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A Bias-Corrected Estimator of Competitive Balance in Sports Leagues

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  • Young Hoon Lee
  • Yongdai Kim
  • Sara Kim

Abstract

The ratio of the actual standard deviation (ASD) to the idealized standard deviation of win percentages (RSD) is the conventional measure of competitive balance (CB). RSD is designed to control for the effect of season length on the sample standard deviation of win percentages (ASD). Theoretically, the RSD should be greater than 1, but empirical values below 1 have been found in previous studies. This article employs a mathematical statistics approach to evaluate the statistical properties of RSD and ASD. In doing so, this study finds that RSD is constructed by an invalid normalization approach and that ASD is biased. It also presents a bias-corrected standard deviation (BCSD) as a new estimator of the standard deviation of true win probabilities. Results from the simulations confirm the following: (i) ASD is prone to underestimate CB levels when the number of games is small, (ii) the RSD values become unreasonably large when the number of games is large, and (iii) BCSD performs well with respect to mean bias and root mean squared errors. According to empirical analysis of the English Premier League (EPL) and the Korea Baseball Organization (KBO), BCSD shows that the KBO was more competitively balanced than the EPL between 2000 and 2015, while the RSD implies that the two leagues were roughly equal.

Suggested Citation

  • Young Hoon Lee & Yongdai Kim & Sara Kim, 2019. "A Bias-Corrected Estimator of Competitive Balance in Sports Leagues," Journal of Sports Economics, , vol. 20(4), pages 479-508, May.
    • Handle: RePEc:sae:jospec:v:20:y:2019:i:4:p:479-508
    DOI: 10.1177/1527002518777974
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    Cited by:

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    2. Young Hoon Lee & Rodney Fort, 2023. "Division Play and Outcome Uncertainty in Sports Leagues," Journal of Sports Economics, , vol. 24(5), pages 639-663, June.
    3. Avila-Cano, Antonio & Owen, P. Dorian & Triguero-Ruiz, Francisco, 2023. "Measuring competitive balance in sports leagues that award bonus points, with an application to rugby union," European Journal of Operational Research, Elsevier, vol. 309(2), pages 939-952.
    4. Young Hoon Lee & Yongdai Kim & Sara Kim, 2018. "Unbiased Estimation of Competitive Balance in Sports Leagues with Unbalanced Schedules," Working Papers 1801, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    5. András Gyimesi, 2020. "League Ranking Mobility Affects Attendance: Evidence From European Soccer Leagues," Journal of Sports Economics, , vol. 21(8), pages 808-828, December.
    6. Hayley Jang & Young Hoon Lee, 2017. "Estimation of Within-Season Competitive Balance Using STATA," Working Papers 1702, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    7. Hojun Sung & Brian M. Mills & Younghoon Lee, 2022. "Moments of Competitive Balance in Major League Soccer," Journal of Sports Economics, , vol. 23(3), pages 329-354, April.
    8. Alexander John Bond & Francesco Addesa, 2020. "Competitive Intensity, Fans’ Expectations, and Match-Day Tickets Sold in the Italian Football Serie A, 2012-2015," Journal of Sports Economics, , vol. 21(1), pages 20-43, January.
    9. Dorian Owen & Caitlin Owen, 2017. "Simulation Evidence on Herfindahl-Hirschman Indices as Measures of Competitive Balance," Working Papers 1715, University of Otago, Department of Economics, revised Dec 2017.
    10. Qi Ge & Brad R. Humphreys & Alexander Eisert, 2022. "Vertical Integration and Competitive Balance in Professional Sports: Evidence from Minor League Baseball," Working Papers 22-07, Department of Economics, West Virginia University.

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