NAIL-RAPM v1.2.3: Free-Throw Profile
NAIL-RAPM v1.2.3 is a strict one-feature extension of v1.2.1. It adds the sum of the five players' forward-safe, stat-specifically padded free-throw attempts per 100 possessions as a ninth additive player-profile coordinate. It deliberately does not include v1.2.2's rejected defensive-rebound percentage term.
The value-conditioned aging prior, exposure-gated cold starts, gap-returner bridge, stat-specific profile padding, Ridge penalty, and the two retained non-additive terms are unchanged.
Contract
For unit \(U\), the new additive coordinate is
where the tilde is the lagged, stat-specifically padded player rate. The home-minus-away coefficient is compiled into the player-attributable additive rating; it is not a new non-additive lineup effect.
Decision Plan
The recursive model will be fitted through 2025-26, then replayed against v1.2.1 on the frozen 2023-24 through 2025-26 regular seasons and playoffs. The audit will report both binary sign share and directional mass:
where \(\beta_t\) is the standardized source-season coefficient. This avoids treating a near-zero crossing as equivalent to a large reversal. We will also report the same statistic for the most recent ten source seasons, so a historical positive effect cannot conceal a currently unresolved direction.
Promotion requires directional stability and a competitive frozen replay. The formal paired full-game-RMSE non-promotion gate is retained as a safety check, but passing it alone does not establish a performance improvement. No website bundle changes until the results are reviewed.
Frozen Result
The 2023-24 through 2025-26 frozen replay does not promote the feature.
| Metric | v1.2.1 | v1.2.3 | Difference (v1.2.3 - v1.2.1) |
|---|---|---|---|
| Regular possession RMSE | 1.197952 | 1.197964 | +0.000012 |
| Regular possession MAE | 1.141355 | 1.141341 | -0.000014 |
| Regular eligible game RMSE | 14.0245 | 14.0456 | +0.0211 |
| Regular full-game RMSE | 14.2521 | 14.2726 | +0.0204 |
| Game-winner accuracy | 68.24% | 68.47% | +0.23 pp |
| Team NetRtg RMSE | 3.2706 | 3.2974 | +0.0268 |
| Pythagorean-win RMSE | 7.0351 | 7.0511 | +0.0160 |
| Playoff possession RMSE | 1.192709 | 1.192714 | +0.000005 |
| Playoff eligible game RMSE | 16.5942 | 16.6157 | +0.0215 |
The paired 2,000-draw bootstrap gives a pooled full-game-RMSE difference of
+0.0204, with 95% interval [-0.0012, +0.0420]; v1.2.3 is better in only
3.3% of draws. It clears the deliberately permissive no-material-harm safety
gate, but it is not competitive with v1.2.1 on the primary margin metrics.
The isolated possession-MAE and winner-accuracy gains do not outweigh that
broader regression.
FTA/100 Stability
FTA/100 is not rejected for instability. Its standardized coefficient is
positive in 27 of 29 completed source seasons (93.1%), with median +1.319.
The positive-directional mass share is 97.3% across the full history and
100.0% in the most recent ten source seasons. The negative result is therefore
useful: the feature is directionally credible, but redundant after the existing
additive profile rather than a source of out-of-sample improvement.
Additive Profile Coefficients
Each panel shows the standardized Ridge coefficient from the completed source-season state. FTA/100 is the ninth panel. The new directional-mass summary weights the visible magnitude of each season rather than treating every sign crossing equally.
Retained Non-Additive Coefficients
The two retained lineup-level terms are unchanged from v1.2.1 and are shown here to verify that adding FTA/100 does not produce an implausible shift in the non-additive component.
The complete fit, frozen replay, paired bootstrap, and directional-mass ledger
are persisted under artifacts/models/forward_nail_rapm_v123_free_throw_profile,
artifacts/models/nail_v123_free_throw_profile_frozen_backtest,
artifacts/models/nail_v123_free_throw_profile_bootstrap, and
artifacts/models/analysis/nail_v123_free_throw_profile_weight_audit.