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NAIL-RAPM v1.2.4: Free-Throw Replacement

NAIL-RAPM v1.2.4 tests the conditional-credit hypothesis exposed by v1.2.3: replace additive usage_per_100 with additive free_throw_attempts_per_100 rather than including both. This is a strict sibling of v1.2.1 with eight additive player profile coordinates and the same two retained non-additive lineup terms.

All other contracts are unchanged: value-conditioned aging, exposure-gated cold starts, gap-returner bridging, forward-safe stat-specific padding, and the Ridge lineup fit.

Contract

For a unit (U), v1.2.4 replaces

\[ \operatorname{Usage}(U) = \sum_{i \in U} \widetilde{\operatorname{USG100}}_i \]

with

\[ \operatorname{FTA100}(U) = \sum_{i \in U} \widetilde{\operatorname{FTA100}}_i. \]

The retained non-additive terms remain top_two_assists and usage_concentration. Thus this tests the additive offensive-load coordinate, not whether distribution of usage within a unit matters.

Decision Rule

Fit recursively through 2025-26, evaluate frozen 2023-24 through 2025-26 regular seasons and playoffs against v1.2.1, then run a paired 2,000-draw game-stratified bootstrap. Promotion requires a competitive primary full-game-margin result, not merely a permissive no-material-harm gate.

The coefficient audit includes binary sign share and directional mass,

\[ D_+ = \frac{\sum_t \max(\beta_t, 0)}{\sum_t |\beta_t|}, \]

so a small sign crossing does not outweigh a persistently material direction.

Frozen Result

v1.2.4 does not promote the FTA/100 replacement. It makes the isolated possession-MAE result better, but the primary regular-season margin metrics remain worse than v1.2.1.

Metric v1.2.1 v1.2.4 Difference (v1.2.4 - v1.2.1)
Regular possession RMSE 1.197952 1.197966 +0.000014
Regular possession MAE 1.141355 1.141328 -0.000027
Regular eligible game RMSE 14.0245 14.0457 +0.0211
Regular full-game RMSE 14.2521 14.2733 +0.0212
Game-winner accuracy 68.24% 68.19% -0.06 pp
Team NetRtg RMSE 3.2706 3.2933 +0.0226
Pythagorean-win RMSE 7.0351 7.0459 +0.0108
Playoff possession RMSE 1.192709 1.192706 -0.000003
Playoff eligible game RMSE 16.5942 16.5988 +0.0046

The paired 2,000-draw bootstrap estimates pooled full-game RMSE at +0.0212 for v1.2.4 relative to v1.2.1, with 95% interval [-0.0025, +0.0433]; the challenger is better in 3.5% of draws. It passes the permissive no-material-harm safety gate but fails to provide a reason to displace v1.2.1.

Profile Coefficients

Removing additive Usage/100 resolves the conditional collinearity seen in v1.2.3. FTA/100 is positive in 28 of 29 source seasons, has median standardized coefficient +1.360, and carries 99.96% positive directional mass over the full history (100% across the latest ten seasons). This is a credible coordinate, but its predictive contribution is redundant after the remaining profile contract.

NAIL-RAPM v1.2.4 additive profile coefficient trajectories

Retained Non-Additive Coefficients

The two retained non-additive lineup terms do not change under this replacement experiment.

NAIL-RAPM v1.2.4 retained non-additive coefficient trajectories

The fit, frozen replay, bootstrap, and directional-mass ledger are persisted under artifacts/models/forward_nail_rapm_v124_free_throw_replacement, artifacts/models/nail_v124_free_throw_replacement_frozen_backtest, artifacts/models/nail_v124_free_throw_replacement_bootstrap, and artifacts/models/analysis/nail_v124_free_throw_replacement_weight_audit.

Reproduction

See Train NAIL-RAPM v1.2.4 Free-Throw Replacement.