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Competitive balance in a football league is extremely important from theperspective of economic growth of the industry. Many researchers have earlierproposed different measures of competitive balance, which are primarily adaptedfrom the standard economic theory. However, these measures fail to capture thefiner nuances of the game. In this work, we discuss a new framework which ismore suitable for a football league. First, we present a mathematical proof ofan ideal situation where a football league becomes perfectly balanced. Next, agoal based index for competitive balance is developed. We present relevanttheoretical results and show how the proposed index can be used to formallytest for the presence of imbalance. The methods are implemented on the datafrom top five European leagues, and it shows that the new approach can betterexplain the changes in the seasonal competitive balance of the leagues.Further, using appropriate panel data models, we show that the proposed indexis more suitable to analyze the variability in total revenues of the footballleagues.

A mathematical take on the competitive balance of a football league