IDEAS home Printed from https://ideas.repec.org/p/sgo/wpaper/1611.html
   My bibliography  Save this paper

A Bias-Corrected Estimator of Competitive Balance in Sports Leagues

Author

Listed:
  • 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, Nam Duck-Woo Economic Research Institute, Sogang University (Former Research Institute for Market Economy).
    • Handle: RePEc:sgo:wpaper:1611
    as

    Download full text from publisher

    File URL: https://tinyurl.com/2x842cu8
    File Function: First version, 2016
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. Simon Rottenberg, 1956. "The Baseball Players' Labor Market," Journal of Political Economy, University of Chicago Press, vol. 64(3), pages 242-242.
    5. Martin B. Schmidt & David J. Berri, 2003. "On the Evolution of Competitive Balance: The Impact of an Increasing Global Search," Economic Inquiry, Western Economic Association International, vol. 41(4), pages 692-704, October.
    6. 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.
    7. 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.
    8. M. Kevin McGee, 2016. "Two universal, probabilistic measures of competitive imbalance," Applied Economics, Taylor & Francis Journals, vol. 48(31), pages 2883-2894, July.
    9. Kelly Goossens, 2006. "Competitive balance in european football: comparison by adapting measures: national measure of seasonal imbalance and Top 3," Rivista di Diritto ed Economia dello Sport, Centro di diritto e business dello Sport, vol. 2(2), pages 77-122, Dicembre.
    10. 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.
    11. Stefan Szymanski, 2003. "The Assessment: The Economics of Sport," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 19(4), pages 467-477, Winter.
    12. Lee Scyoc & M. Kevin McGee, 2016. "Testing for competitive balance," Empirical Economics, Springer, vol. 50(3), pages 1029-1043, May.
    13. Duane W. Rockerbie, 2016. "Exploring Interleague Parity in North America," Journal of Sports Economics, , vol. 17(3), pages 286-301, April.
    14. S. M. Dobson & J. A. Goddard, 1998. "Performance and revenue in professional league football: evidence from Granger causality tests," Applied Economics, Taylor & Francis Journals, vol. 30(12), pages 1641-1651.
    15. Louis P. Cain & David D. Haddock, 2006. "Research Notes: Measuring Parity," Journal of Sports Economics, , vol. 7(3), pages 330-338, August.
    16. Hayley Jang & Young Hoon Lee, 2016. "A Business Analysis of Asian Baseball Leagues," Asian Economic Policy Review, Japan Center for Economic Research, vol. 11(1), pages 95-112, January.
    17. 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.
    18. Dennis Coates & Brad R. Humphreys & Li Zhou, 2014. "Reference-Dependent Preferences, Loss Aversion, And Live Game Attendance," Economic Inquiry, Western Economic Association International, vol. 52(3), pages 959-973, July.
    19. 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.
    20. 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.
    21. Rodney Fort, 2007. "Comments on ``Measuring Parity''," Journal of Sports Economics, , vol. 8(6), pages 642-651, December.
    22. Kelly Goossens, 2006. "Competitive Balance in European Football - Comparison by Adapting Measures: National Measure of Seasonal Imbalance and Top 3," IASE Conference Papers 0620, International Association of Sports Economists.
    23. 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.
    24. Tim Pawlowski, 2013. "Testing the Uncertainty of Outcome Hypothesis in European Professional Football," Journal of Sports Economics, , vol. 14(4), pages 341-367, August.
    25. 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.
    26. P. Dorian Owen, 2012. "Measuring Parity in Sports Leagues With Draws," Journal of Sports Economics, , vol. 13(1), pages 85-95, February.
    27. 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.
    28. Brad R. Humphreys, 2002. "Alternative Measures of Competitive Balance in Sports Leagues," Journal of Sports Economics, , vol. 3(2), pages 133-148, May.
    29. Rodney Fort & Joel Maxcy, 2003. "“Competitive Balance in Sports Leagues: An Introductionâ€," Journal of Sports Economics, , vol. 4(2), pages 154-160, May.
    30. Luigi Buzzacchi & Stefan Szymanski & Tommaso Valletti, 2003. "Equality of Opportunity and Equality of Outcome: Open Leagues, Closed Leagues and Competitive Balance *#We thank the Editor and an anonymous referee for helpful comments," Journal of Industry, Competition and Trade, Springer, vol. 3(3), pages 167-186, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sang Hun Sung & Doo-Seung Hong & Soo Young Sul, 2020. "How We Can Enhance Spectator Attendance for the Sustainable Development of Sport in the Era of Uncertainty: A Re-Examination of Competitive Balance," Sustainability, MDPI, vol. 12(17), pages 1-15, August.
    2. 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).
    3. 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.
    4. 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.
    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. 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.
    7. 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).
    8. András Gyimesi, 2020. "League Ranking Mobility Affects Attendance: Evidence From European Soccer Leagues," Journal of Sports Economics, , vol. 21(8), pages 808-828, December.
    9. 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.
    10. 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.
    11. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dorian Owen, 2014. "Measurement of competitive balance and uncertainty of outcome," Chapters, in: John Goddard & Peter Sloane (ed.), Handbook on the Economics of Professional Football, chapter 3, pages 41-59, Edward Elgar Publishing.
    2. 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).
    3. Hayley Jang & Young Hoon Lee & Rodney Fort, 2019. "Winning In Professional Team Sports: Historical Moments," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 103-120, January.
    4. 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.
    5. Fort, Rodney & Maxcy, Joel & Diehl, Mark, 2016. "Uncertainty by regulation: Rottenberg׳s invariance principle," Research in Economics, Elsevier, vol. 70(3), pages 454-467.
    6. 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.
    7. Meletakos, Panagiotis & Chatzicharistos, Dimitrios & Apostolidis, Nikolaos & Manasis, Vasilios & Bayios, Ioannis, 2016. "Foreign players and competitive balance in Greek basketball and handball championships," Sport Management Review, Elsevier, vol. 19(4), pages 391-401.
    8. Sang Hun Sung & Doo-Seung Hong & Soo Young Sul, 2020. "How We Can Enhance Spectator Attendance for the Sustainable Development of Sport in the Era of Uncertainty: A Re-Examination of Competitive Balance," Sustainability, MDPI, vol. 12(17), pages 1-15, August.
    9. 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.
    10. Rodney Fort & Young Hoon Lee, 2007. "Structural Change, Competitive Balance, And The Rest Of The Major Leagues," Economic Inquiry, Western Economic Association International, vol. 45(3), pages 519-532, July.
    11. Young Hoon Lee, 2009. "The Impact of Postseason Restructuring on the Competitive Balance and Fan Demand in Major League Baseball," Journal of Sports Economics, , vol. 10(3), pages 219-235, June.
    12. Antonio Avila-Cano & Amparo Ruiz-Sepulveda & Francisco Triguero-Ruiz, 2021. "Identifying the Maximum Concentration of Results in Bilateral Sports Competitions," Mathematics, MDPI, vol. 9(11), pages 1-19, June.
    13. Carlos Gomez-Gonzalez & Julio del Corral & R. Todd Jewell & Jorge García-Unanue & Cornel Nesseler, 2019. "A Prospective Analysis of Competitive Balance Levels in Major League Soccer," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 54(1), pages 175-190, February.
    14. 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.
    15. András Gyimesi, 2020. "League Ranking Mobility Affects Attendance: Evidence From European Soccer Leagues," Journal of Sports Economics, , vol. 21(8), pages 808-828, December.
    16. Brian M. Mills & Rodney Fort, 2018. "Team-Level Time Series Analysis in MLB, the NBA, and the NHL," Journal of Sports Economics, , vol. 19(7), pages 911-933, October.
    17. repec:qut:auncer:2013_04 is not listed on IDEAS
    18. Allen R. Sanderson & John J. Siegfried, 2003. "Thinking about Competitive Balance," Journal of Sports Economics, , vol. 4(4), pages 255-279, November.
    19. Franziska Prockl & Dirk Semmelroth, 2018. "Perception Versus Reality - Competitive Balance In Major League Soccer From 1996 – 2016," Working Papers Dissertations 36, Paderborn University, Faculty of Business Administration and Economics.
    20. 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.
    21. Andrew Larsen & Aju J. Fenn & Erin Leanne Spenner, 2006. "The Impact of Free Agency and the Salary Cap on Competitive Balance in the National Football League," Journal of Sports Economics, , vol. 7(4), pages 374-390, November.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sgo:wpaper:1611. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Jung Hur (email available below). General contact details of provider: https://edirc.repec.org/data/risogkr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.