The competitive balance of UEFA and CONMEBOL football leagues: on managing the number of teams in league design

Abstract

This article augments the literature on the analysis of competitive balance, encompassing its measurement, comparisons across leagues and seasons, and ramifications for league management. Central to our examination is the notion of competitive bal- ance, which is intimately tied to the concentration concept. This concept can be depicted as a dual metric—capturing both inequality and the number of competing teams. Historically, its magnitude has been gauged using standardised measures of inequality and concentration. Among these, the Herfindahl–Hirschman index and its subsequent refinements stand out. We employ the distance-to-competitive-balance index, which, contingent upon the metric space chosen, qualifies either as an inequal- ity or concentration measure. Our analysis spans the 2009/2010 to 2018/2019 sea- sons for both the Union of European Football Associations (UEFA) and South American Football Confederation (CONMEBOL) championships in the pre-COVID- 19 era. We discern a tangible and significant correlation between the competitive equilibrium of leagues and the performance metrics of national teams. Both the dis- parities in strengths of teams and the number of participating teams emerged as par- amount variables shaping this competitive balance. Further, we delineate the elasticities of competitive balance relative to these determinants. Our insights bear implications for designing football championship structures and delineating sports policies; thus, they are valuable for relevant sports governing bodies and federations. The strategic decision to enlarge team count vis-à-vis curtailing discrepancies in team competencies is nuanced, varying across federations and confederations. The Big 5 European leagues display heightened sensitivity to inequality factors (with inter- ventions such as financial fair play, salary caps or revenue distribution yielding pronounced effects), whereas for CONMEBOL, elasticity in relation to team count holds greater significance