Quantile regression for rating teams

Abstract

Quantile regression is proposed for modeling game out comes and as the basis for rating teams. The model includes the standard location model for team strength as a special case, while allowing for a richer specification in which teams differ according to the quantiles of the out come distribution. Team ratings are defined as the handicap needed to equalize the out come of a contest. With teams differing by quantiles, this leads to a class of ratings that depend on where in the out come distribution the out come is equalized. Relation ships with betting games are discussed. The approach is illustrated by rating National Football League (NFL) teams based on game results for the 2005 season.