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

Abstract

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.