Arena Model: Inference About Competitions

TL;DR

The paper introduces the arena model, a parametric approach for predicting outcomes in paired competitions that leverages competition structure and quantifies uncertainty, with potential for extensions to multi-individual comparisons.

Contribution

It presents a novel, structure-aware prediction model for competitions, including an invariant Bayes estimator and proofs of estimation consistency.

Findings

Predicts competition results without individual ratings

Provides a method to quantify uncertainty in predictions

Establishes an invariant Bayes estimator and proves its consistency

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.