Optimal stopping in the NBA: Sequential search and the shot clock

Abstract

We study how experienced agents solve a sequential search problem. In professional basketball teams must shoot within 24s of the start of a “possession.” The decision of when to shoot requires weighing the current shooting opportunity against the continuation value of a possession. At each second of the “shot clock,” optimal play requires that a lineup's reservation shot value equals the continuation value. We empirically test this prediction with a structural stopping model. Most lineups adopt a reservation threshold that matches the continuation value closely. Overall, the lineups we study capture 84% of the gains of a dynamic vs. an optimal fixed threshold. Lineups with more shared playing experience performed better on average. Observed mistakes lean towards “impatience” – the adopted threshold is either in too low or has excess steepness – meanings too many shots are taken early in the possession.