Disequilibrium Play in Tennis

Do the world’s best tennis pros play Nash equilibrium mixed strategies? We answer this question using data on serve-direction choices (to the receiver’s left, right, or body) from the Match Charting Project. Using a new approach, we test and reject a key implication of a mixed-strategy Nash equilibrium: that the probability of winning the service game is identical for all possible serve strategies. We calculate best-response serve strategies by dynamic programming (DP) and show that for most elite pro servers, the DP strategy significantly increases their win probability relative to the mixed strategies they actually use.