Arena Model: Inference About Competitions
This work addresses prediction and uncertainty quantification in structured competitions, such as tournaments, but is incremental as it builds on existing parametric models for paired comparisons.
The authors tackled the problem of predicting outcomes in paired competitions with eliminations and bifurcations by proposing the arena model, which predicts results without rating many individuals, leverages competition structure, quantifies uncertainty, and generalizes to comparisons among three or more individuals, with proven consistency in uncertainty estimations.
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.