Winning a Tournament According to Bradley-Terry Probability Model

Abstract

We analyze the chances of winning a tournament under the assumption that the probabilities of winning individual matches follow Bradley-Terry model [2]. We present an exact solution and show a few examples of its use. The examples are from California volleyball tournaments, the round of sixteen in the World Cup and the Champions League, the group stage of the Association of Tennis Professionals tournament, and the volleyball SuperLega in Italy. The computational complexity of the solution grows exponentially fastwith the number of teams and we seek approximations via multivariate Gaussian laws.