Competitive attractiveness measurement in sports leagues: Sequential procedures for heterogeneous competitors

Abstract

The paper proposes three dominance criteria that assess whether one seasonal outcome of a sports league is more attractive than another, taking into account their respective competitive balance levels. Seasonal outcomes are distributions of seasonal points involving heterogeneous competitors (having varying sizes of fan bases). The proposed criteria are the first-degree sequential downward (FSD), second-degree sequential upward (SSU), and third-degree sequential downward (TSD) dominance criteria. The FSD criterion is axiomatically characterized in line with two principles, which require that a famous competitor (with a large fan base) matters more for attractiveness than a common competitor (with a small fan base). The SSU criterion relies on the same principles that characterize the FSD criterion and on two additional ones. First, attractiveness should increase with respect to competitive balance. Second, balance among famous competitors is more important than balance among common competitors. The TSD criterion relies on all the aforementioned principles and incorporates upside sensitivity, emphasizing that a balanced race among many famous competitors enhances attractiveness. An illustrative application provides comparisons of seasonal outcomes of the English Premier League from 2014–2015 to 2018–2019.