Exposure-Gated O/D Cold Starts

This model applies the cold-start exposure gate to the frozen offense/defense RAPM state. It is the first cold-start model that preserves the O/D identification convention rather than assigning a one-number prior to an O/D design.

Returning players retain their completed 2024-25 O/D RAPM values. For each first-NBA-season player \(i\), the common probability of entering the low-exposure pool mixes separately estimated offense and defense priors:

\[ \widehat O_i^{cold} = p_i^{low} O^{replacement} + (1-p_i^{low})\widehat O_i^{draft}, \]

\[ \widehat D_i^{cold} = p_i^{low} D^{replacement} + (1-p_i^{low})\widehat D_i^{draft}. \]

The frozen O/D possession scorer then uses the home offense and away defense with opposite signs:

\[ \widehat y_i = \overline y + \frac{\sum_{p \in O_i}\widehat O_p - \sum_{p \in D_i}\widehat D_p}{100} + s_i\frac{h}{100}. \]

Thus, the model never splits a one-number replacement estimate in half. It fits and retains a distinct value for scoring and for points prevented.

Frozen 2025-26 Inputs

The immutable run is artifacts/models/exposure_gated_offense_defense/2025-26/exposure-gated-od-2025-26-20260806T023559Z-4ffeb2bc/. Every fitted component ends with the 2024-25 regular season.

Component	Training window	Result
Returning O/D state	1996-97 through 2024-25 forward O/D RAPM	462 returning-player priors
Draft offense rate	First-year O/D estimates through 2024-25	Ridge penalty 10.0
Draft defense rate	First-year O/D estimates through 2024-25	Ridge penalty 1.0
Exposure gate	First-year exposure outcomes through 2024-25	Player-specific \(p_i^{low}\)
O/D replacement token	29 completed regular seasons, <5% team opportunity share	offense -2.702; defense -1.175

The token values are equal-season means of independently tokenized O/D RAPM fits. Their net sum is -3.877, but only the separate side values enter the lineup scorer.

The 100 first-year 2025-26 profiles are generated before target outcomes are read. Evaluation uses realized target lineups and exposures only, with no 2025-26 score, possession outcome, target player refit, or playoff outcome in the prior.

Result

The added O/D cold starts reduce regular-season unknown player exposures by 90.4%, from 254,212 in the frozen O/D baseline to 24,356. On the same 1,230 regular-season games, they also improve O/D RAPM's possession RMSE and game-margin RMSE. The one-number exposure-gated prior remains better on game-margin RMSE, and this O/D version is slightly worse than plain frozen O/D RAPM on the 85-game playoff holdout.

Model	Cohort	Possession RMSE	Possession MAE	Game-margin RMSE	Unknown player exposures
Frozen O/D RAPM	Regular season	1.198853	1.142664	14.8901	254,212
Exposure-gated O/D cold starts	Regular season	1.198792	1.142422	14.7631	24,356
Frozen O/D RAPM	Playoffs	1.194642	1.139203	17.8037	5,678
Exposure-gated O/D cold starts	Playoffs	1.194678	1.139209	17.8562	93

See the Frozen Preseason Leaderboard for the comparison against all evaluated preseason models, including team NetRtg and Pythagorean wins.

Artifacts

File	Contents
`rookie_od_draft_rates.parquet`	Outcome-free target draft offense and defense rates
`revised_rookie_od_rankings.parquet`	100 blended first-year O/D priors and net ranks
`season_od_replacement_tokens.parquet`	Per-season separately estimated O/D replacement tokens
`od_rate_cross_validation.parquet`	Six forward validation seasons for each O/D ridge penalty
`frozen_player_priors.parquet`	Final 2025-26 O/D prior vector used for scoring
Evaluation parquet files	Possession, game, team NetRtg, and Pythagorean win outputs
`metadata.json` / `source_state.json` / `manifest.json`	Temporal boundary, input identities, and integrity hashes