"Probabilistic transitivity in sports" by Johannes Tiwisina and Philipp Külpmann has been accepted for publication in Computers & Operations Research.

The paper can be found here.

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.