Ranking structures and Rank-Rank Correlations of Countries. The FIFA and UEFA cases

Ranking of agents competing with each other in complex systems may lead to paradoxes according to the pre-chosen different measures. A discussion is presented on such rank-rank, similar or not, correlations based on the case of European countries ranked by UEFA and FIFA from different soccer competitions. The first question to be answered is whether an empirical and simple law is obtained for such (self-) organizations of complex sociological systems with such different measuring schemes. It is found that the power law form is not the best description contrary to many modern expectations. The stretched exponential is much more adequate. Moreover, it is found that the measuring rules lead to some inner structures, in both cases.Comment: 23 pages, 8 figures, 24 references, 3 tables; to be published in Int. J. Mod. Phys.

A Universal Rank-Size Law

A mere hyperbolic law, like the Zipf’s law power function, is often inadequate to describe rank-size relationships. An alternative theoretical distribution is proposed based on theoretical physics arguments starting from the Yule-Simon distribution. A modeling is proposed leading to a universal form. A theoretical suggestion for the “best (or optimal) distribution”, is provided through an entropy argument. The ranking of areas through the number of cities in various countries and some sport competition ranking serves for the present illustrations

Is football an indicator of development at the international level? (WP)

[spa] El objetivo de este trabajo es examinar si el fútbol puede ser considerado como un indicador de desarrollo a nivel internacional. Se ha diseñado un modelo econométrico empírico con el fin de analizar el desarrollo en términos de niveles de PIB per cápita y del crecimiento del PIB. Se utiliza información transversal y temporal. Los resultados sugieren que la clasificación FIFA de las selecciones nacionales se puede utilizar para complementar nuestra comprensión del desarrollo multidimensional en aquellos países donde la disponibilidad de la información no es tan buena como los investigadores quisieran.[eng] The aim of this paper is to examine whether football can be considered an indicator of development at the international level. An empirical econometric model is designed in order to analyse development in terms of both levels of GDP per capita and GDP growth. Cross-sectional and time series information is used. The results suggest that FIFA rankings of national teams can be used to complement our understanding of multidimensional development in those countries where the availability of information is not as good as researchers would like

Cross Ranking of Cities and Regions: Population vs. Income

This paper explores the relationship between the inner economical structure of communities and their population distribution through a rank-rank analysis of official data, along statistical physics ideas within two techniques. The data is taken on Italian cities. The analysis is performed both at a global (national) and at a more local (regional) level in order to distinguish "macro" and "micro" aspects. First, the rank-size rule is found not to be a standard power law, as in many other studies, but a doubly decreasing power law. Next, the Kendall and the Spearman rank correlation coefficients which measure pair concordance and the correlation between fluctuations in two rankings, respectively, - as a correlation function does in thermodynamics, are calculated for finding rank correlation (if any) between demography and wealth. Results show non only global disparities for the whole (country) set, but also (regional) disparities, when comparing the number of cities in regions, the number of inhabitants in cities and that in regions, as well as when comparing the aggregated tax income of the cities and that of regions. Different outliers are pointed out and justified. Interestingly, two classes of cities in the country and two classes of regions in the country are found. "Common sense" social, political, and economic considerations sustain the findings. More importantly, the methods show that they allow to distinguish communities, very clearly, when specific criteria are numerically sound. A specific modeling for the findings is presented, i.e. for the doubly decreasing power law and the two phase system, based on statistics theory, e.g., urn filling. The model ideas can be expected to hold when similar rank relationship features are observed in fields. It is emphasized that the analysis makes more sense than one through a Pearson value-value correlation analysis.Comment: 34 pages, 13 figures, 6 tables, 81 references; prepared for Journal of Statistical Mechanics: Theory and Experiment (JSTAT

Is football an indicator of development at the international level?

The aim of this paper is to examine whether football can be considered an indicator of development at the international level. An empirical econometric model is designed in order to analyse development in terms of GDP per capita as well as in terms of the Human Development Index. Cross-sectional and time-series information are used. The results suggest that FIFA rankings of national teams can be used to complement our understanding of multidimensional development, in particular, in those countries where the availability of information is not as good as researchers would like

Proceedings of Mathsport international 2017 conference

Proceedings of MathSport International 2017 Conference, held in the Botanical Garden of the University of Padua, June 26-28, 2017. MathSport International organizes biennial conferences dedicated to all topics where mathematics and sport meet. Topics include: performance measures, optimization of sports performance, statistics and probability models, mathematical and physical models in sports, competitive strategies, statistics and probability match outcome models, optimal tournament design and scheduling, decision support systems, analysis of rules and adjudication, econometrics in sport, analysis of sporting technologies, financial valuation in sport, e-sports (gaming), betting and sports