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NAIL-RAPM v1.3.2: Dynamic Additive Profiles

NAIL-RAPM v1.3.2 is the state-space successor to v1.3.1. It keeps the same ten retained additive player-profile terms, player prior, cold starts, gap-returner bridge, non-additive lineup terms, and linear Ridge context fit. Its only change is how the additive coefficients move from one completed season to the next.

Dynamic State Contract

Let \(\theta_{j,t}\) denote raw coefficient \(j\) after completed season \(t\), and let \(\bar\theta_{j,t-1}\) be its running mean over only the prior completed posterior states. Before season \(t\), v1.3.2 uses

\[ \theta_{j,t}^{-} = \bar\theta_{j,t-1} + \phi_{j,t} \left(\theta_{j,t-1} - \bar\theta_{j,t-1}\right), \]
\[ P_t^{-} = \Phi_t P_{t-1}\Phi_t^\top + \operatorname{diag}(q_{1,t}, \ldots, q_{10,t}). \]

The coefficient-specific \(\phi_{j,t}\) is a shrunk AR(1) estimate from the prior completed history. The innovation variance \(q_{j,t}\) is the prior-only empirical AR innovation variance, floored by 10% of the preceding posterior variance. This allows a consistently stable feature to persist while allowing a genuinely changing feature to move.

Nine terms classified as stable material use a persistent default reversion target of 0.90. Unassisted three-point makes, the one sustained-regime-shift term, uses a more responsive target of 0.60 and may estimate a mildly negative AR coefficient. The category-4 zero gate is implemented but empty: v1.3.1 already removed its two insufficiently resolved terms, usage and three-point attempts per 100.

The transition is strictly forward. A state used to forecast 2024-25 can use the complete history through 2023-24, never 2024-25 outcomes or later states.

Coefficient Trajectories

The panel below records the standardized Ridge coefficient for each retained additive term after each completed source season. It uses the same coordinate definition as v1.3.1: the conditional effect of a one-standard-deviation home-minus-away lineup differential, holding the remaining profile and non-additive terms fixed. The dynamic state is used as a forward prior; each point remains the posterior after that season's observed evidence.

NAIL-RAPM v1.3.2 dynamic additive profile coefficient trajectories

The trajectories are visibly more stable for the material terms, especially assists, steals, blocks, defensive rebound percentage, and unassisted rim makes. This supports the intended interpretive behavior. It does not itself establish a predictive gain: the relevant test is the frozen result below.

Evaluation

The full recursive fit, three-season frozen replay, and direct paired game-block bootstrap completed. v1.3.1 is the direct incumbent because v1.3.2 changes only the between-season additive-coefficient state transition.

Model Regular poss. RMSE Regular full-game RMSE Winner accuracy Team NetRtg RMSE Pythagorean-win RMSE Playoff poss. RMSE Playoff eligible-game RMSE
NAIL-RAPM v1.3.1 1.197990 14.307243 68.36% 3.3446 7.1012 1.192646 16.5248
NAIL-RAPM v1.3.2 1.197969 14.282764 68.27% 3.3465 7.0846 1.192690 16.5587

Direct Bootstrap Gate

Positive full-game values mean v1.3.2 has higher error than v1.3.1. Although the pooled estimate favors v1.3.2 by 0.0245 RMSE, its 95% interval crosses zero and the candidate materially worsens two of three individual seasons. It therefore does not meet the stricter per-season promotion requirement.

Scope v1.3.2 minus v1.3.1 Paired 95% interval Gate threshold Gate
Pooled -0.0245 [-0.0778, +0.0290] +0.0715 Pass
2023-24 +0.0676 [-0.0107, +0.1484] +0.0698 Fail
2024-25 -0.2445 [-0.3732, -0.1213] +0.0728 Pass
2025-26 +0.0964 [+0.0288, +0.1643] +0.0719 Fail

v1.3.2 is a useful forward-only state experiment, but it is not promoted over v1.3.1. Its dynamic coefficients improve interpretive stability without a consistent frozen-prediction gain.

Artifacts

  • Recursive fit: artifacts/models/forward_nail_rapm_v132_dynamic_additive_profiles/2025-26/forward-nail-rapm-v132-dynamic-additive-profiles-2025-26-20260822T133348Z-1760349c
  • Frozen replay: artifacts/models/nail_v132_dynamic_additive_profiles_frozen_backtest/frozen_multiseason_backtest/2023-24_to_2025-26/frozen_multiseason_backtest-2023-24-to-2025-26-20260822T161207Z-9c4a6bea
  • Bootstrap gate: artifacts/models/nail_v132_dynamic_additive_profiles_bootstrap/2023-24_to_2025-26/nail-v132-dynamic-additive-profiles-bootstrap-20260822T161422Z-2457d335
  • Coefficient audit: artifacts/models/analysis/nail_v132_dynamic_additive_weight_audit/nail-v132-dynamic-additive-weight-audit-20260822T162754Z-153e3de7

Reproduction

See Train NAIL-RAPM v1.3.2 Dynamic Additive Profiles.