AC-MSP v0.1

Availability-Conditioned Minute-Share Projection is the first game-level conditional rotation model. It answers a narrower question than the preseason rotation models: given the players who were medically available for a game, how should a team allocate its 240 regulation minutes?

It does not yet forecast the availability mask. Forward Availability v0.2 provides a separate season-level probability; integrating that forecast into game scenarios is a later step.

Target and Support

For a regulation team-game \(g\), let \(A_g\) be the players marked medically available in the historical availability mart. Coach DNPs and G-League assignments remain in \(A_g\) with zero observed minutes. Players marked unavailable are not candidates.

\[ y_{i,g} = \frac{m_{i,g}}{240}, \qquad \sum_{i \in A_g} y_{i,g}=1. \]

Only exact-240 team-games with a complete known availability roster are eligible. Overtime, malformed minute totals, and the small number of historical team-games with an ambiguous player status are excluded rather than rescaled or imputed. The initial replay uses all eligible regular-season games in each season, not a first-20-game window; playoffs are excluded.

Pregame Features

Every feature is computed before the current team-game, using only completed earlier games for that same team and season:

\[ x_{i,g} = \left[ \log(1+m^{(1)}_{i,g}), \log(1+\bar m^{(5)}_{i,g}), \log(1+\bar m^{(\mathrm{season})}_{i,g}) \right]. \]

The first three terms are prior-game minutes, mean minutes over the prior five team-games, and season-to-date mean minutes. A player newly acquired by the team starts with zero team-history minutes; the softmax still assigns them positive support when they are available.

Allocation

After standardizing the features on source seasons, a ridge-regularized score is fitted with fractional multinomial loss:

\[ s_{i,g}=x_{i,g}^{\top}\beta, \qquad \widehat y_{i,g}=\frac{\exp(s_{i,g})} {\sum_{j\in A_g}\exp(s_{j,g})}. \]

The primary metric is team-game allocation total variation:

\[ \operatorname{TV}_g = \frac12\sum_{i\in A_g} \left|y_{i,g}-\widehat y_{i,g}\right|. \]

The frozen replay also reports Brier score, cross-entropy, player-share MAE, and player-share RMSE. Its like-for-like control is a lag-five minutes rule with a one-minute floor, normalized over the same observed available roster.

Frozen Replay

The ridge penalty is selected only from 2020-21 through 2022-23, each fit on earlier seasons. The final evaluation is frozen over 2023-24 through 2025-26, with each target season fit only on prior seasons. This establishes the conditional-minutes layer before availability forecasts are coupled to it.

The selected penalty was \(\alpha=0\). The tuning curve was essentially flat through \(\alpha=10\), then worsened at larger penalties; the unpenalized three-feature score is therefore the exact v0.1 contract.

Frozen metric, mean of three seasons	Conditional L5 control	AC-MSP v0.1
Allocation total variation	0.16294	0.16222
Brier score	0.01509	0.01336
Cross-entropy	2.41318	2.38992
Player-share MAE	0.02468	0.02455
Player-share RMSE	0.03380	0.03180

AC-MSP wins the aggregate comparison, but the TV gain is small and reverses in 2025-26. This is not yet a preseason or win-projection model: it receives the observed historical availability roster. Its result only validates the conditional-minute layer and its next-man-up reallocation behavior.

Artifact: artifacts/rotation/availability_conditioned_minutes/ac-msp-20260910T002438Z-7892db2.

Run:

uv run nba-evaluate-ac-minute-share-projection

The command writes predictions, matched-control predictions, frozen metrics, and standardized coefficients beneath artifacts/rotation/availability_conditioned_minutes/.