Sports Ranking with Nonuniform Weighting

Abstract

This paper introduces the integration of nonuniform weighting for sports ranking. While the ideas of the paper can be applied to any ranking method, a careful investigation is conducted on incorporating weighting in two of today's most popular ranking algorithms: the Colley and Massey methods, which were both developed for sports ranking applications and have since become the baseline standards there. The article introduces how to adapt both methods in order to weight some factors, such as late season play, home court advantage, or a winning streak, more heavily in computing the ratings of teams. To illustrate the utility of such weighting, the paper applies the algorithmic ideas in the area in which both Colley and Massey motivated their methods: sports. As such, the target application is producing brackets for the Division I NCAA Men's Basketball Tournament also known as March Madness. All the methods were used to produce brackets in the 2010 tournament and their results are given, including several mathematically-produced brackets that were better than 90 percent of the nearly 5 million brackets submitted to ESPN's Tournament Challenge.