A ranking method based on minimizing the number of in-sample errors.
This article introduces a simple Bayesian method for ranking college football teams. The parameter space is the set of all possible rankings, and individual game results are modeled by taking the odds that the lower ranked team wins to be B : 1, where B < 1. As a result, the likelihood for a given ranking is a function solely of the number of in-sample errors, and by choosing the parameter B to be very close to zero, we may effectively minimize the number of in-sample errors. We propose both a modified Gibbs sampler algorithm for exploring the posterior distribution and an associated importance sampling scheme for examining the impact of individual games on the posterior mean ranks. We rank teams according to their posterior mean ranks, and we use simulations to compare the performance of this ranking to that of rankings produced by standard methods that use the same (win/loss only) information. We find that the new method is almost as good as standard methods in predicting unknown game results, while far outdoing standard methods in matching known game results. An outlier-resistance property of the ranking method is illustrated using the importance sampling scheme.
|Main Author:||Frey, Jesse|