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A Bias-Corrected Estimator of Competitive Balance in Sports Leagues

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  • Young Hoon Lee

    (Department of Economics, Sogang University, Seoul)

  • Yongdai Kim

    (Department of Statistics, Seoul National University, Seoul)

  • Sara Kim

    (Department of Statistics, Seoul National University, Seoul)

Abstract

The ratio of the actual standard deviation 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 one, but empirical values below one have been found in previous studies. This paper 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 on the English Premier League (EPL) and the Korea Baseball Organization (KBO), BCSD shows that the KBO was more competitively-balanced than the EPL between 2000-2015, but the RSD implies that the two leagues were more or less equal.

Suggested Citation

  • Young Hoon Lee & Yongdai Kim & Sara Kim, 2016. "A Bias-Corrected Estimator of Competitive Balance in Sports Leagues," Working Papers 1611, Research Institute for Market Economy, Sogang University.
  • Handle: RePEc:sgo:wpaper:1611
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    References listed on IDEAS

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    Cited by:

    1. Hayley Jang & Young Hoon Lee, 2017. "Estimation of Within-Season Competitive Balance Using STATA," Working Papers 1702, Research Institute for Market Economy, Sogang University.
    2. Young Hoon Lee & Yongdai Kim & Sara Kim, 2018. "Unbiased Estimation of Competitive Balance in Sports Leagues with Unbalanced Schedules," Working Papers 1801, Research Institute for Market Economy, Sogang University.
    3. 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.
    4. Young Hoon Lee & Rodney Fort, 2022. "Division Play and Outcome Uncertainty in Sports Leagues," Working Papers 2204, Research Institute for Market Economy, Sogang University.
    5. 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.
    6. 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.

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