Opponent choice in tournaments: winning and shirking

Abstract

We propose an alternative design for tournaments that use a preliminary stage, followed by several rounds of single elimination play. The conventional “bracket” design of these tournaments suffers from several deficiencies. Specifically, various reasonable performance criteria for the tournament are not satisfied, there is an unnecessary element of luck in the matchups of players, and there are situations where players have an incentive to shirk. To address all these issues, we allow higher ranked players at the single elimination stage to choose their next opponent sequentially at each round. We allow each player’s ranking either to remain static, or to improve by beating a higher ranked player (Guyon, J. 2022. “Choose your opponent”: a new knockout design for hybrid tournaments. J. Sports Anal. 8: 9–29). Using data from 2215 men’s professional tennis tournaments from 1991 to 2017, we demonstrate the reasonableness of the results obtained. We also perform sensitivity analysis for the effect of increasing irregularity in the pairwise win probability matrix on three traditional performance measures. Finally, we consider strategic shirking behavior at both the individual and group levels, and show how our opponent choice design can mitigate such behavior. Overall, the opponent choice design provides higher probabilities that the best player wins and also that the two best players meet, and reduces shirking, compared to the conventional bracket design.