Bradley–Terry modeling with multiple game outcomes with applications to College Hockey

Abstract

The Bradley–Terry model has previously been used in both Bayesian and frequentist interpretations to evaluate the strengths of sports teams based on win-loss game results. It has also been extended to handle additional possible results such as ties. We implement a generalization which includes multiple possible outcomes such as wins or losses in regulation, overtime, or shootouts. A natural application is to ice hockey competitions such as international matches, European professional leagues, and NCAA hockey, all of which use a zero-sum point system which values overtime and shootout wins as 2/3 of a win, and overtime and shootout losses as 1/3 of a win. We incorporate this into the probability model, and evaluate the posterior distributions for the associated strength parameters using techniques such as Gaussian expansion about maximum a posteriori estimates, and Hamiltonian Monte Carlo.