Primacy & Ranking of UEFA Soccer Teams from Biasing Organizing Rules

TL;DR

This paper investigates the structure of UEFA soccer team rankings, revealing a hierarchical class organization influenced by ranking rules, and introduces primacy indices to analyze these patterns as emergent properties of complex systems.

Contribution

It introduces primacy indices and a toy model to explain the hierarchical class structure in UEFA rankings as an emergent property of boundary-constrained nonlinear systems.

Findings

Ranking forms a major class of top teams after each season

Additional classes of regular size emerge in the rankings

Peer classes are an extrinsic property influenced by ranking rules

Abstract

A question is raised on whether some implied regularity or structure, as found in soccer team ranking by the Union of European Football Associations (UEFA), is due to implicit game result value or score competition conditions. The analysis is based on considerations about complex systems, i.e. searching whether power or other simple law fits are appropriate to describe some internal dynamics. It is observed that the ranking is specifically organized: a major class made of a few teams emerges after each game season. Other classes which apparently have regular sizes subsequently occur. Thus, the notion of Sheppard primacy index is envisaged to describe the findings. Additional primacy indices are discussed for enhancing the features. These measures can be used to sort out peer classes in more general terms. A very simplified toy model containing ingredients of the UEFA ranking rules suggests that such peer classes are an extrinsic property of the ranking, as obtained in many nonlinear systems under boundary condition constraints.