Dominance criteria on grids for measuring competitive balance in sports leagues

Abstract

The paper proposes a dominance criterion that assesses whether a seasonal outcome of a sports league is more balanced than another. This criterion is based on a novel third-order stochastic dominance defined on finite sets of evenly spaced seasonal points (seasonal grids), called downward seasonal balance (DSB). The DSB criterion makes the same assessments as the well-known Lorenz criterion. However, the converse is not true: The DSB criterion makes assessments even in cases where the Lorenz criterion cannot. The former is then less incomplete than the latter. The assessments of the DSB criterion reflect the unanimity of a class of competitive balance indices. A seasonal outcome is more balanced than another according to the DSB criterion if and only if every index of the class agrees. Such a class is axiomatically characterized so that the indices place at least as much emphasis on the balance between leading competitors as on the balance occurring among the nonleading competitors. An empirical application provides comparisons of seasonal outcomes of the five most competitive soccer leagues in Europe from 2014–2015 to 2018–2019.