Availability cost

Each absence is weighted by Game Score, a summary of box-score production measured over a longer history than rotation membership.

GmSc = PTS + 0.4·FGM − 0.7·FGA − 0.4·(FTA − FTM)
       + 0.7·ORB + 0.3·DRB + STL + 0.7·AST + 0.7·BLK
       − 0.4·PF − TOV

value = max(0, player's GmSc − the team's own rotation median)

The team’s rotation median is a proxy for replacement production. An absent player above that median contributes a positive missing-value score; one at or below it contributes zero. This does not identify who actually took the missing minutes.

Five weightings were compared against the same baseline: minutes, points, raw Game Score, Game Score above replacement, and a plain best-player-out flag. Value above replacement had the lowest residual error. The comparison is in ml/availability_quality.py; weighting by minutes alone, was the weakest of the continuous measures. This comparison describes model fit, not a held-out forecast evaluation.

Each estimate comes from a regression model of the final score margin. Margin retains the size of each result and expresses the estimated associations in points.

home margin ~ home court
              + team strength (home − away)
              + season position
              + schedule terms      (away − home)
              + absence value       (away − home)

Schedule and absence terms are differenced, away minus home; team strength uses home minus away. Equal values on both sides cancel. Team strength is each side’s win rate in its prior games only, shrunk toward .500 early in a season so an October record is not read as established. It is in the model as a control, never as a published effect: without it, an absence would be credited with some of the fact that weaker teams are missing players more often.

The absence measures are strongly correlated with one another, and entered together their estimates become unstable, including a sign reversal. Each published effect comes from its own specification rather than from a single model carrying all of them, and they should be read as separate answers to separate questions, never summed.

Teams may rest players on the second night of a back-to-back. Adding measured absences to the regression checks how much of the schedule association those absences account for.

backToBack         1.761 → 1.642  (6.7%)
visitingAltitude   1.358 → 1.282  (5.6%)
priorOvertime      0.577 → 0.534  (7.4%)
scheduleDensity    0.275 → 0.265  (3.8%)

Every schedule coefficient moves by under 8%. Measured absences account for little of these associations in this specification. That does not rule out unmeasured absences, changes in playing time, or other confounders.

• —It is not a forecast. Who sat is known only because the game was played. Lineups are not settled until shortly before tip, so nothing here says who will be available tonight.
• —It does not know why a player was out. Injury, load management, suspension and a personal matter are one category here, and they are not the same thing.
• —It does not know who replaced him. Replacement level is the team's own rotation median, which is a reasonable stand-in and not the actual substitute.
• —Game Score captures limited defensive information and may miss part of a defensive player's contribution.
• —Final margins have a standard deviation of 13.6 points. The model's error remains 12.4 points after including team records, schedule, and absences, leaving much of the variation unexplained.
• —Player box-score coverage starts in 1996-97. Earlier games can receive schedule scores but not availability estimates.
• —The effects are averages across three decades. The rate of playing without a best player tripled over that span, so a single figure describes an era that changed underneath it.