A goal based index to analyze the competitive balance of a football league

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, we discuss a new framework which is more suitable for a football league. First, we 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. We 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, we show that the proposed index is more suitable to analyze the variability in total revenues of the football leagues. We also discuss how the methods can be easily extended to develop other goal-based indices under different modeling assumptions.