Linear-Ridge HPM x3 Context

Last updated: 2026-08-15

This is the canonical simplest contextual comparison for HPM x3. It keeps the same forward player prior and 14-feature basketball lineup contract, but replaces bounded hierarchical P-splines with one standardized linear Ridge regression:

\[ C(H,A)=\beta^\top\big(x(H)-x(A)\big). \]

It uses no spline basis, curvature penalty, temporal spline hierarchy, or feature clipping. Because the fitted context is linear in the feature difference, its derived decomposition has no matchup remainder:

\[ C(H,A)=h(H)-h(A),\qquad q(H,A)=0. \]

The model is therefore the appropriate baseline for testing whether the nonlinear spline machinery earns its complexity with the same inputs.

Feature Contract

The current contract excludes imputed_count and replacement_weight. Those are provenance and cold-start calibration diagnostics, not player or lineup basketball attributes. A frozen three-season ablation found no meaningful full-game advantage from retaining them, while possession MAE changed by only 0.000038. The older 16-feature run remains available as a historical artifact; new canonical x3 runs use the 14 basketball features.

Run

uv run nba-train-hpm-x3-linear-ridge --through-season 2025-26

Frozen Result

Metric	HPM x3	Linear Ridge	Ridge minus x3	Paired 95% interval	P(Ridge better)
Full-game RMSE	14.377365	14.352888	-0.024476	[-0.049522, +0.000776]	97.03%
Winner accuracy	67.73%	68.13%	+0.40 pp	[-0.14 pp, +0.94 pp]	91.84%
Possession RMSE	1.198000	1.197978	-0.000022	[-0.000039, -0.000006]	99.66%
Possession MAE	1.141400	1.141349	-0.000051	[-0.000068, -0.000033]	100.00%

The linear model is statistically better on possession RMSE and MAE. Its full-game point estimate is better, but the paired interval crosses zero by 0.0008 RMSE, so it does not meet the strict tournament promotion rule.

Compilation Identity Audit

The NAIL-RAPM Attribution Contract verifies that eight additive basketball context coordinates can move exactly into the player prior, while six lineup-shape coordinates remain context-only. The two forms produce identical frozen forecasts from 2023-24 through 2025-26.