Maximum likelihood ranking in racing sports

Most ranking methods used in racing sports are based on the number of points earned in a series of races. In some applications, this method will fail to provide an accurate ranking of competitors based on ability. In particular, rankings will not accurately reflect ability when competitors enter different numbers of races or when the level of competition varies by race. Additionally, point-based rankings are dependent on a subjective points scale. Three alternative models of performance and corresponding maximum likelihood estimation methods are presented that can be used to rank competitors and overcome the shortcomings of point-based rankings. Two methods are based on paired-comparisons among competitors and can be estimated using common binary-choice regression methods; the other is based on the rank-ordered logit model. These methods are valuable tools for stakeholders who need to evaluate the relative abilities of competitors to efficiently allocate resources. Application is demonstrated using results from the 2012 Formula One season, and the results of the maximum likelihood methods are compared to each other and the official point-based rankings.