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Foul accumulation in the NBA

Abstract This paper investigates the fouling time distribution of players in the National Basketball Association. A Bayesian analysis is presented based on the assumption that fouling time distributions follow a gamma distribution. Various insights are obtained including the observation that players accumulate fouls at a rate that increases with the current number of fouls. We demonstrate possible ways to incorporate the fouling time distributions to provide decision support to coaches in the management of playing time.