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A Bias-Corrected Estimator of Competitive Balance in Sports Leagues

Listed author(s):
  • 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)

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.

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File URL: ftp://163.239.156.99/wpaper/LYH_RIME_2016_11.pdf
File Function: First version, 2016
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Paper provided by Research Institute for Market Economy, Sogang University in its series Working Papers with number 1611.

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Length: 40 pages
Date of creation: 2016
Handle: RePEc:sgo:wpaper:1611
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  1. Martin B. Schmidt & David J. Berri, 2001. "Competitive Balance and Attendance," Journal of Sports Economics, , vol. 2(2), pages 145-167, May.
  2. La Croix, Sumner J & Kawaura, Akihiko, 1999. "Rule Changes and Competitive Balance in Japanese Professional Baseball," Economic Inquiry, Western Economic Association International, vol. 37(2), pages 353-368, April.
  3. Craig Depken, 1999. "Free-Agency and the Competitiveness of Major League Baseball," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 14(3), pages 205-217, May.
  4. Young Hoon Lee & Rodney Fort, 2005. "Structural Change in MLB Competitive Balance: The Depression, Team Location, and Integration," Economic Inquiry, Western Economic Association International, vol. 43(1), pages 158-169, January.
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  9. Rodney Fort & James Quirk, 1995. "Cross-subsidization, Incentives, and Outcomes in Professional Team Sports Leagues," Journal of Economic Literature, American Economic Association, vol. 33(3), pages 1265-1299, September.
  10. Young Lee & Rodney Fort, 2008. "Attendance and the Uncertainty-of-Outcome Hypothesis in Baseball," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 33(4), pages 281-295, December.
  11. Tim Pawlowski, 2013. "Testing the Uncertainty of Outcome Hypothesis in European Professional Football," Journal of Sports Economics, , vol. 14(4), pages 341-367, August.
  12. P. Dorian Owen & Nicholas King, 2015. "Competitive Balance Measures In Sports Leagues: The Effects Of Variation In Season Length," Economic Inquiry, Western Economic Association International, vol. 53(1), pages 731-744, 01.
  13. Stefan Szymanski, 2003. "The Assessment: The Economics of Sport," Oxford Review of Economic Policy, Oxford University Press, vol. 19(4), pages 467-477, Winter.
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  15. Sloane, Peter J, 1971. "The Economics of Professional Football: The Football Club as a Utility Maximiser," Scottish Journal of Political Economy, Scottish Economic Society, vol. 18(2), pages 121-146, June.
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