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

- We study how experienced agents solve an optimal stopping problem.
- Our subjects are professional basketball players.
- The lineups we study capture 84% of the gains of a dynamic optimal threshold.
- Lineups with more shared playing experience performed better on average.
- Observed mistakes lean towards impatience.

We study how experienced agents solve a sequential search problem. In professional basketball teams must shoot within 24 s 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.