NAIL Lower-Quintile Critical-Spacing Candidate

Status: rejected experimental variant. This candidate uses the exact NAIL-RAPM v1.2.1 contract plus one Critical Spacing indicator. It changes only the cutoff from the lower tercile to the lower quintile.

Hypothesis

The lower-tercile test may have included too many merely below-average shooters. This stricter candidate identifies only the bottom 20% of the forward-safe, season-state shrunk three_pm_per_100 profile distribution. A unit activates the term when at least two of its five players fall strictly below that cutoff:

\[ q_t = Q_{1/5}\left(\{\mathrm{3PM100}_{i,t}:i\in P_t\}\right), \qquad \mathrm{CriticalSpacing}_t(U)= \mathbb{1}\!\left[\sum_{i\in U} \mathbb{1}[\mathrm{3PM100}_{i,t}<q_t]\ge2\right]. \]

Every profile and threshold is constructed from information available before the target season. The player prior, additive profile, retained usage_concentration and top_two_assists terms, and Ridge regularization are unchanged from v1.2.1.

Frozen Results

The recursive candidate was fit through 2025-26 and evaluated on the three strict frozen regular-season and playoff holdouts. The stricter cutoff does not improve the incumbent and is modestly worse on the primary aggregate metrics.

Model	Poss. RMSE	Eligible game RMSE	Full-game RMSE	Winner accuracy	Team NetRtg RMSE	Pythagorean-win RMSE	Playoff eligible-game RMSE
NAIL-RAPM v1.2.1	1.197952	14.024550	14.252137	68.24%	3.270613	7.035098	16.594200
Lower-quintile Critical Spacing	1.197960	14.041824	14.272532	68.10%	3.298537	7.090747	16.627064

This was stopped before paired bootstrap because the point estimates are uniformly inferior to v1.2.1 on the primary regular-season and playoff aggregates. It is therefore not a promotion candidate.

Full Non-Additive Audit

The diagnostic includes all three non-additive terms, not only the test candidate. That makes it possible to distinguish a genuinely incremental term from one that merely displaces a retained coefficient.

Lower-quintile Critical Spacing non-additive coefficient trajectories by source season

The new Critical Spacing coefficient is not directionally credible under the agreed total one-sided-mass criterion. It has positive mass 5.24 and negative mass 4.27, so only 55.1% lies on its dominant positive side, despite the hypothesis expecting a negative spacing penalty. Its median standardized weight is +0.04, mean absolute magnitude is 0.33, and range is -0.81 to +0.95.

The candidate also does not explain its failure through displacement of the retained terms: matched source-season weights remain highly aligned with v1.2.1. usage_concentration has Pearson correlation 0.9941 and mean absolute change 0.0303; top_two_assists has correlation 0.9881 and mean absolute change 0.0710. The lower-quintile term is simply too selective and too unstable to add useful residual predictive signal.

Decision

Do not promote. The tercile candidate had a more coherent negative direction but no meaningful aggregate lift; the quintile candidate is both less stable and predictively worse. Future spacing work should test a richer, forward-safe non-additive formulation rather than additional hard quantile cutoffs.

Reproducibility

Recursive fit: artifacts/models/forward_nail_rapm_critical_spacing_quintile/2025-26/forward-nail-critical-spacing-quintile-2025-26-20260823T233944Z-ffce4c9e
Frozen replay: artifacts/models/nail_critical_spacing_quintile_frozen_backtest/frozen_multiseason_backtest/2023-24_to_2025-26/frozen_multiseason_backtest-2023-24-to-2025-26-20260823T234533Z-9470b3b9
Coefficient audit: artifacts/models/analysis/nail_critical_spacing_quintile_weight_audit/nail-critical-spacing-quintile-weight-audit-20260823T234558Z-a241fd1b