Intrinsic classes in the Union of European Football Associations soccer team ranking

Ausloos, Marcel

doi:10.2478/s11534-014-0505-4

Cited by 6 publications

(6 citation statements)

References 26 publications

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“…Second, from a strictly numerical point of view, the γ exponent (≈1) is reminiscent of Zipf's finding about the "least effort law", also understood as an equilibrium process (Zipf, 1949). However, more modernly, it can be understood as resulting from a "self-organizing process" of complex systems, in fact, as recently discussed in a set of papers about soccer team and country ranking (Ausloos, 2014;Ausloos et al, 2014aAusloos et al, , 2014b. The UEFA and FIFA ranking rules lead to a dissipative structure process (Prigogine and Nicolis, 1967), which ends in a stable "dissipative structure" characterized by an "equilibrium exponent" ≈1.…”

Section: Discussion and Interpretationmentioning

confidence: 99%

Rank–size law, financial inequality indices and gain concentrations by cyclist teams. The case of a multiple stage bicycle race, like Tour de France

Ausloos

2020

Physica A: Statistical Mechanics and its Applications

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This note examines financial distributions to competing teams at the end of the most famous multiple stage professional (male) bicyclist race, "TOUR DE FRANCE". A rank-size law (RSL) is calculated for the team financial gains. The RSL is found to be hyperbolic with a surprisingly simple decay exponent ≈-1. Yet, the financial gain distributions unexpectedly do not obey Pareto principle of factor sparsity. Next, several (8) inequality indices are considered : the Entropy, the Hirschman-Herfindahl, Theil, Pietra-Hoover, Gini, Rosenbluth indices, the Coefficient of Variation and the Concentration Index are calculated for outlining « diversity measures ». The connection between such indices and their « concentration aspects » meanings are presented as support of the RSL findings. The results emphasize that the sum of skills and team strategies are effectively contributing to the financial gains distributions. From theoretical and practical points of view, the findings suggest that one should investigate other "long multiple stage races" and rewarding rules. Indeed, money prize rules coupling to stage difficulty might influence and maybe enhance (or deteriorate) purely sportive aspects in group competitions.Due to the delay in the peer review process, the 2019 results can be examined. They are discussed in an Appendix ; the value of the exponent (-1.2) is pointed out to mainly originating from the so called « king effect » ; the tail of the RSL rather looks like an exponential.

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Section: Discussion and Interpretationmentioning

confidence: 99%

Rank–size law, financial inequality indices and gain concentrations by cyclist teams. The case of a multiple stage bicycle race, like Tour de France

Ausloos

2020

Physica A: Statistical Mechanics and its Applications

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“…Again on the UEFA data, we also mention Ausloos et al (2014b) in which the authors discuss the possibility of finding dissipative structures, as in open systems acquiring (and losing) energy. In Ausloos et al (2014a), the authors present the rank-size relationships for the International Federation of Association Football (FIFA) and UEFA rankings to assess ranking differences in terms of the FIFA's and UEFA's coefficients. More recently, Yoon and Sedaghat (2020)'s authors use the ranksize law to fit the ranked attendance data for the games in Major League Baseball (MLB); National Baseball Association (NBA), National Football League (NFL), and National Hockey League (NHL).…”

Section: Introductionmentioning

confidence: 99%

A rank-size approach to analyse soccer competitions and teams: the case of the Italian football league “Serie A"

2022

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In this paper, we present a data-analysis rank-size approach to assess the features of soccer competitions and competitors. We investigate the championships rankings and the teams’ final scores in the most relevant Italian league, the “Serie A”, between 1930 and 2020. We use the final rankings and the teams’ scores to explore the presence of rank-size regimes in the various yearly championships. Besides, we analyse the teams one by one, ranking their performance over the years and using the rank-size law’s parameters to compare their performances across the tournaments. We chose to do so via the Discrete Generalised Beta Distribution, a three-parameter rank-size function. We offer a cluster analysis of the rank-size law parameters based on a k-means algorithm to provide additional insights and capture similarities and deviations among championships and teams. Concluding, we propose a measure of competitiveness within championships and per team. The best fit results are statistically outstanding, and the cluster analysis presents two main clusters capturing teams’ performances and years in which they have competed in the “Serie A”. The competitiveness analysis shows that the teams at the bottom of the championships ranking have obtained decreasing scores in recent years.

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“…Since the introduction of the two-parameter Discrete Generalized Beta Distribution (DGBD) (or Beta-like Rank Function or Cocho Rank Function) [1,2], a wide range of real-life data have been successfully fitted by this function [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. Two questions naturally arise: first, what's the corresponding probability density function (pdf) of the DGBD?…”

Section: Introductionmentioning

confidence: 99%

Beta Rank Function: A Smooth Double-Pareto-Like Distribution

Fontanelli

Miramóntes

Mansilla

et al. 2019

Preprint

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The Beta Rank Function (BRF), x(u) = A(1 − u) b /u a , where u ∈ (0, 1] is the normalized and continuous rank of an observation x, has wide applications in fitting real-world data from social science to biological phenomena. The probability density function (pdf) converted from the BRF, f X (x), does not usually have an analytic expression except for specific parameter values. We show however that it is approximately a unimodal skewed and asymmetric two-sided power law/double Pareto/log-Laplacian distribution. The pdf of the BRF has very simple properties when the independent variable is log-transformed: f Z=log(X) (z) .

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Intrinsic classes in the Union of European Football Associations soccer team ranking

Cited by 6 publications

References 26 publications

Rank–size law, financial inequality indices and gain concentrations by cyclist teams. The case of a multiple stage bicycle race, like Tour de France

Rank–size law, financial inequality indices and gain concentrations by cyclist teams. The case of a multiple stage bicycle race, like Tour de France

A rank-size approach to analyse soccer competitions and teams: the case of the Italian football league “Serie A"

Beta Rank Function: A Smooth Double-Pareto-Like Distribution

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