Bayesian Binomial Regression: Probability of Success in Pro Football

Abstract

Bayesian regression provides a flexible alternative to standard GLM, as it allows for more user control of the data. The Bayesian may use his or her prior knowledge to influence the outcome of an experiment. While GLM is a robust tool that applies to virtually any type of data, there is little room for manipulation on the part of the user, who may have some additional "expert" knowledge beyond the raw data. The assumptions of both practices are outlined and applied to Binomial data acquired from the 2005 NFL season to highlight the advantages and disadvantages of each approach. Under ideal conditions the Bayesian analysis provides more accurate estimators and features relatively simple computations.