Intrinsic Classes in the Union of European Football Associations Soccer Team Ranking

TL;DR

This paper uncovers a structural regularity in UEFA soccer team rankings from 2009 to 2014, identifying three distinct classes of teams and applying a Lavalette function to model rank-size distributions.

Contribution

It introduces a novel classification of European football teams based on rank-size analysis and employs a Lavalette function to characterize the distribution.

Findings

Three classes of teams identified: top, middle, and tail.

Empirical laws describe each class's distribution.

Lavalette function effectively models the rank-size curve.

Abstract

A strong structural regularity of classes is found in soccer teams ranked by the Union of European Football Associations (UEFA) for the time interval 2009-2014. It concerns 424 to 453 teams according to the 5 competition seasons. The analysis is based on the rank-size theory considerations, the size being the UEFA coefficient at the end of a season. Three classes emerge: (i) the few "top" teams, (ii) 300 teams, (iii) the rest of the involved teams (about 150) in the tail of the distribution. There are marked empirical laws describing each class. A 3-parameter Lavalette function is used to describe the concave curving as the rank increases, and to distinguish the the tail from the central behavior.