A Markov process approach to untangling intention versus execution in tennis

Value functions are used in sports to determine the optimal action players should employ. However, most literature implicitly assumes that players can perform the prescribed action with known and fixed probability of success. The effect of varying this probability or, equivalently, "execution error" in implementing an action (e.g., hitting a tennis ball to a specific location on the court) on the design of optimal strategies, has received limited attention. In this paper, we develop a novel modeling framework based on Markov reward processes and Markov decision processes to investigate how execution error impacts a player's value function and strategy in tennis. We power our models with hundreds of millions of simulated tennis shots with 3D ball and 2D player tracking data. We find that optimal shot selection strategies in tennis become more conservative as execution error grows, and that having perfect execution with the empirical shot selection strategy is roughly equivalent to choosing one or two optimal shots with average execution error. We find that execution error on backhand shots is more costly than on forehand shots, and that optimal shot selection on a serve return is more valuable than on any other shot, over all values of execution error.