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Competitive balance with unbalanced schedules

Author

Listed:
  • Lee Young Hoon

    (Department of Economics, Sogang University, Mapo-Gu, Korea)

  • Kim Yongdai
  • Kim Sara

    (Department of Statistics, Seoul National University, Seoul, Korea)

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, which confirm that the debiasing strategy to obtain the unbiased estimator of within-season CB is still effective for unbalanced schedules.

Suggested Citation

  • Lee Young Hoon & Kim Yongdai & Kim Sara, 2019. "Competitive balance with unbalanced schedules," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 15(3), pages 239-260, September.
    • Handle: RePEc:bpj:jqsprt:v:15:y:2019:i:3:p:239-260:n:1
    DOI: 10.1515/jqas-2017-0100
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    Citations

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    Cited by:

    1. András Gyimesi, 2020. "League Ranking Mobility Affects Attendance: Evidence From European Soccer Leagues," Journal of Sports Economics, , vol. 21(8), pages 808-828, December.
    2. 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.
    3. 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.
    4. Rodney Fort & Young H. Lee, 2020. "Transition to an unbalanced Sports League schedule: adding the analysis of outcome uncertainty," Applied Economics, Taylor & Francis Journals, vol. 52(51), pages 5629-5638, November.

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