Model review / 2025-26

What a One-Season RAPM Can Establish

This case study starts with an untouched one-year RAPM ranking, then asks which positions survive resampling, time, regularization, data-construction, influence, and lineup-context checks.

1,230 gamesregular season

200 bootstraps complete-game resamples

452 eligible players 500-possession floor

Experimental, not promoted

The review bands below are editorial screening aids, not hypothesis tests, causal conclusions, or a replacement player metric. "Fragile" means the exact top-25 position is not robust in this one-season specification; it does not mean the player is poor or that the coefficient must be false.

Starting point

The source model is a signed, one-number ridge RAPM fit to 39,918 regular-season stints. It selected lambda 0.03 through expanding chronological validation and then refit all 1,230 games. The table below is the initial exposure-eligible top 25 before applying any diagnostic screen.

Rank	Player	Team	RAPM	Possessions	Raw on-court
1	Victor Wembanyama	SAS	6.34	3,896	17.53
2	Shai Gilgeous-Alexander	OKC	6.13	4,730	16.47
3	Kawhi Leonard	LAC	5.50	4,167	8.28
4	Chet Holmgren	OKC	5.43	4,129	16.40
5	Nikola Jokić	DEN	5.02	4,786	11.14
6	Derrick White	BOS	4.85	5,180	11.60
7	Neemias Queta	BOS	4.31	3,752	13.38
8	Dyson Daniels	ATL	4.08	5,317	6.26
9	Donovan Mitchell	CLE	4.00	4,925	7.70
10	Alex Caruso	OKC	3.96	2,125	18.92
11	Cade Cunningham	DET	3.93	4,490	11.09
12	Marcus Smart	LAL	3.89	3,607	6.85
13	Jimmy Butler III	GSW	3.84	2,449	7.76
14	Bam Adebayo	MIA	3.81	5,031	6.06
15	Moussa Diabaté	CHA	3.76	3,790	10.42
16	Julian Champagnie	SAS	3.71	4,745	11.87
17	Devin Vassell	SAS	3.51	4,258	11.72
18	Devin Booker	PHX	3.42	4,442	4.46
19	Amen Thompson	HOU	3.38	5,936	6.74
20	Ajay Mitchell	OKC	3.38	3,075	16.00
21	OG Anunoby	NYK	3.30	4,531	8.85
22	Ausar Thompson	DET	3.11	3,897	11.57
23	Donte DiVincenzo	MIN	3.11	5,223	6.05
24	Jalen Smith	CHI	3.10	2,316	4.27
25	Brandon Miller	CHA	3.08	3,968	9.15

Review bands

The bands deliberately remain separate from RAPM. They summarize whether a top-25 position survives several diagnostics; they do not alter coefficients.

Band	Rule
Stable core	Bootstrap top-25 probability at least 75% and no structural warning
Qualified	Bootstrap top-25 probability at least 50% and at most one structural warning
Fragile	Below the qualified bootstrap threshold or carrying multiple structural warnings

A structural warning is triggered by a chronological or lambda eligible-rank range above 40, an allocation-policy rank change above 20, an exact delete-game coefficient change above 0.45, or more than 80% of possessions beside one teammate. These are transparent case-study thresholds chosen for review readability, not estimated statistical cutoffs.

The screen retains 5 players in the stable core, qualifies 9, and marks 11 initial top-25 positions as fragile.

Rank	Player	Review	Boot top 25	Chronology range	Lambda range	Allocation move	Delete-game move	Teammate share
1	Victor Wembanyama	Stable Core	100%	6	2	2	0.41	66.2%
2	Shai Gilgeous-Alexander	Stable Core	98%	2	2	1	0.33	57.3%
3	Kawhi Leonard	Qualified	91%	31	16	3	0.50	60.8%
4	Chet Holmgren	Stable Core	93%	12	3	2	0.34	60.6%
5	Nikola Jokić	Stable Core	91.5%	2	5	15	0.34	74.7%
6	Derrick White	Stable Core	82%	16	8	6	0.37	66.5%
7	Neemias Queta	Qualified	71%	26	12	10	0.36	82.4%
8	Dyson Daniels	Qualified	62%	36	17	3	0.34	77.7%
9	Donovan Mitchell	Qualified	54%	5	12	17	0.36	63.7%
10	Alex Caruso	Qualified	60%	5	21	15	0.43	60.1%
11	Cade Cunningham	Qualified	62.5%	5	8	22	0.31	65.4%
12	Marcus Smart	Qualified	54%	27	29	19	0.32	66.4%
13	Jimmy Butler III	Fragile	55.5%	3	50	35	0.38	55.9%
14	Bam Adebayo	Qualified	60.5%	48	18	8	0.44	60.4%
15	Moussa Diabaté	Fragile	49%	25	21	8	0.41	71.5%
16	Julian Champagnie	Qualified	58.0%	7	35	26	0.32	61.6%
17	Devin Vassell	Fragile	48.5%	49	16	9	0.37	60.7%
18	Devin Booker	Fragile	38%	12	48	10	0.43	63.7%
19	Amen Thompson	Fragile	44%	14	4	6	0.25	73.5%
20	Ajay Mitchell	Fragile	42.5%	12	71	12	0.42	51.6%
21	OG Anunoby	Fragile	39.5%	85	10	32	0.30	72.5%
22	Ausar Thompson	Fragile	32.5%	83	31	50	0.22	72.9%
23	Donte DiVincenzo	Fragile	34.5%	16	16	4	0.32	74.4%
24	Jalen Smith	Fragile	34.5%	15	73	13	0.38	53.0%
25	Brandon Miller	Fragile	28.0%	73	28	9	0.42	64.6%

Sampling stability

Each horizontal interval is the 5th to 95th percentile of a player's coefficient across 200 complete-game bootstrap samples. The dot is the original full-season RAPM estimate. Positive intervals support positive one-season impact, but the top-25 probability is the stricter question used by the review bands.

Bootstrap coefficient intervals for the initial RAPM top 25 — Coefficient uncertainty and review band for the initial eligible top 25.

Specification and time

The next view separates two different failure modes. Horizontal movement means the rank depends on ridge strength; vertical movement means it changed across expanding season windows. Circle size increases with the largest rank movement under an alternate possession-allocation policy.

Lambda and chronological rank sensitivity for the initial RAPM top 25 — Dashed lines mark the case-study structural-warning thresholds.

Five diagnostic stories

1. Wembanyama and Gilgeous-Alexander: convergent evidence

Victor Wembanyama begins first at 6.34 RAPM and remains top 25 in 100% of bootstrap samples. His chronological, lambda, and allocation rank ranges are only 6, 2, and 2. Shai Gilgeous-Alexander is similarly consistent: 98% top-25 retention with rank movements of 2, 2, and 1. The diagnostics cannot prove either coefficient is causal, but they find no material internal reason to reject these positions.

2. Kawhi Leonard: strong estimate, influential game

Kawhi Leonard ranks third at 5.50 and remains top 25 in 91% of bootstrap samples. Lambda and allocation changes are modest, but deleting his most influential screened game moves the coefficient by 0.50 points, the largest effect among the reviewed leaders. The ranking remains plausible, but its support is less diffuse than the point estimate alone suggests, so the screen labels it qualified.

3. Neemias Queta: positive signal, entangled context

Neemias Queta is the most useful surprising result. His bootstrap interval is entirely positive at [2.12, 6.37] and he remains top 25 in 71% of samples. However, 82.4% of his modeled possessions are beside Derrick White. His raw on-court net rating of 13.38 is adjusted down to 4.31. This is not evidence to discard him; it is evidence that one season has limited leverage for separating his contribution from a recurring successful context.

4. Jimmy Butler III: stable over time, unstable by specification

Jimmy Butler III barely moves chronologically, with a rank range of 3, but moves 50 places across the lambda path and 35 under alternate possession allocation. His 55.5% bootstrap retention is not the main concern. The disagreement instead comes from modeling choices, which is why a single bootstrap interval would have missed the fragility.

5. Ausar Thompson and Brandon Miller: rank precision breaks down

Ausar Thompson and Brandon Miller begin 22nd and 25th, but retain a top-25 position in only 32.5% and 28.0% of bootstrap samples. Their chronological rank ranges reach 83 and 73; Thompson also moves 50 places under allocation alternatives. Both bootstrap intervals remain positive, so the evidence challenges their precise top-25 placement rather than their positive estimated impact.

Model-level checks

Nearby lambda values preserve broad ordering, while the ends of the tested path change the membership of the leaderboard materially.

Lambda	Coefficient correlation	Rank correlation	Top-25 overlap
0.003	0.917	0.921	16/25
0.01	0.974	0.974	19/25
0.03 selected	1.000	1.000	25/25
0.1	0.961	0.954	21/25
0.3	0.897	0.879	18/25

Possession-allocation policies tell a similar two-level story: held-out game-margin performance is stable, but some individual ranks move sharply. Each skill score is computed against the mean model under the same target construction.

Allocation policy	Test possessions	Game-margin RMSE	Skill vs mean
`equal_segments`	18,562	15.81	0.013
`starting_lineup`	18,562	15.87	0.012
`terminal_lineup`	18,562	15.80	0.013
`boundary_split`	18,562	15.83	0.015
`exclude_multi_lineup`	16,586	15.95	0.010

Conclusion

The diagnostics narrow the initial ranking rather than simply approving or rejecting it. Five players form a stable one-season core. Nine remain credible with a specific qualification. Eleven top-25 positions are too sensitive to sampling or specification to publish without prominent uncertainty.

The important distinction is between coefficient sign, coefficient magnitude, and rank precision. Several fragile top-25 players still have bootstrap intervals above zero. The tests are saying that the season supports positive impact more strongly than it supports an exact leaderboard position. Multi-season RAPM is the next direct test of whether these signals persist.

Reproduce this page

uv run --group docs nba-build-rapm-case-study 2025-26 \
  --diagnostics-run-id diagnostics-2025-26-20260728T043406Z-32196bfa

Provenance	Value
Diagnostics run	`diagnostics-2025-26-20260728T043406Z-32196bfa`
Source model run	`baseline-2025-26-20260727T230533Z-72eac627`
Diagnostics manifest SHA-256	`f3d2eb563f69137284fb50d790a6a1ec12c70bccaa7ccb672584bc85ed16c91b`
Generator source SHA-256	`cafe92b109cea921f43b62189843ce1354a2c468e399dcb00c2a514738b58b6f`
Player population	582 total / 452 eligible
Bootstrap samples	200

See the RAPM training and diagnostics guide for the methodological references and complete artifact definitions.