Primacy & Ranking of UEFA Soccer Teams from Biasing Organizing Rules

A question is raised on whether some implied regularity or structure, as found in soccer team ranking by the Union of European Football As-sociations (UEFA), is due to implicit game result value or score compe-tition conditions. The analysis is based on considerations about complex systems, i.e. searching whether power or other simple law fits are appro-priate 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 sub-sequently occur. Thus, the notion of Sheppard primacy index is envisaged to describe the findings. Additional primacy indices are discussed for en-hancing 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. ∗Associate researcher 1 a