Nate Sandholtz, Luke Bornn
Abstract: In basketball, the shot clock makes evaluating shot selection a difficult task. For example, a mid-range jump shot is a relatively inefficient decision early in the shot clock, but it gradually becomes more efficient relative to expectation as the shot clock winds down. These subtle dynamics often get overlooked when evaluating shot selection, which in turn leads to slightly misguided conclusions. Though mid-range jumpers are on average the least efficient shot in the NBA, we cannot simply conclude that teams should take fewer of them across the board — we must consider when and whom should take fewer shots, and how these changes would affect the team’s overall production. This is the key point of interest in this project. In pursuit of answers, we’ve developed statistical methods to simulate, or “re-play”, a team’s regular season plays under different shot probabilities. This entails simulating plays not simply by outcome but rather at the sub-second level, incorporating every intermediary and terminal on-ball event over the course of a play. We do this with respect to time, player, court-region, and defensive pressure, allowing us to explore incredibly nuanced changes to team shot policies. To this end, we model possessions from the 2015-2016 NBA regular season as Markov chains realized from team-specific non-stationary Markov decision processes. Using the estimated decision processes and the initial states of regular season plays, we simulate seasons for each NBA team and forecast the consequences under two alternate mid-range shot policies.