Arena Model: Inference About Competitions

Abstract: The authors propose a parametric model called the arena model for prediction in paired competitions, i.e. paired comparisons with eliminations and bifurcations. The arena model has a number of appealing advantages. First, it predicts the results of competitions without rating many individuals. Second, it takes full advantage of the structure of competitions. Third, the model provides an easy method to quantify the uncertainty in competitions. Fourth, some of our methods can be directly generalized for comparisons among three or more individuals. Furthermore, the authors identify an invariant Bayes estimator with regard to the prior distribution and prove the consistency of the estimations of uncertainty. Currently, the arena model is not effective in tracking the change of strengths of individuals, but its basic framework provides a solid foundation for future study of such cases.