HIPSTER PM v2.1: Empirical Rebound Capacity
HIPSTER PM v2.1 is a feature release built on HPM v2's depth-aware shooting representation. It preserves the value-conditioned aging player prior, exposure-gated cold-start path, rolling information boundary, bounded hierarchical P-spline penalties, and portable-matchup decomposition. Only the rebounding context representation changes.
Rebound Capacity
The prior feature for player \(i\) is standard box-score rebound percentage:
with the analogous offensive formula using \(\mathrm{TmORB}+\mathrm{OppDRB}\). Percentages are calculated game by game from the prior regular season's cached player box scores, then minute-weighted to the player-season profile. First-year profiles use the existing draft-cohort/replacement blend of the same percentage traits.
For a rebound opportunity, let \(D\) be the defending unit and \(O\) the offensive unit. v2.1 first sums their prior-season player claims:
It then fits a regularized logistic spline on the completed season's actual, non-dead-ball rebound events:
The two smooth functions and their coefficients are empirical: they are learned from observed rebound opportunities rather than chosen as a hard 25%/75% cap. A unit's portable features are its expected ORB% and DRB% against the completed season's reference opponent-claim distribution. This gives Kevin Love plus Steven Adams less than additive realized rebound credit when their individual claims compete for the same opportunities, while leaving the degree of saturation to the data.
Feature Registry
| Rebound feature | HPM v2 | HPM v2.1 | Reason |
|---|---|---|---|
| Raw offensive rebounds per 100 | Active | Retired | Volume is not normalized to available opportunities. |
| Raw defensive rebounds per 100 | Active | Retired | Same opportunity problem. |
| Square-root offensive rebounds | Active | Retired | Generic concavity does not encode rebound competition. |
| Square-root defensive rebounds | Active | Retired | Same limitation. |
| Rebounding by usage | Active | Retired | Depends on the retired volume proxy. |
| Expected offensive rebound rate | None | Added | Empirical ORB% against reference defensive claims. |
| Expected defensive rebound rate | None | Added | Empirical DRB% against reference offensive claims. |
Evaluation Contract
For a forecast of season \(t\), every player percentage and the rebound realization calibration come from completed data through \(t-1\). The contextual state fitted in \(t-1\) is then applied to target lineups. Target-season regular and playoff outcomes are evaluation-only.
Frozen Result
Across the frozen 2023-24 through 2025-26 regular-season evaluation, v2.1 records a possession RMSE of 1.198010 and an eligible game-margin RMSE of 14.1340. It is effectively tied with the incumbent HPM on possession error while modestly improving eligible game-margin error. See the Three-Season Frozen Leaderboard for the complete regular-season and playoff comparison.
Response-Curve Audit
The completed-history audit evaluates each stored rebound calibration across its own 5th--95th percentile claim support. All 29 seasons have the expected overall direction: higher defensive claims increase defensive-rebound probability and higher offensive claims decrease it. The central-support median effect is +4.73 percentage points for defensive claims and -6.28 points for offensive claims. Five seasons contain tiny local spline reversals; the largest is only 0.020 percentage points over one of 100 grid intervals. That is negligible relative to the learned season-level effect, but the audit remains part of the release contract rather than assuming monotonicity.
Reproduce it with:
uv run nba-audit-rebound-capacity
Reproduce
uv run nba-train-hpm-v21 --through-season 2025-26 \
2>&1 | tee artifacts/logs/train-hpm-v21-2025-26.log
Follow progress with:
tail -f artifacts/logs/train-hpm-v21-2025-26.log
The immutable outputs are stored in:
artifacts/models/forward_hpm_v21_empirical_rebound_capacity/2025-26/