Competitive Balance Index
Competitive balance indices quantify how evenly matched the teams in a sports league are — the parity that the 'uncertainty of outcome' hypothesis says fans value and that economists treat as central to a league's product. The workhorse measure is the Noll-Scully ratio, which compares the actual standard deviation of teams' win percentages to the standard deviation that would arise in an idealized league where every team had equal playing strength, so that a value near one signals balance and large values signal dominance by a few clubs. Brad Humphreys's 2002 paper showed the limits of single-season dispersion measures and proposed the Competitive Balance Ratio to capture how standings change over time, while Owen, Ryan, and Weatherston's 2007 work adapted the Herfindahl-Hirschman index of concentration to wins, correcting it for the number of teams. Together these give a toolkit of dispersion and concentration indices for measuring league parity.
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- Humphreys, B. R. (2002). Alternative measures of competitive balance in sports leagues. Journal of Sports Economics, 3(2), 133-148. · DOI 10.1177/152700250200300203
- Owen, P. D., Ryan, M., & Weatherston, C. R. (2007). Measuring competitive balance in professional team sports using the Herfindahl-Hirschman index. Review of Industrial Organization, 31(4), 289-302. · DOI 10.1007/s11151-008-9157-0
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