A Model Based Ranking System for Soccer Teams

Abstract

In competitive sports, the design of an effective ranking system attracts increasing interests. For sports with 2-way results, the Bradley-Terry model has proven to be an effective approach. However, a well-known limitation of standard Bradley-Terry models is that they cannot be applied to sports which allow to end with a tie after regular playing time. During the past decades various methods have been explored to model soccer games in the literature. In this paper, a new extended Bradley-Terry model with various covariates is devised to construct a more advanced ranking system for international soccer teams based on their games played within the past 4 years. First a standard likelihood (ML) estimation method was employed. A weighted likelihood (WML) estimation procedure was run for further improvement. Finally an evolutional model was developed to capture the dynamic trend in performance during big events. This paper examines the extent to which our ranking differs from the existing FIFA ranking. In addition, the 2012 UEFA European Football Championships was analyzed.

Keywords: Bradley-Terry model, Evolutionary model, Multinomial distribution, Strength of soccer teams, Weighted likelihood