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.An important feature of a sport competition is the uncertainty about the outcome. Sport industry, governments and followers are interested in having some degree of uncertainty about the competition. In the field of sport rankings the term "competitive balance" attends to measure this degree of uncertainty about the result of a competition. A high competitiveness means that there is high uncertainty about the teams ranking. Classical measures of competitiveness are based on the ratio of wins of each team or other related measures. In this paper we show a new perspective by using techniques from complex networks. We show how to use an ad hoc graph, that we called "competitivity graph", to give some measures of the competitiveness of a family of rankings. As an application we make a comparison of the four major European soccer leagues during 2011-12 season and 2012-13 season.

Comparing series of rankings with ties by using complex networks: An analysis of the Spanish stock market (IBEX-35 index)

“…. , σ m } contains any tie, then there are no weighted edges in the semi-crossing label, no weighted edges in the long-term-crossing layer and no weighted edges in the tie label of the multiplex evolutive competitivity network of R, so the evolutive competitivity graph defined in [14] corresponds to the projected evolutive competitivity network associated to R with fixed α = 1. These rankings were obtained with a precision threshold ∆ = 0.5 from the family of scores {s 1 , · · · , s 5 } (see Table 2).…”

On graphs associated to sets of rankings

“…In a recent work (see [11]) we introduced a new method to compare a set of rankings. We based our method on counting crossings but using tools from Complex Networks Analysis, or put in other words, using structural properties of some graphs defined ad hoc.…”

A modified weighted TOPSIS to identify influential nodes in complex networks

“…Firstly, we investigate the correlations between node's influence measured by the two methods and F (t) via 25 Kendall's tau coefficient τ [43]. Kendall's tau coefficient τ is widely used for correlation analysis [6,44,45]. The Kendall's 26 tau coefficient considers a set of joint observations from two random variables X and Y .…”