Forward Conditional Minutes

Forward Conditional Minutes forecasts a player's regular-season NBA minutes per medically available game before the team-level rotation allocation. It is paired with Forward Availability in the preseason minutes stack.

Current Contract

For a player-season with \(A_{i,t}\) medically available games and total NBA minutes \(M_{i,t}\), the observed target is:

\[ m_{i,t}^{\mathrm{avail}} = \frac{M_{i,t}}{A_{i,t}}. \]

A pooled quadratic age curve predicts \(\log(1+m_{i,t}^{\mathrm{avail}})\). Returning players carry an exposure-shrunk deviation from that curve forward; available games are measurement exposure, so a 10-game observation moves the state less than a 70-game observation:

\[ z_{i,t}^{\mathrm{post}} = \frac{q z_{i,t}^{\mathrm{prior}} + A_{i,t}\log(1+m_{i,t}^{\mathrm{avail}})} {q + A_{i,t}}. \]

The current rookie branch adds a regularized, draft-informed residual to the age baseline:

\[ \log(1+\widehat m_{i,t}^{\mathrm{avail}}) = b(\mathrm{age}_{i,t}) + \gamma_0 + \sum_{k=1}^{6}\gamma_k\,\widetilde{x}_{i,t,k}^{\mathrm{rookie}}. \]

The six rookie inputs are draft capital, undrafted status, rookie age, and listed guard/forward/center indicators. A non-rookie with no usable NBA minutes state remains on the age baseline; the model does not invent a veteran role from draft information.

The two forward components form raw expected minutes:

\[ r_{i,t}=82\,P(\mathrm{available}_{i,t}) \,\widehat m_{i,t}^{\mathrm{avail}}. \]

Roster Squashing

The availability-times-conditional-minutes product is an independent player forecast, so player raw totals do not normally add to the team's fixed 19,680-minute regular-season budget. The downstream Win Projections model converts those raw totals into a feasible active-15 rotation before it builds team strength. See Roster Squashing In Win Projections.

Current Production State: v0.2

The returner-state configuration is full one-season persistence, a 15-game later-update strength, and a 30-game initial-state strength. The rookie ridge penalty \(\alpha=0.01\) was selected on completed 2020-21 through 2022-23 targets. The final comparison uses frozen 2023-24 through 2025-26 seasons.

Mean frozen metric	v0.1	v0.2	Change
Conditional minutes MAE	6.14	5.60	-0.53
Conditional minutes RMSE	8.03	7.55	-0.48
Available-game-weighted MAE	5.44	5.06	-0.38
Available-game-weighted RMSE	7.11	6.67	-0.44
Raw expected-total-minutes MAE	505.9	455.0	-50.9
Raw expected-total-minutes RMSE	632.4	583.4	-49.0
Rookie weighted RMSE	10.09	7.63	-2.45

Artifact: artifacts/rotation/forward_conditional_minutes/forward-conditional-minutes-20260910T163017Z-fe2dd1d.

Update History

v0.1: Age And Player-State Prior

The initial release established the age baseline, exposure-shrunk returner state, availability-times-conditional-minutes combination, top-15 rotation constraint, and exact team-minute conservation. It beat the age-only control on every frozen aggregate metric, but a true rookie received only the pooled age baseline.

v0.2: Draft-Informed Rookie Prior

v0.2 keeps the returner model unchanged and adds the rookie residual above. It improves every aggregate held-out metric and every individual held-out season. The change is concentrated where intended, but also improves overall allocation because a rookie's raw expected minutes are normalized jointly with their teammates.

For current top prospects, the practical effect is substantial: AJ Dybantsa changes from 9.8 to 21.5 conditional MPG, Darryn Peterson from 9.8 to 21.2, and Cameron Boozer from 9.8 to 20.0.

Win-Loss Envelope

Win Projections exposes projected available games and conditional MPG as separate controls. It then simulates 82 games 10,000 times using the same minute-weighted strengths, home-court term, back-to-back term, and logistic game probabilities as the win-total table. The resulting Win-Loss Envelope shows 1st--99th and 5th--95th percentile cumulative-win intervals, opponent and back-to-back detail, toughest-game annotations, and a self-contained PNG export.