The ranking lasso and its application to sport tournaments

Abstract

Ranking a vector of alternatives on the basis of a series of paired comparisons is a relevant topic in many instances. A popular example is ranking contestants in sport tournaments. To this purpose, paired comparison models such as the Bradley–Terry model are often used. This paper suggests fitting paired comparison models with a lasso-type procedure that forces contestants with similar abilities to be classified into the same group. Benefits of the proposed method are easier interpretation of rankings and a significant improvement of the quality of predictions with respect to the standard maximum likelihood fitting. Numerical aspects of the proposed method are discussed in detail. The methodology is illustrated through ranking of the teams of the National Football League 2010–2011 and the American College Hockey Men’s Division I 2009–2010.