Bayesian Optimal Design of Fixed Knockout Tournament Brackets

• Activity Number: 184
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics in Sports
• Author(s): Jonathan Hennessy* and Mark Glickman
• Companies: The Houston Rockets and Boston University
• Keywords: Tournament design ; Bayesian optimal design

Abstract

We present a methodology for finding optimal knockout tournament designs when the strengths of the players are uncertain. Following Glickman (2008), we model player strengths using a multivariate normal distribution. We consider 4, 8, and 16 player knockout tournaments and find the tournament brackets that maximize a variety of utility functions, for instance, the probability the best player wins the tournament and the probability the two best players meet in the final. We apply Bayesian optimal design approaches, including Monte Carlo integration and simulated annealing, to identify the optimal tournament bracket. We also compare the optimal brackets to other knockout tournament designs, including brackets following the standard seeding.