Tick Tock Shot Clock: Optimal Stopping in NBA Basketball

Abstract

We study how highly experienced agents, professional basketball players, solve an optimal stopping problem. By rule, teams must shoot within 24 seconds of the start of a possession. The decision of when to shoot requires weighing the current shooting opportunity against the continuation value of the possession. At each second of the clock, optimal play requires that a lineup's reservation shot value equals the continuation value of the possession. We empirically test this prediction with a structural stopping model. Most lineups adopt a reservation threshold that matches the continuation value function very closely. These lineups tend to be those with more shared playing experience. Mistakes we do observe come in the form too low a threshold and excess steepness. Overall, the lineups we study capture 84% of the gains of a dynamic threshold vs. an optimal fixed threshold, with only a single lineup estimated to capture less than 66%.