A short study of pairwise comparison methods applied to the ranking of sport teams

Details

Supervisors

Marco Saerens

Faculty

Louvain School of Management

Degree label

Master [60] en sciences de gestion (horaire décalé)

Abstract

This paper studies pairwise comparison methods and ranking mechanisms. It delves into the theoretical background before applying these principles on a practical example. First of all, the theoretical study introduces key concepts in voting systems. The fundamentals of these voting systems rely on pairwise comparisons, which means they can provide valuable insights in establishing rankings. Next, graph theory is introduced through the Floyd-Warshall algorithm, followed by an introduction of the Elo rating. To conclude the theory, the randomised shortest path theory is introduced. But, regardless of its potential, this theory will not return later on as it would drive us too far in our practical implementation. From this theoretical background, the paper continues to the practical implementation of four ranking mechanisms on a real-world scenario: The points based ranking, the Elo ranking, the Schulze ranking and the Floyd-Warshall ranking. Seasons ’20-’21 and ’21-’22 of the Belgian Jupiler Pro League will serve as the two primary case studies. Interpreting match outcomes as pairwise preferences between teams, the different ranking mechanisms are evaluated on their ability to reflect team performances and predict match outcomes. A cross-validation technique is used to assess predictive accuracy and the mean squared error between an expected outcome and an actual outcome. This paper aims to provide valuable and comprehensive insights about the question: How do different pairwise comparison methods fare in a dynamic, competitive, real-world environment and what can we learn from their practical implementation?