Bayes-ically fair: A Bayesian Ranking of the Olympic Medal Table

Abstract: Evaluating a country's sporting success provides insight into its decision-making and infrastructure for developing athletic talent. The Olympic Games serve as a global benchmark, yet conventional medal rankings can be unduly influenced by population size. We propose a Bayesian ranking scheme to rank the performance of National Olympic Committees by their "long-run" medals-to-population ratio. The algorithm aims to mitigate the influence of large populations and reduce the stochastic fluctuations for smaller nations by applying shrinkage. These long-run rankings provide a more stable and interpretable ordering of national sporting performance across games compared to existing methods.