Forward Availability v0.1

Superseded by Forward Availability v0.2.

This pilot estimates a player's medical availability share for a future season. It is deliberately separate from the minutes-allocation model: a player may be available and still receive no minutes because the coach does not select them.

Its training panel and binary label are defined in the player-game availability contract. The target is a player's available games divided by their known rostered player-games, not games played.

Forward Contract

For target season \(t\), the model uses only information from completed seasons before \(t\):

\[ \operatorname{logit}(p_{i,t}) = a(\operatorname{age}_{i,t}) + \rho^{g_{i,t}}\left(z_{i,t-1} + w\,\widetilde{m}_{i,t-1}\right). \]

\(a(\cdot)\) is an exposure-weighted quadratic age baseline. \(z\) is the player's prior filtered deviation from that baseline, \(g\) is the number of seasons since that observation, and \(\widetilde{m}\) is prior-season NBA minutes per available game after standardization. The observed availability share updates the player state with a beta-binomial-style pseudo-game strength \(q\):

\[ \widehat{p}^{\mathrm{post}}_{i,t} = \frac{q p_{i,t} + A_{i,t}}{q + N_{i,t}}, \]

where \(A\) is available games and \(N\) is known rostered player-games.

This is a state model for medical availability, not a claim that a player's availability is determined by prior minutes. The workload term is a small, lagged candidate transition signal and must earn its place in forward tests.

First Frozen Replay

The panel contains every completed season from 2015-16 through 2025-26. For each target season, the age curve and each player's filtered state use every earlier available season; no target-season availability leaks into its prediction. The model selected its hyperparameters on the three completed tuning targets, 2020-21 through 2022-23, then evaluated once on frozen 2023-24 through 2025-26. Thus the first tuning target already has five source seasons, 2015-16 through 2019-20, behind it. The selected configuration was:

Parameter	Value
State persistence \(\rho\)	0.50
Pseudo-game strength \(q\)	60
Lagged workload weight \(w\)	-0.25

The artifact is artifacts/rotation/forward_availability/forward-availability-20260909T225142Z-94dee6f.

Frozen metric, mean of three seasons	Age-only control	Forward availability v0.1
Exposure-weighted Brier score	0.06044	0.06093
Binomial log loss	0.55965	0.58250
Player-share MAE	0.19704	0.19201
Player-share RMSE	0.25452	0.25604

The player-state model modestly improves average absolute error, but it loses on both probability-sensitive measures. It also overpredicts availability on the first two frozen seasons. Therefore v0.1 is the documented first benchmark for this new model family; it is not yet integrated into the minutes or win-projection pipeline.

Next Decision

The next slice was to improve first-state calibration while preserving the same binary contract and frozen splits. That work produced v0.2. Candidate changes must be tested against the age-only control and v0.2 before they can affect expected minutes:

\[ E[\mathrm{minutes}_{i,t}] = P(\mathrm{available}_{i,t}) \times E[\mathrm{minutes}_{i,t}\mid\mathrm{available}_{i,t},\ \mathrm{team}]. \]

The availability probability is player-specific. The conditional-minutes allocation remains a joint team problem, so changing one player's availability will ultimately require a team-level reallocation only after this layer has earned promotion.