  Value functions are used in sports applications to determine the optimal
action players should employ. However, most literature implicitly assumes that
the player 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.
