title: A new method for comparing rankings through complex networks: model and analysis of competitiveness of major European soccer leagues.
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.
authors.affiliation: Department of Applied Mathematics, Rey Juan Carlos University, Madrid, Spain.
authors.forename: Regino
authors.initials: R
authors.lastname: Criado
authors.affiliation: Department of Applied Mathematics, Rey Juan Carlos University, Madrid, Spain.
authors.forename: Esther
authors.initials: E
authors.lastname: García
authors.affiliation: Institut de Matemàtica Multidisciplinària, Universitat Politècnica de València, Valencia, Spain.
authors.forename: Francisco
authors.initials: F
authors.lastname: Pedroche
authors.affiliation: Department of Applied Mathematics, Rey Juan Carlos University, Madrid, Spain.
authors.forename: Miguel
authors.initials: M
authors.lastname: Romance
mesh_terms: D005060:Europe; D006801:Humans; D008962:Models, Theoretical; D011237:Predictive Value of Tests; D012916:Soccer