Prediction and Evaluation in College Hockey using the BradleyTerryZermelo Model
Abstract
We describe the application of the BradleyTerry model to NCAA Division I Men's Ice Hockey. A Bayesian construction gives a joint posterior probability distribution for the logstrength parameters, given a set of game results and a choice of prior distribution. For several suitable choices of prior, it is straightforward to find the maximum a posteriori point (MAP) and a Hessian matrix, allowing a Gaussian approximation to be constructed. Posterior predictive probabilities can be estimated by 1) setting the logstrengths to their MAP values, 2) using the Gaussian approximation for analytical or Monte Carlo integration, or 3) applying importance sampling to reweight the results of a Monte Carlo simulation. We define a method to evaluate any models which generate predicted probabilities for future outcomes, using the Bayes factor given the actual outcomes, and apply it to NCAA tournament results. Finally, we describe an online tool which currently estimates probabilities of future results using MAP evaluation and describe how it can be refined using the Gaussian approximation or importance sampling.
 Publication:

arXiv eprints
 Pub Date:
 January 2020
 arXiv:
 arXiv:2001.04226
 Bibcode:
 2020arXiv200104226W
 Keywords:

 Statistics  Applications;
 62F15 (Primary) 62F07 (Secondary)
 EPrint:
 21 pages, 8 figures, proceeding for the 2019 UPSTAT conference