Assessing competitive balance in the English Premier League for over forty seasons using a stochastic block model

Abstract: Competitive balance is the subject of much interest in the sports analytics literature and beyond. In this paper, we develop a statistical network model based on an extension of the stochastic block model to assess the balance between teams in a league. Here we represent the outcome of all matches in a football season as a dense network with nodes identified by teams and categorical edges representing the outcome of each game as a win, draw or a loss. The main focus and motivation for this paper is to provide a statistical framework to assess the issue of competitive balance in the context of the English First Division / Premier League over more than 40 seasons. The Premier League is arguably one of the most popular leagues in the world, in terms of its global reach and the revenue which it generates. Therefore it is of wide interest to assess its competitiveness. Our analysis provides evidence suggesting a structural change around the early 2000's from a reasonably balanced league to a two-tier league.