Predictive Power of Elo Rating Systems and Markovian System on Association Football

1. Introduction This independent study is about the predictive power of Elo rating systems and other ranking procedures in sports. Rating system has been a topic of interest. One reason is that a reasonable rating system could provide appropriate seeding, grouping players of similar skill levels. Besides, many rating systems also yield prediction on a specific match, which could be used in betting and pricing. The Elo rating system is a widely accepted rating system that is used to quantify the skill levels of game players, and it was initially created by Arpad Elo, a Hungarian-born American physics professor. The Elo system was initially applied to rank the chess players, however, it gradually was applied to many other sports and games, including baseball, basketball, and association football. The Elo rating system can also be used to generate an expected winning probability of a team, once given the team's Elo rating and the opponent's rating. This is one reason why we are interested in the Elo system-it could be extended to generate prediction of a match outcome. We decide to study the performance of Elo rating system on the association football dataset. One reason is that FIFA (Fédération Internationale de Football Association) maintains monthly world ranking for men's association football and quarterly world ranking for women's association football. FIFA has different ranking procedures for men's and women's football, however, both ranking procedures could be considered as Elo variants. In addition to the Elo system, we are also curious about other rating systems. One system being studied this time is the Markovian rating system, which utilizes the equilibrium distribution of winning probabilities. Details about both systems will be explained in Section 4.