Skip to content

Additive Prior Plus Linear Non-Additive Context

Last updated: 2026-08-15

This is the controlled test of the project’s attribution contract:

  1. Player-additive profile information belongs in a strictly lagged player prior.
  2. Only genuinely non-additive five-player properties remain in lineup context.

The player prior is the existing eight-feature Additive Profile-Prior RAPM: three-point attempts and makes, assists, turnovers, usage, offensive rebound percentage, steals, and blocks. Its coefficients are learned recursively using only completed prior seasons.

The context layer is standardized linear Ridge over exactly six non-additive features:

\[ C(H,A)=\sum_{k=1}^{6}\gamma_k\,[z_k(H)-z_k(A)]. \]

The six (z_k) values are bottom-two three-point makes, credible-shooter count, top-two assists, usage concentration, shooting-by-usage, and shooter-by-passing. They are handcrafted nonlinear functions of the five players, but their effects on net rating are deliberately linear. There are no P-splines, quadratic terms, thresholds beyond the declared shooter definition, or target-season outcomes in the fitted state.

Evaluation

The primary comparison is against additive profile-prior RAPM with no context. The frozen evaluator will replay 2023-24, 2024-25, and 2025-26 from the state available before each season, then report regular season and pooled playoff metrics separately.

Frozen Result

The three-season replay covers 584,970 eligible regular-season possessions (3,284 games) and 39,967 playoff possessions (238 games).

Cohort Metric Additive player prior only Additive prior plus linear non-additive context Non-additive minus control
Regular season Possession RMSE 1.198042 1.198026 -0.000015
Regular season Possession MAE 1.141429 1.141366 -0.000063
Regular season Eligible game RMSE 14.2457 14.2154 -0.0303
Regular season Full-game RMSE 14.4902 14.4542 -0.0360
Regular season Winner accuracy 68.07% 67.76% -0.31 pp
Playoffs Possession RMSE 1.192751 1.192814 +0.000063
Playoffs Eligible game RMSE 16.6886 16.7224 +0.0339

The non-additive lineup layer improves every regular-season error metric versus the exact additive-prior-only control. Its paired full-game RMSE interval is \([-0.0765, +0.0047]\), with a 95.84% bootstrap probability of improvement, but the upper endpoint remains above zero. It therefore does not yet meet the project’s strict primary-metric promotion rule. The playoff check favors the control.

This establishes that the declared non-additive lineup features contain some incremental regular-season signal after additive player profile credit is moved into the prior. It does not establish that they outperform the current NAIL-RAPM v1.0 reference.

Artifact: artifacts/models/analysis/additive_profile_linear_shape_context_frozen/frozen_multiseason_backtest/2023-24_to_2025-26/frozen_multiseason_backtest-2023-24-to-2025-26-20260816T063830Z-ae6c82db.