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Unbiased Estimation of Competitive Balance in Sports Leagues with Unbalanced Schedules

Author

Listed:
  • Young Hoon Lee

    () (Department of Economics, Sogang University, Seoul)

  • Yongdai Kim

    (Department of Statistics, Seoul National University)

  • Sara Kim

    (Department of Statistics, Seoul National University)

Abstract

Many empirical studies on competitive balance (CB) use the ratio of the actual standard deviation to the idealized standard deviation of win percentages (RSD). This paper suggests that empirical studies that use RSD to compare CB among different leagues are invalid, but that RSD may be used for time-series analysis on CB in a league if there are no changes in season length. When schedules are unbalanced and/or include interleague games, the final winning percentage is a biased estimator of the true win probability. This paper takes a mathematical statistical approach to derive an unbiased estimator of within-season CB that can be applied to not only balanced but also unbalanced schedules. Simulations and empirical applications are also presented.

Suggested Citation

  • 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.
  • Handle: RePEc:sgo:wpaper:1801
    as

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    File URL: ftp://163.239.156.99/wpaper/LYH_RIME_2018_01.pdf
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    References listed on IDEAS

    as
    1. Walter C. Neale, 1964. "The Peculiar Economics of Professional Sports," The Quarterly Journal of Economics, Oxford University Press, vol. 78(1), pages 1-14.
    2. 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.
    3. Martin B. Schmidt & David J. Berri, 2001. "Competitive Balance and Attendance," Journal of Sports Economics, , vol. 2(2), pages 145-167, May.
    4. 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.
    5. 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.
    6. 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.
    7. Simon Rottenberg, 1956. "The Baseball Players' Labor Market," Journal of Political Economy, University of Chicago Press, vol. 64, pages 242-242.
    8. 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, January.
    9. Trandel Gregory A & Maxcy Joel G, 2011. "Adjusting Winning-Percentage Standard Deviations and a Measure of Competitive Balance for Home Advantage," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 7(1), pages 1-17, January.
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    11. Martin B. Schmidt & David J. Berri, 2004. "The Impact of Labor Strikes on Consumer Demand: An Application to Professional Sports," American Economic Review, American Economic Association, vol. 94(1), pages 344-357, March.
    12. Liam J. A. Lenten, 2008. "Unbalanced Schedules And The Estimation Of Competitive Balance In The Scottish Premier League," Scottish Journal of Political Economy, Scottish Economic Society, vol. 55(4), pages 488-508, September.
    13. Liam J. A. Lenten, 2015. "Measurement of Competitive Balance in Conference and Divisional Tournament Design," Journal of Sports Economics, , vol. 16(1), pages 3-25, January.
    14. E. Eckard, 1998. "The NCAA Cartel and Competitive Balance in College Football," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 13(3), pages 347-369, June.
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    Keywords

    Competitive Balance; Unbalanced Schedule; Unbiased Estimation;

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