Measurement of competitive balance in professional team sports using the Normalized Concentration Ratio

Competitive balance is an important concept in professional team sports; its measurement is, therefore, a critical issue. One of the most widely used indices, which was introduced for the estimation of seasonal competitive balance is the Concentration Ratio, which is a relatively simple index and measures the extent to which a league is dominated by a particular number of teams. However, it is shown that both the total number of league teams and the number of dominant teams under examination affects the index's boundaries, which results in a misleading interpretation concerning the level of competitive balance. Thus, we introduce the Normalized Concentration Ratio for the study of competitive balance across leagues or seasons.