Offense/Defense RAPM

This model separates each player's offensive contribution from their defensive contribution while retaining the project's ridge-regularized RAPM framework. It is evaluated as a frozen preseason forecast, not with a target-season player refit.

Identification

A net-rating row alone cannot identify separate offensive and defensive player coefficients: both sides of a player's contribution enter the same lineup difference. Instead, every lineup stint supplies two offensive-rating rows.

For home offense in stint \(s\),

\[ 100\frac{P_{H,s}}{N_{H,s}} = \alpha + \sum_{p\in H_s}o_p - \sum_{p\in A_s}d_p + h + \epsilon_{H,s}, \]

and for away offense,

\[ 100\frac{P_{A,s}}{N_{A,s}} = \alpha + \sum_{p\in A_s}o_p - \sum_{p\in H_s}d_p - h + \epsilon_{A,s}. \]

\(o_p\) is offensive RAPM and \(d_p\) is defensive RAPM measured as points prevented per 100 possessions, so a stronger defender has a larger positive value. \(N_{H,s}\) and \(N_{A,s}\) are the separate offensive-possession exposures, which are also the row weights. \(h\) is the home-offense shift; its net home margin implication is \(2h\).

Ridge regularization centers otherwise arbitrary offense/defense level shifts. The identifiable net contribution for a player is \(o_p+d_p\).

Forward Prior

The first exemplar uses regular seasons only. It fits seasons 1996-97 through 2024-25 in chronological order. Each completed season's offense and defense coefficients become the ridge center for the following season; unseen players receive zero on both dimensions. Lambda is selected separately for every season with the established expanding chronological game folds.

The completed 2024-25 O/D state is then frozen and scored on every 2025-26 regular-season and playoff possession using realized lineup exposure as the explicit oracle. No 2025-26 outcome is used in fitting a coefficient.

First Result

Cohort	One-number lagged RAPM RMSE	Frozen O/D RAPM RMSE	Difference (O/D - one-number)
Regular-season possessions	1.199000	1.198853	-0.000147
Regular-season game margin	14.8894	14.8901	+0.0007
Playoff possessions	1.192895	1.194642	+0.001747
Playoff game margin	17.5409	17.8037	+0.2627

The regular-season possession improvement is real in this single frozen holdout but extremely small and does not extend to game-margin or playoff prediction. The O/D model is therefore not promoted over one-number lagged RAPM yet. It establishes a useful two-dimensional player representation for subsequent side-specific priors and nonlinear models.

The immutable run is frozen-offense-defense-rapm-2025-26-20260805T050511Z-62b718bd under artifacts/models/frozen_offense_defense_rapm/2025-26/. It contains the historical season-by-season coefficients and lambda selections, frozen player priors, regular/playoff predictions, team evaluations, and file hashes.

2025-26 Retrospective Rankings

The following rankings are a separate completed-season descriptive fit. They start from the frozen 2024-25 O/D state, select lambda with chronological folds within the 2025-26 regular season, and refit all 1,230 regular-season games. They must not be read as a preseason forecast or compared directly to the Frozen Preseason Leaderboard. The selected lambda was 0.03. Each list requires at least 500 side-specific possessions.

Offense is points added per 100 possessions. Defense is points prevented per 100 possessions, so larger positive values are better on both lists. Overall RAPM is their sum, which is the identifiable net contribution from the joint fit. Click any column header in the three tables to sort it.

Top 25 Overall

Rank	Player	Team	Net RAPM	Total possessions	Offense RAPM	Defense RAPM
1	Nikola Jokić	DEN	11.89	4,786	9.73	2.16
2	Shai Gilgeous-Alexander	OKC	9.59	4,730	7.75	1.84
3	Giannis Antetokounmpo	MIL	8.76	2,129	5.25	3.51
4	Joel Embiid	PHI	7.77	2,479	3.74	4.03
5	Alex Caruso	OKC	7.72	2,125	1.14	6.58
6	Stephen Curry	GSW	7.50	2,822	8.43	-0.93
7	Jimmy Butler III	GSW	7.38	2,449	5.42	1.96
8	Victor Wembanyama	SAS	7.00	3,896	1.57	5.43
9	Derrick White	BOS	6.99	5,181	2.53	4.45
10	Rudy Gobert	MIN	6.75	4,951	-0.59	7.33
11	Bam Adebayo	MIA	6.66	5,031	2.60	4.06
12	Franz Wagner	ORL	6.48	2,190	2.91	3.56
13	Jrue Holiday	POR	6.35	3,295	2.72	3.64
14	Aaron Gordon	DEN	6.25	2,057	3.51	2.74
15	Jayson Tatum	BOS	6.23	1,046	4.86	1.37
16	Kawhi Leonard	LAC	6.22	4,167	4.49	1.72
17	Jarrett Allen	CLE	5.88	3,191	3.91	1.97
18	Devin Booker	PHX	5.73	4,442	5.76	-0.04
19	Pascal Siakam	IND	5.64	4,322	3.44	2.19
20	Paul George	PHI	5.51	2,328	1.91	3.60
21	Donovan Mitchell	CLE	5.49	4,925	5.10	0.39
22	Cade Cunningham	DET	5.26	4,490	3.71	1.56
23	Luka Dončić	LAL	5.16	4,759	5.30	-0.14
24	Lauri Markkanen	UTA	5.02	3,080	3.21	1.81
25	Herbert Jones	NOP	5.01	3,289	1.79	3.23

Top 25 Offense

Rank	Player	Team	Offense RAPM	Offensive possessions	Net RAPM
1	Nikola Jokić	DEN	9.73	4,795	11.89
2	Stephen Curry	GSW	8.43	2,823	7.50
3	Shai Gilgeous-Alexander	OKC	7.75	4,735	9.59
4	James Harden	LAC	5.95	4,944	4.02
5	Trae Young	ATL	5.94	853	1.90
6	Devin Booker	PHX	5.76	4,448	5.73
7	LaMelo Ball	CHA	5.62	4,120	4.00
8	Jimmy Butler III	GSW	5.42	2,448	7.38
9	Luka Dončić	LAL	5.30	4,758	5.16
10	Giannis Antetokounmpo	MIL	5.25	2,128	8.76
11	Donovan Mitchell	CLE	5.10	4,927	5.49
12	Karl-Anthony Towns	NYK	4.95	4,722	4.80
13	Jayson Tatum	BOS	4.86	1,048	6.23
14	Jalen Brunson	NYK	4.85	5,245	3.07
15	Kawhi Leonard	LAC	4.49	4,169	6.22
16	Michael Porter Jr.	BKN	4.11	3,402	2.99
17	Kevin Durant	HOU	3.97	5,739	4.81
18	De'Aaron Fox	SAS	3.92	4,707	2.90
19	Jarrett Allen	CLE	3.91	3,190	5.88
20	Luke Kennard	ATL	3.90	3,472	2.26
21	Joel Embiid	PHI	3.74	2,484	7.77
22	Cade Cunningham	DET	3.71	4,490	5.26
23	CJ McCollum	ATL	3.70	4,776	3.87
24	Julius Randle	MIN	3.69	5,476	3.07
25	Jamal Murray	DEN	3.60	5,453	1.52

Top 25 Defense

Rank	Player	Team	Defense RAPM	Defensive possessions	Net RAPM
1	Rudy Gobert	MIN	7.33	4,961	6.75
2	Alex Caruso	OKC	6.58	2,124	7.72
3	Victor Wembanyama	SAS	5.43	3,892	7.00
4	Wendell Carter Jr.	ORL	4.49	4,770	4.51
5	Derrick White	BOS	4.45	5,178	6.99
6	Draymond Green	GSW	4.24	3,874	2.16
7	Jaren Jackson Jr.	MEM	4.17	3,066	4.31
8	Bam Adebayo	MIA	4.06	5,027	6.66
9	Joel Embiid	PHI	4.03	2,474	7.77
10	Clint Capela	HOU	3.96	1,849	3.80
11	Jrue Holiday	POR	3.64	3,292	6.35
12	Matisse Thybulle	POR	3.63	1,008	2.62
13	Paul George	PHI	3.60	2,325	5.51
14	Franz Wagner	ORL	3.56	2,191	6.48
15	Giannis Antetokounmpo	MIL	3.51	2,130	8.76
16	Jusuf Nurkić	UTA	3.48	2,337	2.32
17	OG Anunoby	NYK	3.43	4,537	4.55
18	Herbert Jones	NOP	3.23	3,293	5.01
19	Chet Holmgren	OKC	3.15	4,127	4.94
20	Anthony Davis	DAL	3.09	1,295	4.27
21	Brook Lopez	LAC	2.99	3,278	2.74
22	Evan Mobley	CLE	2.97	4,319	4.37
23	Aaron Gordon	DEN	2.74	2,056	6.25
24	Dillon Brooks	PHX	2.68	3,506	4.28
25	Jalen Suggs	ORL	2.67	3,373	2.10

The immutable ranking run is all-season-offense-defense-rapm-2025-26-20260805T125051Z-7f5ef527 under artifacts/models/offense_defense_rapm/2025-26/. It includes both published tables, all coefficients and exposures, the 2025-26 lambda-selection evidence, and hashes of the exact 2024-25 frozen source state.

Verification

tests/test_offense_defense_rapm.py verifies that the two-row sparse design places the offense lineup in offensive columns and the opponent lineup in defensive columns with the required sign. It also verifies that frozen scoring uses the two coefficient types separately and that published side rankings use the corresponding offensive or defensive possession exposure threshold.