IDEAS home Printed from https://ideas.repec.org/p/otg/wpaper/1715.html
   My bibliography  Save this paper

Simulation Evidence on Herfindahl-Hirschman Indices as Measures of Competitive Balance

Author

Listed:
  • Dorian Owen

    (Department of Economics, University of Otago, New Zealand)

  • Caitlin Owen

    (Department of Information Science, University of Otago, New Zealand)

Abstract

Measurement of the degree of competitive balance, how evenly teams are matched, is central to the economic analysis of professional sports leagues. A common problem with competitive balance measures, however, is their sensitivity to the number of teams and the number of matches played by each team, i.e., season length. This paper uses simulation methods to examine the effects of changes in season length on the distributions of several widely used variants of the Herfindahl- Hirschman index applied to wins in a season. Of the measures considered, a normalized measure, accounting for lower and upper bounds, and an adjusted measure perform best, although neither completely removes biases associated with different season lengths.

Suggested Citation

  • 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.
    • Handle: RePEc:otg:wpaper:1715
    as

    Download full text from publisher

    File URL: http://www.otago.ac.nz/economics/research/otago671741.pdf
    File Function: First version, 2017
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Owen, P. Dorian, 2010. "Limitations of the relative standard deviation of win percentages for measuring competitive balance in sports leagues," Economics Letters, Elsevier, vol. 109(1), pages 38-41, October.
    2. Simon Rottenberg, 1956. "The Baseball Players' Labor Market," Journal of Political Economy, University of Chicago Press, vol. 64(3), pages 242-242.
    3. Young Hoon Lee & Yongdai Kim & Sara Kim, 2019. "A Bias-Corrected Estimator of Competitive Balance in Sports Leagues," Journal of Sports Economics, , vol. 20(4), pages 479-508, May.
    4. Brian Mills & Rodney Fort, 2014. "League-Level Attendance And Outcome Uncertainty In U.S. Pro Sports Leagues," Economic Inquiry, Western Economic Association International, vol. 52(1), pages 205-218, January.
    5. Scott Tainsky & Jie Xu & Qian Yang, 2017. "Competitive balance and the participation–spectatorship gap in Chinese table tennis," Applied Economics, Taylor & Francis Journals, vol. 49(3), pages 263-272, January.
    6. Nicholas King & P. Dorian Owen & Rick Audas, 2012. "Playoff Uncertainty, Match Uncertainty and Attendance at Australian National Rugby League Matches," The Economic Record, The Economic Society of Australia, vol. 88(281), pages 262-277, June.
    7. 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.
    8. Wen-Jhan Jane, 2014. "The Relationship Between Outcome Uncertainties and Match Attendance: New Evidence in the National Basketball Association," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 45(2), pages 177-200, September.
    9. Lee Scyoc & M. Kevin McGee, 2016. "Testing for competitive balance," Empirical Economics, Springer, vol. 50(3), pages 1029-1043, May.
    10. Joshua Utt & Rodney Fort, 2002. "Pitfalls to Measuring Competitive Balance With Gini Coefficients," Journal of Sports Economics, , vol. 3(4), pages 367-373, November.
    11. Liam J. A. Lenten, 2017. "A Formal Test for Asymmetry in the Uncertainty of Outcome Hypothesis," Journal of Sports Economics, , vol. 18(3), pages 253-270, April.
    12. Tim Pawlowski & Christoph Breuer & Arnd Hovemann, 2010. "Top Clubs’ Performance and the Competitive Situation in European Domestic Football Competitions," Journal of Sports Economics, , vol. 11(2), pages 186-202, April.
    13. 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.
    14. Lief Brandes & Egon Franck, 2007. "Who Made Who – An Empirical Analysis of Competitive Balance in European Soccer Leagues," Eastern Economic Journal, Eastern Economic Association, vol. 33(3), pages 379-403, Summer.
    15. P. Owen & Michael Ryan & Clayton Weatherston, 2007. "Measuring Competitive Balance in Professional Team Sports Using the Herfindahl-Hirschman Index," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 31(4), pages 289-302, December.
    16. 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.
    17. John Goddard & Peter Sloane (ed.), 2014. "Handbook on the Economics of Professional Football," Books, Edward Elgar Publishing, number 14821.
    18. Walter C. Neale, 1964. "The Peculiar Economics of Professional Sports," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 78(1), pages 1-14.
    19. 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.
    20. Misael Martinez & Jonathan Willner, 2017. "Competitive Balance and Consumer Demand in the English Football League," Applied Finance and Accounting, Redfame publishing, vol. 3(2), pages 49-60, August.
    21. Aju Fenn & Peter Allmen & Stacey Brook & Thomas Preissing, 2005. "The Influence of Structural Changes and International Players on Competitive Balance in the NHL," Atlantic Economic Journal, Springer;International Atlantic Economic Society, vol. 33(2), pages 215-224, June.
    22. Evan S. Totty & Mark F. Owens, 2011. "Salary Caps and Competitive Balance in Professional Sports Leagues," Journal for Economic Educators, Middle Tennessee State University, Business and Economic Research Center, vol. 11(2), pages 46-56, Fall.
    23. M. Kevin McGee, 2016. "Two universal, probabilistic measures of competitive imbalance," Applied Economics, Taylor & Francis Journals, vol. 48(31), pages 2883-2894, July.
    24. E. Woodrow Eckard, 2017. "The Uncertainty-of-Outcome Hypothesis and the Industrial Organization of Sports Leagues," Journal of Sports Economics, , vol. 18(3), pages 298-317, April.
    25. Francesco Addesa, 2011. "Competitive Balance In The Italian Basketball Championship," Rivista di Diritto ed Economia dello Sport, Centro di diritto e business dello Sport, vol. 7(1), pages 107-125, June.
    26. John Goddard & Peter J. Sloane, 2005. "Economics of sport," Chapters, in: Simon W. Bowmaker (ed.), Economics Uncut, chapter 12, Edward Elgar Publishing.
    27. 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.
    28. 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.
    29. Girish Ramchandani, 2012. "Competitiveness of the English Premier League (1992-2010) and ten European football leagues (2010)," International Journal of Performance Analysis in Sport, Taylor & Francis Journals, vol. 12(2), pages 346-360, August.
    30. Kahane, Leo H. & Shmanske, Stephen (ed.), 2012. "The Oxford Handbook of Sports Economics Volume 1: The Economics of Sports," OUP Catalogue, Oxford University Press, number 9780195387773.
    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. 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.
    2. repec:beo:swcetp:23-12 is not listed on IDEAS
    3. Dejan Trifunovi? & Vito Pipitone, 0000. "Welfare Maximizing Competitive Balance: the Evidence from Top European Football leagues," Proceedings of International Academic Conferences 11113139, International Institute of Social and Economic Sciences.
    4. Dejan Trifunović & Bojan Ristić, 2023. "The Impact Of The Horizontal Distribution Of Media Rights Revenues In Sports Leagues On Competitive Balance," Shaping Post-COVID World – Challenges for Economic Theory and Policy, in: Aleksandra Praščević & Miomir Jakšić & Mihail Arandarenko & Dejan Trifunović & Milutin Ješić (ed.),Shaping Post-COVID World – Challenges for Economic Theory and Policy, chapter 12, pages 263-285, Faculty of Economics and Business, University of Belgrade.

    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. 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.
    2. 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.
    3. 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.
    4. 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).
    5. András Gyimesi, 2020. "League Ranking Mobility Affects Attendance: Evidence From European Soccer Leagues," Journal of Sports Economics, , vol. 21(8), pages 808-828, December.
    6. Fort, Rodney & Maxcy, Joel & Diehl, Mark, 2016. "Uncertainty by regulation: Rottenberg׳s invariance principle," Research in Economics, Elsevier, vol. 70(3), pages 454-467.
    7. 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.
    8. 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.
    9. Young Hoon Lee & Yongdai Kim & Sara Kim, 2019. "A Bias-Corrected Estimator of Competitive Balance in Sports Leagues," Journal of Sports Economics, , vol. 20(4), pages 479-508, May.
    10. Daniel Read & Aaron C.T. Smith & James Skinner, 2021. "A Comparative Analysis of Competitive Balance Between a Closed and an Open League in Rugby League," Journal of Sports Economics, , vol. 22(8), pages 871-892, December.
    11. Francisco Triguero Ruiz & Antonio Avila-Cano, 2019. "The distance to competitive balance: a cardinal measure," Applied Economics, Taylor & Francis Journals, vol. 51(7), pages 698-710, February.
    12. Lee, Travis, 2020. "Competitive Balance in the National Hockey League after Unrestricted Free Agency and the Salary Cap," MPRA Paper 108400, University Library of Munich, Germany.
    13. Dubois, Marc, 2022. "Dominance criteria on grids for measuring competitive balance in sports leagues," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 1-10.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Dejan Trifunovi? & Vito Pipitone, 0000. "Welfare Maximizing Competitive Balance: the Evidence from Top European Football leagues," Proceedings of International Academic Conferences 11113139, International Institute of Social and Economic Sciences.
    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. Budzinski, Oliver & Kunz-Kaltenhäuser, Philipp, 2020. "Promoting or restricting competition? - The 50plus1-rule in German football," Ilmenau Economics Discussion Papers 141, Ilmenau University of Technology, Institute of Economics.

    More about this item

    Keywords

    Herfindahl-Hirschman; Competitive balance; Simulation;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism
    • Z20 - Other Special Topics - - Sports Economics - - - General

    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:otg:wpaper:1715. 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: Janet Bryant (email available below). General contact details of provider: https://edirc.repec.org/data/etotanz.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.