Foul Accumulation in the NBA
This project investigates the fouling time distribution of players in the National Basketball Association. A Bayesian analysis is presented based on the assumption that fouling times follow a Gamma distribution. Various insights are obtained including the observation that players accumulate their $n$th foul more quickly for increasing $n$. Methods are developed that will allow coaches to better manage playing time in the presence of fouls such that key players are available in the latter stages of matches.