I developed a Bayesian model for ranking ultimate teams that compete in the leagues run by USA Ultimate. This approach facilitates predicting future matches as well as tournaments. The paper that describes the proposed approach has been accepted to the Journal of Quantitative Analysis and Sports. As soon as I am able, I will provide a link to the paper; I provide R software for implementation below. I also wrote an article for Ultiworld, located here, but have since slightly revised my approach.
R software (I am currently using R/3.3.2, which is freely available here)
functions.R – contains relevant functions, requires “rjson” and “BayesLogit” packages.
analysis.R – contains code that downloads the data, fits the proposed model (as well as win-loss and point-scoring models) and generates the rankings in a similar format to the rankings that I report below.
I will try to provide rankings that correspond to each week of the season (based on 200,000 posterior samples). The following information is provided for each team: rank, record (W-L), weighted strength of schedule (“wSoS,” which is the weighted average of each team’s opponents posterior mean strength), posterior mean rank and its corresponding 90% credible interval, and posterior mean strength and its corresponding 90% credible interval. I will also try to provide predictive placement probabilities for the National Championships (based on 20,000 posterior samples/iterations of the tournament). I will try to keep everything up-to-date as the results are made available at Nate Paymer’s website. Nate, thank you for this invaluable resource. ***Nate’s webpage is now defunct, and thus I am not able to maintain current rankings.***
Results reported below reflect the proposed model with a prior standard deviation set to 15. I now use a data-driven approach to choosing the prior standard deviation, which usually results in values between 5 and 12.
Men: Nationals Predictions; Post Regionals; End of Regular Season
Women: Nationals Predictions; Post Regionals; End of Regular Season
Mixed: Nationals Predictions; Post Regionals; End of Regular Season