NAIL Context Block-Penalty Study

This study tests whether NAIL-RAPM should regularize its eight additive profile terms and two non-additive lineup terms at different strengths. Everything else is fixed to the production NAIL-RAPM v1.2.1.3 contract, including the residualized player-lambda selection, aging and cold-start priors, Medvedovsky profile padding, B2B control, fit ordering, and frozen evaluator.

Candidate Contract

The context Ridge objective is

\[ \sum_k w_k\left(y_k-X_{k,A}\beta_A-X_{k,N}\beta_N\right)^2 + \alpha_A\lVert\beta_A\rVert_2^2 + \alpha_N\lVert\beta_N\rVert_2^2, \]

where \(X_A\) contains the eight additive profile coordinates and \(X_N\) contains top_two_assists and usage_concentration. The additive penalty is fixed at \(\alpha_A=10{,}000\), while

\[ \alpha_N=r\alpha_A, \qquad r\in\{0.25,0.5,1,2,4,8,16\}. \]

A structural additive-only control omits both non-additive coefficients. The development window is 2019-20 through 2022-23. The registered selection rule chooses the largest ratio within one paired-season standard error of the lowest equal-season full-game MSE; it selected \(r=16\).

Development Result

Ratio	Full-game RMSE	Winner accuracy	Team NetRtg RMSE	Pythagorean-win RMSE
1	13.5048	64.27%	2.8675	6.6076
4	13.5017	64.20%	2.8613	6.5875
8	13.5005	64.23%	2.8582	6.5742
16	13.5002	64.32%	2.8563	6.5616
Additive only	13.5160	64.15%	2.9125	6.6852

Locked Frozen Result

Both rows below use the corrected evaluator over the same 625,615 regular possessions, 3,511 regular games, and 39,967 playoff possessions. Lower is better except winner accuracy.

Metric	Production shared penalty	Candidate \(r=16\)
Regular possession RMSE	1.198147	1.198144
Regular possession MAE	1.141455	1.141478
Regular eligible-game RMSE	14.0051	14.0134
Regular full-game RMSE	14.2166	14.2327
Winner accuracy	68.30%	68.30%
Team NetRtg RMSE	3.2351	3.2735
Pythagorean-win RMSE	6.9423	7.0265
Playoff possession RMSE	1.192728	1.192719
Playoff eligible-game RMSE	16.5782	16.5595

The candidate's tiny possession and playoff gains do not offset its losses on regular game and team outcomes. The shared 10,000 penalty remains the production contract. The candidate is not added to the production leaderboard or model tree.

Coefficient Histories

The completed 1996-97 through 2025-26 fit provides the required annual review. Blue panels are additive profile terms; orange panels are genuinely non-additive lineup terms.

r=16 non-additive coefficient trajectories

The stronger penalty does not erase the retained non-additive signals. top_two_assists has 99% one-sided coefficient mass and usage_concentration has 81%. This supports retaining both features while rejecting the larger penalty on frozen predictive grounds.

Artifacts

Completed r=16 fit: artifacts/models/forward_nail_rapm_v1213_block_penalty_r16/2025-26/forward-nail-rapm-v1213-block-penalty-r16-2025-26-20260828T213200Z-5630f328
Frozen candidate replay: artifacts/models/nail_v1213_block_penalty_locked_backtest/frozen_multiseason_backtest/2023-24_to_2025-26/frozen_multiseason_backtest-2023-24-to-2025-26-20260828T213732Z-3ab0b3fc
Corrected production replay: artifacts/models/nail_v1213_block_penalty_locked_incumbent_backtest/frozen_multiseason_backtest/2023-24_to_2025-26/frozen_multiseason_backtest-2023-24-to-2025-26-20260828T214328Z-0ac35125
Coefficient review: artifacts/models/analysis/nail_v1213_block_penalty_r16_review/nail-v1213-promotion-review-20260828T214530Z-f59a9881

See the reproduction guide.