A Goal-based Index to Analyse the Competitive Balance of a Football League

Journal: Quantitative Analysis in Sports 

Abstract: Competitive balance in a football league is extremely important from the perspective of economic growth of the industry. Many researchers have earlier proposed different measures of competitive balance, which are primarily adapted from standard economic theory. However, these measures fail to capture the finer nuances of the game. In this work, the authors discuss a new framework which is more suitable for a football league. First, they present a mathematical proof of a theoretically optimal situation where a football league becomes perfectly balanced. Next, a goal-based index for competitive balance is developed. They present relevant theoretical results and show how the proposed index can be used to formally test for the presence of imbalance. The methods are implemented on the data from the top five European leagues, and it shows that the new approach can be helpful in explaining the changes in the seasonal competitive balance of the leagues. Further, using panel data models, the authors show that the proposed index is more suitable to analyse the variability in total revenues of the football leagues. They also discuss how the methods can be easily extended to develop other goal-based indices under different modelling assumptions.