Ranking ultimate teams using a Bayesian score-augmented win-loss model

Ultimate is a field sport played by two teams, each with seven players on the field. USA Ultimate administers nationwide leagues that consist of a regular season and post-season with Sectional, Regional, and National Championship tournaments. USA Ultimate ranks teams by applying an algorithm to the regular season results, and distributes the sixteen bids for the National Championship to the eight regions based on these rankings. Teams then compete at Regionals to earn the bids granted to their region. This article presents a novel score-augmented win-loss model for ranking Ultimate teams and distributing National Championship bids. The proposed approach facilitates predicting the placement of each qualifying team at the 2016 Club National Championships as well. The key innovations are the use of a pseudo-outcome called the win fraction that splits a win between the two teams based on the final score of their match, and a weighted quasi-likelihood function that facilitates discounting older results. The proposed approach is applied to the 2016 Club Division results. Rankings, bid allocations, and predictive placement probabilities are reported, as well as a comparative evaluation with the USA Ultimate algorithm, a win-loss model, and a point-scoring model.