Probabilistic transitivity in sports

Abstract

We seek to find the statistical model that most accurately describes empirically observed results in sports. This model has only two assumptions: a trinomial distribution of outcomes and a transitive relationship between these probabilities. The latter is implemented by imposing constraints on the outcome probabilities. To find the most likely correct ranking, we propose a Branch-and-Bound algorithm and a quicker, heuristic method.

We apply the model to panel data from soccer, American football and tennis. Due to the transitivity assumption, our model has a natural application in comparing ranking systems. Therefore, we use it to evaluate empirically applied ranking schemes.