Stated, Realized, and Optimal Aiming Strategies for the Tennis Serve: Experimental Evidence from Collegiate Athletes

Abstract

We study where, within a chosen Wide or T region, a tennis player should aim a serve. Aiming near a service-box boundary makes a serve harder to return but raises the probability of a fault, creating a trade-off that depends on the player's execution error. Ordinary match data provide limited information about execution error because players' intended targets are unobserved. We therefore conducted an experiment with members of the Brigham Young University men's tennis team. Each player identified targets they believed to be optimal, which we marked on the court. Players then served repeatedly toward each target while we recorded precise bounce locations. From these data, we estimate player-specific serve distributions while accounting for serves censored by net contact, then combine them with an estimated point-win reward surface in a Bayesian, two-period Markov decision process with a continuous spatial action space. We find that the estimated optimal second-serve target is more conservative than its first-serve counterpart in every player-region combination, consistent with prior theory. Also, while players' stated targets were generally more aggressive than optimal, their realized serve centers were more conservative than those targets and markedly closer to the estimated optima.