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NAIL Quartile Critical Spacing Plus Standard USG%

Status: experimental, not promoted. This candidate jointly changes the Critical Spacing threshold and its usage coordinate relative to the production NAIL-RAPM v1.2.1.

Contract

For each source-season player-profile pool \(P_t\), let \(q_t\) be the lower quartile of shrunk three-point makes per 100 possessions:

\[ q_t = Q_{0.25}\left(\{\mathrm{3PM100}_{i,t}: i \in P_t\}\right). \]

For five-man unit \(U\), Critical Spacing is the non-additive threshold event

\[ \mathrm{CriticalSpacing}_t(U) = \mathbb{1}\!\left[ \sum_{i \in U}\mathbb{1}[\mathrm{3PM100}_{i,t} < q_t] \geq 2 \right]. \]

Thus, the feature activates when at least two players are below the prior-season lower-quartile shooting threshold. It does not credit or penalize one low-threat player by itself. Across the frozen 2023-24 through 2025-26 regular-season samples, it activated for 26.0% of lineup sides on average (22.9%, 24.5%, and 30.6% by season).

The candidate also replaces the internal usage-events rate with conventional box-score usage percentage:

\[ \mathrm{USG\%}_i = 100\, \frac{\mathrm{FGA}_i + 0.44\,\mathrm{FTA}_i + \mathrm{TOV}_i} {\mathrm{TeamPossessions}_i}. \]

It then retains the same two non-additive terms as v1.2.1: usage_concentration and top_two_assists. All player profiles, threshold values, and context coefficients obey the forward information boundary.

Frozen Three-Season Results

The recursive model was fit from 1996-97 through 2025-26. The strict replay predicts 2023-24, 2024-25, and 2025-26 using only the relevant preseason player-prior state and the immediately preceding completed context state.

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
Quartile Critical Spacing + standard USG% 1.197954 14.030448 14.258396 68.10% 3.278702 7.045978 16.614526

The new candidate is effectively tied at the possession level, but it is worse on every primary pooled game-level metric. Its full-game RMSE increases by 0.0063, winner accuracy falls by 0.14 percentage points, and playoff eligible-game RMSE increases by 0.0203. It modestly improves possession MAE and Pythagorean-win rank correlation, but neither offsets the losses in the primary scorecard.

Coefficient Diagnostics

The chart shows the full non-additive contract, so the new term can be evaluated together with possible displacement of the two retained terms.

Quartile Critical Spacing plus standard USG% non-additive coefficient trajectories

Feature Median standardized weight Dominant directional mass Interpretation
Usage concentration +1.01 100.0% positive Stable retained signal
Top-two assists +0.60 89.1% positive Stable retained signal
Critical Spacing -0.10 61.2% negative Expected sign, but weak and inconsistent

The quartile threshold is more targeted than the previous lower-tercile candidate, but its coefficient is too unstable and it does not improve the frozen scorecard. The standard-USG% coordinate also does not recover an edge.

Decision

Do not promote this candidate. NAIL-RAPM v1.2.1 remains the production model. This result narrows the spacing hypothesis: a two-or-more low-threat event is directionally plausible, but this particular lower-quartile and standard-USG% formulation does not provide sufficient incremental predictive value.

Artifacts

  • Recursive candidate: artifacts/models/forward_nail_rapm_critical_spacing_quartile_standard_usage/2025-26/forward-nail-critical-spacing-quartile-standard-usage-2025-26-20260824T052154Z-9e32f2d8
  • Frozen replay: artifacts/models/nail_critical_spacing_quartile_standard_usage_frozen_backtest/frozen_multiseason_backtest/2023-24_to_2025-26/frozen_multiseason_backtest-2023-24-to-2025-26-20260824T053055Z-d8a33cc7
  • Coefficient audit: artifacts/models/analysis/nail_critical_spacing_quartile_standard_usage_weight_audit/nail-critical-spacing-quartile-standard-usage-weight-audit-20260824T053116Z-1d5bbe2c

Reproduction

See Train NAIL Quartile Critical Spacing Plus Standard USG%.