 (2023): Per 100 possessions and centred per season; not otherwise relevant; LC-PPP-2023 (2023): Regular-season participation rule: may raise star minutes in RS, not preseason; not modelled; LC-CBA-2023 (2023): Per 100 possessions and centred per season; not otherwise relevant

Do Kostya's preseason correlations replicate on our seasons?

On NBA.com logs 2005-06..2025-26, preseason net correlates 0.34 with regular-season net (Kostya: 0.32); R-squared rises 0.354 to 0.407 when added to last season's net (Kostya: 0.27 to 0.35).

Sample: 630 team-seasons

Because starters sit in preseason, do games with more regulars' minutes carry more signal?

Head to head, regulars-weighted preseason net (F3) against raw net (F1): MSE change -0.04, not distinguishable from zero; regulars' plus-minus (F4) scored no better.

Sample: 480 team-seasons; regulars = top 8 by forecast minutes; regulars played 55% of preseason minutes

How much of the SiPM team forecast's error comes from not knowing minutes?

Giving SiPM the real minutes instead of last season's cuts squared error by 4.16, about 4 times what preseason net adds. Feasible SiPM r = 0.69; real minutes r = 0.81.

Sample: 480 team-seasons

Does Kostya's recursion (box prior -> RAPM -> refit box to that RAPM -> repeat) beat the project's one-step box prior on held-out next-season lineups?

No. After 10 rounds the production lineup rating predicts next season's lineups worse than round 1 (the current one-step prior): difference -0.086 (90% -0.111 to -0.062 over seasons); one-season rating -0.096.

Sample: 18 held-out target seasons

Is ridge toward zero the wrong prior for RAPM?

Yes, by a wide margin: the one-season rating with a walk-forward box prior removes +0.148 more next-season lineup error than plain RAPM (+0.133 to +0.163); the production chain +0.197. Ahead in 18 of 18 seasons. Kostya's first point; the project has used it since xRAPM.

Sample: 18 held-out target seasons

Does swapping V3 for the recursive version improve SiPM on its declared test?

No. SiPM refit with the round-10 lineup part scores 0.023 below SiPM held out (-0.030 to -0.017); with round 2 (added afterwards) -0.007 (-0.011 to -0.003).

Sample: 18 held-out target seasons

Is there a useful early stop in the recursion?

Narrowly, for the one-season rating only: round 2 minus round 1 +0.007 (+0.001 to +0.013 over seasons; +0.010 with a learned scale). The production chain gains nothing (-0.001), and SiPM loses with it.

Sample: 18 held-out target seasons

Does the recursion change the LR02 residual?

No, it widens it: top-60 gap -0.11 (-0.22 to -0.01 over seasons), top-30 -0.09 (-0.25 to +0.06); more non-creating bigs reach the top 30 (82 to 110 rows).

Sample: 4,209 player-seasons, targets 2008-09 to 2025-26

Does the recursion change how SiPM grades primary creators' defense, and does next season agree?

No, it lowers the grade further: primary creators' defensive rating minus everyone else's moves -0.29 (-0.32 to -0.27), and their lineups then defend +0.05 better than the new grade says (+0.04 to +0.06).

Sample: 1,073 primary-creator rows of 4,209

Is the LR02 gap larger in recent seasons, and do season-specific type values shrink it?

No. The top-60 gap is the same in every era (2021-26 minus 2014-21 −0.12, −0.63 to +0.36), and the season-to-season part of the type's lineup miss explains −9% of it (−47 to +20%).

Sample: 1,080 top-60 rows, 229 non-creating-big rows

Holding each player's SiPM forecast fixed, do lineups with LR02's non-creating bigs beat or miss the forecast, season by season?

Yes at the lineup level: lineups with last season's non-creating bigs fall short of SiPM's forecast by −0.36 per 100 per such big (−0.59 to −0.15). Removing it closes LR02's top-60 gap (+93% explained, overstated). Player-level LR02 found no type-wide miss (−0.06). Updated 2026-10-15: was −0.57 points per 100 per non-creating big on the floor (18-season mean) (−0.80 to −0.35 (90%, team-season bootstrap)) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 1,314,446 stint sides; 10.9% of player slots unrated (nuisance counts)

Over ordinary offseasons, does the calendar-day decay over- or under-forget?

Yes: the best clock speed across a healthy offseason gap is 1.25, the opposite of injury absences.

Sample: 5,696 season openers, 1327 players

Do the two approved box-input changes, together, beat production SiPM on the declared held-out test, and do their gains add?

Yes: SiPM with each box stat's memory fitted for next season (FT% and 3P% included) and old games aging at about 0.6 of calendar speed during 41+ game injury absences removes +0.0044 more next-season lineup error than the previous production SiPM (90% +0.0030 to +0.0057), ahead in 14 of 18 held-out seasons. Nearly all of the gain is the memory change; the clock adds +0.0001 (not distinguishable). Adopted 2026-10-07.

Sample: 18 held-out seasons of lineup stints

With LR02's rows and CV06's lineup data in one model (unshrunk group terms, shrunk players), how large is SiPM's miss on non-creating bigs?

Held on the 2026-10-08 production: -0.42 (-0.72 to -0.14) points per 100 over LR02's rows. On current production (re-run 2026-10-10) it is -0.20 (-0.50 to +0.08), which includes zero. The SiPM reruns of 2026-10-09 (age term, one height standard, rim deterrence) closed about half of the over-forecast; LR02's top-30 version still holds at -0.36 (-0.72 to -0.04).

Sample: 4,209 player-seasons (852 NCB, 947 players); 18 seasons of stints, 540 team-season clusters

Is the non-creating-big miss concentrated at the top of SiPM's board?

No: top-60 NCBs minus other 1,000-minute NCBs −0.17 (−0.65 to +0.20) at the lineup level. LR02's larger top-of-board gap comes from the comparison group: top-60 players who are not NCBs beat their forecasts by +0.34 (+0.12 to +0.59). Updated 2026-10-15: was −0.11 and +0.27 before the 2026-10-09 SiPM reruns.

Sample: 4,209 player-seasons (852 NCB, 947 players); 18 seasons of stints, 540 team-season clusters

Is the NCB miss concentrated in lineups without a star creator, or in NCBs who lost the creator they played with?

No, once each NCB is compared with other role players in the same context: star kept and on the floor −0.22 (−0.64 to +0.17), star kept but sitting −0.37 (−0.84 to +0.16), star gone −0.49 (−1.30 to +0.13), no star −0.52 (−0.92 to −0.15). Unmatched, NCB lineups without a star looked worse; every role player shares that. Updated 2026-10-15: was −0.47, −0.66, −0.58 and −0.75 before the 2026-10-09 SiPM reruns; the first two intervals now include zero (status question already open from the 2026-10-10 audit).

Sample: 4,209 player-seasons (852 NCB, 947 players); 18 seasons of stints, 540 team-season clusters

Do non-additive lineup features built from last season's box lines account for the NCB lineup miss?

No. Adding each lineup feature (applied to every lineup) leaves the NCB miss in place: M1 explains 6%; M2 explains 5%; M3 explains -2%; M4 explains -11%; all explains -2%. Updated 2026-10-15: was all four together explain -4% of the NCB miss (-25% to 20% (90%)) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 4,209 player-seasons (852 NCB, 947 players); 18 seasons of stints, 540 team-season clusters

Does the NCB miss depend on age in the target season?

Lead: NCB minus other survivors of the same age −0.68 (−1.04 to −0.35) at 25 or under, −0.35 at 26-29, −0.11 at 30+. Updated 2026-10-15: was −1.07, −0.31 and −0.38 before the 2026-10-09 SiPM reruns.

Sample: 4,209 player-seasons (852 NCB, 947 players); 18 seasons of stints, 540 team-season clusters

Does a skill-profile age curve improve held-out lineup error and shrink the non-creating-big miss?

Partly. Role plus reliance age curves (AB, adopted 2026-10-08) cut the young-NCB miss from -1.05 to -0.60 per 100 (-0.93 to -0.30 (90%)) and are level on held-out lineups (-0.13 per 1,000, -1.82 to +1.75 (90%)). What is left sits in 2008-13 targets; 2021-25 +0.08 (-0.45 to +0.67 (90%)).

Sample: T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons (1,312 players) next season; 4,365 three-season windows. Profiles 2007-25 (250+ min): NCB 1906, CRE 1441, OBG 407, REST 3938.

Is the NCB miss in the box layer or the lineup layer of SiPM (LR13's question, as a split)?

Box part above lineup part: NCB minus matched others −0.50 (−0.84 to −0.18); lineup part above box part: −0.15 (−0.50 to +0.11), not distinguishable from zero. Updated 2026-10-15: was −0.69 and −0.38 before the 2026-10-09 SiPM reruns.

Sample: 4,209 player-seasons (852 NCB, 947 players); 18 seasons of stints, 540 team-season clusters

Is CV06's lineup miss the 1,000-minute filter LR02 applies (survivors) rather than a type miss?

No. Players who fall below 1,000 minutes miss their forecasts badly, but NCBs who do miss no more than other players who do (+0.30 (−0.12 to +0.72)). Updated 2026-10-15: was +0.14 before the 2026-10-09 SiPM reruns.

Sample: 4,209 player-seasons (852 NCB, 947 players); 18 seasons of stints, 540 team-season clusters

Do profile age terms reduce error against next-season and three-season RAPM for every player?

Yes, on offense: role plus reliance curves (AB) cut next-season error -0.44% and three-season error -1.36%; the shipped pipeline reproduces both.

Sample: T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons (1,312 players) next season; 4,365 three-season windows. Profiles 2007-25 (250+ min): NCB 1906, CRE 1441, OBG 407, REST 3938.

Is SiPM's NCB miss confined to young ages?

Calibrated next-season miss on NCBs by age band: -0.63 / -0.41 / -0.38 / -0.34 / -0.27 per 100 (22 or under to 33+), including 26-29.

Sample: T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons (1,312 players) next season; 4,365 three-season windows. Profiles 2007-25 (250+ min): NCB 1906, CRE 1441, OBG 407, REST 3938.

Does an additive role + reliance curve keep the reliance version's player gains and the role version's young-big cut?

Yes. AB matches LB's player gains (next season -0.09% vs LB, -0.34 to +0.14 (90%)) and LA's young-big cut (gap change vs LB +0.39, vs LA +0.01).

Sample: T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons (1,312 players) next season; 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples.

Do role x reliance cell terms (shrunk toward role + reliance) beat the additive version?

No. ABX is worse than AB on held-out lineups (-4.87 per 1,000, -7.19 to -2.49 (90%)) and on defense at the player level; shrinkage toward the parents does not save it.

Sample: T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons (1,312 players) next season; 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples.

Do the test's gains survive the production code path?

Yes. With AB wired into dpm_v3 (Revision 6), the shipped forecasts give next-season player error -0.44% (-0.80 to -0.10 (90%)) and three-season -1.36%, matching the test; the switch-off mode reproduces the old SiPM exactly.

Sample: T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons (1,312 players) next season; 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. Per-player shipped vs test forecasts on 9,097 player-seasons.

Does letting the box part's weights on rebounds, blocks and interior scoring drift with the era (trailing window or trend terms, walk-forward) shrink the 2008-13 young-NCB gap and the 26-29 NCB miss?

No. Drifting box prices barely move SiPM's young-NCB miss: -0.60 now, -0.57 with random-walk prices (change +0.03); the 2008-13 miss stays at -1.59 and the 26-29 miss at -0.34.

Sample: Box: 11,929 player-seasons 2002-25. T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons next season, 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. Drift description: 14,569 player-seasons, 2,859 players, 300 player resamples.

Do the weights of SiPM's box model (fitted pooled across seasons) differ by 5-season window, and does the pooled price mis-value player types?

Yes, in sample. Assists lost offensive value after 2015, height lost value, offensive rebounds cost less on defense; at the pooled price young NCBs' box line is over-valued by 0.55 per 100 in 2011-15 and 0.52 in 2016-20.

Sample: Box: 11,929 player-seasons 2002-25. T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons next season, 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. Drift description: 14,569 player-seasons, 2,859 players, 300 player resamples.

Does pricing each season's box line at a trailing-window price, shrunk toward the pooled price with a walk-forward chosen pull, beat SiPM's pooled box prices?

No on lineups: held-out lineup error worse (-2.93 per 1,000, -4.36 to -1.33 (90%)), in 2014-25. The box fit improves (-6.7%) and next-season player error improves (-0.39% (-0.67 to -0.11 (90%))), offense only.

Sample: Box: 11,929 player-seasons 2002-25. T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons next season, 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. Drift description: 14,569 player-seasons, 2,859 players, 300 player resamples.

Does a Kalman random walk on the box prices (speed chosen walk-forward) beat SiPM's pooled box prices?

No on lineups: held-out lineup error worse (-3.80 per 1,000, -6.04 to -1.61 (90%)), in 2014-25. The box fit improves (-9.5%) and next-season player error improves (-0.57% (-0.93 to -0.19 (90%))), offense only.

Sample: Box: 11,929 player-seasons 2002-25. T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons next season, 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. Drift description: 14,569 player-seasons, 2,859 players, 300 player resamples.

Does rescaling the 16 rate stats within each season, with pooled prices, beat SiPM's raw per-36 box inputs?

Mixed. Held-out lineups level (+0.95 per 1,000, -0.89 to +2.69 (90%)); next-season player error better (-0.47% (-0.84 to -0.09 (90%))); three seasons level (-0.52% (-1.37 to +0.32 (90%))).

Sample: Box: 11,929 player-seasons 2002-25. T2: 18 held-out target seasons of stints. Player level: 6,458 player-seasons next season, 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. Drift description: 14,569 player-seasons, 2,859 players, 300 player resamples.

Does choosing the drift speed by walk-forward lineup error (or using a fixed-penalty RAPM target) turn the player-level gain into a lineup gain?

No. Tuning the drift speed on lineup error removes most of LR30's lineup loss but not all of it: -0.87 per 1,000 (-2.14 to +0.44 (90%)). Every fixed drift speed above zero is worse on lineups; the player gain shrinks to -0.28% (-0.44 to -0.10 (90%)).

Sample: T2: 18 held-out target seasons of stints; lineup-tuned selection over target seasons 1999..s-1. Player level: 6,458 player-seasons next season, 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. RAPM refit: 30 seasons x 2 penalties.

Does the 2008-13 young-NCB miss shrink when V3's prior or the minutes-selection of young bigs is modelled?

No. V3's prior carries the 2008-13 miss but changing it (age, a 5-season window, one height standard) moves the 2008-13 gap by at most +0.03; the miss holds whether minutes rose (-1.58) or fell (-1.37). A quarter is the back-test learning late.

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Does the 2008-13 young-NCB gap shrink when the same model is forecast with weights fitted on every season instead of walk-forward weights?

Yes, a quarter. Refitting SiPM's layer on every season cuts the 2008-13 gap from -1.60 to -1.18; in 1999-2007 it removes the whole miss (-0.78 to -0.03).

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Does adding on-floor opponent rim frequency and accuracy to SiPM's inputs move the 2008-13 young-NCB defensive gap toward zero?

No. A play-by-play rim input (make effect, deterrence, blocks and shooting fouls per opponent rim attempt) added to SiPM's defensive box model moves the 2008-13 young-NCB defensive gap from -0.98 to -1.00. It improves SiPM for everyone instead (LR30f10c).

Sample: Rim shots 1996-97 to 2025-26 placed in lineup stints; tracking check 2013-14 to 2025-26 (6,942 player-seasons); T2 18 held-out seasons, 500 game and 500 team resamples; PL1 1,000 player resamples; young-big measure 400 team-season resamples.

Fitted on each season's own lineups, how far is V3's prior (walk-forward box prices plus carried correction) off for young NCBs?

Yes in the seasons behind 2008-13 forecasts: -1.31 net, -0.80 on defense; V3 keeps -0.55 after that season's lineups. Small or positive in other eras.

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Does the 2008-13 young-NCB gap sit with young bigs whose minutes rose, with dropouts, with a few players or with a lineup context?

No. The 2008-13 miss holds whether minutes rose (-1.58) or fell (-1.37), at any experience and with or without another big; it is spread across 126 players.

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Does the young-NCB gap vary with league style across seasons, and with team or opponent style within a season?

No. Over 2008-25 the per-season gap tracks every league trend, but with a consistent forecaster over 1999-2025 the link vanishes (three-point share implies -0.18 of an observed -1.06); within-season team style is level.

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Which side of the young-NCB comparison moves in 2008-13: young NCBs falling short or young others beating forecasts?

Partly. Against players aged 26-29, in 2008-13 young NCBs fall short by -0.90 (defense -0.78) and other young players come in +0.70 above (offense +0.50). Added after the first run.

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Does SiPM with VH (see page section 4) beat production on held-out next-season lineups (T2)?

Yes: T2 +1.33 per 1,000 (+1.10 to +1.55 (90%)), better, ahead in 15 of 18 seasons. It does not fix the young-big miss.

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Does SiPM with VA (see page section 4) beat production on held-out next-season lineups (T2)?

Yes: T2 +0.72 per 1,000 (+0.38 to +1.11 (90%)), better, ahead in 15 of 18 seasons. It does not fix the young-big miss.

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Does SiPM with VAH (see page section 4) beat production on held-out next-season lineups (T2)?

Yes: T2 +2.06 per 1,000 (+1.67 to +2.52 (90%)), better, ahead in 18 of 18 seasons. It does not fix the young-big miss.

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Does SiPM with VW (see page section 4) beat production on held-out next-season lineups (T2)?

No: T2 -0.71 per 1,000 (-1.76 to +0.33 (90%)), level, ahead in 6 of 18 seasons. It does not fix the young-big miss.

Sample: Young-big measure: every regular-season stint of 18 target seasons (27 for E1 / A1 / D2), 400 team-season resamples. Young player-seasons 2008-13: 249 NCB, 580 other. T2: 18 held-out target seasons, 500 game and 500 team resamples.

Does replacing the box target's season-by-season penalty (2,000 to 2014, 2,828 from 2015/2017) with one penalty (2,000) improve SiPM?

Mixed. Lineups better (+0.45 per 1,000 (+0.21 to +0.67 (90%))), all in 2014-25; next-season player error slightly worse (+0.06% (+0.01 to +0.10 (90%))).

Sample: T2: 18 held-out target seasons of stints; lineup-tuned selection over target seasons 1999..s-1. Player level: 6,458 player-seasons next season, 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. RAPM refit: 30 seasons x 2 penalties.

On a target refitted at one penalty, does the box-fit-tuned drift slow down and stop hurting lineups?

No. On the fixed-penalty target the random walk still picks its fastest speed in 23 of 24 seasons and still hurts lineups (BRF minus B0F -2.32 per 1,000 (-4.49 to -0.26 (90%))).

Sample: T2: 18 held-out target seasons of stints; lineup-tuned selection over target seasons 1999..s-1. Player level: 6,458 player-seasons next season, 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. RAPM refit: 30 seasons x 2 penalties.

How much does the cross-validated penalty's move from 2,000 to 2,828 shrink 3-season RAPM, and what does it bias?

Yes. In the 10 changed seasons the top 30 players' 3-season RAPM is 0.886 of its one-penalty value; the spread is 1.86 / 1.39 (offense / defense) against 2.08 / 1.57. LR30's 'defensive spread fell' is this. It does not cause the young-big miss.

Sample: 30 seasons, 2 refits each

Does BSF (16 rate stats z-scored within season, pooled prices, target refitted at one penalty) beat SiPM now?

Yes on players, level on lineups. Next-season player error -0.47% (-0.84 to -0.09 (90%)); lineups +1.49 per 1,000 (-0.34 to +3.27 (90%)); three seasons level. Adoption plan drafted, not applied.

Sample: T2: 18 held-out target seasons of stints; lineup-tuned selection over target seasons 1999..s-1. Player level: 6,458 player-seasons next season, 4,365 three-season windows. Young-big measure: 18 seasons, 400 team-season resamples. RAPM refit: 30 seasons x 2 penalties.

Do young bigs allow more rim points than their blocks, rebounds and height predict, compared with bigs aged 26-29?

Yes, slightly. After the box defensive inputs, young NCBs allow +0.20 more rim points per 100 than NCBs aged 26-29 (2008-13 targets); the forecast miss on defense is about four times larger.

Sample: Rim shots 1996-97 to 2025-26 placed in lineup stints; tracking check 2013-14 to 2025-26 (6,942 player-seasons); T2 18 held-out seasons, 500 game and 500 team resamples; PL1 1,000 player resamples; young-big measure 400 team-season resamples.

Does adding play-by-play rim inputs to SiPM's defensive box model improve held-out forecasts?

Yes. Deterrence alone (RIMD) improves held-out lineup forecasts by +2.71 per 1,000 and three-season player error by -0.75%; next-season player error is level. All four inputs (RIM) are not better than deterrence alone. Adoption is Griffin's call.

Sample: Rim shots 1996-97 to 2025-26 placed in lineup stints; tracking check 2013-14 to 2025-26 (6,942 player-seasons); T2 18 held-out seasons, 500 game and 500 team resamples; PL1 1,000 player resamples; young-big measure 400 team-season resamples.

Can a box-to-lineup value model be applied to seasons before lineup data exist?

Fitted on 2011-25 and tested on 1996-2010, the box model explains 0.63 of offensive and 0.38 of defensive 3-season RAPM variance (reverse: 0.56 / 0.32). The reduced 1951-72 version keeps offense (0.62) but loses most of defense (0.24).

Sample: 14562 windows

Does a BPM-style team adjustment improve a box model of 3-season RAPM?

Adding the team's rating gap (team rating minus its players' box values) cuts held-out error of the full box model: offense 0.075, defense 0.274 (squared points per 100).

Sample: 14562 windows

Does the box-to-RAPM model over-value a player type, inflating pre-1997 players of that type?

Out of sample, the box model's error does not move with assist rate (-0.00 per SD) or steal rate (-0.00). The 100 seasons most like Stockton's prime show -0.27 (-0.79 to +0.12): a lean, not a finding.

Sample: 14562 windows, 2856 players

Is the box model calibrated at the extremes of the value scale?

The top tenth of box values beat their box value in 3-season RAPM by +0.38 per 100 (+0.13 to +0.61); the bottom tenth by +0.53. Both ends are pulled to the middle.

Sample: 14562 windows, 2856 players

Does a lineup correction learned late in a career (Stockton: ages 34-40) apply to the player's prime?

Fitted only on 2011-26 lineups, a player's correction predicts his 1996-2007 box residual with slope 1.46 (0.93 to 1.96); 1 = full carry-over. Players 33+ when it was learned: 1.51.

Sample: 276 players

Does height predict the box model's error?

Residual rises +0.08 per 100 per SD of height (3.5 inches), +0.01 to +0.15: small, and the all-time box model has no height input.

Sample: 14562 windows, 2856 players

Is the reduced pre-1973 model biased by player type?

Without steals and blocks, the reduced model's residual rises +0.47 per SD of steal rate and +0.31 per SD of box value, tested on 1996-2026.

Sample: 14562 windows, 2856 players

How sensitive is the all-time ranking to a type correction and to the lineup correction's reach?

Not robust: across type corrections and lineup-correction variants his rank runs 2-12; box only 5. Paul runs 6-12. Top-20 membership is stable (17-20 of 20 kept).

Sample: top 20 by peak score

Does production SiPM's box prior have the same top-end calibration gap?

Weaker and U-shaped: 3-season RAPM exceeds SiPM's walk-forward box prior by +0.26 (-0.02 to +0.53) per 100 in the prior's top decile (not distinguishable from zero) and by +0.54 (+0.44 to +0.66) in its bottom decile. The top-end gap sits with heavy-minute players and creators and is explained by exposure (RAPM is shrunk more for low-minute players), not a star effect. The final SiPM forecast under-rates its top decile (+0.19 (+0.02 to +0.34) next season, +0.43 (+0.08 to +0.74) three seasons) whatever the box prior.

Sample: 11,929 player-seasons

Do the three changes tested in sandboxes on 2026-10-09, together or in subsets, beat production SiPM on held-out lineups without hurting players?

Yes: SiPM with these changes removes +4.10 more per 1,000 of next-season lineup error than the previous production SiPM (90% +2.20 to +6.06), ahead in 11 of 18 held-out seasons, and changes next-season player squared error by -0.68% (-1.03 to -0.30), a gain. The lineup-rating prior part (age, heights) carries the steady lineup gain; the season-scaled box stats carry the player gain. Adopted 2026-10-09.

Sample: 18 held-out seasons of lineup stints; player tests 6,458 next-season and 4,365 three-season player-seasons; young-big measure 18 seasons

Should the single-season RAPM fit, the target of V3's box prior, also move to one penalty?

No: with V3's prior fitted on single-season RAPM at one penalty (2,000) instead of the per-season choice, SiPM's held-out lineup forecast is level or slightly worse (-0.86 per 1,000, -1.65 to +0.02) and its next-season player error is worse (+0.12% (+0.01 to +0.22)). So scripts/rapm.py keeps the cross-validated penalty for single seasons.

Sample: 18 held-out seasons; 6,458 next-season player-seasons

Is a box-score assist worth the same in lineup (RAPM) terms in every season?

A smooth trend in the value of creation stats beats a single-era box model out of sample (held-out error -0.029, -0.053 to -0.006). The net assist term rises +0.40 per 100 per unit of league-relative assist rate per decade.

Sample: 14562 windows, 2856 players

Did the illegal-defense rules (before 2001-02) change what box creation stats are worth?

A step at 2001-02 fits (net assist interaction -0.38, -0.66 to -0.09), but the 2006-11 period, under the new rules, shows the same assist slope (-0.45) as 1996-2000 (-0.47). The data show a steady drift, not a step at the rule change.

Sample: 2199 old-rule windows

Is the box model less reliable for seasons whose box profile is unlike any 1996-2026 season?

Out of sample, the excess error variance rises from 0 at the median distance (0.872) to 0.75 at distance 2.0 and 2.41 at 3.0 (per 100 squared).

Sample: 14562 windows

Does the box model flatter seasons whose profile is unlike modern ones?

Far-out seasons are, on average, under-rated, not over-rated: mean residual 2.3-2.6: +1.25 (+0.54 to +2.20); 2.6-3.0: +1.44 (-0.38 to +2.92).

Sample: 222 far-out windows

Is playoff over- or under-performance (box score) a trait?

Barely: consecutive-postseason correlation +0.05 (+0.01 to +0.09), 1943 pairs. Small playoff samples are shrunk toward the regular season with k = 687 minutes (offense).

Sample: 1943 pairs

Do playoff lineups show players who are persistently better or worse in the playoffs than in the regular season?

Pooled over 30 postseasons, cross-validation gains 0.0079% at best; the one-standard-error rule keeps penalty 4,096,000 (top of grid: True). SD of the fitted deviation 0.00 per 100.

Sample: 138141 stint rows, 1666 players

How much less certain is a pre-1973 season's value?

The 1951-72 box model's persistent error variance is 0.55 (per 100 squared) above the full model's (+0.45 to +0.67).

Sample: 14562 windows

Does the rim-deterrence input (LR30f10c) still improve SiPM after rerun 2 changed its V3 prior and box inputs?

Yes: adding rim deterrence (opponent rim attempts per 100 possessions with the player on, lineup-adjusted) to the defensive box model removes +2.53 more per 1,000 of next-season lineup error (90% +0.64 to +4.54), ahead in 12 of 18 seasons, and changes three-season player error by -0.59% (-1.02 to -0.14); next-season player error is level. Adopted 2026-10-09 (SiPM rerun 3).

Sample: 18 held-out seasons; 6,458 next-season and 4,365 three-season player-seasons

Does a monotone (isotonic or spline) calibration of the box prior against 3-season RAPM, fitted on earlier seasons only, improve held-out lineups and players?

Mixed: a smooth monotone map (linear spline, slopes kept non-negative) of the box prior improves next-season player error (-0.19% (-0.32 to -0.07)) and three-season error (-0.34% (-0.57 to -0.12)), but held-out lineups are level (-0.44 per 1,000, -1.35 to +0.48). Not adopted: the rule needs lineups and players both better.

Sample: 18 held-out seasons; player tests as SP11

Whom does SiPM agree with?

Rank agreement with the model median 0.75 vs the editorial median 0.38; models and editorial lists agree at 0.55.

Sample: 124 players; 8 public sources (4 editorial, 3 model, 1 game)

Are SiPM's divergences unusual for a model?

Mean distance from the other rankings: SiPM 0.58, DARKO 0.46, EPM 0.51, xRAPM 0.71; editorial lists 0.16 to 0.23.

Sample: 124 players; 8 public sources (4 editorial, 3 model, 1 game)

Which part of SiPM puts consensus top-40 players 20+ places lower than the public consensus?

Against the players SiPM ranks at their consensus spot, the 16 bearish stars give up −1.97 per 100 on defense (−2.40 to −1.52) and are level on offense (+0.02, −0.45 to +0.50). The lineup rating's defense carries most of it (−1.37); luck and gravity adjustments add little. Updated 2026-10-15: was Defense gap to consensus-rank peers −2.00 per 100; offense +0.19 (90% player bootstrap −2.43 to −1.59; −0.32 to +0.76) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 14 bearish stars, 23 other consensus top-40 players, 363 rated players in the universe

How does the composition of SiPM's bullish divergence list differ from the consensus top 30?

24% of SiPM's 25 bullish divergences are primary creators vs 77% of the consensus top 30 (difference -53 points, -71 to -34); non-creating bigs 40% vs 3%.

Sample: 25 and 30 players; player bootstrap

Which part of SiPM makes it disagree with public rankings?

Among the 50 largest gaps between SiPM's 2026-27 rank and the pooled consensus median, the lineup rating is the main part for 33; luck adjustment 6, age 6, box score 5, gravity 0.

Sample: 124 players; 8 public sources (4 editorial, 3 model, 1 game)

Why does SiPM rank Anthony Edwards 37th for 2026-27 when the pooled consensus has him 7th?

General finding first: SD01 (bearish stars lose on defense). Edwards is one row: SiPM ranks his offense 15th and his defense 246th of 363; with his consensus-rank peers' defense he ranks 9th. Box model and lineup rating agree on both sides. His own SiPM residuals: under-forecast in 4 of 5 seasons, but −1.39 in 2025-26.

Sample: 14 bearish stars, 23 other consensus top-40 players, 363 rated players in the universe

Where does the Wolves' 2025-26 defensive credit go, and is Edwards short-changed?

No. The Wolves' players' ratings add up to +2.36 points per 100 of credit against an actual +2.64; Gobert carries +1.69, Edwards -0.55 (luck-adjusted -0.30).

Sample: Regular-season lineup stints

When SiPM disagreed most with the preseason consensus, where did the players land?

Backtest on 2025-26: SiPM's 50 largest disagreements with the 4-outlet editorial consensus won a balanced 0.58 of calls on 2025-26 on-court impact (0.47 to 0.70): not distinguishable from a coin flip. On the crowd's own lists a year later the consensus won (0.22, 0.12 to 0.32).

Sample: 125 players in the comparison set; 50 large calls, 40 scored on on-court impact

Are SiPM's disagreements with the crowd better than a public model's?

Backtest on 2025-26: SiPM's balanced win share minus DARKO's preseason disagreements, same rule and consensus: +0.24 (+0.07 to +0.40). DARKO's own disagreements lost to the consensus (0.34, 0.23 to 0.47).

Sample: 50 large calls each; scored SiPM 40, DARKO 38; DARKO as of 2025-10-20 (data through 2025-06-22)

How far does a value-based sustained-peak ranking depart from expert lists?

Rank correlation with the NBA-Ranker seed top 100 0.78; with the published lists' median 0.73.

Sample: 880 players

Can a before-the-season forecast of each dimension of a player's season be calibrated?

Forecasting each player's efficiency, usage, creation, minutes, availability and value separately, walk-forward, its 80% ranges cover 78-84% of outcomes. Efficiency R-squared is 0.61, against 0.44 for last season alone.

Sample: About 5,900 player-seasons per dimension, walk-forward

How predictable are breakouts, and when do they happen?

The baseline expected a median 17% of an efficiency breakout and 10% of a value breakout. Value breakouts fall from about 7.2 per 100 seasons at 21 and under to 0.3 at 31 and over.

Sample: 108 efficiency, 197 value breakouts

Which knowable causes mark efficiency and value breakouts?

Young high picks (picks 1-10 in seasons 2-4) are 4.97x over-represented among impact breakouts and 3.61x among value breakouts. A new team is under-represented (0.53x and 0.36x).

Sample: 108 impact and 197 value breakouts

Were the biggest usage and creation surprises predictable from team context?

Most of the largest usage surprises had a specific cause known before the season: a star teammate left or was out at the start, the player became the top option, he returned from a lost season, or his team had a top-decile opening. 40 of the top 50 usage surprises had one, against 47% of all player-seasons.

Sample: Walk-forward baseline rows

Which knowable causes mark usage and creation breakouts?

Among one-season usage breakouts, a star teammate leaving appears 2.15x as often as in all player-seasons, promotion to top option 2.37x and a top-decile opening 2.42x. Creation breakouts show the same pattern. Descriptive tags, not causes.

Sample: 148 usage and 144 creation breakouts

Do richer role-opening inputs shrink the biggest usage and creation surprises?

Better role-opening inputs improve usage and creation forecasts slightly but remove only a few percent of each top surprise; every top-50 surprise stays outside the forecast's 80% range.

Sample: Placebo = inputs permuted within season

Does knowing what roles are open on a team help forecast a player's season?

Vacated usage and minutes improve the usage (+2.3%), creation and minutes forecasts, intervals clear of zero, and slightly worsen the efficiency forecast (-0.6%).

Sample: About 5,900 player-seasons per dimension, walk-forward

Which traits decline with age, and when?

Rim shots, dunks, fast-break shots, blocks and offensive rebounds peak at 21-24 and slide from there; shooting, passing and ball security hold until about 26-28. From 27 to 31 the explosive group falls 0.13 league spreads more than the skill group (-0.17 to -0.08).

Sample: Player-season pairs, 200 player resamples

Do skills age more slowly than explosive traits after 31?

From 31 to 35 both groups fall by about 0.18 league spreads; the gap is 0.00 (-0.08 to +0.06).

Sample: Player-season pairs, 200 player resamples

Do breakouts on different dimensions happen together?

Usage and creation break out together 12.8 times as often as chance (10.3 to 15.5); efficiency and usage 4.4 times (2.8 to 6.3). Brunson broke out on usage and creation in 2022-23, then on efficiency, usage and value in 2023-24.

Sample: 4,673 seasons eligible on three dimensions

Are staircase risers a distinct, identifiable group?

Yes, with no window cap. About 1 in 8 players beat their draft-slot path on efficiency at every draft range; 15% of plateaus are followed by a rise beyond forecast, often on another dimension; early underperformers rarely recover. Rolling outperformance is no more common than chance (TB24).

Sample: 1,135 draft-scored players; 2,184 plateaus; 223 early underperformers

Does the breakout definition catch slow-grind improvers?

Kawhi Leonard and Jimmy Butler never cross the efficiency bar in one season: their efficiency rose 2 to 2.7 points per 100 in several seasons, each below the 3.1 bar. They show up only on usage, creation, minutes and value.

After a player plateaus, how often does he rise again (climber type 2)?

Of 2,184 plateaus, 336 were followed by a rise beyond forecast (15%); in 249 the rise was on another dimension (e.g. Butler's usage after 2012-14). The chance falls from 42% (38-46%) for plateaus ending at 23 and under to 4% (3-5%) at 30+.

Sample: 2,184 plateaus, 1,173 players

How often do players beat what their draft slot implied (climber type 1)?

Draft outperformers (above the draft model's 80% range in 2+ seasons from year three): 145 of 1,135 on efficiency (13%). Late picks and top picks outperform at similar rates because the expectation is set by slot.

Sample: 1,135 players (efficiency)

How often do players rise beyond the forecast made after two seasons (climber type 5)?

351 of 1,509 players rose beyond the forecast made after their first two NBA seasons: undrafted 15%, second round 20%, first round 26% (Ingles, VanVleet, Covington). Descriptive.

Sample: 1,509 players

How common is a late peak (climber type 7)?

58 of 361 good players (16%) set their career-best impact (+2.0 or better) at 30 or older (Jokic, Stockton, Kawhi, Olajuwon, Malone). Descriptive.

Sample: 361 players

Do climbs follow a change of team (climber type 6)?

151 of 336 plateau rises (45%) came on a new team: 74 talent climbs and 77 role unlocked (e.g. role: Millsap; talent: Pau Gasol, Korver). Without a move: 110 and 75. Descriptive.

Sample: 336 rises

Do early-career underperformers catch up (climber type 3)?

Of 223 players below the draft model's 25th percentile in 2+ of their first 3 seasons, 12 recovered (5%, 3 to 8%); among those who kept playing, 11%.

Sample: 223 players

Do mid-career skill jumps lead to climbs (climber type 8)?

Of 378 skill jumps at 24 or older, 56 led to a climb within two seasons: 18% of three-point-volume jumps and 8% of FT% jumps. Brook Lopez's 2016-17 three-point jump is found, but his impact did not climb beyond forecast.

Sample: 378 skill jumps

Is rolling outperformance a real type (climber type 4)?

Not above chance: runs of seasons above the one-season forecast happen as often as when each player's seasons are shuffled (efficiency 32 vs 39 by chance). The baseline already absorbs persistent outperformance.

Do breakouts last?

Under the design's talent definition, 106 player-seasons broke out from 1997-98 to 2025-26 (about 3.7 a season), and 58 of the 106 held up the next season. A quick read-only look, no interval.

Sample: 106 breakouts

Does the precedent lookup add forecasting information beyond age?

Held out, the share of a player's 40 nearest historical precedents who broke out next season ranks players no better than the breakout rate for his age band (AUC 0.701 vs 0.708). The lookup is a reading aid, not a better forecast.

Sample: 7,356 queries, 1,358 players; breakout rate 6.7%

Used as an input rather than a replacement, does the precedent share help?

Added to age in a walk-forward logistic, the fitted precedent share raises held-out AUC by +0.018 for next-season breakouts and +0.065 for a breakout or climb within three seasons; it still adds on top of age plus the baseline.

Sample: 6,365 and 5,040 queries

Do learned similarity weights make the precedent breakout share a better forecast than age alone?

It does not. Weights learned walk-forward to predict breakouts, climbs and value changes over the next 1-3 seasons give a held-out breakout AUC of 0.695 vs 0.708 for age alone; no fitted variant beats age (best 0.711).

Sample: 7,356 queries, 1,358 players; breakout rate 6.7%

Does the fitted lookup beat the trajectory baseline at ranking who breaks out next season?

Against the declared baseline comparator (forecast turned into a probability with its spread, AUC 0.580) the fitted lookup wins, but that comparator is weak. Against a fairer baseline score added after the first run (logistic on the forecast gaps, AUC 0.697) it ties.

Sample: 7,356 queries, 1,358 players; breakout rate 6.7%

Can the lookup replace the baseline for value forecasts?

It does not. Predicting next season's change from the precedents' changes beats age alone but falls short of the baseline forecast (R² imp 0.14 vs 0.18, usg 0.11 vs 0.23, cre_pct 0.08 vs 0.18, mpg 0.23 vs 0.27, value 0.13 vs 0.18).

Sample: 4,720 queries (usage)

Does the lookup forecast development over 1-3 seasons better than age?

On its own, the fitted lookup's share of precedents with a breakout or climber event within three seasons gives held-out AUC 0.724 vs 0.663 for age; the current lookup gives 0.720. Updated 2026-10-15: was AUC 0.725 vs 0.664 (difference +0.047 to +0.075 (90% player bootstrap, 200)) before the 2026-10-05/07 re-runs; numbers refreshed from the current output.

Sample: 6,721 queries

How much of a young high pick's growth was expected from draft day?

For a top-3 pick, the baseline expected a median 54% of his breakout-sized minutes rise; for picks 31+, 30%. For efficiency and value, even top picks' breakouts were mostly unforeseen. Added after the first results.

Sample: About 5,900 player-seasons per dimension, walk-forward

Can anyone predict a late (25+) jump in three-point volume (the Brook Lopez question)?

No. Lasting jumps are rare (111 of 4,025 seasons at 25+, 2.8%), and nothing measured in advance predicts them: out-of-sample AUC 0.56 vs 0.54 for season and prior volume alone.

Sample: 4,025 seasons

Is a rookie's second-half jump real?

Mostly not: about 85% noise. Splitting his games odd and even produces almost the same spread.

Where does a departing player's share of plays go over a season?

Yes. Of the share of team plays that departing players leave, arrivals take 87.1% and the players who stay take 12.9% (11.6 to 14.2). Pre-season veteran arrivals take 47.4%, rookies 23.1%, in-season arrivals 16.6%.

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

When stayers' share of team plays rises after departures, is it a bigger role per game or more games?

Of departed plays, stayers' role growth (share of plays in the games they play) is 4.3% and their availability growth (playing more of the team's games) 8.6%.

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

When a high-usage player leaves, does his share go to the remaining players the way it does on nights he sits?

No. Held out on 2013-14 to 2025-26 departures, splitting the opening with the game-level model changes season forecast error 0.4% vs no allocation, and ranks within teams worse than the proportional split. Stayers pick up only 11% of a departure's share combined. Updated 2026-10-15: was season error 0.4% (game-level split) and -0.1% (proportional) vs drift only (-1.1 to 2.0%; -1.4 to 1.2%; stayers' combined share of the opening 8 to 13%) before the 2026-10-05 game-order fix re-run; numbers refreshed from the current output.

Sample: 1,991 test rows on 217 team-seasons with net opening 10+ points (2013-14 on)

Does a team play faster or slower (more or fewer plays per game) to absorb a departure?

No. In per-game terms the change in the team's total plays covers -0.7% of departed plays; arrivals 87.3%, stayers 13.4%.

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

Does a team-level replacement-plan signal predict how much stayers absorb on held-out seasons?

Yes. Adding the arrivals' predicted share (from prior shares and draft slots) cuts the error in predicting the stayers' role growth by 8.4% for plays and 11.0% for created baskets on 2013-14 to 2025-26.

Sample: 390 held-out team-seasons

Do stayers absorb more when the arrivals are weak relative to the opening?

Yes. When the arrivals' predicted share covers little of the opening (bottom third), stayers' role growth is 10.9% of departed plays; when it covers the opening (top third), -3.5%.

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

Do stayers absorb more when the arrivals are few?

Weakly. With 0-3 pre-season arrivals stayers' role growth is 7.3% of departed plays; with 6+, 3.0%.

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

Does the replacement-plan signal improve the hm baseline's season creation % forecast?

Yes, slightly. On established players (1,000+ minutes), adding the uncovered opening, heir and top-option-gone terms to the history-mean baseline cuts held-out error by 1.6%; the plain opening term does less.

Sample: 5,914 established rows, 9,850 all rows

Does the replacement-plan signal improve the hm baseline's season usage % forecast?

Yes, slightly. On established players (1,000+ minutes), adding the uncovered opening, heir and top-option-gone terms to the history-mean baseline cuts held-out error by 0.8%; the plain opening term does less.

Sample: 5,914 established rows, 9,850 all rows

Does team context predict which stayer gains, on held-out seasons?

No. At the player level the full model (replacement plan, heir, second option, top option gone) changes held-out error -1.1% for plays and -2.2% for creation, not distinguishable from zero; it picks the top absorber no better than the simple model.

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

How much does a role opening add to a player's usage beyond the forecast?

Only top-decile openings push usage above the forecast (+0.41, 0.23 to 0.59) and creation (+0.66). Sharing an opening in proportion to current usage over-predicts badly (usage MSE 6.19 to 47.7).

Do stayers absorb more when the departure is a star (top-1 usage) rather than a role player?

Yes. When the top option (highest role share) is not on the opening roster, stayers' role growth is 8.6% of departed plays, vs 2.4% otherwise.

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

Do Griffin's examples of stayers who exploded fit a describable pattern, or are they outliers?

Partly. Brown 2025-26, Westbrook 2016-17 and Harden 2024-25 are all heirs (the top claim after the top option left); heirs are 3.68x over-represented among the 50 largest usage jumps. But 60% of those jumps had no ex ante opening flag, and the model predicted almost none of each example's jump (z 2.09, 3.17, 2.54). Kobe 2005-06 sits only in the large-opening cell, with no top-option departure (his 2004-05 jump, after the Shaq trade, is in the 'top option stays, co-star left' cell).

Sample: 4,232 stayer rows; top 50 role-share gains

Does the stayer who becomes the top remaining option grab more of the plays?

Mixed. Heirs gain 0.9 points of team plays on average vs 0.1, but the model's heir term is not distinguishable from zero.

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

Do stayers absorb a lot when they are already the second option?

No. When the top option leaves, the former second option gains 0.5 points of team plays per game played on average, no more than the third (0.9) or lower options (0.8).

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

Do players whose games rest on skill (Durant, Curry) decline less than explosive players of the same age and level?

Not supported among players who keep playing: per SD of reliance on explosiveness, the yearly impact change is +0.002 points per 100 (-0.037 to +0.050). Among stars the gap leans Griffin's way (-0.11 a year, -0.30 to +0.07), but the interval reaches zero. Updated 2026-10-15: was Impact change per SD of explosive reliance: -0.006 points per 100 per year (-0.043 to +0.037) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 1,127 season pairs

Does SLAP-lite (frame plus combine athleticism) predict slower aging?

No reliable difference: a slower decline after 28 shows in a simple model, but not once each band and role gets its own age curve. Headline withdrawn in the critic round.

Does explosive reliance predict exits rather than decline among stayers?

58% of explosive-reliant players are gone by 33 against 50% of skill-reliant ones. Counting leavers as replacement level, each SD of explosive reliance costs -0.103 points of impact at 33 (-0.190 to -0.011). The evidence for Griffin's idea sits in who leaves, not how fast stayers decline. Updated 2026-10-15: was Impact at 33 per SD of explosive reliance, leavers at replacement: -0.092 (-0.174 to -0.004) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 696 players

Until a veteran shows tangible decline, should we assume less decline?

Players 31+ with no decline signal did not beat the age curve the next year; they did slightly worse than the rest (difference -0.101, -0.202 to -0.009). Decline signals did not improve forecasts either. Updated 2026-10-15: was No-signal minus rest, next-season result vs age curve: -0.049 (-0.139 to +0.038) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 222 no-signal vs 578 other seasons at 31+

Does a count of high-level seasons since 30 help aging forecasts?

The only signal pointing Griffin's way: +0.54% of error removed (-0.02 to +1.16), not distinguishable from zero. Players with 3+ such seasons beat the curve by +0.11 (descriptive). Not yet tested inside SiPM (Option C). Updated 2026-10-15: was Error removed by the Lindy count, ages 30+: +0.59% (-0.02 to +1.26) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 114 seasons with 3+ high-level seasons

Do season-end decline signals sharpen aging forecasts?

Adding the signals to the age curve removes -0.70% of error at 30+ (-1.36 to -0.07): no gain; the signals make the forecast slightly worse. A drop in true shooting predicts a slightly better next season, because it is mostly luck. Updated 2026-10-15: was Error removed by decline signals, ages 30+: -0.86% (-2.23 to +0.31) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: Walk-forward

When does each skill peak, and how fast does it fall?

Blocks, offensive rebounds and steals peak by 23; overall value (BPM) at 26; assists 27; 3P%, FT%, 3PA at 28 or later. After 31 the steepest falls are shot volume, free throws and true shooting.

Does the age drift of the latent level depend on career stage and pre-NBA years, not only on age?

At about 23, a second-year player (entered at 22.5) is expected to gain +0.30 impact per 100 next season; a fifth-year player of the same age is flat (0.00). Growth stops around 23-26 for early entrants and decline starts near 27.

Sample: Full-sample state-space fit

Does composition-adjusted foul-drawing skill fall less with age than raw FT rate?

About half. From 24 to 35, shooting fouls per attempt fall 30% of the league rate for the typical player, and shot mix accounts for 47% of that. Composition dominates at 24-27 (about 90%); at 31-35 the decline is mostly lost foul drawing (FT05).

Sample: 200 player bootstraps

Does FT-based explosiveness still fall with age once shot mix is fixed?

Mix-adjusted foul drawing peaks at 27 (raw FT rate at 24) and falls 0.33 league spreads from 31 to 35 (-0.44 to -0.24), about as much as raw FT rate (-0.30). So the late decline is not composition (declared H3b not supported).

Sample: 200 player bootstraps

Does the make/miss mix change the free-throw count with age?

From 31 to 35, and-ones per make fall 0.31 league spreads (-0.47 to -0.15), so free throws per shooting foul rise +0.22 (0.05 to 0.46). Raw FT rate hides part of the finishing decline. Updated 2026-10-15: was And-ones per make 31-35: -0.31 spreads; FTs per shooting foul +0.22 (-0.47 to -0.15; 0.04 to 0.46) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Are persistently missed players missed mainly early (draft) or late (aging)?

Not supported. Both top-20 groups miss by about the same amount at every age band and career stage until 34+; league-wide no age band or career stage differs from zero. Individuals differ (Hill best after 30, Rondo worst after 30).

Sample: 4,311 player-seasons, 947 players

Does being fast for one's size predict beating the model (the size-speed frontier)?

Weakly: peak speed for size vs the factor model's miss, rank correlation 0.10 (0.002 to 0.20), just above zero; speed with the ball alone is not significant. LeBron, Giannis and Durant are fastest with the ball for their size. Updated 2026-10-15: was 0.11 (0.02 to 0.20) before the 2026-10-01 re-run chain.

Sample: 328 players

Does the baseline handle injury seasons well (climber type 9)?

Not on all returners. After 41+ missed games, return-season impact runs -0.69 per 100 below the forecast and lands above the 80% range 7.2% of the time (10% expected). The 16-18% counted only returners with 1,000+ minutes, a condition on the outcome.

Sample: 2,217 returns

Is there an injury over-penalty once playing time is held equal?

Yes, slightly. Holding realized minutes equal, first seasons after 41+ missed games beat the impact forecast by +0.18 per 100. Neither injury block removes it (M1 +0.19, M2 +0.20).

Sample: 2,217 return seasons

Does weighting earlier seasons fix the over-penalty for injury-shortened seasons (TB28)?

After a season with 41+ missed games, the old baseline saw impact above its 80% range in 18.2% of return seasons (10% expected). With the history mean it is 16.2%: closer, still above 10%.

Sample: 587 return seasons with impact

Does a model of the baseline's miss on knowable inputs (cause of the short season, last healthy level, age, injury type, team need) beat the baseline on returning players?

Yes. Held out 2009-10 to 2025-26, squared error vs the baseline with M1: gp82 9.4% lower (6.4% to 12.5%); mpg 12.1% lower (8.4% to 16.1%); min82 11.2% lower (7.4% to 15.8%).

Sample: 1,634 rows (1,520 short, 114 gap), 826 players; 1,032 held out

Does a model of the baseline's miss on knowable inputs (cause of the short season, last healthy level, age, injury type, team need) beat the baseline on returning players?

Yes. Held out 2009-10 to 2025-26, squared error vs the baseline with M1: value 5.1% lower (2.8% to 7.5%); imp 4.1% lower (2.0% to 6.2%).

Sample: 1,634 rows (1,520 short, 114 gap), 826 players; 1,032 held out

Does a model of the baseline's miss on knowable inputs (cause of the short season, last healthy level, age, injury type, team need) beat the baseline on returning players?

No. Held out 2009-10 to 2025-26, squared error vs the baseline with M1: usg 1.4% lower (-0.2% to 3.2%); cre_pct 0.6% lower (-1.3% to 2.4%).

Sample: 1,634 rows (1,520 short, 114 gap), 826 players; 1,032 held out

Does a typed injury block forecast next season better than games missed alone?

Splitting games missed into injury and other absences, with a major-injury flag, an injury still running at season's end and a major injury two seasons back, cuts held-out error for role minutes (1.5%), games (3.6%), value (1.1%) and impact (0.7%); not usage or creation.

Sample: 9,850 evaluation rows; 1,043 after a major injury

Which granularity of injury category is worth carrying in a forecast?

Walk-forward: subcategory x type cuts the return-year impact error by 2.8%; location alone does not help significantly; no granularity helps games. Griffin's four groups cut minutes error 3.1% and value 2.1%.

Sample: 585 events (impact), 683 (games)

Do injury types add forecasting power beyond an overall injury effect?

No. Adding subtype terms to the overall block (M2 vs M1) improves no dimension on major-injury rows and worsens usage and creation. The Achilles term moves Achilles rows' impact residual from -1.23 to +0.07, on about 30-40 cases.

Sample: 1,043 rows (Achilles 30, ACL 64)

For gap returners (Klay Thompson 2021-22, Durant 2020-21), does propagating the latent level through the gap beat persistence?

The baseline cannot forecast a player with no minutes last season. A state-space model, which carries the hidden level through the gap with the age drift, beats "his last full season" on usage, minutes, games, value and defense (52 returns).

Sample: 52 returns (usage), 82 (games)

For gap returners, does composing value from state-space efficiency, minutes and games beat 'his last full season'?

Yes. RMSE 69.1 vs 110.0 points of value. It is no better than the state-space value forecast itself (-7.8 to 2.1).

Sample: 82 seasons

When a star's last season was short (Curry 2019-20, 5 games), does the state-space model forecast his return better?

Partly. For stars back from a short season (43 seasons) the state-space forecast still has lower RMSE than the current baseline (usage 3.87 to 3.17, creation 5.11 to 4.51), but none of the three intervals is below zero: not distinguishable from zero. Against baseline Revision 2 all three were. Value is not fixed.

Sample: 43 seasons, 38 players (usage)

Does (efficiency + 2) x minutes per game x games x pace, each from the state-space model, forecast returning stars' value better?

Not supported. Value built from its parts (efficiency + 2) x minutes per game x games x pace misses returning stars by more than the direct forecast: RMSE 119.6 vs 110.8. With state-space efficiency and minutes it ties (112.1).

Sample: 52 seasons, 42 players

Which part of value (efficiency, minutes, games, pace) carries the returning-star miss?

Yes. The spread of the miss (SD of log actual/forecast) is 0.74 for games, 0.44 for efficiency, 0.19 for minutes per game and 0.02 for pace.

Sample: 48 seasons

Are the misses on a returning star's efficiency, minutes and games correlated?

Yes. When a returning star beats his forecast on games he tends to beat it on minutes (+0.53) and efficiency (+0.43). So the product of three cautious part forecasts is too low.

Sample: 48 seasons

Can injury-driven athleticism loss be seen in public data?

Partly. Against same-age uninjured players, dunks per 36 fall in the injury season (-0.050; Achilles year 1 -0.123); rim-attempt rate does not move; free-throw rate is lower by year 2 (-0.008).

Sample: 1,892 injury events (926 major, 21+ games), 932 players

Compared with players who did not break out, did efficiency rise earlier for players who broke out on usage or creation?

Before a usage breakout, efficiency had already risen 20+ percentile points and held in 38% of cases vs 17% of eligible non-breakouts. Before creation breakouts: 34% vs 18%.

Sample: 10,228 player-seasons, 1,820 players

Within rise episodes, does efficiency lead usage?

Where both rose, efficiency crossed first in 38% of 128 episodes (chance 34%); usage first in 23% (chance 31%). Efficiency first is inside the chance band; usage first is at its low edge.

Sample: 10,228 player-seasons, 1,820 players

Do minutes (role) move before usage?

Minutes per game rose early before 44% of usage breakouts vs 18% of controls. Over all players, a minutes rise with usage flat raises next season's chance of a usage rise from 9% to 18%.

Sample: 10,228 player-seasons, 1,820 players

When usage and creation both rise, which moves first?

In 100 rise episodes where both rose, usage and creation crossed in the same season 60% of the time; random timing gives 35%. Usage first (19%) and creation first (21%) are both below chance.

Sample: 10,228 player-seasons, 1,820 players

Does a usage rank far below efficiency close from below?

At the same usage quintile, players whose efficiency ranks 2+ quintiles higher are no more likely to gain a usage quintile (-0.2 points). They are more likely to gain minutes (+9.3).

Sample: 10,228 player-seasons, 1,820 players

Does a usage rank far above efficiency close from above?

At the same usage quintile, players whose efficiency ranks 2+ quintiles lower are +12.7 points more likely to drop a usage quintile.

Sample: 10,228 player-seasons, 1,820 players

Held out, do transition states improve next-season forecasts of usage, efficiency and minutes?

No variant improves usage, efficiency or minutes forecasts on established players; efficiency gets about 1.5% worse under every variant. A forecast from transitions alone is 8-19% worse than the baseline.

Sample: 10,228 player-seasons, 1,820 players

Held out, do transition states improve next-season creation forecasts?

Not against the current baseline. No creation variant's interval excludes zero in its favour; even the best adds error (-0.3% change), and 1 of 7 make it worse beyond chance. Against baseline Revision 2 one variant cut creation error by 0.9%; the history mean (Revision 3) took that gain.

Sample: 10,228 player-seasons, 1,820 players

Do usage, creation and efficiency moves this season predict each other's moves next season beyond each one's own move?

Once a dimension's own last move is known, the other two add little: the lookup's best smoothing strength is 500-1373 player-seasons, and held out the move pattern improves the next-quintile log score by only +0.004 (usage) to +0.002 (creation).

Sample: 10,228 player-seasons, 1,820 players

Given one dimension leads, how likely are the others to move, and which way?

Pairwise, with the follower flat: usage rise -> efficiency rise next season 23% vs 14%; within two seasons +13.3 points. Most pairs move the follower's odds by under 5 points.

Sample: 10,228 player-seasons, 1,820 players

Griffin's example: usage and efficiency rose but creation has not; what next?

After a season in which usage and efficiency rose and creation stayed flat (196 player-seasons), creation rose next season 8% of the time, the same as any player whose creation was flat (8%).

Sample: 10,228 player-seasons, 1,820 players

Which dimensions of a player's season are stable?

Year to year, creation repeats most (r 0.92), then usage (0.87), offensive impact (0.76), role minutes (0.77) and defensive impact (0.66). Games played barely repeats (0.21).

Sample: About 5,900 player-seasons per dimension, walk-forward

What explains a player's next three seasons of value (the factor model)?

Current value 29%, scoring 14%, vision 8%, age/experience/draft 7%, athleticism stand-ins 6.5%, touch 2%, size about 1% (Shapley shares, 12,448 player-seasons 1982-2021, in sample).

Sample: 12,448 player-seasons

Which skills change most from one year to the next?

True one-year change as a share of the league spread: FTA/36 0.51, 3P% 0.50, FGA/36 0.49, turnovers 0.47 … blocks 0.30, offensive rebounds 0.28.

Do public tracking summaries add to the factor model?

No. Future BPM explained: 66% from what the market knows, 69% with box factors, 69% with tracking added.

Are outlier skills worth more than a straight line says (the Curry question)?

No: gradient boosting 0.640 vs linear 0.639 out of sample. Every model is about 1 point too cautious on its own top forecasts.

Does value = efficiency x possessions work as a forecasting structure?

Direct and parts-built value forecasts are equally accurate (R-squared 0.65 vs 0.65). Of the variance in value surprises, the efficiency part carries 62%, the possession part 28%.

Sample: About 5,900 player-seasons per dimension, walk-forward

Are some players persistently under- or over-forecast by the baseline?

They do not: lag-1 r +0.001 (-0.030 to 0.027), permutation p 0.47; the stable player share of the misses is 1.0% (null 95th percentile 1.3%). Updated 2026-10-15: was Lag-1 r +0.003; player share 1.1% (null 95th pct 1.3%) (-0.028 to 0.029) before the 2026-10-05/07 re-runs; numbers refreshed from the current output.

Sample: 6,525 rows, 1,288 players

When the model misses a player badly, do his 20 look-alikes miss too (type or individual)?

About 47-48% of look-alikes also beat the model, close to the 50% chance rate: type and individual are not separated.

Do players who defy their height bucket (Harden, Giannis, Draymond) beat forecasts?

No. Defiers beat the factor model as often as everyone else; adding the mismatch makes star forecasts slightly worse and value forecasts no better (−0.1 R² points, −0.5 to +0.1, earlier run). 1,073 players defied their bucket in at least one season.

Sample: 1,073 players

Does a coach's player-growth record travel with him?

As a lead, yes: +0.36 (+0.11 to +0.60) at his new team. One test of about 19, so it needs confirming on another rating.

Does any organization grow players faster in a way that lasts?

No: an organization's past player growth does not carry to its next players (slope −0.09, −0.20 to +0.00); young players and shooting show no carry-over either.

Do players who join a team whose players are growing improve through skill or setting?

Joiners rise at once: +0.35 (+0.13 to +0.55), which points to the setting rather than learned skill.

Do players who join a team whose players are growing improve through skill or setting?

Leaving such a team costs nothing measurable: -0.20 (-0.42 to +0.06).

Where does each Bulls player's level usually go in one and three seasons?

A normal path with an 80% band for every skill of each Bull with a 2025-26 season. On 2010-15, a window the rule was not chosen on, the band covers 81% at three seasons; three-point volume bands run narrow (75%).

Does Durant's skill-based game age better than the curve says?

His skill index held after 30 (+1.02 at 28, +1.06 at 37) but his explosiveness proxies fell by more than a league spread. His impact fell 0.36 points a year after 31, close to the 0.39 the age curve predicts. He has not beaten the curve.

Sample: 5 seasons at 31+

Does LeBron beat every aging trajectory, as Griffin thinks?

LeBron beat the age curve by +0.27 points a year over 10 seasons from 31, and kept his explosiveness proxies near his 27-30 level into his 40s (rim share 44% at 41). Kawhi (+0.85) and Butler (+0.46) beat it by more.

Sample: 10 seasons at 31+

Does the history-mean input (F1) help dimensions beyond usage and creation?

Adding the mean of a player's last three seasons, weighted by how much he played in each, cuts held-out forecast error on 19 of 24 dimensions. Established players: creation 10.0%, usage 1.8%, impact 1.4%, value 1.5%.

Sample: 5,914 established rows (impact, usage, creation); 6,203 (value)

Does the baseline over-weight a short last season?

Yes, and fixed: the history mean entered the baseline as Revision 3 and stays in Revision 4. Taking it out of the current baseline raises established-player error by 10.0% (creation) and 1.8% (usage). Returning stars stay under-forecast (Curry 2020-21: 25.8 vs 34.9).

Does a state-space model with exposure-weighted observation noise improve on ARMA?

Letting a season's noise grow as its minutes shrink cuts held-out error vs ARMA on every dimension with an exposure: efficiency +3.9%, usage +6.7%, creation +5.8%.

Sample: 5,914 established player-seasons (9,850 all) per rate dimension

Does an ARMA model per dimension, pulling in all previous seasons on an age-and-stage time axis, beat the baseline walk-forward?

It does not. For established players ARMA(1,1) has higher forecast error than the baseline on efficiency (-7.4%), usage (-13.3%) and minutes (-10.1%) and ties on creation, value and defense.

Sample: 5,914 established player-seasons (9,850 all) per rate dimension

Does a Kalman-filter model with a latent level drifting by age and stage beat the baseline for established players?

Not against the current baseline (Revision 4, which holds the history mean). It is better only on defense (+1.0%, 0.3 to 1.7%) and worse on the other six dimensions, including creation (-4.9%, -6.9 to -3.0%). Against baseline Revision 2 it was better on creation (+5.6%) and defense (+3.2%).

Sample: 5,914 established player-seasons (9,850 all) per rate dimension

Where does each model win, by the target season's minutes?

Added after. Error vs the baseline, efficiency: +19.9% when the target season has under 500 minutes, -8.2% at 2,000+.

Sample: 5,914 established player-seasons (9,850 all) per rate dimension

Does a fixed 50/50 average of models 2 and 4 improve on model 2?

Added after. Not for established players (usage -1.1%); it helps returning stars (usage +27.8%) and defense (+1.3%).

Sample: 5,914 established player-seasons (9,850 all) per rate dimension

What state resolution does the data support?

Held out, deciles beat quintiles on log density for every dimension (+0.033 to +0.118); a smooth percentile model ties deciles except a +0.010 gain for defense.

Sample: 10,228 player-seasons, 1,820 players

Does the foul-drawing skill swap move the explosiveness index, its age curves, or the named players?

With shot-mix-adjusted foul drawing in place of FTA/FGA, the reliance index correlates 0.9954 with the old one and 30 of 696 players change tertile. The free-throw trait now peaks at 27 (was 24); the other curves do not change.

Sample: 696 players

Can a model give calibrated probabilities for each kind of breakout over the next one to three seasons, for every player, better than age and draft slot?

A walk-forward logistic model gives every player the chance of seven breakout types (jump or multi-season climb) and of a first starter-level or star-level season within 1-3 seasons. Pooled over the seven types, its three-season forecasts beat age plus draft slot by 4.2% in Brier score (3.3% to 5.3%); any-breakout AUC 0.76 vs 0.72. The probabilities are calibrated.

Sample: 32,683 type-rows (4,669 player-seasons), 1,253 breakouts

Does a full-history model with age as the time axis forecast better than the three-season history mean?

Answered by SS01: an ARMA model on an age-and-career-stage axis forecasts next season worse than the trajectory baseline for established players (efficiency, usage and minutes), and ties on creation, value and defense. It wins only for returning stars and low-minute seasons (see SS08).

Does beating one's regular season in the playoffs signal real improvement?

Yes: each point of playoff lift predicts 0.14 points of next-season improvement (+0.12 to +0.17), beyond his level and age.

Sample: 1924 consecutive player-seasons

Where does the overall-impact age curve peak once survival is modelled separately and leavers count at replacement level?

Yes. Survival times change-if-he-stays, with leavers at replacement level, peaks at 26 (90% 25 to 26) for a player in the league at 21, against 28 for the front-page curve; prime window 24-29 vs 25-30. At 28 the front-page curve is 0.28 league spreads higher (0.22 to 0.33).

Sample: Overall impact Q (front-page measure), pairs 1996-97 to 2025-26

Does modelling who stays in the league separately improve the trajectory baseline's multi-season value forecast?

Yes. Out of sample on 7,501 origins (2001-02 to 2022-23), multiplying the baseline's value forecast by each player's chance of playing cuts its squared error on value over the next three seasons by 4.5% (1,205; 90% 892 to 1506); seasons with no minutes count zero.

Sample: 7,501 origins, 1,417 players, walk-forward

Is the gain from counting leavers, or from splitting the model?

Yes, modestly. The split beats a one-equation model with the same inputs by 419 squared points (90% 227 to 626), 1.6% of that model's error.

Sample: 7,501 origins

Is an age table enough, or does survival need player-level inputs?

No. Multiplying the baseline by the share of players his age who keep playing changes its squared error by +550 (90% -428 to 1670): not distinguishable from zero, and worse in the point estimate, because exits fall on low-value players and a flat discount shrinks stars.

Sample: 7,501 origins

Is there selection on the season a player leaves that no model of observables removes?

Yes. Players who dropped out for a season and returned were -0.20 league spreads (90% -0.29 to -0.12) below stayers with the same age, rating, minutes and injuries two seasons later (170 returners). Updated 2026-10-15: was Returners minus stayers, two-season change in Q: -0.23 spreads (-0.31 to -0.13 (90%)) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: Q, 1996-97 to 2025-26

Do the trait peaks and the explosive-versus-skill contrast survive season-y weights?

Tested. Explosive peaks did not move (5 of 6 still peak at 21); skill peaks moved later, not earlier (three-point % 26 to 36, mid-range 28 to 32); overall impact moved earlier (28 to 26).

Sample: 200 player bootstraps

Is this season's exposure a safe weight for a delta-method age curve of a rate?

A player's attempts track his luck that season (3P attempts vs 3P%, ages 25-30: r = 0.35), so season-y weights tilt every step down: under them the skill group falls 0.31 spreads from 27 to 31 and Figure 3 reverses.

Sample: 200 player bootstraps

Where does the overall-impact age curve peak with weights known in season y?

Refit peak 26 (26 to 28); 26 and 28 are tied (+0.00). The old curve rose too steeply from 21 (level at 28 +0.66 vs +0.84 spreads).

Sample: 200 player bootstraps

Does Figure 4's offense curve survive counting players who lose their minutes?

Offense change at 27-28 (age in the later season): -0.19 per 100 (report -0.07); flat at 25-26. Defense unchanged.

Sample: 200 player bootstraps

When do shooting percentages peak with weights known in season y?

Refit peaks: three-point % 36 (32 to 36), mid-range 32 (27 to 33); last-season weights agree on no decline but show a flat, not rising, three-point curve.

Sample: 200 player bootstraps

At each career-minute checkpoint, does a forecast built only from the first N minutes explain more of the career peak (best 3 seasons of SiPM) than draft slot and age, out of sample?

Yes, from the first 100 minutes, also with no look-ahead in SiPM. At 1,143 minutes the as-of forecast explains 0.36 of the spread in career peaks; draft slot and age 0.02. The leaky original's box forecast said 0.42 and 0.10; most of the drop is the stricter yardstick (draft slot drops too).

Sample: 1,416 players; fit 694 (1997-2006 debuts), test 722 (2007-16 debuts)

At how many career minutes does a forecast made only from those minutes explain half the variance of the realized career peak?

Not as a constant. As of each checkpoint, the forecast reaches R^2 0.5 at 3,680 minutes (2,414 to 4,701; 24% of resamples never reach it); fitted the other way round, 880 minutes. The leaky original said 2,549 minutes and 445 minutes.

Sample: 1,416 players; fit 694 (1997-2006 debuts), test 722 (2007-16 debuts)

Does a model with draft slot and early production beat production alone at forecasting the career peak?

No detectable gain from 250 minutes, with no look-ahead in SiPM: adding draft slot and age to the as-of forecast changes R^2 by at most 0.010 from 250 minutes on, in both directions (reverse at most 0.018); every interval includes zero. At 100 minutes it adds +0.019 (+0.000 to +0.044), at the edge of detection; on the measured-impact peak +0.023 (+0.002 to +0.042).

Sample: 1,416 players; fit 694 (1997-2006 debuts), test 722 (2007-16 debuts)

At matched experience, does the full production SiPM (lineup and box parts) forecast the career peak better than the first-N-minutes box forecast?

Among careers of 3,000+ minutes, as-of SiPM after season 1 against the as-of forecast at 1,000 minutes: R^2 difference -0.00; after season 3 against 3,000 minutes +0.18.

Sample: 1,416 players; fit 694 (1997-2006 debuts), test 722 (2007-16 debuts)

Does early production reveal the career peak better for some positions?

Suggestive only (group differences not tested): at 500 minutes the as-of forecast explains 0.35 of the spread in bigs' peaks, 0.39 for guards and 0.21 for wings.

Sample: 1,416 players; fit 694 (1997-2006 debuts), test 722 (2007-16 debuts)

Is the early edge over draft slot coming from box production, or only from the coach's minutes allocation?

Production alone (no minutes per game) gains +0.15 R^2 over draft slot at 250 minutes and +0.30 at 1,143, with the peak on a scale no test player shaped.

Sample: 1,416 players; fit 694 (1997-2006 debuts), test 722 (2007-16 debuts)

Does knowing how roster competition moved improve held-out forecasts of next-season rebounding, steals, blocks, fouls, assists and defensive RAPM?

No. Adding the two usage-shift terms to a walk-forward model (age curve, last season, teammates' stat competition) changes held-out error by -0.16% to +0.10%; steals and blocks get slightly worse.

Sample: 5,691 held-out pairs; player bootstrap of errors

At a career-minute checkpoint, does the full rating computed as of that day forecast the career peak better than box rates from the same minutes?

A little, and only when SiPM is also the yardstick: adding as-of SiPM (lineup part included) to the first-N-minutes box forecast adds +0.03 R^2 at 500 minutes and +0.04 at 1,143 on the SiPM peak, but -0.00 on the measured-impact peak.

Sample: 1,416 players; fit 694, test 722; 10,430 as-of checkpoint ratings on 3,123 days

Do young NCBs' own season-to-season changes show slower defensive growth?

No. Their one-season defensive change relative to others at the same age and level is +0.10 per 100 at 22 or under and +0.05 at 23-25: as fast or faster.

Sample: 11,630 pairs at risk, 9,139 observed, 2,091 players

Does adding LB's terms to the multi-season value forecast reduce held-out error?

No, a tie: adding the five profile indicators to the engine changes three-season VORP error by -0.5% (engine minus profiles +0.018, -0.022 to +0.058 (90%)); the engine stays as it is.

Sample: 5,688 test origins, 1,468 players

Does the overall-impact age curve differ by position?

Guards gain +0.86 (+0.72 to +0.96) spreads of overall impact from 21 to 27, bigs +0.40 (+0.29 to +0.53); guards peak at 28 (26-30), bigs and wings at 26. The curves are 0.73 spreads apart at 31 (0.53 to 0.95). Updated 2026-10-15: was 0.87 (0.66 to 1.09) apart, guards +0.93 and bigs +0.38, before the 2026-10-09 SiPM reruns lowered guards' gain; the gap is still well above the label-shuffle 95th percentile (0.37).

Sample: 12382 pairs; 200 player bootstraps; 100 label shuffles

Does ball security age differently by position?

Guards cut their turnover rate through their 20s and peak at 30 (25-30); bigs peak at 25 (21-25) and turn the ball over more from 27 to 31 (-0.44 (-0.63 to -0.24) spreads, up = better). Updated 2026-10-15: interval bounds moved by 0.01 after the 2026-10-09 SiPM reruns.

Sample: 12382 pairs; 200 player bootstraps; 100 label shuffles

Do explosive traits fade at the same pace for every position?

From 21 to 27 bigs' blocks change by -0.47 (-0.61 to -0.32) spreads while guards' barely move (-0.00 (-0.05 to +0.05)); dunks peak at 21 for all three, but bigs' dunks change by -0.52 (-0.65 to -0.39) against guards' -0.26 (-0.30 to -0.21). Updated 2026-10-15: small moves (0.01) after the 2026-10-09 SiPM reruns.

Sample: 12382 pairs; 200 player bootstraps; 100 label shuffles

Does free-throw shooting develop differently by position?

From 21 to 27 guards gain +0.49 (+0.30 to +0.64) spreads of FT%, wings +0.48 (+0.30 to +0.69), bigs +0.03 (-0.16 to +0.22); bigs peak at 24 (22-28). Updated 2026-10-15: the largest gap was 0.94 (0.63 to 1.28) before the 2026-10-09 SiPM reruns.

Sample: 12382 pairs; 200 player bootstraps; 100 label shuffles

Does forecast = w(minutes) x draft expectation + (1 - w) x the baseline without draft terms, w fitted walk-forward, beat the production next-season value forecast?

No. Moving draft slot from the baseline's fixed terms into a prior that fades with minutes changed error by -0.5% on all rows and -12.0% under 250 career minutes. Production unchanged.

Sample: 9,850 rows, 1,935 players

Does blending the draft-and-age model into the box + as-of SiPM peak forecast with a weight fading in minutes beat that forecast?

A tie: +0.1% (-0.8 to +0.8%). Draft slot refit as a covariate at each minutes checkpoint does at least as well (+1.1%) and helps at 100 minutes (+2.6%, +0.6 to +4.6%).

Sample: 5,293 player-checkpoints, 628 players

Does w = error of the performance forecast / (sum of both errors), by minutes, beat production?

No, worse on all three targets: next-season value -12.3%, three-season value -12.6%, peak -4.5%. The weight ignores that the two forecasts' errors move together, so it leans on the draft prior far too long.

Sample: As DP01-DP03

When the breakout model says X%, do about X% happen?

Held out, forecasts match outcomes: breakout within three seasons, mean forecast 3.91% vs 3.83% happened, calibration slope 0.98. Players in their first three seasons: slope 1.01.

Sample: Ten bins of forecast probability, seven types pooled

Does a fitted logistic on player history, age, draft, position and roster context forecast breakouts better than the 'players like him' lookup?

On the precedent study's own rows and labels: next-season breakout Brier skill 3.8% (AUC 0.77 vs 0.71); breakout or climber event within three seasons 2.4% (AUC 0.74 vs 0.72).

Sample: 5,351 and 4,596 player-seasons

How does the chance of each breakout type change with age?

Chance of any breakout within three seasons: 31.4% at 21-23, 17.6% at 25-27, 5.8% at 29-31. Efficiency breakouts fall 44-fold over that span; defensive ones 2.6-fold.

Sample: 8,880 player-seasons

Do breakout odds differ by position for young players?

At 21-25, any breakout within three seasons: guards 32.6%, wings 25.4%, bigs 22.4%. Creation: guards 12.8% vs bigs 2.2%.

Sample: 3,323 player-seasons

Does position change a young player's chance of reaching star level?

Not supported: a first top-15 value season within three seasons, ages 21-25, guards 6.8%, wings 4.0%, bigs 5.6%; the guard-big difference is not distinguishable from zero.

Sample: 3,182 player-seasons

Do role openings known before the season improve breakout forecasts, beyond the player's own history?

Removing the team-context inputs (team change, vacated minutes and plays, opening and unclaimed share, heir, star gone) makes next-season usage-jump forecasts 2.0% worse and creation-jump forecasts 2.4% worse, held out. Other types are untouched; the help fades over three seasons.

Sample: 5,439 player-seasons per type

Can the model foresee a player's first starter-level or star-level season?

First top-15 value season within three seasons: AUC 0.94 vs 0.77 for age plus draft slot; Brier skill 20.1%. Starter level (top 60): AUC 0.83.

Sample: 4,162 player-seasons, 123 star arrivals

Did the age curve of breakouts change between eras?

Mixed: for players 25 and under the chance of any breakout within three seasons fell (-9.6 pts at 22 and under), with defense and value down and usage and creation up. From 26 on, no change is distinguishable from zero.

Sample: 8,880 player-seasons

Which traits does a team buy at their peak when it adds a 19-21-year-old?

5 of 6 explosive traits (rim-shot share, dunks, transition shots, blocks, offensive rebounds) peak at 19 or 20; dunks per 36 fall -0.29 from 19 to 27.

Sample: 13,987 season pairs; 74-162 pairs at age 19; 200 player resamples

How does a young player's shot diet change with age?

Rim attempts per 36 peak at 23 and fall -0.41 from 21 to 27; corner-three attempts per 36 change +0.02 from 19 to 27.

Sample: 13,987 season pairs; 74-162 pairs at age 19; 200 player resamples

How much of the 25-27-year-old is visible at 19-21?

Own value at 19-21 explains 0.71 of dunks, 0.76 of blocks, 0.69 of assists at 25-27 (out of sample). Updated 2026-10-15: was Blocks per 36 at 25-27, R^2 from own value at 19-21: 0.76 (0.66 to 0.82) before SiPM rerun 3 (2026-10-09); numbers refreshed from the current output.

Sample: Walk-forward; outcome at ages 25-27; 1,000 player resamples

Is it true of the top 20 by sustained peak, and more than of ranks 21-100? (Best 3-year run centred inside the league-wide prime window (24-29))

Best 3-year run centred inside the league-wide prime window (24-29): 17 of 20 in the top 20 vs 58 of 80 in ranks 21-100.

Sample: Top 100 by sustained-peak score (top 20 vs ranks 21-100)

Is it true of the top 20 by sustained peak, and more than of ranks 21-100? (Built the peak as a staircase (largest one-season rise under half of the climb))

Built the peak as a staircase (largest one-season rise under half of the climb): 6 of 20 in the top 20 vs 14 of 78 in ranks 21-100.

Sample: Top 100 by sustained-peak score (top 20 vs ranks 21-100)

Do analytics-forward teams push each shot type until the marginal values equalize?

Three minus two with fouls, 2025-26: -0.093 (-0.102 to -0.083) points per attempt (replicated). In the half court, counting offensive rebounds and the opponent's next trip, the gap is +0.009 (-0.006 to +0.024). Non-rim twos still trail threes by +0.129 (+0.118 to +0.139). Updated 2026-10-15: was Three-minus-two value with fouls, 2025-26: -0.093 points per attempt; half court with full accounting +0.009 (-0.102 to -0.083; half court -0.006 to +0.024 (90%, games resampled)) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: All regular-season shots

Once transition, putbacks and rebounds are accounted for, do half-court threes and twos differ in value?

Half court, no putbacks, heaves or garbage time, net of the opponent's next possession: 2025-26 +0.009 (-0.006 to +0.024); 2021-25 +0.008 (+0.001 to +0.015).

Sample: 2025-26: 96,892 twos, 64,942 threes

Are the twos a team could take instead of threes worth more or less than threes?

2025-26, with fouls: three minus short two +0.100 (+0.089 to +0.111), minus long two +0.222 (+0.208 to +0.237); three just outside the arc minus long two just inside +0.347 (+0.317 to +0.377). Updated 2026-10-15: was Three minus non-rim two, with fouls, 2025-26: +0.129 (+0.118 to +0.140) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: All regular-season shots

Does the three-versus-two comparison depend on who shoots the three?

2021-25, threes by prior-season 3P% minus the average two: 38%+ -0.010 (-0.017 to -0.003); below 33% -0.111 (-0.120 to -0.099); no prior record -0.146 (-0.154 to -0.138). Updated 2026-10-15: was Below-33% shooters' threes minus the average two, 2021-25: -0.111 (-0.121 to -0.100) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: Share of threes: 38%+ 32%, below 33% 12%, no prior 22%

Has the spread of values across shot zones shrunk as teams optimized?

They have not: rim attempts got more valuable (1.21 to 1.34 points per attempt) and long twos stay far below threes. The weighted spread of zone values barely shrank (0.204 then, 0.183 now; flat since 2008).

Sample: All regular-season shots

Is there a visible diminishing return on threes across teams?

They do the opposite: within each season, a higher three-point rate goes with higher three-point value, before and after adjusting for shot type. So the data cannot show the margin; teams that shoot more threes have better shooters.

Sample: 863 team-seasons

Which traits stay stable when a player's role changes?

Among 1,286 role changers, FT%, 3P%, blocks and rebounding keep noise-corrected year-to-year r of 0.83-0.96, barely below same-role players. Fouls, turnover %, 2P%, assist %, steals and shot mix repeat less well, because they depend on the role.

Sample: 1,286 role changers, 3,764 same-role

Does shooting rise when a player's role grows?

Role changers' FT% (+1.79, 1.41 to 2.17), 3P% and pull-up eFG rise against same-role players. FT% barely depends on role, so its rise suggests players given more role were already improving: selection. The test cannot tell selection from flow.

Sample: 1,286 vs 3,764 pairs

Does shooting rise with role, for flow or hot-hand reasons, compared with a bench player who gets two shots and is pulled?

Not supported: when an absence hands players a bigger role, bench players' shot-making falls 0.52 per 100 shots per 10 points of dose (-0.83 to -0.21) and starters' 0.14. Players believe in flow anyway; the narrower warm-up effect is real (UE10).

Sample: 5,934,240 shots

How reliable are Hawk-Eye shot-quality stats over one season?

Shot difficulty 0.98; FG% above expected 0.71 (0.57 on self-created shots); FT% 0.85 (odd vs even games). From regular season to playoffs, FG% above expected repeats at only 0.14 (54 players).

Sample: 54 players

Does half a season of Hawk-Eye shot-making beat raw efficiency at predicting the next half?

Slightly, on Hawk-Eye's own scale (+0.02 to +0.12), not on raw points. Last season's history is as good or better.

Is the hot hand real?

Small: raw, players shoot 1.1 points worse after a make because they take harder shots; adjusted for the shot (label-safe model), -0.01 after one make and +0.41 after three (+0.29 to +0.53).

Sample: , players

Does pricing defender distance change the shot-adjusted hot-hand estimate?

In the 2015-16 SportVU games, adding the closest defender's distance at release raises the shot-adjusted hot-hand estimate by 0.14 points (0.07 to 0.21), from -0.05 to +0.09; small next to the estimate's own uncertainty.

Sample: 106,426 shots

How much of free-throw rate is shot mix rather than foul-drawing skill?

Yes. Most free throws come from fouled missed twos, and paint and rim attempts draw shooting fouls far more often than jumpers. A foul-drawing measure that holds shot mix fixed is nearly as stable as raw FT rate and reorders players: raw FT rate flatters ball-handling guards with bonus FTs and rim-heavy bigs.

Sample: 3,759 pairs

Where do free throws come from, by foul type and shot type?

Fouled missed twos give 63% of free-throw attempts, bonus fouls 18% (23% in 1996-2015), and-ones 10%, fouled threes 5%. Shooting fouls per attempt: paint 0.19, rim 0.16, mid-range 0.07, threes 0.01.

Sample: No sampling interval (league totals)

Can foul-drawing skill be separated from shot mix?

Shooting fouls drawn against what a player's shot mix implies is nearly as stable year to year as raw FT rate (r 0.81 vs 0.85) and robust to the allocation and location choices (correlations 0.999 and 0.958 with alternatives).

Sample: 3,759 pairs

Among guards, does height go with defense, and does poor shooting cost value?

A measurable cost of poor shooting shows only among guards who shoot often (about 0.54 BPM); not across all guards.

When did this tactic change in our data, and does that match the told date (2012-13 on (Rockets, Warriors); the told acceleration is 2014-15 to 2018-19)?

Three-point share of FGA crossed halfway from its 1980s level to today's in 2012-13; largest single shift before 2014-15.

Sample: Team box scores

When did this tactic change in our data, and does that match the told date (2012-13 on, with pace and space)?

Long-two share fell from about 30% to 7%; corner threes rose steadily from 1997-98.

Sample: Team zone tables

When did this tactic change in our data, and does that match the told date (2016-17 on (told: Brook Lopez 2016-17, then league-wide))?

Share of big-man minutes (83 in+) from players taking 3+ threes per 36 roughly doubled in 2016-17 and 2017-18 (series added after the first run).

Sample: Player-seasons

Does a career-to-date shooting estimate beat both kinds of prior?

For veterans, yes: FT% +16.7% and 3P% +6.2% better than both kinds of prior.

Does a career-to-date shooting estimate beat both kinds of prior?

Not for rookies' three-point percentage, where there is no career yet to lean on.

Does shrinking a shooter toward players like him (size, height, volume) beat shrinking toward the league?

Within a season, yes: 3P% error -8.6% (7.5 to 9.9), FT% -3.7% (3.0 to 4.3), walk-forward over 39 seasons.

Sample: 39 seasons

Does shrinking a shooter toward players like him (size, height, volume) beat shrinking toward the league?

No better for next season's 3P%: +1.8% (-0.2 to +3.9). Not adopted. Updated 2026-10-15: was +1.7% (-0.3 to +3.7) before the 2026-10-01 rebuild; numbers refreshed from the current output.

Sample: 39 seasons

Does playoff-minus-regular-season true shooting repeat across a player's postseasons?

No: true-shooting lift next-postseason r -0.025 (-0.065 to +0.015); a trait above 1.1 TS points is ruled out (regular-season spread 4.5).

Sample: 3782 player-postseasons, 1061 players; 1924 consecutive pairs

How much does a 19-year-old's shooting improve, zone by zone?

Within players, from 19 to 27: rim +4.4 pp, short two +8.3 pp, long two +8.4 pp, corner three +6.3 pp, above-the-break three +5.8 pp, free throws +6.1 pp (vs league).

Sample: 13,987 season pairs; 74-162 pairs at age 19; 200 player resamples

Does early three-point accuracy tell you the later shooter?

Own 3P% at 19-21 (shrunk) explains 0.03 of 3P% at 25-27; every young trait together 0.22.

Sample: Walk-forward; outcome at ages 25-27; 1,000 player resamples

Does the threes-versus-twos ordering change with the shooter's age?

2021-22 to 2025-26, field-goal points per attempt: shooters 21 or younger rim 1.26, above-break three 1.00, long two 0.77; three minus non-rim two +0.24 at 21 or younger and +0.22 at 31+.

Sample: Regular-season shots, heaves dropped

When a player's usage rises because a teammate is out, how much does his efficiency change?

When a teammate's absence hands a player one more point of usage, his true shooting falls 0.52 points (0.42 to 0.61). The result holds for injury-only absences, in every era, and in a plain with/without split.

Sample: 561,831 player-games, 10,401 player-team-seasons, 892 team-seasons; intervals resample team-seasons

Does usage moved by season-level roster changes cost the same as usage moved by a teammate's absence (UE01)?

Yes. Instrumenting a player's season usage with roster competition, team openings, absences and coach changes gives 0.59 TS points per usage point on the 2022-23 to 2025-26 core; the game-level absence method on the same seasons gives 0.54.

Sample: 1,533 player-team-seasons, 564 players; 90% intervals from a player-cluster bootstrap (400)

Which part of a player's usage change carries the efficiency cost in next-season forecasts?

Yes, held out. In next-season TS forecasts, the usage change explained by roster, opening, absences, coach and the player's shot habit costs about 0.35 per usage point; the unexplained rest costs -0.01. Separating them cuts error 2.7% against one cost on the whole change; splitting asked from chosen adds nothing (-0.05%). Applying UE01's 0.52 to every usage change makes forecasts 18% worse. (Numbers above are from the 2019-20-onward run. Re-run on 2022-23 to 2025-26: MSE gain, explained/unexplained split vs one cost: 3.5%; fixed 0.52 on all change: -36%.)

Sample: 237 test rows, 237 players; paired player bootstrap (500)

Does the efficiency cost of more usage depend on what kind of player he is?

Per usage point gained, spacers lose 1.26 TS points and on-ball creators 0.16; the declared contrast is -1.10 (-1.54 to -0.71). High free-throw shooters and self-creators lose less.

Sample: 561,831 player-games, 10,401 player-team-seasons, 892 team-seasons; intervals resample team-seasons

When usage rises, does a player get worse, or is he handed worse shots?

About 69% of the drop in points per shot is a worse shot diet and the rest is making fewer of the same shots (label-safe shot model; 64% with the published model). Tracking data (2020-26) confirm the shots get more contested.

Sample: 5.9M priced shots

Why do the obvious usage-efficiency comparisons show little cost?

Across players the slope is flat (-0.005 TS per usage point, -0.037 to +0.031) and within a player from season to season it is small (-0.067). Coaches give the ball to players who can carry it, which hides the cost the absence experiment shows.

Sample: 7,146 player-seasons

Is the efficiency cost from taking more shots, or from losing the teammate who created them?

Hold fixed how much passing left the floor, and the cost of the extra shots alone shrinks to -0.06 TS per usage point (-0.21 to +0.08), not distinguishable from zero. Players lose efficiency when the guy who set them up is gone.

Sample: 561,831 player-games, 10,401 player-team-seasons, 892 team-seasons; intervals resample team-seasons

When a high-usage player sits, does each teammate gain in proportion to his current share?

No: the split is about halfway between equal and proportional. A teammate's share of what the star leaves rises with his current share at 0.45 of the proportional slope. Held out, the strict proportional rule explains 3% of who gains what; a fitted usage-only model 10%.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

Does a teammate's creation skill predict how much of a sitting star's usage he takes?

Yes. Unassisted scorers absorb more of the star's share; dropping creation traits raises held-out error 2.8%. Per SD of the creation composite, a teammate gains 1.2 more points of the star's share, mostly through on-court usage rate.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

When the lead creator sits, who takes over his shots?

Last season's creation score (θ) predicts who absorbs the usage (+0.27 usage per 36 per SD, 0.17 to 0.36) beyond prior usage, but not who keeps his efficiency; prior usage alone flags step-ups better (68% vs 62%). 2,213 teammate cases, 289 team-seasons.

Sample: 289 team-seasons

Does tracking-data creation predict absorption beyond box-score creation?

Small. Last season's drives and pull-ups per 36 cut held-out error 1.3% (0.2 to 2.4%) once box-score creation traits are in (after the 2026-10-07 game-order fix; before: -0.8%, interval including zero). Status changed 2026-10-15: the held-out error change (-1.3%, 90% -2.4 to -0.2%) excludes zero, so tracked creation does add to the forecast; the gain is small. The 2026-10-07 entry had left this call open. Updated 2026-10-15: was held-out error change -1.2% (leave-one-season-out, 2013-14 on) (-2.4 to -0.2%) before the 2026-10-05/07 re-runs; numbers refreshed from the current output.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

How do players become their team's lead creator?

Of 203 seasons where a player became his team's top creator, 45 were creation breakouts, 27 had a usage breakout that season or the one before, and 61 followed a move to a new team. Most inherited the role at a modest level after a teammate left.

Sample: 203 seasons

Does the stayer who becomes the top remaining creator grab more of the opening?

Yes. 'Heirs' (highest prior creation share on the opening roster, not the old top option) gain 2.4 points of team created baskets on average, vs 0.1 for other stayers; 33% gain 5+ points.

Sample: 862 team-season transitions, 8,161 arrivals, 6,163 stayer rows

Do certain players consistently create 'lucky' teammate shooting, or is it luck?

Teammates' three-point luck carries over for players who change teams (r 0.040, 0.006 to 0.075), beating shuffle and noise nulls. A typical player's true effect is about 0.47 pp on each teammate three (0.18 to 0.65), about 0.41 points per 100 possessions. The free-throw placebo shows nothing.

Sample: 2,458 season pairs; 1,195 players in the multi-season estimate

On which shot types does the teammate effect show?

For team changers, above-the-break persistence is r 0.056 (0.020 to 0.093) and corner threes 0.000 (-0.038 to 0.037). Corner threes are almost all catch-and-shoot, so this is not a clean catch-and-shoot gravity result.

Sample: 2,458 season pairs

Do teammates shoot better with the lead creator on the floor (the Curry lift)?

Teammates shoot +1.2 TS points better in games he plays. Per-player estimates are mostly noise, and the effect of who replaces him is not separated.

How much of one season's teammate shooting lift is signal?

One season of the teammate-shooting measure is about 98% sampling noise; the multi-season estimate's uncertainty (about +/-0.34 pp) is larger than most gaps between players.

Sample: 200 simulated seasons at expected rates

Does the gravity estimate split credit correctly between teammates who share the floor?

Supported, but small. Fitting all players on the floor at once moves about 18% of the top players' raw teammate lift to their teammates (+0.24 pp, +0.20 to +0.28) and predicts next season better, yet the list barely reorders (rank correlation 0.985). Murray stays above Jokic (0.72 vs 0.60 pp); the gap's interval (-0.28 to +0.47) cannot say which of them carries it.

Sample: 1.6M threes; held-out targets 2002-03 to 2025-26

Is a non-scorer's teammate shooting lift explained by screens and passing rather than gravity?

Mixed. Across 518 players (2016-26), joint gravity tracks potential assists (+0.077 pp per SD, +0.059 to +0.095, height fixed), not scoring volume. Screen assists link to it only through height (+0.018, -0.009 to +0.043). Draymond: joint +0.47 pp, rank 7 of 518; his passing and screening profile predicts +0.26.

Sample: 518 players; 1,000 player resamples

Does the efficiency cost of usage depend on whether the team asked for it?

Not shown. On the 2022-23 to 2025-26 core (pull-up labels reliable), usage the roster hands a player costs 0.59 TS points per usage point and usage he takes himself costs 0.30. The gap, 0.29 (-0.14 to 0.65), includes zero; the direction does not hold in both halves, and the held-out prediction no longer beats predicting no change.

Sample: 1,533 player-team-seasons, 564 players; 90% intervals from a player-cluster bootstrap (400)

Is discretionary (self-chosen) shot volume a stable player trait?

Yes. Early-clock pull-ups, step-backs and fadeaways above his team's norm correlate 0.92 between halves of a season and 0.87 year to year. (Numbers above are from the 2019-20-onward run. Re-run on 2022-23 to 2025-26: year-to-year r 0.89; split-half r 0.93.)

Sample: 1,533 player-team-seasons, 843 consecutive-season pairs; player bootstrap (400)

Is on-court yield (design 3) stable enough to measure a player's choice?

No. A player's share of shots with a better teammate on versus off correlates 0.36 within a season but only 0.16 year to year; it mostly reflects the teammates and the minutes structure. (Numbers above are from the 2019-20-onward run. Re-run on 2022-23 to 2025-26: year-to-year r 0.14; split-half r 0.34.)

Sample: 1,209 player-team-seasons, 636 consecutive-season pairs; player bootstrap (400)

Does chosen usage travel with a player beyond what his old usage already says?

No. For 533 team changes, adding the old-team chosen-shot excess and yield to old usage and the new roster changes held-out error by -0.9% (-2.0 to +0.4); old usage already carries the habit. (Numbers above are from the 2019-20-onward run. Re-run on 2022-23 to 2025-26: held-out MSE gain -1.2%; chosen-excess coefficient +0.17 usage points per point.)

Sample: 268 moves; fit into 2022-23 to 2023-24, test into 2024-25 to 2025-26; player bootstrap

Priced against the team alternative, do a player's excess self-chosen plays cost points?

Not on average. Excess discretionary plays are small (about 0.39 per 100 team plays) and score about what teammates would: -0.01 points a season (-0.25 to +0.25) on non-rebuilding teams. Rebuilding teams (own category): +0.34 (-0.01 to +0.71). (Numbers above are from the 2019-20-onward run. Re-run on 2022-23 to 2025-26: excess value -0.24 points per season (non-rebuilding); +0.33 (rebuilding).)

Sample: 779 non-rebuilding and 199 rebuilding rows; player bootstrap

When a star sits, is the team's next-highest-usage player the one who absorbs most?

No in total share. He is the biggest gainer in 19% of held-out absences (chance 8%) and gains less than his share predicts. His on-court usage rate does rise.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

Is Griffin's case (usage grows while efficiency drops only a little) common?

Of 227 role breakouts (usage or minutes), 197 (87%) kept impact within 1 point per 100 of the player's past or raised it. Usage and efficiency surprises move together (r 0.24), so roles grow mostly when a player is playing well.

Sample: 227 role breakouts

Do traits (creation, position, shooting, pedigree, age) predict who absorbs a sitting star's usage?

Yes, modestly. Held out, the full trait model cuts error 3.4% against a usage-plus-minutes model and 9.5% against the proportional rule (after the 2026-10-07 game-order fix; before: 4.7% and 12.1%).

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

Does position overlap with the absent star predict who absorbs his share?

Yes, mostly through minutes: the player at the star's position gets his minutes. Height overlap adds 2.1 points of the star's share per SD; dropping overlap raises held-out error 2.3%.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

Do a teammate's shooting skills by shot type predict how much usage he absorbs?

Partly: only shot type matters. Rim finishers absorb less (-1.1 points of the star's share per SD of rim share); shot-making, 3P% and FT% do not predict absorption.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

Do higher picks get more of a sitting star's usage than their traits imply?

No. Dropping draft slot changes held-out error 0.05%; its coefficient is indistinguishable from zero.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

Do younger (or older) players absorb more of a sitting star's usage?

No. Dropping age and career season changes held-out error 0.01%.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

Do some coaches concentrate a missing star's usage in one player while others spread it?

Not detectable. Between-coach variance in how concentrated the split is does not exceed a shuffled-coach null (p 0.10, 56 coaches with 3+ events).

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

On Hawk-Eye's shot-quality outcome, which predicts next season's self-created shot-making: touch or history?

History: rank correlation 0.51 vs 0.31 for touch (206 players, 2024-25 → 2025-26). For players with thin histories the edge is borderline.

Sample: 206 players

After a role jump, does shooting touch predict pull-up shot-making as well as creation history does (hidden creators)?

Touch matches history, and it is available when history is not. On 64 wing role-player jumps, touch minus shrunk history is +0.075 to +0.521, but 0 of 18 contrasts survive a multiple-test correction; walk-forward, touch adds +0.34 (0.12 to 0.54).

Do screen-setters add value beyond their rating?

Screen assists are among the most stable numbers in basketball (season to season 0.94), but players who set more do slightly worse next season than their rating says (−0.06 per SD); neither shot-quality measure links them to better shots.

Does creation skill protect a teammate's efficiency when he absorbs a sitting star's usage?

Not shown in this design. Teammates' TS falls 0.44 points on average; creation changes that by 0.22 points per SD, indistinguishable from zero, with no creation x expected-gain interaction. Only ball-handling overlap with the star helps slightly.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

When a star's absence raises a teammate's usage, is 'role grew, efficiency held' more common than noise would produce?

No. Absences create real usage jumps (740 rows with +3 usage-rate points vs 283 in random game splits), but 49% keep TS, vs 54% in random splits.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

Does Hawk-Eye's "creation leverage" measure creation skill?

No: it ranks players almost exactly as assists per 36 do (rank correlation 0.95); once volume is removed it carries no skill signal.

Do the teammates who grab more of a sitting star's usage than predicted keep their efficiency?

Slightly. Split each absence's games in two: the extra share a player grabs beyond prediction in one half correlates r = 0.031 with his TS change in the other half.

Sample: 368 absence events, 308 team-seasons, 4,433 teammate rows; held out = fit 1996-2012, test 2013-2025

Do latent usage and efficiency move in opposite directions within players?

Not in true levels. In a multivariate state-space model, season-to-season changes in true efficiency and true usage correlate +0.32; same-season noise is unrelated (-0.03). The joint model adds no accuracy.

Sample: Full-sample fit

Does creation depend on who feeds the player the ball (pass networks)?

No: feeder dependence moves rank R² from 0.235 to 0.243 (105 players).

Sample: 105 players

Do lucky kick-outs teach a passer better habits?

No sign at the season level: −0.08 kick-rate points per SD of luck (−0.23 to +0.06), against a typical season-to-season change of 2.2.

Does Durant's teammate shooting lift persist across his career?

Not found: across his career his teammates shot only +0.40 pp above their norms; his multi-season estimate is +0.24 pp, rank 192 of 1,195. His 2024-25 Phoenix figure (+2.73 pp) was mostly luck by this test.

Sample: 18 seasons

How should a value metric credit a high-volume scorer whose team needed him to take hard shots?

With a shot model that no longer leaks the result, Kobe's shot diet was harder than average (rank 135 of 602) and he made those shots +2.9 points per 100 above expected (rank 211). His usage credit still depends on the assumed usage cost: rank 25 at the all-player cost, 85 at the creator cost.

Sample: Career shot logs

What do worked examples of role-to-creator jumps show?

Five cases picked by a fixed rule: touch flagged Bane before his record did (+15.5 pull-up points per 100, rough 90% +6.6 to +24.3), raised a false alarm (Murray) and narrowly missed (Podziemski).

When a teammate is injured, how much does a player's role grow that night?

Clearly, in the short run (2020-26 game logs, 2,364 player-seasons): per 10 points of assist share freed by injured teammates, assists per 36 rise +0.21 (0.19 to 0.22); per 10 points of usage freed, shots per 36 +0.66 (0.63 to 0.69).

Sample: 2,364 player-seasons; , shots

Can a public creation-skill score (θ) stand in for Hawk-Eye shot-making back to 2013?

Partly: θ tracks 2025-26 Hawk-Eye FG% above expected at rank correlation 0.70 (naive version 0.57); walk-forward from 2024-25, 0.60.

Does our 2015-16 raw-tracking gravity match Hawk-Eye gravity a decade later?

Partly: rank correlation 0.51 (0.25 to 0.70; 30 players). How often a player stands on the perimeter alone matches better (0.66), so location does much of the work.

Sample: 30 players

Does an open creator role predict who becomes a creator?

Tested 2026-10-09 inside the breakout model: removing only the creator-role openings (creation opening, unclaimed creation, heir to the lead creator, lead creator gone) changes next-season creation-jump forecasts by +0.3% (-0.2 to +0.9), not distinguishable from zero. The general roster-opening block helps (BK06); the creator-specific part adds nothing on top.

Sample: 5,439 player-seasons

Does a player's playoff increase in usage, scoring and minutes repeat?

Yes: usage lift repeats (r +0.184, +0.137 to +0.229), as do points per 75 (+0.103) and minutes (+0.188). Roles repeat; efficiency does not rise with them.

Sample: 3782 player-postseasons, 1061 players; 1924 consecutive pairs

In games a teammate primary creator misses, do the remaining handler's lineups (him the only handler) defend worse than in games all handlers play, beyond the change for lineups with no handler?

Not distinguishable from zero, and not in conflict with RU03: +0.15 (-0.46 to +0.83) on the rerun SiPM. A handler-out night raises a creator's usage only 1.55 points; the one-night cost that survives RU03's checks predicts +0.18 per 100 on such a night. Measured directly for creators (in-season ratings, no garbage time): +0.41 (-0.10 to +0.92).

Sample: 816 handler-team-seasons; 20,884 of 76,399 handler-games with a teammate handler out; placebo 462 team-seasons

Does a tracking gravity number put the league's best shooters at the top?

Yes. The 10 leaders in threes made average the 95th percentile (92 to 99); Curry and Korver lead; split-half reliability 0.94.

Sample: 631 SportVU games, off-ball half-court frames

Is there defense a player creates beyond his individual numbers?

Individual numbers explain 26-42% of a player's single-season defensive RAPM. Most of the rest is noise; a small part persists (r 0.19 season to season).

Do award votes, including down-ballot ones, carry defensive signal our numbers miss?

All-Defense vote share predicts next season's defensive xRAPM (+0.67, 95% +0.39 to +1.01) even with this season's and 3-season defensive xRAPM in the model. Out of sample the votes remove 0.5% of error (0.15% to 1.0%).

Sample: 8,475 player-seasons; 95% intervals, 2,000 player resamples

Does a single down-ballot vote carry signal?

A player named by any voter but not selected defends about 0.15 points per 100 better next season than the model expects (95% +0.09 to +0.21), with box score and measured defense controlled.

Sample: 925 cases

Is a single vote noise (e.g. a hometown reporter) while agreement is signal?

Not supported: on published ballots 2014-15 to 2024-25, a single vote predicts as well as several (+0.17 vs +0.17; difference +0.01, 95% -0.16 to +0.17). The test can only detect a gap of about 0.24 or more.

Sample: 125 one-voter, 212 two-plus, 3,021 none

Do DPOY votes add beyond All-Defense votes?

DPOY vote share adds nothing once All-Defense share is in the model: -0.22 (95% -0.92 to +0.34).

Sample: 8,475 player-seasons; 95% intervals, 2,000 player resamples

Do All-Defensive voters lag behind measured defense?

Not against play-by-play defense: lag +0.07 (-0.07 to +0.22).

Do All-Defensive voters lag behind measured defense?

Against box-score defense, voters lean on last season: +0.53 (+0.31 to +0.75).

Does defensive impact decline with age like offense?

Only weakly: measured defensive impact changes little with age (-0.03 a season at 33+, -0.07 to 0.00) while offense falls fast (-0.46). The flat curve may partly reflect a weak measure.

Sample: Delta method

Do defensive breakouts happen young?

Not supported: 33% of defensive breakouts came at 24 or under, against 52% of offensive ones (difference -0.19, -0.30 to -0.09). Median age 25.7 vs 23.9.

Sample: 111 defensive, 109 offensive

Do bigs grow more on defense early in their careers?

Both groups rise (bigs +0.068 a season, others +0.040), but the difference is not distinguishable. Gobert looks like a big who arrived early rather than one who improved.

Does defense rise more in the playoffs for high-usage creators than for others?

No. Per primary creator on the floor, lineup defense changes -0.21 points per 100 (playoffs vs the same teams' regular season) relative to other players.

Sample: 226,164 playoff possessions per side, 480 playoff team-seasons

Does a player's defensive playoff lift in one postseason predict the next?

No. Lift in one postseason vs the next: r -0.00; career lifts spread by 2.1 points where noise alone gives 2.1.

Sample: 1349 pairs, 464 players

Does playoff defense beat what regular-season defense predicts for creators?

No. Regular-season defensive xRAPM carries into the playoffs about point for point (slope 0.93); the creator flag adds -0.21 beyond its regular-season value.

Sample: 3,563 player-postseasons

Do public effort proxies rise more for creators in the playoffs?

No. Hustle activity (deflections, contests, loose balls, charges) changes +0.03 SD relative to others; creators move slower on defense (-0.18 SD).

Sample: 809 player-seasons (activity)

Do offenses target weak defenders more in the playoffs?

Yes. The weakest fifth by regular-season defensive xRAPM is attacked +0.047 more (target index) than the rest, playoffs vs regular season; in the regular season they are not attacked more.

Sample: 806 defender-seasons, 317 players

Is the extra hunting costly per attempt?

No. Points per attempt above expected do not rise for weak defenders in the playoffs (slope +0.013 per SD of defense, the wrong sign for a cost).

Sample: 806 defender-seasons

Do creators guard tougher or easier players in the playoffs?

Yes. The usage of the man a creator guards, relative to his team, falls 0.51 points more than for others from regular season to playoffs.

Sample: 806 defender-seasons

Is lineup defense sub-additive in its players' defensive ratings when an elite anchor is on the floor?

No. Beside a top-5% defender the other four's prior ratings convert 1.06 times as well as elsewhere (90% +0.94 to +1.19); total rating shows no diminishing returns (squared term +0.006). Updated 2026-10-15: was Anchor x other-four interaction +0.03 per rating point (90% −0.09 to +0.16) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 1,879,558 stint sides; about 17 elite anchors a season

Within a team-season, does a teammate's on/off defense shrink when an award-recognised anchor plays?

Yes, small: −0.24 points per 100 against comparison pairs (90% −0.37 to −0.10), mostly before 2016-17. Secondary definition; the rating-defined anchors do not show it. Updated 2026-10-15: was Award-anchor pairs minus comparison pairs −0.24 per 100 (90% −0.37 to −0.11) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 2,800 award-anchor pairs

Is DC03 shooting luck?

Yes. With opponents' threes and free throws at expected rates (SiPM's luck adjustment), the award-anchor interaction is −0.29 per 100 against comparison pairs (90% −0.41 to −0.18), against −0.24 on actual points. Updated 2026-10-15: was Award-anchor pairs minus comparison pairs, luck-adjusted, −0.29 per 100 (90% −0.42 to −0.17) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 2,800 award-anchor pairs, 44,499 comparison pairs

Within a team-season, does a teammate's on/off defense shrink when the anchor is on the floor?

Not distinguishable from zero: −0.08 points per 100 against comparison pairs (90% −0.19 to +0.04).

Sample: 4,168 anchor pairs, 44,499 comparison pairs

Within player across seasons, does gaining an anchor lower his single-season defensive RAPM?

No, it rises: +0.49 points per 100 from no anchor minutes to all (90% +0.39 to +0.58), within player. Ridge leakage explains +0.37; the remainder +0.10 (90% +0.01 to +0.20) is now just above zero (its 90% interval excludes zero). Updated 2026-10-15: was Anchor share coefficient +0.47 per 100 (90% +0.37 to +0.57) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 9,832 player-seasons, 1,771 players

Does a teammate's target index (attacks vs expected) rise in games the rim anchor plays?

No. With the anchor in, teammates are attacked −2.0% relative to expectation vs −1.2% when a non-elite big is out (difference −0.8%).

Sample: 466 rim-anchor pairs, 4,249 comparison pairs

Does any ceiling effect differ before and after 2016-17?

No. From 2016-17 the anchor interaction is −0.08 (90% −0.36 to +0.15) and the pair test −0.02; the award-anchor effect is concentrated before 2016-17. Updated 2026-10-15: was Pair test from 2016-17 −0.03 per 100 (90% −0.20 to +0.17) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 10 later seasons vs 19 earlier

Do offenses hunt particular defenders, and does defending wear a star down?

Split-half 0.91, season to season 0.66.

Do offenses hunt particular defenders, and does defending wear a star down?

Being hunted does not mean being scored on efficiently; Jokic is attacked more than other bigs in most seasons.

Does measurable length predict defense?

Yes on most declared composites: wingspan and reach beyond height go with better defense for players and teams (intervals such as +0.03 to +0.25); some composites failed their checks.

Among guards, does height go with defense, and does poor shooting cost value?

Guard height shows no link to defensive RAPM (-0.04 per 100 per inch, -0.13 to +0.04); for bigs, +0.21 per inch.

Is a defender's assignment difficulty stable?

The average offensive quality of the players a defender guards repeats (split-half 0.81, next season 0.65). It measures assignment, not success.

Sample: 2,013 rows

Does the playoff-minus-regular-season defensive lift, read as regular-season coasting, cost teams wins and seeding?

Not supported on public data: the playoff defensive lift (the coasting proxy) is mostly noise, so shrunk per-player costs are a few hundredths of a win (upper spread at most 0.9). As a scenario, a star holding back 0.78 points per 100 all season costs about 0.3-1.3 wins; for Durant's Rockets (one win behind 4th) that is 0.61 home playoff games.

Sample: 372 players, 30 teams; 10,000 simulated postseasons per version

Do Edwards, LeBron, Giannis, Durant, Doncic, Kawhi and Harden show more playoff defensive lift than the all-player baseline?

Leans yes, fragile. His seven names lift +0.78 points per 100 above the season baseline; luck-adjusted and on-off versions cross zero, and the names were chosen from memory of the same postseasons.

Sample: 3,563 player-postseasons, 969 players

Do rim protectors and defense-first guards and wings (already at maximum effort) show no lift beyond the league shift?

Consistent: B1 lifts +0.16 (-0.17 to +0.49); the test could detect about 0.5. His eight named defenders alone: -1.04.

Sample: 3,563 player-postseasons, 969 players

Do weak defenders who always give full effort (Curry, Jokic) show no lift?

Consistent but uninformative: -0.38 (-1.85 to +1.10).

Sample: 3,563 player-postseasons, 969 players

Do Tatum and Cunningham show little lift above the baseline?

Not distinguishable: +0.46 (-1.55 to +2.48).

Sample: 3,563 player-postseasons, 969 players

Do the two names Griffin flagged as ambiguous show playoff defensive lift?

Leans no: together -1.67 (-3.68 to +0.34); SGA -1.08, Mitchell -2.13.

Sample: 3,563 player-postseasons, 969 players

Do very young players, already at full effort, show no lift beyond the league shift?

No: young players lift more than the baseline, +0.38 (+0.03 to +0.73). In-season development may explain it.

Sample: 3,563 player-postseasons, 969 players

Do all 13 named switch-on players together beat the baseline?

Leans yes: +0.71 for 13 players; carries Set 1's in-sample and luck caveats.

Sample: 3,563 player-postseasons

Does the A2 group show lift above the all-player baseline?

Not distinguishable: +0.49; the test could only detect about 2.2 points.

Sample: 3,563 player-postseasons

Does the B2 (Set 2) group show no lift above the baseline?

Consistent but uninformative: -0.90; Flagg and Ball have no qualifying postseason.

Sample: 3,563 player-postseasons

A2 minus B2 (Set 2).

Not distinguishable: +1.39.

Sample: 3,563 player-postseasons

Does Brown show lift above the baseline?

Not distinguishable: -0.29.

Sample: 3,563 player-postseasons

Is the switch-on list's playoff defensive lift larger than that of calling-card defenders (his named defenders plus guards and wings with prior All-Defensive or DPOY recognition)?

Not distinguishable. A minus B1 = +0.62 points per 100; the test could detect about 1.2.

Sample: 3,563 player-postseasons, 969 players

Does the list's lift concentrate in late rounds, game 4 and later, and close series, beyond the baseline's own pattern?

No. Conference finals and Finals vs rounds 1-2: list minus all players -0.54 (-2.23 to +1.15); game 4+ -0.00; close series -0.14.

Sample: 3,563 player-postseasons, 969 players

Within all players, does series-level defensive lift fall with usage in that series?

No measurable trade-off: -0.14 per 10 usage points (-0.39 to +0.10).

Sample: 6,612 player-series, 951 players

Does lift rise with experience, and is Edwards's lift smaller in his first seasons?

No: +0.007 per season (-0.029 to +0.042). Edwards's later postseasons sit above his early ones at the point estimates, within noise.

Sample: 3,563 player-postseasons, 969 players

Among starters, do All-NBA or MVP-vote players show more lift, holding rating and usage fixed?

No: visibility coefficient -0.11 (-0.69 to +0.45). Consistent with Griffin's idea that the 'phones it in' story tracks visibility.

Sample: 1,853 player-postseasons

Do hustle counts and matchup defense, which do not depend on lineup credit, show the list's playoff lift?

No: hustle activity +0.11 SD (-0.04 to +0.27); matchup points saved -0.36 per 100 (-1.45 to +0.73).

Sample: 801 (hustle), 806 (matchups) player-seasons

Among team #1 options, is the lift of prior-season plus defenders lower than that of minus defenders?

Reversed: plus defenders lift +0.04, minus defenders -0.91; gap +0.95. Hunting of weak defenders (PE07) may explain it.

Sample: 428 player-postseasons (78 plus, 96 minus players)

Does Davis play more of his playoff possessions as the only big, and is his lift concentrated there?

Unresolved: his center share rises 57% to 63%, but center-minus-other lift +0.40 is far within noise.

Sample: 2923 center and 1695 other playoff defensive possessions

Across all bigs, does a larger playoff center share (vs the regular season) go with more lift?

No: +0.11 per 10 points of center share; center minus other lift across bigs +0.30.

Sample: 859 big postseasons, 229 players

Does one defender embolden his teammates, so they steal more with him on the floor (the Claxton question)?

No sign. The published spillover estimator produces the same spread when nobody affects anybody; a corrected estimator finds nothing beyond noise and team scheme.

Does defender pressure lower shooting?

Not identifiable from public data: pressure follows the shooters defenses fear. The most-pressured third beat expected more often (20 of 42 vs 23 of 83; +20 points, 6 to 35).

When did this tactic change in our data, and does that match the told date (2015-16 to 2017-18 (Warriors, then the 2017-18 Rockets))?

Top defender's share of an attacker's matchup possessions in a game fell from about 42% to 33%.

Sample: NBA.com matchups

When did this tactic change in our data, and does that match the told date (2017-18 / 2018-19 (Rockets in the playoffs); spread since)?

Slope of target index on defensive xRAPM moved from clearly positive toward zero in the regular season; playoffs mostly negative from 2019-20.

Sample: Matchup defender-seasons

On like-for-like plays, do player speed, distance and closeout measures from tracking data separate effort from skill and role, including regular-season coasting?

Mixed. On 2015-16 SportVU, a like-for-like speed measure (speed above defenders in the same situation) is a stable trait (split-half 0.98; within height groups 0.97) and survives a broadcast-camera simulation (0.99). But it sorts players by position and does not line up with defensive xRAPM (-0.12), so it is not yet shown to be effort.

Sample: 630 games

In lineup stints, do lineups with 2+ primary creators allow fewer points than the sum of their players' prior-season defensive ratings predicts?

No. The second handler costs about what the first does: L (second's cost minus first's) -0.31 (-0.79 to +0.18) points allowed per 100. Lineups with 2+ handlers allow +0.80 (+0.44 to +1.16) more than their SiPM rating sum, against lineups with none. Updated 2026-10-15: was L (2+ term minus 2.17 x 1-handler term) -0.30 points allowed per 100; 2+ term +0.75 (90% team-season bootstrap -0.79 to +0.18; +0.38 to +1.11) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 1,190,442 defensive stints, 4,201,860 possessions, 540 team-seasons

Within a handler-team-season, is his lineups' defensive residual lower when another primary creator is on the floor?

No. Within player-season, his lineups allow +0.28 (-0.00 to +0.57) more per 100 when paired, about the second handler's own cost. Updated 2026-10-15: was Paired minus alone +0.24 points allowed per 100 (90% team-season bootstrap -0.04 to +0.54) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 1,190 handler-team-seasons with 200+ defensive possessions in each state

On nights when absent teammates push a player's usage up, do his rebounds and steals per 36 fall, holding fixed the rebounds and steals the absent players free?

No. Per 5 usage points: defensive rebounds +0.04 (-0.02 to +0.08), offensive +0.02 (-0.01 to +0.05), steals +0.01 (-0.01 to +0.04) per 36; none distinguishable from zero.

Sample: 561,831 player-games, 1,782 players; 90% player-cluster bootstrap (400)

Do blocks and fouls per 36 fall on nights when absences raise a player's usage?

Yes, modestly. Per 5 usage points: blocks -0.04 (-0.05 to -0.02) per 36 (about 5% of the average), fouls -0.13 (-0.16 to -0.10) (about 4%). Shifted-date placebo is zero.

Sample: 561,831 player-games, 1,782 players; 90% player-cluster bootstrap (400)

Within a game, does a player's on-court minus off-court defensive rating worsen on nights when absences raise his usage?

Yes, but smaller than first reported. Raw on-off +2.39 (+1.76 to +2.98) per 5 usage points (2008-09 on); after removing opponents faced, garbage time, in-season rating error and controls, +0.57 (+0.07 to +1.26), all in his on-court minutes. Close-game stints only +0.46 (-0.21 to +1.16), not distinguishable from zero.

Sample: 561,831 player-games, 1,782 players; 90% player-cluster bootstrap (400)

When a departed or weaker-scoring roster raises a player's usage, do his rebounding, steals, blocks and one-season defensive RAPM fall?

No. With usage pushed up 5 points by falling roster competition: defensive rebounds +0.13 (-0.01 to +0.29), steals -0.02 (-0.07 to +0.03), blocks -0.01 (-0.06 to +0.06) per 36, defensive RAPM -0.14 (-0.39 to +0.12).

Sample: 7,390 pairs, 1,353 players (2,259 after a team change); 90% player-cluster bootstrap (400)

When a higher-usage teammate arrives and pushes a player's usage down, do his rebounding, steals, blocks and defensive RAPM rise?

No. With usage pushed down 5 points by a higher-usage arrival: defensive rebounds -0.04 (-0.21 to +0.14), steals -0.02 (-0.08 to +0.04), blocks +0.02 (-0.03 to +0.07) per 36, defensive RAPM -0.21 (-0.51 to +0.06). The forward case is also null (RU04), so there is nothing to mirror.

Sample: 7,390 pairs, 1,353 players (2,259 after a team change); 90% player-cluster bootstrap (400)

Over a season, do fouls per 36 fall when roster changes push usage up and rise when they push it down, by the same amount?

Probably. Pooled: -0.12 (-0.17 to -0.06) fouls per 36 per 5 usage points (Holm p 0.001). Forward -0.11 (-0.19 to -0.03) and reverse (usage down 5) +0.13 (+0.02 to +0.22); difference +0.01 (-0.15 to +0.17). Each direction alone misses the declared Holm bar, so symmetry is formally undetermined.

Sample: 7,390 pairs, 1,353 players (2,259 after a team change); 90% player-cluster bootstrap (400)

When roster changes push a player's usage down, do his screen assists, contested shots and rim contests rise?

Yes in tracking seasons (exploratory, unadjusted). Usage down 5: screen assists +0.38 (+0.14 to +0.59), contests +0.63 (+0.25 to +1.04), shots defended at the rim +0.33 (+0.01 to +0.71) per 36. The forward direction does not show matching drops.

Sample: 2,485 hustle pairs; 1,413 tracking pairs

Among players who were creators the season before, does a higher-usage arrival that lowers their usage raise their rebounding or defense?

No. Creators whose usage falls 5 points: defensive rebounds +0.14 (-0.11 to +0.45), defensive RAPM -0.06 (-0.52 to +0.57), steals -0.16 (-0.27 to -0.06) per 36 (steals fall).

Sample: 1,469 creator pairs; reverse first-stage F 41

How much of RU03's one-night on-off cost do the ratings of who was on the floor and the game state explain?

Yes. Of the raw +2.39 per 5 usage points, opponents' ratings explain +0.76 (more minutes against starters) and garbage time about +0.69; 76% of the raw cost goes once those, in-season ratings and controls are removed.

Sample: 345,262 player-games, 1,266 players; 90% player bootstrap (400)

Do the same defenders close out faster in both halves of the sample?

Moderately. Split-half reliability 0.60 league-wide and 0.40 within height groups; peak speed in closeouts 0.83. Guards close faster than bigs.

Sample: SportVU catch-and-shoot jumpers, contester 6+ ft away at the catch

Do reputed elite defenders close out faster than others of their size?

Not found. The 10 All-Defensive players average the 40th percentile of closeout speed above expected within their height group (25 to 53); closeout speed shows no link to defensive xRAPM (0.02).

Sample: SportVU

Does a defender's speed beyond what his situation demands repeat across games?

Yes, as a trait: split-half reliability 0.98, 0.97 within height groups. Whether it is effort is not shown: it runs slightly against defensive xRAPM (-0.12).

Sample: 631 SportVU games, half-court frames

Is it true of the top 20 by sustained peak, and more than of ranks 21-100? (Defense supplied at least a third of the best 5-year value)

Defense supplied at least a third of the best 5-year value: 5 of 20 in the top 20 vs 34 of 80 in ranks 21-100.

Sample: Top 100 by sustained-peak score (top 20 vs ranks 21-100)

How many games will a player miss next season?

Only loosely: out-of-sample R² 0.14 (0.125 to 0.155) vs 0.08 for last season's absences alone; chance of missing 20+ games AUC 0.69 (0.68 to 0.71).

Sample: 15 games

Why do players sit, and can injuries be predicted?

Of established players' missed games 2020-26, 56% were injury or illness and 23% coach's decisions. The all-absence forecast predicts benchings; injury games themselves are barely predictable from public history.

Does a player's injury history sharpen projections?

Walk-forward, injury history improves next season's minutes and games-missed forecasts.

Does a player's injury history sharpen projections?

It does not sharpen the projection of per-minute impact or VORP.

Does a player's games-missed history improve the value forecast?

Barely: out-of-sample R² 0.688 → 0.690. The injuries that matter come after the season the model sees (Rose 2011-12: forecast +5.6, actual +0.4).

How much does each kind of injury cost, and does it depend on career stage?

A major injury (21+ games) leaves impact -0.58 per 100 below the pre-injury forecast in the injury season, -0.40 in year 1 and -0.29 in year 2, net of same-age uninjured players. A 10-20 game injury costs -0.10 in year 1.

Sample: 1,892 injury events (926 major, 21+ games), 932 players

Does surgery mark a larger trajectory cost?

Major injuries with surgery: year 1 impact -0.56 per 100 vs -0.28 without (or unknown); value -33 vs -19.

Sample: 1,892 injury events (926 major, 21+ games), 932 players

Does age at injury change the efficiency cost?

Not among those who play again. Year 1 impact: age 24 and under -0.61, 25-28 -0.38, 29-31 -0.25, 32+ -0.28 per 100. Older players who never return drop out, so this cannot show the old recover better.

Sample: 1,892 injury events (926 major, 21+ games), 932 players

Does the trajectory residual after return differ by injury type and career stage?

Yes. Year 1 after a major injury, impact against the pre-injury forecast: ACL -1.29, Achilles -1.02, other knee -0.56, foot or ankle -0.27, back -0.03 per 100. ACL and Achilles also cut role minutes (-5.5, -3.2). Updated 2026-10-15: the blurb still carried the pre-M1 numbers (ACL -1.30, Achilles -1.07, minutes -5.7 and -3.6); the key effect was refreshed on 2026-10-08 but the blurb was not.

Sample: 1,889 injury events (925 major, 21+ games), 929 players

Which injuries change a player's per-minute level?

Half right. ACL and Achilles tears cut per-minute level most (year 1: -1.30 and -1.07 per 100), and ACL's cut lasts past year 2 (-0.91), against a published 'back by year 2'. But other injuries also cut level (other knee -0.55, foot or ankle -0.27), not only games.

Sample: 1,892 injury events (926 major, 21+ games), 932 players

Do Achilles and ACL tears need separate treatment?

Return-year impact Achilles -1.07, ACL -1.23; the difference (+0.17) is not distinguishable from zero on impact or games in either year.

Sample: 925 major events; 57 without text left out

Should ACL tears be separated from other knee injuries when forecasting the return?

Return-year impact: ACL -1.23, other knee -0.47 per 100; difference -0.76. Games: -16.6 vs -4.9 per 82.

Sample: 925 major events; 57 without text left out

Beyond location, does the type of injury change the return?

Return-year impact: tear -0.76, fracture -0.16, sprain -0.14, strain -0.40. Tears also cost -1.8 TS points.

Sample: 925 major events; 57 without text left out

Does a major injury predict another, in the same place or anywhere?

26.3% of returners have a new 21+ game injury within two seasons vs 15.6% of healthy same-age players; same subcategory 7.3% vs 1.5%.

Sample: 925 major events; 57 without text left out

Does a hampered player (e.g. a finger injury) show a shooting dip while playing his minutes?

Across 12,469 played-through games (2018-26), true shooting is not distinguishable from the player's own baseline: -0.002 (95% -0.006 to +0.001). The exception is hand, wrist, finger and thumb listings (IR04).

Sample: 12,469 games, 806 players

Does an upper-extremity injury a player plays through show up in his shooting?

In 945 played-through games with a hand, wrist, finger or thumb listing, true shooting is 1.3 points below the player's own baseline (95% -0.024 to -0.003), while minutes do not change. Ankle and knee listings show no shooting change.

Sample: 945 games, 296 players

Which listed injuries cost shooting efficiency when the player plays?

TS while listed and playing: hand-wrist group -1.3 points, hamstring -1.5, shoulder -1.6, illness -1.0; ankle +0.3, knee +0.3.

Sample: 12,469 games, 806 players

Do listed players who play get their usual minutes?

In played-through games (2018-26) players log about 1 minute below their own baseline: -0.96 (95% -1.15 to -0.76).

Sample: 12,469 games, 806 players

Do major hand-area injuries carry into the next season, as knee injuries do?

They do not: return-year impact -0.00, games +0.8 per 82. The cost appears while playing through (IR04).

Sample: 925 major events; 57 without text left out

Is the baseline's miss on Achilles and ACL returners different from zero?

Yes. Held-out mean miss on value -34.6 points per 82 and games -10.3; the returning-player model cuts them to -3.7 and -0.4.

Sample: 58 held-out Achilles or ACL returning rows

How has the season profile of absences changed?

Season regulars who played every game: 20% in 1983-84 to 1999-00, 4% since 2019-20. The one-game share of misses changed little.

Sample: 11,960 player-seasons

When a regular misses exactly one game, what is the labeled reason?

Not by the league's labels: of regulars' one-game misses, 18% are labeled rest or injury management, 52% injury, 25% coach's decision. On a back-to-back the rest share is 30%.

Sample: 5,399 one-game misses, 723 players

How restricted are minutes on return, by absence length?

Minutes in the first 3 games back fall from 0.92 of the pre-injury average after 2-4 games out to 0.73 after 20+.

Sample: 13,610 episodes

Do contracts price in serious injuries?

Contracts discount ACL and Achilles injuries (210 deals since July 2021); the trade test (about 25 trades) is too small to show a move.

Sample: 210 deals; 69 trades

How much do rookies who lose their first season to injury go on to play?

0.57 of the minutes their draft slot predicts (0.40 to 0.75; 21 players). The asset engine now cuts their minutes, not their per-minute impact, by that ratio.

Sample: 21 players

Does the opening report status add to the returning-player model?

Yes, on 2019-20 to 2025-26 (leave-one-season-out): games squared error 26.8 lower (11.3 to 41.7). Listed Out at the opener: -10.1 games per 82 beyond the model.

Sample: 444 rows, 56 listed Out at the opener

Among short-season players with an established level, does the cause predict leaving the league?

Yes. Share with no NBA game the next season: trade, waiver or unsigned 63%, coach decision 31%, other major injury 16%, Achilles or ACL 11%.

Sample: 2,059 seasons

What did games sat by healthy players cost teams in wins, seeding, home playoff games and gate in 2025-26?

Mixed: clean rest codes cost the league about 15 wins and 2.9 home playoff games in 2025-26 ($7.5M of gate); counting every isolated one-game injury miss as rest, 46 wins and 8.1 games. Real but small, concentrated on teams at a seed line.

Sample: 372 players, 30 teams; 10,000 simulated postseasons per version

Did Edwards, LeBron, Giannis, Kawhi, Embiid, Durant, Harden and Doncic lose their teams seeding by sitting healthy?

Not supported except for Embiid: 8 clean rest games cost the 76ers about 0.6 wins and 0.34 home playoff games. Edwards, LeBron, Giannis, Kawhi, Durant, Harden and Doncic sat 0-1 clean rest games; at most 1.1 wins and 0.05 home games under the high rule.

Sample: 372 players, 30 teams; 10,000 simulated postseasons per version

Do isolated one-game injury absences behave like rest (back-to-back timing)?

Not supported on this check: clean rest games fall on the second night of a back-to-back 51% of the time, multi-game injuries 18%, isolated one-game injury misses 22%. A mixture reading says about 9% of them are rest.

Sample: 739 short rest-coded games; 4263 isolated misses

Does explosive reliance improve forecasts of games missed and exits?

Partly. A more explosive game forecasts fewer games, more so each year past 30: the held-out gain is small but its interval excludes zero (all players 0.88, 0.45 to 1.31; 30+ 1.53, 0.34 to 2.64). It does not help the minutes forecasts or the forecast of who leaves the league.

Does a vague label on a long absence signal an unresolved problem?

Games per 82 in the year after the return: -17.6 for major 'contusion or soreness' events vs -4.5 for tears. Added after seeing results.

Sample: 925 major events; 57 without text left out

What does a major back or core injury do to the next two seasons?

Return-year impact +0.01 (no loss); games per 82 -5.1 in the return year and -5.9 the year after.

Sample: 925 major events; 57 without text left out

When did this tactic change in our data, and does that match the told date (2012-13 (Spurs rest stars); named 2018-19; 65-game award rule 2023-24)?

Core players (28+ mpg) played 95% of roster games in 1983-84 and 77% in 2025-26.

Sample: Player-seasons

What is the expected cost of each player's missed games next season?

A heavy-minute player is forecast to miss about 21 games to injury; the cost is mostly his value per game. Jokić tops the 2026-27 board at 11.4 wins; the largest Bull is Giddey at 2.7.

Sample: 21 games

Do SiPM's misses differ in seasons with injury absences?

A season with 10+ games lost to runs of 2+ missed games falls 0.30 points per 100 further below the SiPM forecast than a clean season. The season after such an injury is not distinguishable from clean (+0.07).

Sample: 4,311 player-seasons, 947 players

Does a player's injury history before the season predict his SiPM miss?

Not supported; it hurts held out: gain -0.0091 (-0.0150 to -0.0018). Inputs: games lost in the two previous seasons, a return flag, and quality x games lost.

Sample: 3,618 scored player-seasons

Can injury returns be separated from real breakouts?

A breakout after a season with 30+ games missed that does not beat the player's best healthy season is labelled an injury return and removed. Kevin Love 2013-14 is an injury return on efficiency but still a value surprise; Kawhi 2025-26 an injury return on four dimensions; Lillard 2022-23 is not a breakout.

How often is a multi-game, non-coach absence of a regular an injury?

81% of such labeled episodes are injury or illness; most of the rest are protocols, G League stints and personal leave.

Sample: 4,350 episodes, 674 players

How accurate are the rules usable for 1983-2019 (row type, transactions, calendar)?

When the rules call a regular's absence an injury, league labels agree 84% (held-out 2022-23 on) and the injury reports 83% (2018-19 and playoffs). They find only 47% of labeled injuries, because one-game misses are called rest.

Sample: 6,862 labeled episodes

Does multiplying the decayed pre-absence history by (1 + L/10)^-theta (theta fitted per stat) beat the current calendar-day decay on the first 25 games back?

No. Fitted walk-forward, the rate function's exponent sits near zero and changes sign across stats. Held-out per-game error of the 14 SiPM box stats: -0.01%; SiPM box rating +0.09% (worse).

Sample: 4,762 returns, 1,283 players; held out 2,485 returns, 721 players

Does keeping the pre-absence estimate, with weight (pre-absence weight) x (1 + L/10)^-theta, beat the current layer on the first 10/25/82 games back?

Mixed. At the return it cuts the first-25-game error of the box stats (-1.59%) and minutes (-15.63%); per game the box stats do not change distinguishably. After 82+ games out it helps box stats (-8.1% of reducible error) and hurts minutes (+47.3%).

Sample: 4,762 returns, 1,283 players; held out 2,485 returns, 721 players

With one free multiplier per layoff bin, fitted walk-forward, which direction does the data want?

Yes, for box rates (added after). The best multiplier on the decayed history is about 2.0 after 41-81 games out and 3.4 after 82+; held out, 82+ reducible error -5.5%. After short absences it is slightly below 1.

Sample: 4,762 returns, 1,283 players; held out 2,485 returns, 721 players

Does the return treatment change SiPM's box rating forecast?

Yes. No method moves its per-game error by more than a fraction of a percent (-0.11% at best). The box model weighs makes against attempts, so a pull toward average volume cancels. Durant: points per 36 fell from 26.2 to 21.0 at the return, box rating +6.43 vs realized +6.18.

Sample: 4,762 returns, 1,283 players; held out 2,485 returns, 721 players

How far below the pre-absence level do returners play in their first 25 games back?

Yes. Against the pre-absence minutes estimate, the first 25 games back average -1.0 minutes for all returns and -6.4 after 82+ games out. Points per 36 after 82+: -0.78, not distinguishable from zero.

Sample: 4,762 returns, 1,283 players; held out 2,485 returns, 721 players

Does a pre-absence minutes level scaled by a ratio per layoff length beat the current layer and the unscaled held level on minutes after a return?

Yes. Scaling the pre-absence minutes level by a ratio per layoff length (fitted 1996-2019) cut held-out per-game minutes error after 41+ games out by 5.4%; a planning forecast of the first 25 games (ratio 0.76 after 82+) cut its error 39%.

Sample: Test window 1,399 returns by 462 players (104 after 41+ games out, 26 after 82+)

After 82+ games out, do box rates come back below the held pre-absence level?

No shift needed in the test window: after 82+ games out, realized points per 36 minus the held level is +0.27 (interval includes zero).

Sample: 26 test returns after 82+ games out

Does the direction of the best layoff adjustment depend on whether the decay ages history by calendar days or by games?

Yes. Refit on a player-games clock, the best multiplier on pre-absence history after 82+ games out is 0.27 (Kostya's direction); on calendar days 3.80 (the opposite).

Sample: All 4,762 returns 1996-97 to 2025-26

Does a pre-registered clock-speed rule beat the current layer on returns 2020-21 to 2025-26?

Yes, out of sample. Clock speeds 0.61 (41-81 games out) and 0.55 (82+) fitted on 1996-2019 and frozen cut 2020-21..2025-26 reducible error by 7.4% after 41+ games out.

Sample: Test window 1,399 returns by 462 players (104 after 41+ games out, 26 after 82+)

How much of the long-layoff gain is the level (pull to average) and how much the learning rate?

Partly. Removing the pull (own-level prior) gets -8.0% of reducible error after 82+ games out vs -14.6% for the clock rule; with the pull gone the clock still wants speed 0.55.

Sample: Test window 1,399 returns by 462 players (104 after 41+ games out, 26 after 82+)

Does the pre-registered rule improve the season-end projections SiPM's box part reads, scored on next season's box stats?

Yes: next-season box-stat error of season-end projections after a 41+ return falls 2.3%; nobody else's inputs change.

Sample: 304 player-seasons with a 41+ return

Does replacing the production minutes forecast for returning players with pre-injury level x a season ratio by layoff length cut held-out error?

No. Inside the production pipeline, the LY06 form forecast next-season minutes per game +32.2% worse (-0.4 to +71.9%) than the production model after 41+ games out, test seasons 2020-21 to 2025-26. Not switched.

Sample: 837 player-seasons (817 with a production forecast); test 57 rows after 41+ games, 273 after 5-40

Do injury details add to breakout forecasts?

Not supported: removing injury games, major injury and 'ended the season injured' changes next-season breakout forecasts by -0.13% (-0.29 to +0.01), and three-season forecasts by +0.04%.

Sample: Seven types pooled

Is it true of the top 20 by sustained peak, and more than of ranks 21-100? (Played 90% or more of the games in the best 5-year run)

Played 90% or more of the games in the best 5-year run: 17 of 20 in the top 20 vs 59 of 80 in ranks 21-100.

Sample: Top 100 by sustained-peak score (top 20 vs ranks 21-100)

Which player types fit together in lineups?

Next to a star creator, spacers add +0.38 per 100 (0.26 to 0.54) and interior bigs +0.29; a second star creator costs −0.90 (−1.21 to −0.56). 12 of 28 pair cells exclude zero (2.8 by chance), and pair effects fitted on 1996-2013 carry into 2013-26 at 1.19 of their size (0.69 to 1.69).

What fits around Wilson (lineup test)?

Held out one season at a time, a lead creator lifts lineups +1.41 per 100 beyond the ratings (0.75 to 2.07). Shooters −0.23 (−0.53 to +0.05) on a career rule; spacing centers add nothing measurable.

Sample: 27 team-seasons

Do switchable defenders make lineups better than their ratings?

Switchability is a stable trait (reliability 0.71). Lineups with more switchable defenders allow 0.28 fewer points per 100 per SD (0.12 to 0.45) than ratings predict, also with prior-season switchability.

Beyond player types, does a specific lineup have its own fit?

Not clearly: lineup-specific fit does not repeat within a season (halves correlate 0.017, −0.010 to 0.048); its spread is at most about 1.9 per 100.

Next to the two star types Wilson could become, does any supporting type add a fit bonus?

No: 3 of 16 type cells exclude zero (1.6 by chance), and type effects fitted on 1996-2013 carry into 2013-26 at only 0.18 (−0.05 to +0.34). Even at the top of its interval, fit is worth at most about $9.6M a season, against $18.2M for picking a 75th- over a 25th-percentile player.

Does a non-shooting forward star need shooters around him?

The data do not show it: spacers add +0.63 per 100 next to a non-shooting forward star and +1.08 next to a shooting one (difference −0.45, −1.64 to +0.91).

Does how a player's impact changes with teammate quality depend on age?

At 22 and under, each point of teammate quality lowers a player's apparent impact by 0.125 per 100 (-0.168 to -0.078); by 25-27 the effect is near zero.

Sample: 7,028 rows

Can a player's impact with stronger vs weaker teammates be measured as his own trait?

Not at the player level: a player's portability score does not repeat (split-half 0.11, next season r 0.04). Griffin agreed to drop it as a per-player label and keep the league-level pattern (TB15).

Sample: 7,028 rows

When did this tactic change in our data, and does that match the told date (2014-15 / 2015-16 (Warriors' small lineups))?

Share of team minutes with no player 82 in+ held at 10-15% until 2016-17, doubled by 2020-21, then eased.

Sample: Lineup stints

When injuries force lineup changes, does fit around a Wilson-type forward show up?

No: 0 of 19 trait comparisons exclude zero against a plain teammate's absence (which itself costs −0.41 per 100, −0.71 to −0.15). The lead creator: +2.6 (−0.3 to +5.4), consistent with B21.

Do lineups with 2+ primary creators score less than a straight-line sum of the first handler's lineup effect?

Yes. 1 handler scores +2.11 (+1.75 to +2.46) beyond the offensive rating sum, 2+ +2.82 (+2.35 to +3.27); the second adds much less than the first (L -1.77 (-2.27 to -1.24)). Larger since 2021-22. Updated 2026-10-15: was L -1.76 points scored per 100 (2+ term minus 2.17 x 1-handler term) (90% team-season bootstrap -2.27 to -1.23) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 1,190,442 defensive stints, 4,201,860 possessions, 540 team-seasons

Holding a player's box profile at fixed prices, does a traditional center (6-10+, under 10% threes) add more to lineup margin in 2021-26 than in 2014-21?

Not under the declared rule. Lineups gain +0.24 points per 100 more per traditional center in 2021-26 than in 2014-21 (90% −0.43 to +0.95), beyond the value of his box line. 2025-26 alone is high (+2.67 to +5.10).

Sample: 1,314,446 stint sides, 18 seasons, 540 team-season clusters

Holding box profile fixed, does any 6-10+ big add more to lineup margin in 2021-26 than in 2014-21?

Mixed. Any listed 6-10+ big adds +0.90 more per 100 in 2021-26 (90% +0.40 to +1.38), but the height-free rebounding non-shooter type does not (−0.02), and listed heights drift across the 2019 re-measurement (CV08).

Sample: 1,314,446 stint sides

Does a champion need a star creator?

Teams with one won 32 titles where the bracket-aware odds expected 26.7 (1980-81..2025-26); odds x1.86 (1.12 to 3.18); series odds x1.55 (1.24 to 1.93).

Sample: 46 seasons, 724 team-seasons, 678 series

Does a smooth weight in usage rank and relative true shooting tie or beat the yes/no star-creator flag on hits and halve its rank jumps?

Title equity with the soft weight beats the yes/no flag on All-NBA (+1.1 points, +0.4 to +2.0) and top option on a playoff team (+1.3, +0.4 to +2.4); a 1-point shooting change moves no top-30 player 10+ places (flag: 34 of 570). Rule D: adopt.

Sample: 4718 player-seasons, 18 seasons; 19 boards for stability

Does the best soft weight on a roster predict champions better than the yes/no flag?

Held-out champion log loss 1985-86..2025-26: soft 1.583 vs gate 1.691; difference -0.109 (-0.192 to -0.022).

Sample: 41 champions

Does a premium fitted on 1980-2008 forecast 2008-26 series better than the bracket odds alone?

The premium replicated (x1.56 fitted early, x1.64 refitted late) but the out-of-sample log-loss gain is not distinguishable from zero (-0.0055, -0.0195 to +0.0097). Rule C fails; the test passes only 33% of the time if the premium is real.

Sample: 270 test series, 131 with a star-creator difference

Does the true-shooting condition in B03's star-creator flag carry information beyond high usage?

On held-out champions the gate does not beat the same flag without it (-0.051 to +0.006 log loss), so the declared rule renames the premium a lead-option (usage) premium. At series level the gate does help (-0.0064, -0.0119 to -0.0010).

Sample: 46 champions, 678 series; 82 team-seasons where the flags differ

Does B03's premium disappear when team strength is built from SiPM forecasts corrected for the creator under-forecast?

Correcting creators' SiPM forecasts walk-forward moves star-creator teams by +0.009 points; the premium moves from x1.81 to x1.75. The declared rule fired (interval includes 1), but real margin on the same 18 seasons also includes 1.

Sample: 18 seasons, 270 series

Is the star-creator premium different in the three-point era (2016-17 on)?

Series odds x1.53 before 2016-17 and x1.67 after; difference in log-odds +0.09 (-0.54 to +0.88). No change detectable.

Sample: 36 vs 10 seasons; 528 vs 150 series

Can role-player teams win titles?

Yes, less often than their margins suggest: 13 of 45 champions lacked a star creator under the declared rule; such teams won 13 titles where their odds implied 19.0.

Do teams with two star creators win more titles than their margins predict?

In sample, yes: 18 titles vs 10.9 expected (+7.1, +3.6 to +10.7). On fresh seasons (1980-81 to 1995-96), 3 titles vs 2.6 expected without a premium and 5.3 with it: not replicated (only 16 two-star playoff teams).

Does a team's playoff edge rise with how high its best creator ranks in usage?

Not measurably: +0.61 points per game from no creator to the league's top creator (−0.21 to +1.53).

Does team strength built from players (rating × expected playoff minutes) beat margin at predicting champions?

Yes: log loss 1.458 vs 1.651 on 29 seasons the models did not see (−0.361 to −0.032). Still too flat at the top (calibration slope 1.49).

Sample: 29 seasons

Does simulating the real playoff bracket predict champions better than regular-season margin?

Yes: log loss 1.63 vs 1.74 for margin alone, each season predicted by a model fitted without it (difference about −0.11; 90% −0.20 to −0.03 in the 10-01 run).

Does adding February 21 rosters improve the trade-deadline title forecast?

Yes: champion log loss 1.440 vs 1.482 (−0.070 to −0.013), better in 8 of 10 seasons.

Sample: 10 seasons

How did the 2025-26 forecast do?

At the end of the regular season the Thunder were 48%; the champion Knicks 4.5% (5th-highest); on February 21, 4.6% (5th). One champion cannot validate a probability model.

How well can public data rank who becomes All-NBA (the star baseline)?

Age, BPM, scoring and usage per 36, draft slot and minutes give average precision 0.587 on 26 future stars (1,523 rows). The baseline under-forecasts its top bands by +7, +10, +5 and +11 points.

Sample: 26 future stars

Is the star baseline getting worse as more is priced in?

No: average precision 0.30 (1988-89), 0.44 (1990s), 0.47 (2000s), 0.60 (2010s). With a fixed training window and a box composite that is not BPM, the edge over draft slot still grows.

Is the star baseline calibrated at the top?

No, too low: players forecast 65%+ made All-NBA 94% of the time. A Platt correction fixes the level (top observed/expected 1.20 → 1.04; Flagg 85% → 91%, 84 to 95), but no correction that reorders the list beat the plain one on later seasons.

Where do #1 options come from?

Of 114 star creators since 1979-80: 46 were top-3 picks, 37 picks 4-10, 23 picks 11-30, 8 second-rounders; 70% of their star seasons came on the team that drafted them (Gilgeous-Alexander is the acquired-as-prospect route).

When do #1s arrive, and who stands beside a #2?

#1s first reach the role in a median year 4 (69-91% by year 5); 78-85% are still with their first team. The #1 beside a #2 was older in 66-73% of cases and a top-10 pick in 66-71%.

Does style uniqueness ("singularity") predict All-NBA?

No. It changes average precision by −0.039 (it slightly hurts); a learned style embedding does worse.

Does rare skill for size flag the next singular star?

No. None of 22 declared comparisons excludes zero once models are refit in every draw (about 1.1 each way by chance).

Do rare combinations of skills for size flag future stars?

No: 0 of 16 tests clear zero either way (0.8 expected each way by chance); real combinations do no better than shuffled ones.

Are there two kinds of stars, and do models miss the singular kind?

62% of All-NBA seasons show breadth. "Singular only" seasons are as common among All-NBA players (11%) as among near-stars (10%).

Which grounded ranking best predicts the outcomes a 'best player' ranking should predict?

Top 30 by title equity made All-NBA 37.6% of the time vs SiPM 34.6% (+3.0 points, +1.7 to +4.3 points) and were a playoff team's top option 30.2% vs 26.3% (+3.9, +2.6 to +5.2 points). Updated 2026-10-15: was All-NBA top-30 hit rate +2.2 points vs SiPM (+1.5 to +3.0 points) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 4,718 player-seasons, 18 seasons; season bootstrap 2,000

Does SiPM after pricing the efficiency cost of a lead-role usage load predict best-player outcomes better?

Not supported. The lead-role rating's top 30 made All-NBA 34.1% of the time (-0.6 points vs SiPM, -2.0 to +0.9 points); no best-player outcome improves. Updated 2026-10-15: was All-NBA top-30 hit rate -0.9 points vs SiPM (-2.0 to +0.4 points) before SiPM rerun 3 (2026-10-09); numbers refreshed from the current output.

Sample: 4,718 player-seasons, 18 seasons; season bootstrap 2,000

Does subtracting each UE02 type's 31st-best rating (supply) improve a best-player ranking?

Not supported: worse. Top-30 All-NBA hit rate -0.9 points vs SiPM (-1.9 to -0.0 points); salary rank correlation 0.44 vs 0.53. Updated 2026-10-15: was All-NBA top-30 hit rate -1.9 points vs SiPM (-3.0 to -0.9 points) before the 2026-10-07 SiPM re-run; numbers refreshed from the current output.

Sample: 4,718 player-seasons, 18 seasons; season bootstrap 2,000

Does evaluating the title-equity model at a player's demonstrated role capacity (usage and minutes) instead of his current role improve a best-player ranking?

Not supported. R5 (title equity at the largest load carried in the last three seasons with impact held) put 38.1% of its top 30 on All-NBA vs R2's 37.6% (+0.6 points, -0.4 to +1.5); top option on a playoff team +0.9 (-0.4 to +2.0). Updated 2026-10-15: was All-NBA top-30 hit rate +0.9 points vs R2 (+0.0 to +1.9) before the re-runs after 2026-10-08 (SiPM reruns and the ordered re-run of 2026-10-09/10); numbers refreshed from the current output.

Sample: 4,718 player-seasons, 18 seasons; season bootstrap 2,000

Is absence of lead-load evidence some evidence of absence: do first-time lead-load seasons hold less often?

Supported in sample. Their first lead-load seasons hold (impact within 1 point per 100 of their lower-load level) 86% of the time vs 95% for players who carried one before (-9 points, -15 to -3).

Sample: 70 first-time and 292 repeat rows; player bootstrap 2,000

Within a player-team-season, does a higher share of team plays (usage x minutes) caused by teammate absences lower his lineups' margin beyond the other nine players' ratings?

Not supported. Instrumented by absent teammates' load, impact changes +0.01 points per 100 per load point (-0.04 to +0.06); the naive slope is +0.54.

Sample: 701,124 player-games, 2,188 players; player bootstrap 2,000

Does the per-possession cost of extra load depend on how much load the player already carries?

Mixed. By the season's load band the instrumented slope is <10%: +0.16, 10-15%: -0.09, 15-20%: -0.14 (-0.27 to -0.02), 20-25%: -0.07, 25%+: -0.11 (wide).

Sample: 701,124 player-games, 2,188 players; player bootstrap 2,000

Is SiPM's forecast too high for players handed their first lead load?

Not supported. At a first lead load the residual vs SiPM's walk-forward forecast is +0.34 vs +0.45 for repeat lead players (difference -0.12, -0.52 to +0.30).

Sample: 70 first-time and 292 repeat rows; player bootstrap 2,000

Do the top usage creators (B03 rule) defend better in the playoffs than their regular season predicts?

Leans yes but not distinguishable from zero: +0.21 points per 100 per star creator on the floor; the regular-season-to-playoff residual test gives +0.39.

Sample: 226,164 playoff possessions per side, 480 playoff team-seasons

Does offense rise more in the playoffs for creators?

No: +0.02 points per 100 per creator on the floor. Griffin's contrast (offense cannot be switched on) holds, but defense does not switch on either.

Sample: 226,164 playoff possessions per side, 480 playoff team-seasons

What separates future #1s from #2s before they arrive?

Growth, not shooting accuracy: future #1s add free-throw attempts per 36 and xRAPM faster under all three definitions (e.g. FTA/36 +0.45 per year, +0.17 to +0.71, earlier run).

Does a champion need a top-5 player?

21 of 30 champions since 1996-97 had one (70%, 55 to 82%): more often than not. They won 21 titles where their odds implied 16.7 (range 12 to 21), so a premium beyond the player's rating is not established.

How often does the team with the better regular season lose a series?

27% of series (24 to 30%); a margin gap of 6 to 8 points still loses 13% of the time. 663 series, 1980-2025.

Sample: 663 series

How much does each player add to his team's title odds (championship probability added, CPA)?

Gilgeous-Alexander about 43 points with a replacement rule (38 to 48), about 48 (34 to 61) with the lineup model; depth players on deep teams are worth far less than a replacement rule says.

Does resembling an all-time great at 19-23 predict a star?

No: 85 box-score-era greats fall into 10 weakly stable shapes, and resemblance adds nothing to an All-NBA forecast (average precision −0.000, −0.006 to +0.005).

In January 2016, could public tracking have flagged the future stars?

No: adding 4 pre-declared movement features dropped average precision from 0.41 to 0.30 (change −0.21 to +0.05); 12 future All-NBA among 285 players. Updated 2026-10-15: was adding 4 pre-declared movement features dropped average precision from 0.42 to 0.29 (change −0.22 to +0.002) before the 2026-10-01 re-run chain; numbers refreshed from the current output.

Sample: 285 players

Does a head coach's effect travel to his next team?

Barely: a coach's result beyond the roster at his old teams predicts his next team's at slope 0.07 (−0.09 to +0.23); the portable effect is at most about 1.1 points per 100 (90% upper bound).

Do an executive's past trades predict his next ones?

No: r −0.02 (−0.17 to +0.13), split by date within each executive's record (pick values not counted).

Does the star-creator bonus help a pre-season ranking pick who adds the most on-court playoff margin, on a label with no usage in it?

Not supported. On a usage-free playoff outcome, title equity's top 30 hit 29.8% vs margin added 30.6% (-0.7 points, -1.7 to +0.2). Rule written before the run: within 1 point, so the bonus is a column, not a rank input.

Sample: 4,718 player-seasons, 18 postseasons, 3,817 player-postseason labels; season bootstrap 2,000

How much is the star-creator flag worth on the usage-free playoff label, beyond margin added?

Not supported (added after the declared test). Across the pool, with a smooth curve in margin added, the flag is worth +0.37 points of margin added (-0.04 to +0.88), below the 1.27 title equity adds.

Sample: 4,718 player-seasons, 18 postseasons, 3,817 player-postseason labels; season bootstrap 2,000

Does pricing players at their demonstrated role capacity pick better playoff performers than margin added?

Not supported. R5's top 30 hit 30.9% vs margin added 30.6% (+0.4 points, -0.7 to +1.5); within 1 point, so a column, not a rank input.

Sample: 4,718 player-seasons, 18 postseasons, 3,817 player-postseason labels; season bootstrap 2,000

Does the usage part of the star flag, on its own, pick better playoff performers?

Not supported. Margin added plus the bonus for any 28+ minute top-15 usage player hit 30.0% vs 30.6% (-0.6 points, -1.5 to +0.6).

Sample: 4,718 player-seasons, 18 postseasons, 3,817 player-postseason labels; season bootstrap 2,000

Which sort key, rate or rate x minutes, better picks next-season playoff performers?

Not separated. Margin added minus SiPM: -0.2 points of top-30 hit rate (-1.1 to +0.6). The sort stays where earlier evidence put it (margin added, on All-NBA average precision).

Sample: 4,718 player-seasons, 18 postseasons, 3,817 player-postseason labels; season bootstrap 2,000

Does a team-level decomposition of margin into P2's eight parts beat net rating alone at predicting held-out playoff games and series?

No. Held out one season at a time, the model with the eight parts (weights shrunk toward their regular-season values) changes playoff game error by -0.15 squared points per game (-1.03 to +0.66) and series log loss by -0.0025 (-0.0104 to +0.0049). Under the declared rule two parts still pass the weight test (TOV, DSHOT), both as playoff discounts.

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Beyond net rating, does a point of margin from avoiding turnovers pay differently in playoff games?

Passes the declared rule: beyond net rating it pays 0.62 points per point less in the playoffs (difference -0.62, -0.96 to -0.21), and passes within both eras. It fails the eight-test correction and adds nothing held out.

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Beyond net rating, does a point of margin from holding opponents' shooting down pay differently in playoff games?

Passes the declared rule beyond net rating (-0.25, -0.47 to -0.03), but within eras only from 2016-17 on. As a total weight it grows in the playoffs as much as net rating (0.98x, added after), so this is not evidence that defense is worth less per point.

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Does a point of margin from unassisted half-court scoring pay more in playoff games?

No. Playoff minus regular-season weight, beyond net rating: +0.01 (-0.13 to +0.15).

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Does a point of margin from free throws drawn pay differently in playoff games?

No. Playoff minus regular-season weight, beyond net rating: -0.25 (-0.47 to +0.01). Passes within one era only (before 2016-17), an era-specific candidate.

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Does a point of margin from threes pay differently in playoff games?

No. Playoff minus regular-season weight, beyond net rating: -0.09 (-0.19 to +0.03).

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Does a point of margin from offensive rebounding pay differently in playoff games?

No. Playoff minus regular-season weight, beyond net rating: -0.25 (-0.64 to +0.14). Passes within one era only (from 2016-17), an era-specific candidate.

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Does a point of margin from forced turnovers pay differently in playoff games?

No. Playoff minus regular-season weight, beyond net rating: -0.26 (-0.66 to +0.14).

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Does a point of margin from defensive rebounding pay differently in playoff games?

No. Playoff minus regular-season weight, beyond net rating: -0.01 (-0.68 to +0.70).

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Does a point of regular-season net rating buy more margin in playoff games than in regular-season games between playoff teams?

Yes, as a by-product of this test. Between playoff teams, a point of net-rating gap buys +0.75 points of regular-season margin (that game left out) and +1.19 of playoff margin (difference +0.44, +0.27 to +0.60).

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Does a net-rating model with round-specific weights predict held-out playoff series better than one weight for all rounds?

Mixed, found after seeing results. From 2016-17 on, letting net rating's playoff weight differ by round improves held-out series log loss by -0.0172 (-0.0267 to -0.0072); pooled 1996-2025 it does not (-0.0036).

Sample: 2,440 playoff games, 450 series, 30 seasons; 9,912 regular-season games between playoff teams

Do broad college producers, or the best combine athletes, become #1s?

Broad producers became #1s 12-13% of the time vs 1-2% (not adjusted for draft slot).

Do broad college producers, or the best combine athletes, become #1s?

The top 10% in combine athleticism for height did not: 2-5% vs 4-6%.

Measured only where all-out speed pays (fast breaks he leads), does speed for size mark future stars?

Suggestive only: 4 of 9 tests exclude zero; elite-for-height players became first-time All-NBA 7.4% vs 3.7% (2 of 27 players). Some stars could not be measured (Kyrie had 3 such breaks in the window, while returning from injury).

Sample: 27 players

Do teams that beat their regular season in the playoffs do it again?

No sign: next-postseason r +0.063 (-0.019 to +0.136) over 1983-2026. One postseason's team residual is about 2% team; a repeating team edge above about 1.1 points per game is ruled out.

Sample: 688 team-seasons; 508 consecutive pairs

Do champions carry more SLAP-lite (measurable frame and combine athleticism)?

No: champions' top-8 rotations carry no more than other playoff teams (−0.01, −0.09 to +0.06, earlier run), and SLAP-lite adds nothing to title odds beyond margin.

What was one more point of margin worth at the 2026 deadline?

8.1 title points to the Thunder and 6.3 to the Pistons; to the Bulls, 1.1 points of playoff odds and no title odds (playoff odds 48% even at +10 per game).

Was Jokić visible in January 2016?

The baseline model ranked him 43rd of 285 (his draft slot weighed on him). Judged against his age, experience and slot he was 5th (2nd among 48 players 22 and under).

Sample: 48 players; 12 stars

Do the definitions of a "#1" and a "#2" agree?

No: 51-58 #1s and 49-73 #2s among 1,360 players drafted 1996-2018, depending on the definition; the definitions agree on only 50-69% of each other's #1s.

Sample: 1,360 players

Recent playoff upsets come from the play-in and rested stars making regular-season records less telling?

Not supported. Upsets by record rose +10.3 points; strength from star games or the game-1 roster does not remove a measurable part, and play-in series had fewer upsets (7 of 31).

Sample: 663 series; 75 recent

Does a continuous star-creator weight beat margin added on the usage-free playoff outcome?

Not supported. Margin added plus the soft lead-creator bonus (b03-refit's declared soft measure) put 30.4% of its top 30 in the next postseason's top 30 vs 30.6% for margin added (-0.2 points, -1.3 to +0.7): within 1 point, so a column, not a rank input.

Sample: 4,718 player-seasons, 18 postseasons; season bootstrap 2,000

How closely does regular-season level predict playoff level?

Yes: playoff box production tracks regular-season production at correlation 0.82 (slope 0.88); playoff level repeats next postseason at r 0.67.

Sample: 3782 player-postseasons, 1061 players; 1924 consecutive pairs

Do the best regular-season players rise or fall relative to others in the playoffs?

Yes: the top 5% by regular-season Game Score per 75 change -0.74 (-1.19 to -0.35) relative to the typical player, with true shooting -1.16, while taking more usage.

Sample: 210 top-tier player-postseasons, 58 players

How much of a great playoff record is a playoff-specific edge?

Yes, on the example Griffin raised: Jordan ranks 2 of 294 in playoff box production per possession, but his lift above the typical playoff drop is +1.10 raw and +0.45 after shrinkage.

Sample: 259 players

Is it true of the top 20 by sustained peak, and more than of ranks 21-100? (A top-15 season (by total value) by age 22)

A top-15 season (by total value) by age 22: 15 of 20 in the top 20 vs 19 of 80 in ranks 21-100.

Sample: Top 100 by sustained-peak score (top 20 vs ranks 21-100)

Is it true of the top 20 by sustained peak, and more than of ranks 21-100? (A top-15 season within his first three seasons)

A top-15 season within his first three seasons: 18 of 20 in the top 20 vs 49 of 80 in ranks 21-100.

Sample: Top 100 by sustained-peak score (top 20 vs ranks 21-100)

Is it true of the top 20 by sustained peak, and more than of ranks 21-100? (Ten or more top-15 seasons)

Ten or more top-15 seasons: 18 of 20 in the top 20 vs 10 of 80 in ranks 21-100.

Sample: Top 100 by sustained-peak score (top 20 vs ranks 21-100)

Is it true of the top 20 by sustained peak, and more than of ranks 21-100? (Won a title inside the best 5-year run)

Won a title inside the best 5-year run: 12 of 20 in the top 20 vs 21 of 80 in ranks 21-100.

Sample: Top 100 by sustained-peak score (top 20 vs ranks 21-100)

Does the draft order beat a public pre-draft model, and why?

On four-year value the draft wins 57% of disagreements (52 to 64), 63% (55 to 71) when it separated players by 10+ picks. Once both players reached 1,000 minutes: 46% (42 to 52), and on per-minute impact the model wins 58%. Updated 2026-10-15: was On four-year value the draft wins 56% of disagreements (51 to 62) before the 2026-10-01 rebuild; numbers refreshed from the current output.

Which college stats carry to the NBA, and does any beat draft slot?

Within position, 3PA rate, block %, offensive rebound % and steal % carry best (r 0.64 to 0.72); 3P% barely (0.26). No college number predicts NBA value beyond slot out of sample (0 of 15 cells).

Does a rookie's box score beat the draft order at spotting future All-NBA players?

Clearly in 4 of 6 decades (1960s, 1970s, 2000s, 2010-16; e.g. 2000s 0.52 vs 0.32 average precision), not in the 1980s or 1990s. Each decade is fit only on earlier classes.

Does the box-score model beat what teams learned from the same rookie season (their year-2 minutes)?

Only in 1 of 6 decades. Teams' minutes also use practice, scouting and medical files.

Does a rookie season help say who becomes a #1 or #2?

Brier better in 3 of 5 definitions; impact definition +0.020 (0.007 to 0.029).

Do an executive's past drafts predict his next ones?

Yes: r 0.32 (0.11 to 0.53); 0.33 (0.11 to 0.54) after removing how good the team was before the draft.

Can draft slot and age tell a future #1 from a future #2?

Mostly no: AUC 0.49 (option definition), 0.54 (impact), 0.60 (All-NBA tier, the one definition where they separate). The test had 80% power to see 0.69-0.71.

Counting only contenders, can slot and age tell a #1 from a #2?

No under the main version: AUC 0.44 (0.31 to 0.57). 3 of 14 versions separate (about 1 expected by chance).

Does a rookie season help say who becomes a #1 or #2?

It barely separates #1s from #2s: the AUC gain excludes zero in only one definition.

Does age at the draft sharpen the draft-day forecast?

Younger draftees become All-NBA more often (top-10 picks: 30% of the youngest third vs 15% of the oldest), but on unseen classes adding age does not measurably improve log loss (−0.002, −0.009 to +0.004).

Did the prep-to-pro and one-and-done eras change what age means?

No: age × era terms change out-of-sample R² by −0.0002 (−0.003 to +0.002).

Do recruiting rankings add anything?

No: the recruit score adds nothing beyond slot (−0.007 R², −0.018 to +0.003). AAU and high-school stats are not public in usable form.

Do college free throws or combine drills better predict NBA shooting?

College FTs beat drills for NBA FT%: +0.25 (+0.07 to +0.42).

Do college free throws or combine drills better predict NBA shooting?

For threes the drill leans ahead but cannot be separated: -0.30 (-0.75 to +0.12).

How do EuroLeague and other leagues translate?

A EuroLeague scorer keeps about 78% of his points per 40; domestic leagues and the EuroCup 69-72%. For international draftees, production adds nothing beyond slot (a weak test).

Do late picks playing far above their slot (draft-slot flags) become stars more often?

In sample, yes: 27% vs 21% expected, which met the declared rule. Out of sample it adds nothing.

What path would Wilson need to become a #1?

Among 6'8"-6'10" forwards, every #1 path needs more usage by years 4-5: +3.5 to +6.9 points from his projected 21% start (15.6 to 26.5); 4-15% of players his age made that move.

Did players built like Wilson reach #1 or #2 at their slot's rate?

Less often (option 2 vs 5.0 expected; impact 1 vs 3.7; All-NBA tier 3 vs 5.8), but a shortfall this size happens 8-12% of the time by chance.

What does Wilson's body say?

For his height he jumps higher than 94-98% of combine participants and is quicker than 79-81%, but lighter than 90% and shorter-armed than 69%.

Which college seasons look most like Wilson's?

Murray-Boyles, Sullinger, G. Williams, Simmons, Zeller, Draymond Green, W.

What does Bryson Graham's draft record show?

His front offices took players about where ESPN's board ranked them (the test catches only large reaches). Against same-slot picks, his picks differ on no combine part (composite +0.31; p 0.20; Holm 1.00).

Do draft slot and age at entry explain SiPM's misses in career seasons 1-4?

Not supported held out: gain -0.0031 (-0.0073 to 0.0011). SiPM has no draft input, and the persistent misses continue years after the draft (Jokic, Hill).

Sample: 3,618 scored player-seasons

Do rookies' preseason box stats improve a forecast of their rookie-season impact beyond draft slot and age?

Over 463 rookies with 500+ minutes (2008-09..2025-26, walk-forward), shrunk preseason per-36 rates cut squared error by 0.25; correlation with rookie impact rises 0.24 to 0.39.

Sample: 463 rookies

Does a draft-slot curve forecast rookie-season value better than the average rookie?

Yes. A curve in log pick, fitted on earlier rookie classes, removes 10.4% of the squared error of the rookie average (R^2 0.10). Production has no next-season forecast for players without NBA minutes.

Sample: 2,097 rookies

Does weighting recent rookie classes (or adding an era term) remove the high bias for picks 1-20 without losing the gain over the rookie average?

No. Weighting recent classes (half-life chosen walk-forward) changed rookie forecast error by -0.1% (-1.1 to +0.9%); an era trend -0.0% (-0.8 to +0.9%). The picks 4-10 gap is real, but fixing it costs as much at picks 1-3. Production keeps the pooled curve, plus a monotone hold past pick 40.

Sample: 2,097 rookies, 25 first-season classes

Do public college numbers improve a draft-slot forecast of peak SiPM in years 2-5, on classes the model has not seen?

Yes: slot + 38 college and combine inputs remove +10.1% of the slot's squared error on peak SiPM, walk-forward over 11 classes; better in 9 of 11. Updated 2026-10-15: was +9.9% of slot squared error removed (MSE 2.874 to 2.589) (+3.5% to +15.8% (90%, players); +2.4% to +16.8% (classes)) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Do college numbers improve a draft-slot forecast of reaching 15+ minutes per game in a season of years 2-5?

No: -0.005 log loss per player; the college model alone is clearly worse than the slot (-0.057). Minutes follow the slot.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Do college numbers improve a draft-slot forecast of a top-60 SiPM season (1,000+ minutes) in years 2-5?

Yes, modestly: log loss +0.024 per player, AUC 0.747 to 0.778; better in 9 of 11 classes.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Without the draft order, how close does a public college model come to the market?

Mixed: on peak SiPM it ties the slot (+2.7%); among players who earned minutes it beats it (+15.1%); on rotation it is clearly worse. Updated 2026-10-15: was Peak SiPM +3.2%; top-60 log loss +0.017; rotation -0.057 (-6.2% to +11.1%; -0.007 to +0.042; -0.087 to -0.026 (90%)) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Where in the draft does the college model add to the slot?

Picks 1-14: +31.9% of slot error removed on peak SiPM; picks 15-30 -0.3%; 31-60 -0.3%. Updated 2026-10-15: was Picks 1-14: +31.2% (n 131) (+19.5% to +41.1% (90%, players)) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Which college inputs carry the model's gain over slot?

BPM alone with slot removes +11.6% of peak-SiPM error; dropping it from the full model costs +7.4%. Career BPM outweighs final-season BPM; a final-season jump is marked down. Updated 2026-10-15: was add to slot +11.9%; drop from full +7.7% (+7.0% to +16.3%; +4.3% to +10.6% (90%)) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Does age at the draft improve a draft-slot forecast of peak SiPM out of sample?

No: adding age at the draft to draft slot changes peak-SiPM squared error by -1.5% (-4.2% to +0.9%). Its weight inside the full model is in the heterogeneity field. Updated 2026-10-15: was add to slot -1.1%; drop from full model +2.5% (-3.6% to +1.3%; -1.2% to +6.5% (90%)) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Does steal % and block % improve a draft-slot forecast of peak SiPM out of sample?

On their own, yes (+5.0%); once BPM is in the model they add nothing (+0.0%): BPM already holds them. Updated 2026-10-15: was add to slot +4.2% (+1.3% to +6.8% (90%); beyond the full model -0.9% to +1.0%) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Does college free-throw shooting improve a draft-slot forecast of peak SiPM out of sample?

No: adding college free-throw shooting to draft slot changes peak-SiPM squared error by +0.3% (-1.1% to +1.8%). Its weight inside the full model is in the heterogeneity field.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Does college assist rate improve a draft-slot forecast of peak SiPM out of sample?

No: adding college assist rate to draft slot changes peak-SiPM squared error by +0.7% (-0.7% to +2.0%). Its weight inside the full model is in the heterogeneity field. Updated 2026-10-15: was add to slot +0.5%; drop from full model +0.4% (-1.3% to +2.2%; -0.1% to +1.0% (90%)) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Does combine size, length and athletic tests improve a draft-slot forecast of peak SiPM out of sample?

No: adding combine size, length and athletic tests to draft slot changes peak-SiPM squared error by -1.1% (-3.5% to +1.0%). Its weight inside the full model is in the heterogeneity field. Updated 2026-10-15: was add to slot -1.8%; drop from full model -1.2% (-4.0% to +0.3%; -2.2% to -0.2% (90%)) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

When the model and the pick order rank two classmates differently, whose ranking does the outcome follow?

Mixed: the 10% the model liked most beat their slot's expectation by +0.53 SiPM and the 10% it liked least fell short by -0.78; but over all opposite-ranked pairs the draft is right 53%.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Do non-linear trees find interactions the linear model misses?

No: trees did worse than the ridge model on all three outcomes (peak SiPM -12.3% vs the linear model). Updated 2026-10-15: was peak SiPM: trees' squared error +11.8% vs the linear model's (+5.2% to +18.6% (90%)) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Is a public pre-draft board a better market benchmark than the pick?

No: on peak SiPM the board ties the slot (+0.6%); on rotation it is worse. The college model adds as much to the board (+10.1%) as to the slot. Updated 2026-10-15: was peak SiPM +0.1% (-4.1% to +4.3% (90%); rotation -0.044 to -0.004) before SiPM rerun 2 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes; 90% intervals from 2,000 player bootstraps unless noted

Can the model, applied to all college seniors, flag undrafted players who later earn NBA minutes?

Partly: a college model trained on draftees puts 17 of 53 undrafted future rotation players inside its top 60 of their class; ranking by college BPM alone finds about as many.

Sample: 53 undrafted rotation players in test classes; 342 undrafted NBA players matched by name

Does a translated international profile forecast NBA impact beyond slot, as college numbers do?

Partly: international box scores translated to a college scale and scored by the college model sharpen the top-60 forecast for international draftees (+0.113 log loss) but the scale runs high: they finish -0.69 xRAPM below the college model's forecast.

Sample: 89 test players

Is the high reading for picks 4-10 in recent classes larger than class-to-class noise?

Yes. In first seasons 2013-25, picks 4-10 averaged 5.3 value points against a walk-forward forecast of 28.61; 10 of 13 classes fell short. Not noise.

Sample: 91 rookies, 13 classes

Is the drop in first-season value of picks 4-10 a change in rookie roles (minutes) or in rookie play (impact per minute)?

Yes, in sample. Picks 4-10: impact per 100 possessions changed -0.97 (2013-25 vs 1996-2012); minutes changed -131 (interval spans zero). With the early impact, recent value would be 24.91 instead of 5.3.

Sample: 91 rookies 2013-25; 119 in 1996-2012

Can a pre-debut version forecast first-three-season breakouts and arrivals better than draft slot alone?

Tested: for arrivals in the first 1-3 NBA seasons, slot + college BPM is no better than slot alone (starter level within 3 seasons: -0.0004 log loss, -0.0164 to +0.0141). The 2026 draftees' arrival rows are written for the breakout board anyway.

Sample: 864 players (starter, 3 seasons); 6 outcome x horizon cells

Is the scouting rule 'trust his free throws' right for accuracy?

R^2 for 3P% at 25-27: FT% 0.12, 3P% 0.09, both 0.18. The FT-over-3P gap is not distinguishable from zero. Updated 2026-10-15: was FT% minus 3P% models, R^2: +0.034 (-0.079 to +0.151) before SiPM rerun 3 (2026-10-09); numbers refreshed from the current output.

Sample: 206 players with a 25-27 3P%

Does free-throw shooting predict who starts shooting threes?

Among the third of young players who took the fewest threes, FT% at 19-21 explains 0.12 of threes per 36 at 25-27; their 3P% explains -0.09.

Sample: 72 low-volume players

Once a player has played, does his draft slot still tell you about his traits?

Adding draft slot to the 19-21 values never improved the 25-27 forecast in 31 traits; for three-point volume it hurt (-0.164). Updated 2026-10-15: was Three-point attempts per 36, R^2 change from adding draft slot: -0.167 (-0.324 to -0.043) before SiPM rerun 3 (2026-10-09); numbers refreshed from the current output.

Sample: Walk-forward; outcome at ages 25-27; 1,000 player resamples

Which profile at 19 returns the most value beyond draft slot and early production?

Adding the explosive-versus-skill profile to draft + production changes the R^2 of value at 22-27 by -0.012; the shooting profile by +0.002.

Sample: Value = points above replacement per 82 games, summed over ages 22-27, 0 when not playing

Should the draft board use free throws as a three-point-volume signal?

Yes: college FT% adds +2.6% (+1.4% to +3.9%) to slot + BPM + college threes for NBA three-point volume in years 2-5; +4.9% in years 5-7.

Sample: 619 players (years 2-5), 435 (years 5-7)

Does a two-number college model (BPM, final and career) plus slot match the 38-input model out of sample?

Yes: slot + college BPM (final and career) removes +11.9% of slot error on peak SiPM; the 38-input model +10.1%; adding four more inputs changes nothing (+0.1%). Updated 2026-10-15: was +12.2% of slot squared error removed (slot + BPM) (+7.8% to +16.5% (90%, players)) before SiPM rerun 3 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes

On the same test classes, does a model fitted from 1995 beat the same model fitted from 2008?

No measurable gain: fitting from 1995 instead of 2008 changes peak-xRAPM error on 2011-2021 classes by +1.3%.

Sample: 971 test players, 22 classes

Does the gain survive removing the players who contribute most to it?

Supported for slot + BPM: dropping the 20 players it helped most (of 524) still leaves +4.0%; dropping them and the 20 it hurt most leaves +9.9%. Updated 2026-10-15: was +10.1% after symmetric trimming of 20 + 20 players (+5.8% to +14.6% (90%, players, trimming redone per draw)) before SiPM rerun 3 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes

Is the gain smaller in recent draft classes, as if teams have learned the college signal?

Not supported: slot + composite gains by era are 2000-05 +5.7%, 2006-10 +2.5%, 2011-15 +5.3%, 2016-21 +1.4%, with overlapping intervals.

Sample: 971 test players, 22 classes

Does the team's rating (or schedule strength) add beyond BPM, which already adjusts for opponents?

Not distinguishable from zero: +1.4% on peak SiPM; schedule strength -0.3%. Updated 2026-10-15: was +1.3% of squared error (-0.9% to +3.5% (90%, players)) before SiPM rerun 3 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes

Does college usage add beyond BPM?

No: -0.4% on peak SiPM. Updated 2026-10-15: was -0.3% of squared error (-1.0% to +0.4% (90%, players)) before SiPM rerun 3 (2026-10-09); numbers refreshed from the current output.

Sample: 524 test players, 11 classes

Does a public scouting rank add information beyond the pick and college BPM?

No: adding ESPN's final board rank changes peak-SiPM error by -1.6%; the bar an eye-test grade must clear. Updated 2026-10-15: was -1.2% of squared error (-6.2% to +3.4% (90%, players)) before SiPM rerun 3 (2026-10-09); numbers refreshed from the current output.

Sample: 520 players

Is it true of the top 20 by sustained peak, and more than of ranks 21-100? (Drafted in the top 3 (players with a recorded pick))

Drafted in the top 3 (players with a recorded pick): 10 of 19 in the top 20 vs 27 of 76 in ranks 21-100.

Sample: Top 100 by sustained-peak score (top 20 vs ranks 21-100)

Does slot + a BPM with possessions, team-mates' shares and a team-rating adjustment beat slot + college-2's composite out of sample?

Not measurably: slot + the new BPM +4.2% of slot error on peak xRAPM vs +3.7% for the old composite; difference +0.6% (-1.7% to +2.5%).

Sample: 971 test players, 22 classes; outcome peak xRAPM years 2-5

Does college FT% add to college 3P% and volume when forecasting NBA 3P%?

Yes: added to slot + BPM + college threes, FT% removes +5.8% (+2.7% to +8.7%) of the error on NBA 3P% (years 2-5); +6.6% (+2.0% to +10.9%) in years 5-7.

Sample: 477 players (years 2-5), 337 (years 5-7)

Do college shooting signals (FT%, FT rate, threes) add to slot + BPM for peak impact?

No: FT% added to slot + BPM -0.3% (-0.8% to +0.1%) on peak xRAPM; college threes -0.3%.

Sample: 971 test players

On the board's own target, does slot + Barttorvik BPM beat slot + the rebuilt team-page BPM?

On the 500 college draftees of 2011-2021 with both, slot + Barttorvik BPM (final and career) removes +4.0% more of the squared error of peak xRAPM (NBA years 2-5) than slot + the rebuilt BPM (+1.5% to +6.3%, 90% players). Same direction as CP27/the +5.0% on peak SiPM.

Sample: 500 players

Can players and picks be priced in one currency (the asset engine)?

Yes, as a yardstick: one VORP costs about $14.4M on today's market; a #4 pick returns about $56M more than it costs. Projections tie a linear model 1-2 seasons ahead and beat it 3-4 ahead (+0.03 R²).

Sample: 2 seasons

Do engine prices predict what teams actually pay in trades?

No: on 69 trades, rank correlation −0.05 with picks paid, below the declared bar of 0.30. Engine dollars are an internal yardstick, not a trade-price forecast.

Sample: 69 trades

How much did 2026 trades of past All-Stars pay over the engine's price?

Five trades paid −$2M to $182M over the engine price ($23M to $179M with veteran contracts at zero); median premium about $14.2M.

Sample: 2026 trades

What is a draft pick worth by slot?

A #1 pick is worth about 2.8 tenth picks in value over eight seasons, and the chance of an All-NBA player falls faster than value does. Draft-class bootstrap intervals on the tab.

Why is #1 worth more than the curve says?

#1 is worth about 1.50× the average of picks 2 and 3 (1.07 to 2.02); the #1 was his class's best in 8 of 28 drafts, more than any other slot (no other slot more than 3). How big the premium looks depends on the yardstick. Updated 2026-10-15: the count was 10 of 28 before the 2026-10-02 full re-run (BPM fix and 82-game minutes basis), which made Paul George (#10) the best of 2010 over John Wall and Kawhi Leonard (#15) the best of 2011 over Kyrie Irving.

What do protections and swap rights do to a pick's value?

Top-4 protection removes about 31% of a mid-table pick's value, because it removes the rare hit. A swap right is worth more three drafts out than one (it behaves like an option).

Do pick prices follow the title odds a player adds (convex) or his production (linear)?

Production, at least as well: on 69 pick-for-player trades since 2019, mean miss 3.89 vs 4.46 (difference +0.57, −0.09 to +1.28: cannot separate); 0 of 66 variants favor title odds.

Does the market misprice player types?

The obvious pattern (scorers overpaid, role players underpaid) is mostly a measurement artifact. Under both directions of the regression, 1 of 15 types is mispriced: big interior finishers, overpaid by $1.1-6.4M a season.

Do buyers pay more at the trade deadline?

For time, not talent: per game delivered before the next offseason, deadline buyers pay 1.65× the offseason price in picks (1.33 to 2.08); per unit of recent form about the same, 1.11× (0.89 to 1.40).

Priced by what the buyer controls, is there a timing premium?

No consistent one: deadline buyers paid 1.41× (1.03 to 1.96) over 1999-2026, but only 0.88× (0.61 to 1.46) in 2019-26, and the trailing-form yardstick shows none.

Do buys made after the deadline cost more?

Withdrawn. All six such trades were June trades counted as if the season were nearly over; priced as offseason trades they cost no more (0.86×, 0.46 to 1.82).

How long do bad teams stay bad (lottery recovery)?

A bottom-five team stays bottom-five the next season 47% of the time; three seasons later, about as often as a random team.

Once cap holds and extensions count, how many teams really have max room?

About 2.0 teams expected to fit a 25% max, not the 6.6 a maximum-room view shows.

Sample: 2.0 teams

Which teams are squeezed by the tax and aprons?

For 2026-27, 12 teams are over the tax (5 by under $10M) and none over the second apron. In 2027-28 the Thunder are over the second apron on signed contracts with probability 0.74. 11 of 28 projected taxpayers ducked the tax at the last two deadlines (39%, 26 to 55).

Sample: 12 teams

Do teams trading up on draft night overpay?

They give 1.22× the curve value they receive (1.05 on the 29 trades with no future picks). The players they move up for do no better than their slot; the data cannot say whether the premium is earned back.

Sample: 29 trades

Who signs a rookie-scale extension, and when?

Predictable from years 1-3: 2022 class out of sample AUC 0.87 (0.74 to 0.97), 10.8 predicted vs 9 signed. About 60% come in the October rush; 4.2 more 2023-class extensions expected before opening night (2 to 7).

Can contract decisions be predicted from production?

On later seasons: rookie extensions Brier 0.184 vs 0.196; restricted free agents staying 0.246 vs 0.287.

Can contract decisions be predicted from production?

No: Brier 0.269 vs 0.264 for the baseline.

Does winning fill seats, and what would a rebuild cost the Bulls at the gate?

Ten more wins draw about 4.3% more fans a game that season (3.4 to 5.1) and 6.4% over three seasons, then the effect is gone. A two-season rebuild path goes with about 119,000 fewer Bulls tickets over five seasons (66,000 to 169,000).

Do salaries discount players expected to miss games?

Cannot tell: one measure says yes (discount share −4.3, −9.0 to −0.5), the check measure cannot rule a full discount in or out (0.0, −1.6 to +1.2).

Are SLAP-lite players traded or paid differently?

At equal production and age they are traded less often (−0.088 log-odds per SD, −0.127 to −0.046, earlier run), weaker with role bands; the market pays them no premium.

How often does a cheap contract hold a top-quarter player (climber type 10)?

15 of 497 low-contract players (3%; paid 3% of the cap or less, rookie-scale first-rounders excluded) had 2+ seasons in the top quarter of value, 1999-2025 (Parsons, Jokic, Whiteside). Descriptive.

Sample: 497 players

What are the Bulls' assets worth?

Wilson $56M, Giddey $47M, Buzelis $33M; Patrick Williams's contract is the largest liability (−$37M). Valued partly at his slot, Essengue ($23M at the deadline) stops counting as filler.

What are the Bulls' own firsts worth?

Chicago's 2027-33 firsts are worth about 46 VORP together, or 2.5 average #1 picks. From four drafts out, a Bulls first is best priced as league average.

How much cap room will the Bulls have in summer 2027?

Median maximum room $40M (10th-90th percentile $26-59M); a 46% chance of fitting a 25%-of-cap max contract. Simulation spread, not a confidence interval.

Which summer-2027 plan gives the Bulls the most?

The three room plans end with 6.4-7.5 projected VORP kept and signed, against 4.8 staying over the cap, and leave $3-26M of 2028 room against $59M.

Which players can the Bulls reach, and at what price?

Every target is priced with the cheapest legal Bulls package (checked with the CBA engine). Wembanyama tops the price list at $274M; the star tier holds 21 players at 3+ projected VORP.

Sample: 21 players

Which lead creators (the one piece type with support) are affordable?

26 of 27 lead creators under contract are reachable with picks and filler at the engine's price, but 16 of those are priced below zero. Cheapest above zero: Lillard $6.6M; with the median $14.2M star premium, Maxey $35.3M; 4 lead creators in the 2027 free-agent class fit the Bulls' room.

Who runs the other 29 front offices, and how do they trade?

30 top executives, 1,912 trades since 1980-81; 9 are in the job under two years. Since Graham took over, the most active traders across from the Bulls are Winger, Peterson and Stevens.

Sample: 1,912 trades

Has the salary premium for traditional centers, at equal prior-season VORP and age, risen from 2014-21 to 2021-26?

No: it fell. At equal past production and age, teams paid traditional centers +4.1% of the cap more than other veterans in 2008-13, +1.1% in 2014-21 and −1.4% in 2021-26 (change −2.6 points, −3.7 to −1.5).

Sample: 4,484 player-seasons, 17 seasons (2013-14 lacks payroll pages)

Does P(plays in t+k) x an engine refit on players who play beat the asset engine, whose target already counts exits as zero?

No. On the engine's own validation split, the split changed three-season squared error by -1.1% (a tie); multiplying the current output by the chance he plays made it worse. The engine already counts seasons with no minutes as zero. Not switched.

Sample: 5688 test origins, 1468 players

Does a fitted minutes-fading draft prior beat the shipped asset engine (v1 projection + v2 slot blend) on three-season VORP?

A tie: +1.5% of the shipped engine's error (-1.0 to +4.3%). The fitted weight is flat and small (0.11 at 0 minutes, 0.06 at 1,000): log pick inside the engine already holds what slot knows. Production unchanged.

Sample: 5,688 test origins, 1,468 players

Does asset_values_v2.py's slot blend beat the v1 projection on the players it applies to?

No. On the 827 held-out rows the rule applies to, dropping it removes 12.6% of the squared error (+5.1 to +21.7%). Low-minute young players fall short of their slot's average. Not changed here (not a declared candidate); Griffin's decision.

Sample: 827 test rows, 513 players

Is clutch performance a trait?

Mostly no. A player's late-and-close edge carries into the next season at r 0.10 on court and 0.02 (−0.03 to +0.07) for players who change teams; his own shooting 0.07, and −0.003 under the top-10% leverage definition.

Do players miss more free throws under pressure (the "unclenching" question)?

Yes: 1.8 fewer per 100 in the last two minutes of a close game than of a decided one, and 3.8 fewer when the throw can tie or take the lead in the last 30 seconds (1.7M throws, each player against himself).

How much of a playoff game is three-point luck?

About 31% of what regular-season margins leave unexplained; the side with better three-point luck won 69% of games (e.g. the 2018 Rockets' Game 7).

Can score, clock and possession give a calibrated win probability for every possession since 1996?

Yes: calibration slope 0.98 when each season is predicted from the others. Fit on 1996-2015 and tested on 2016-25, every model is too confident (0.88): leads are less safe since 2016.

Who adds the most win probability, and does it repeat?

Gilgeous-Alexander led 2025-26. One season's total tracks the next (r 0.48 per possession); rank agreement with NBA.com's own leverage table 0.50.

How much is transition worth?

17.2% of possessions, 0.16 points more per possession than the half court (2025-26). How often a team runs is stable (0.94); transition is 15.1% of the spread in team net ratings.

Sample: Team-seasons

Is drawing fouls a skill?

As stable as free-throw shooting: year to year r 0.84 for free-throw rate and 0.86 for shooting fouls per shot, against 0.82 for FT%.

Do referee crews differ?

Yes: one crew calls about 1.2 more or fewer fouls per game than another (1 SD), and most of it carries over to the next season. Home-whistle differences (about 0.7 free throws a game) cannot be tested for persistence.

Do stars get a reputation whistle after their first All-NBA team?

No clear effect: free-throw rate rises +0.010 per shot more than look-alikes' (−0.000 to +0.021); the shooting-foul rate does not move.

When did this tactic change in our data, and does that match the told date (long-standing; pushed by analytics in the 2010s)?

Excess early first actions at 30-42 s before quarter ends rose from about 12% to 19% (2008-09) and fell to about 15% by 2025-26.

Sample: Play-by-play

When did this tactic change in our data, and does that match the told date (peak 2014-15 / 2015-16; rule change 2016-17 (last 2 minutes of every quarter))?

Early-in-possession fouls sending sub-55% shooters to the line peaked in 2014-15 and fell by about two-thirds after the rule (series added after the first run).

Sample: Play-by-play fouls

When did this tactic change in our data, and does that match the told date (rising through the 2010s; rule change 2022-23)?

Non-shooting fouls within 3 s of a live-ball start fell by about 40% in 2022-23.

Sample: Play-by-play

When did this tactic change in our data, and does that match the told date (conventional wisdom; analytics argued against it from about 2012)?

On-court share of the rest of the first half after a first-quarter second foul rose from about 20 points below normal to about 12.

Sample: Play-by-play and stints

When did this tactic change in our data, and does that match the told date (2004-05 rule change)?

Not in this signature: guards' FT rate rose slightly but bigs' rose as much.

Sample: Player-seasons

When did this tactic change in our data, and does that match the told date (2001-02 rule change (with defensive three seconds))?

Small: unassisted share +0.7 points, rim share flat; only four seasons before the rule.

Sample: Play-by-play shots

The two-for-one fade since 2022-23 is a real change in end-of-quarter play?

Supported. Excess early first actions fell -2.6 points (-3.3 to -1.9) in 2022-23..2025-26 vs 2016-17..2021-22; teams acted early less often and the baseline did not move.

Sample: about 3,200-3,900 possessions a season (play-by-play)

Has the traditional center's share of on-court possessions and opening lineups risen from 2014-21 to 2021-26?

No. Traditional centers held +11.0% of on-court spots in 2014-21 and +7.0% in 2021-26 (−4.1 points, −5.1 to −3.0); flat since 2019-20.

Sample: 1,314,446 stint sides

Do players shoot worse right after they check in, compared with their own later shots in the same kind of stint?

A player's first shot after he enters is worse than his later shots, by 1.9 points per 100 shots. The deficit fades over about three minutes.

Sample: Every regular-season FGA 1996-97..2025-26 (5,933,661 shots, 2,839 players). Expected make rate from a league shot model (distance, shot type, clock, score, period) plus court location plus the shooter's own skill by shot class. Player-season fixed effects; player-cluster bootstrap. Replicates in each era alone: 1997-2009 -1.88 (90% interval -2.31 to -1.43); 2010-19 -2.22 (90% interval -2.70 to -1.75); 2020-26 -1.22 (90% interval -1.78 to -0.70).

How do usage and efficiency change with time into a player's shift?

In the first two minutes of a shift, players take fewer shots and make fewer than expected. Their team also scores less. This holds for starters and bench players, every type and every era.

Sample: Every player-minute 1996-97..2025-26, cut into lineup-stint rows; within-player-season deviations; player bootstrap.

Is there a cold start in free throws, where shot selection cannot explain it?

With shot selection removed, the first free-throw trip after a player enters is about 2 percentage points worse. The longer he sat, the bigger the drop.

Sample: Every regular free throw 1996-97..2025-26 (technical, flagrant, take and clear-path FTs excluded), controls for position in the trip (1 of 2, 2 of 2 and so on), clutch and period. Eras alone: 1997-2009 -1.78 (90% interval -2.09 to -1.52); 2010-19 -2.01 (90% interval -2.33 to -1.71); 2020-26 -2.39 (90% interval -2.76 to -1.98).

Is the cold start caused by the dead-ball restart (a called play, a set defence) or by sitting on the bench?

The first shot after a timeout, by a player who stayed on the floor, is as good as his later shots. Bench time is what makes the first shot worse; a dead-ball restart alone does not.

Sample: Timeout restarts identified from possessions with a timeout before the first attempt (the timeout clock itself is not in every feed).

Is the cold start specific to checking in mid-quarter, or does it follow any entry off the bench?

Bench players who enter at the start of a quarter start just as cold. Starters opening the second half do not start cold.

Sample: Same data and model as cold-start-1. Quarter-break entry = a player who sat at the end of one quarter and opened the next.

Griffin's idea: shooters may start cold while post players score best from the post right after checking in. Does the data agree?

Spacers and post players show the same first-shot deficit. Post players' post-ups and rim shots right after entry are also below expected.

Sample: Player types per player-season (200+ FGA): post (top 15% in hook / short turnaround share), creator, spacer (top quarter in 3PA share), big (6-10+), other. Post-ups are a shot-label proxy, not play-type data.

How does shot-making vary with shot number in the game?

Descriptive: a player's first shot of the game is 1.23 points per 100 shots below his average (-1.44 to -1.02); shots 4-6 are +0.31. Players who start hot get more shots, so this table leans against flow.

Sample: 5.9M shots

Griffin's hypothesis: catch-and-shoot role players start cold on threes at their first first-half entry, but not in the second half once they have played.

Low-usage shooters' first three after their first entry is well below expected. Their first three after re-entering in the second half is less cold, but the gap is not clear.

Sample: Catch-and-shoot role players = 1,790 player-seasons with usage below the median and 3PA share in the top third (examples: Joe Johnson 2004, Dorell Wright 2010, Quentin Richardson 2004, Peja Stojakovic 2007). Non-self-created threes; non-starter stints.

Does shot-making fall with minutes into a stint (fatigue)?

Starter-level players shoot 2.34 points per 100 shots worse at 9+ minutes into a stint than at 3-6 minutes (-2.65 to -2.01). Bench players look better the longer they stay, but that is mostly coaches keeping hot players on.

Sample: 5.9M shots

What do back-to-backs, travel and altitude cost?

A back-to-back costs 1.8 points of margin on the road and 1.5 at home; the cost has not shrunk over time.

How do players who play the second night of a back-to-back perform?

0.3 TS points worse and 0.17 game score per 36 lower; the drop does not grow with age, and those who play get slightly more minutes.

Beyond back-to-backs and three-in-four, does a crowded week cost?

Yes, but smaller than a back-to-back. Each extra game in the previous 7 days costs -0.34 (-0.50 to -0.21) points of margin, about a fifth of a back-to-back (-1.67), on top of the back-to-back, rest and three-in-four terms. It runs through defense (+0.40 (+0.24 to +0.52) points per 100 allowed). Four games in five nights: -0.39 (-0.82 to +0.07).

Sample: 68,414 team-games (34,207 games); ratings from games before each game

Does regular-season rest pay off in the playoffs?

No design shows a payoff: playoff TS per 3 fewer minutes a game +0.04 (−0.11 to +0.22; effects under about 0.26 could not show). The one estimate clear of zero runs through injury: 10 points more games missed goes with 5.7 points less playoff availability.

Do teams score or defend worse when the game runs faster or slower than they are used to?

Not detectable. Per 3 possessions per 48 of mismatch (either direction), a team's own offense changes by +0.05 (-0.09 to +0.18) points per 100 against its pre-game expectation; both offenses together change by +0.11 (-0.18 to +0.37). Held-out years agree (+0.07 (-0.13 to +0.30)) and the next-opponent placebo is +0.11 (-0.02 to +0.22).

Sample: 68,414 team-games (34,207 games); ratings from games before each game

Does a team's result against its pre-game rating expectation change with the game's pace?

No. Against the pre-game gap the margin residual moves +0.18 (-0.04 to +0.45) points per 3 possessions per 48 (curvature -0.10 (-0.25 to +0.02)). By actual pace minus the team's norm, the average margin residual stays within about 0.1 points in every bin except the slowest (more than 6 below the norm: +0.32 (+0.07 to +0.55)).

Sample: 68,414 team-games (34,207 games); ratings from games before each game

Do half-court teams lose more than transition teams when the opponent plays faster?

The declared test is null: +0.10 (-0.11 to +0.34) points of margin per 3 possessions per 48 (half-court minus transition), but its placebos were not centred on zero. With own-pace controls (added afterwards) the contrast is -0.24 (-0.53 to +0.02), in the hypothesised direction but including zero; it is -0.57 (-1.01 to -0.18) in 2015-2025 and -0.13 (-0.45 to +0.18) in 1997-2014.

Sample: 68,414 team-games (34,207 games); ratings from games before each game

Do teams built on defense hold up better than others when the opponent plays faster?

A small lead. Defense-first teams beat their rating expectation by +0.31 (+0.11 to +0.55) points of margin more than other teams per 3 possessions per 48 that the opponent is faster. The next-opponent placebo is -0.03 (-0.30 to +0.29); the held-out years give +0.43 (+0.05 to +0.87) and the early years +0.24 (-0.01 to +0.47).

Sample: 68,414 team-games (34,207 games); ratings from games before each game

What is playoff home court worth beyond the skill difference between the teams?

Within-series estimate 4.09 points (90% 3.61 to 4.57), 1996-2026; regular season 2.77 (2.56 to 2.96) by the same method; difference 1.32 (0.82 to 1.84).

Sample: 435 series, 1692 always-played games; 34,487 regular-season games

Does the playoff home edge survive without fans and travel?

Supported by the 2020 bubble: same nominal hosts and 2-2-1-1-1 order, no fans or travel, home edge -0.07 (-2.58 to 2.45), 4.5 below nearby postseasons.

Sample: 435 series, 1692 always-played games; 34,487 regular-season games

Does home court change the chance of winning the series, beyond skill?

Supported (model-implied): hosting is worth 6.6 percentage points against the opponent hosting (5.8 to 7.4), 8.0 for even teams. The direct series test (70 underdog-hosted series) gives 14.6 (5.5 to 23.6), consistent but noisy. Updated 2026-10-15: the model-implied value was 5.8 (5.1 to 6.5) before the 2026-10-09 fix that moved the mixed-model fit to its true optimum (series-skill spread omega 4.37 -> 1.70; agents/statsmodels-port/verify.json); a wider skill spread had been absorbing part of home court. The direct test did not move.

Sample: 435 series, 1692 always-played games; 34,487 regular-season games

What does one extra point of regular-season margin buy in seeding, home court, playoff games and title odds, by team?

Supported in simulation: one point of margin per game adds 0.25 home playoff games for the average team (0.31 hosted as series host) and 5.2 points of round-1 hosting odds; 0.42 home games for teams ranked 4th-8th; near zero for lottery teams and top seeds.

Sample: 10,000 simulated seasons per team and margin step

How often were seeds, and series hosts, within one or two wins?

Mixed: adjacent seeds are often close (4th and 5th within 2 wins in 57% of conference-seasons; 6th and 7th within 1 win in 65%), but the host of a real best-of-7 series led its opponent by 2 wins or fewer in only 19% (median edge 7 wins).

Sample: 40 conference-seasons; 330 series

Does the playoff home edge change in games 5, 6 and 7, once the selection of series that reach them is removed?

Yes: games 5-7 pooled carry 3.6 points beyond skill after correcting for which series reach them, -0.5 (-1.6 to 0.6) against games 1-4; the within-series design gives -0.5.

Sample: 387 series, 2160 games; secondary 1983-2026 sample 478 series, 2680 games

Does the playoff home edge follow the regular season's decline since about 2010?

Not supported: since 1983 the regular-season edge fell 0.72 points per decade, the playoff edge 0.22 (interval includes no decline); trends differ by 0.50 per decade.

Sample: 435 series, 1692 always-played games; 34,487 regular-season games

How much of the raw playoff home margin is skill rather than venue?

No: skill explains 4.1% of the raw home margin (-2.0 to 10.7%); the lower seed hosts games 3, 4 and 6, so home teams are only slightly better on average.

Sample: 435 series, 1692 always-played games; 34,487 regular-season games

Does the playoff home edge differ by round?

Not supported: conference finals and Finals minus rounds 1-2 = +0.39 points (-0.61 to 1.39).

Sample: 435 series, 1692 always-played games; 34,487 regular-season games

Is the home edge larger in game 7s and other deciding games?

Not distinguishable: the deciding-game term is -0.08 (-1.83 to 1.66), selection-bias corrected. Updated 2026-10-09 after the mixed-model fit was moved to its true optimum (it was +0.71 before). Hosts won 77 of 107 game 7s, about what home court plus skill predicts.

Sample: 435 series, 1692 always-played games; 34,487 regular-season games

Does the side facing elimination outperform its series level?

Not supported, and the sign runs the other way: the side facing elimination plays about 1 point below its level (-0.97, 90% -1.81 to -0.12, selection-bias corrected). Corrected 2026-10-09: the earlier +0.08 (-0.79 to 0.95) came from a mixed-model fit that had stopped before its optimum (REML log-likelihood 16.4 lower). The numpy port (agents/statsmodels-port/verify.json) finds the true optimum (omega 4.37 -> 1.70). The fixed-effects version, corrected, agrees in sign (-1.37). One test among several in this family, so treat it as small and borderline.

Sample: 435 series, 1692 always-played games; 34,487 regular-season games

Is the home edge in game 6 different from games 1-4?

Unsettled: game 6 sits about 2 points below games 1-4 (-1.8 prior skill, -2.1 within series); only the within-series interval excludes zero, and 1983-2026 data give -0.8.

Sample: 387 series, 2160 games; secondary 1983-2026 sample 478 series, 2680 games

Does the home edge change with the series score, in particular for a home team facing elimination?

Suggestive: the home team's edge in this state is about zero (0.6 / -0.3 points), -3.5 and -4.4 against the constant edge; fails the multiple-comparison bar for 15 states.

Sample: 387 series, 2160 games; secondary 1983-2026 sample 478 series, 2680 games

Does the result of game 1 change the host's game-2 margin beyond what skill predicts?

Suggestive: after a game-1 loss the host's game-2 margin beats the constant-skill model by +3.2 points (1.1 to 5.2); after a game-1 win it trails by -1.0. Both games are at the host, so venue cannot explain it.

Sample: 387 series, 2160 games; secondary 1983-2026 sample 478 series, 2680 games

Does running a play for the new player right away help or hurt?

First shots taken in the team's first possession after a player enters are much worse than first shots that come later.

Sample: Mid-quarter entries. Shot model already adjusts for shot type, distance, location and shot clock.

Do some players reliably start colder than others?

Players who start cold in even seasons are no more likely to start cold in odd seasons. Individual cold-start numbers are noise.

Sample: Players with 100+ mid-entry first FGAs in each half. Shrunk table covers 1352 players.

Who controls pace when two teams with different norms meet?

No one gets extra say. A game's pace is the league average plus each team's own pace deviation. The share of control is +0.49 (+0.48 to +0.50) for the faster team, +0.50 (+0.49 to +0.51) for the home team and +0.51 (+0.50 to +0.51) for the better team (0.5 = equal say).

Sample: 68,414 team-games (34,207 games); ratings from games before each game

How do playoff games differ from the regular season?

Slower (−2.1 possessions per 48), lower-scoring (−3.5 per 100 raw; −1.3 beyond the better opponents) and more concentrated on the top two players (usage share 41% → 44%).

Do bigs or guards change most, against their own baseline, when the opponent plays faster?

Yes, slightly. Per 3 possessions per 48 of opponent pace, bigs (82 in and up) gain +0.26 (+0.17 to +0.35) points per 100 possessions and +0.38 (+0.24 to +0.53) TS percentage points relative to guards (75 in and under). Guards' own TS slope is -0.12 (-0.22 to -0.03); bigs' is +0.26 (+0.16 to +0.37).

Sample: 603,408 player-games, 2,591 players

Do young or athletic players gain in fast games relative to their own baseline?

No. Every group gains a little when the opponent plays faster, by about the same amount. Young (23 and under) minus 30-and-over: +0.04 (-0.05 to +0.13) game score per 100 possessions per 3 possessions per 48. Athletic (top third of 2015-16 fast-break speed for height) minus others: +0.11 (-0.04 to +0.25).

Sample: 603,408 player-games, 2,591 players

Do high-usage creators gain or lose in fast games relative to their own baseline?

Unclear. Creators' TS changes like everyone else's (contrast +0.00 (-0.11 to +0.11) percentage points). Their points per 100 contrast is -0.07 (-0.14 to -0.01), but it flips sign between 1997-2014 (-0.20 (-0.26 to -0.12)) and 2015-2025 (+0.20 (+0.11 to +0.34)), and its placebo is not null (+0.07 (+0.01 to +0.13)).

Sample: 603,408 player-games, 2,591 players

What do back-to-backs, travel and altitude cost?

Denver and Utah have the largest home edges, about 2.0 points beyond the league's.

Do visitors fade late in games at Denver and Utah?

Only on the second night of a back-to-back. Visitors' fourth quarter minus their first three, in net points per 100 possessions, is -1.4 (-3.3 to +0.2) at altitude beyond other arenas (includes zero). On a back-to-back it drops a further -2.6 (-4.4 to -0.6). The Q2 placebo is +0.8 (-1.4 to +2.9).

Sample: 34,207 visitor games, 2,302 at Denver/Utah

Does a player's usage change with the quality of the opposing unit?

When 0-1 opposing starters are on the floor, a player's usage share rises about one point above his own norm.

Sample: Opposing starters = players on court at the opening tip of that game.

How does foul trouble change a player's game?

In foul trouble, players shoot less often and foul less, with no change in shot-making.

Sample: Foul trouble at the start of a lineup stint: 2+ fouls in Q1, 3+ in Q2, 4+ in Q3, 5+ in Q4/OT.

Is there a fatigue interaction between pace and back-to-backs or fourth quarters?

No. Being forced faster on the second night of a back-to-back changes the margin residual by -0.04 (-0.26 to +0.14) per 3 possessions per 48. In fourth quarters, a faster predicted game changes a team's own offense (Q4 minus Q1-Q3) by -0.17 (-0.37 to +0.04) per 100; the back-to-back interaction is +0.35 (+0.08 to +0.63), the opposite sign to fatigue.

Sample: 68,414 team-games (34,207 games); ratings from games before each game

How do teams do in the first home game after a long road trip, and late in long trips?

No letdown. The first home game after a 4+ game trip: -0.14 (-0.55 to +0.38) points against the pre-game expectation; after a 6+ trip -0.42 (-1.24 to +0.28). The last game of a 4+ trip: -0.39 (-0.99 to +0.17). Games 5+ of a trip: +0.62 (+0.18 to +1.14), but not in the held-out years (+0.12 (-0.58 to +0.85)).

Sample: 68,414 team-games (34,207 games); ratings from games before each game

When did this tactic change in our data, and does that match the told date (late 2000s on; told partial reversal in the 2020s)?

League offensive rebound rate fell from about 33% to 22% (low 2019-20) and is back near 26%.

Sample: Team box scores

How do usage, shot mix and efficiency differ by when and how a player enters (starter vs bench, first vs re-entry, each half)?

Against their own norms, starters re-entering in the second half draw more free throws and run less in transition. Bench players' first stints are below their norm in shot-making.

Sample: Contexts S1-S4 (starters) and N1-N5 (bench) defined in agents/cold-start/plan.md.

The back-to-back cost grew because teams rest stars on the second night?

Only a small part. The second-night cost grew -0.92 points (-1.47 to -0.22) from 1997-2021 to 2021-26; the part running through top-two absences grew -0.11 (-0.21 to -0.01), about 12% of it.

Sample: 34269 games

How well is each input measured?

Counting stats are reliable at 500+ minutes (0.85 to 0.98). The noisy inputs are true shooting (0.70) and 3P% (half weight needs about 193 attempts); steals for size need about 316 minutes.

How wrong are listed heights?

The database stores one final height per player. Listings run +1.24 in over barefoot for players retired before 2019-20 and +0.61 in after.

Can a box-score stand-in measure athleticism?

No: the stand-in tracks 2015-16 in-game peak speed at rank correlation 0.09. Athleticism is unmeasurable from box scores before the combine era.

How much does survivorship distort aging curves?

Without a survivor correction, the 31-35 drop in 3P% is -0.47 league spreads; with it, -0.18. Shooters who keep playing are partly the lucky ones, and their next season regresses.

Sample: Player-season pairs, 200 player resamples

Do shrinkage strengths fitted by prediction (empirical Bayes) beat hand-set ones?

Mostly close. Catch-and-shoot shrinkage was far too weak (k 49 → 215) and play-type efficiency badly under-shrunk (25 → 125-370).

Does weighting each pair by next season's minutes bias the survivor age curve?

Yes. The front-page delta weights each pair by the harmonic mean of both seasons' minutes; next season's minutes are an outcome. With equal weights the survivor curve peaks at 26 (26 to 28) and sits 0.18 spreads (0.14 to 0.23) lower at 28.

Sample: 10,827 at-risk pairs, 200 player bootstraps

How do ABA values translate to the NBA scale?

ABA-to-NBA movers kept 0.76 of their ABA value spread (90% [0.608, 0.945]) with a level shift of -0.64 per 100 (90% [-1.04, -0.232]).

Sample: 104 ABA->NBA pairs, 1788 NBA pairs

How strong was each era's league in absolute terms?

Untested: values here are relative to each season's league; an era-bridging model (players' value changes across league changes, with an age curve) could estimate absolute league strength.