Expectation Propagation for Rating Players in Sports Competitions

Rating players in sports competitions based on game results is one example of paired comparison data analysis. Since an exact Bayesian treatment is intractable, several techniques for approximate inference have been proposed in the literature. In this paper we compare several variants of expectation propagation (EP). EP generalizes assumed density filtering (ADF) by iteratively improving the approximations that are made in the filtering step of ADF. Furthermore, we distinguish between two variants of EP: EP-Correlated, which takes into account the correlations between the strengths of the players and EPIndependent, which ignores those correlations. We evaluate the different approaches on a large tennis dataset to find that EP does significantly better than ADF (iterative improvement indeed helps) and EPCorrelated does significantly better than EP-Independent (correlations do matter).