A new method for comparing rankings through complex networks: Model and analysis of competitiveness of major European soccer leagues

TL;DR

This paper introduces a novel network-based method to analyze and compare the competitiveness of European soccer leagues by examining the structural properties of teams' ranking dynamics.

Contribution

It presents a new technique that models team competitions as a graph, generalizes Kendall's correlation, and enables dynamic and comparative analysis of league competitiveness.

Findings

The method reveals differences in competitiveness among leagues.

Structural properties correlate with traditional measures of competitive balance.

The approach provides a dynamic perspective on league competitiveness.

Abstract

In this paper we show a new technique to analyze families of rankings. In particular we focus on sports rankings and, more precisely, on soccer leagues. We consider that two teams compete when they change their relative positions in consecutive rankings. This allows to define a graph by linking teams that compete. We show how to use some structural properties of this competitivity graph to measure to what extend the teams in a league compete. These structural properties are the mean degree, the mean strength and the clustering coefficient. We give a generalization of the Kendall's correlation coefficient to more than two rankings. We also show how to make a dynamic analysis of a league and how to compare different leagues. We apply this technique to analyze the four major European soccer leagues: Bundesliga, Italian Lega, Spanish Liga, and Premier League. We compare our results with the classical analysis of sport ranking based on measures of competitive balance.