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

The article focuses on developing a Bayesian stochastic block model (SBM) to assess competitive balance in the English First Division/Premier League over more than 40 seasons. By representing match outcomes as a network with teams as nodes and game results (win, draw, loss) as categorical edges, the model probabilistically partitions teams into blocks with similar competitive characteristics, allowing inference on the number of competitive tiers within the league. Analysis reveals that the league was relatively balanced until the early 2000s, after which it shifted to a more imbalanced, two-tier structure with a smaller strongest block of teams, supporting the emergence of a dominant "big-six" group. The SBM approach offers a richer, game-level statistical framework compared to traditional season-end summary indices and provides insights into the evolution of competitive balance, with potential applications for league policy and further methodological extensions.