Quantification of competitive balance in European football: development of specially designed indices

The common competitive balance indices have not been designed to fully account for the complex structure of European football leagues. Domestic championships are multi-prize tournaments since, in addition to the competition for the championship, the best teams also compete to qualify for the lucrative European tournaments, whereas the worst teams struggle to avoid relegation. This article introduces a new measure, the Special Concentration Ratio (SCRK^I), which captures the degree of competition for winning any of the important prizes awarded in the league. This approach not only leads to a new perspective for the overall level of competitive balance but it also enables us to identify its ingredient sources.