IDEAS home Printed from https://ideas.repec.org/a/taf/applec/v51y2019i7p698-710.html
   My bibliography  Save this article

The distance to competitive balance: a cardinal measure

Author

Listed:
  • Francisco Triguero Ruiz
  • Antonio Avila-Cano

Abstract

Competitive balance is a key variable in the analysis of sports competitions. There are several indexes that measure competitive balance but, either they are not a mathematical metric or they do not have the unit interval as a range. Therefore, these indexes do not indicate the magnitude of the differences, and the measurements cannot be interpreted as percentages. We characterize the space of all admissible configurations of the results of a competition. Then, we construct a new index, based on the concept of distance, whose range is the unit interval, and define it as a function in a metric space. So, it solves issues linked to the limited cardinality of most existing indexes, and we can answer this question: What is the meaning of the differences between the levels of competitive balance? We applied this index to the major European soccer leagues over the last twenty seasons.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:applec:v:51:y:2019:i:7:p:698-710
    DOI: 10.1080/00036846.2018.1512743
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00036846.2018.1512743
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00036846.2018.1512743?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Andrew S. Zimbalist, 2002. "Competitive Balance in Sports Leagues," Journal of Sports Economics, , vol. 3(2), pages 111-121, May.
    2. Vani K. Borooah & John Mangan, 2012. "Measuring competitive balance in sports using generalized entropy with an application to English premier league football," Applied Economics, Taylor & Francis Journals, vol. 44(9), pages 1093-1102, March.
    3. Martin B. Schmidt & David J. Berri, 2001. "Competitive Balance and Attendance," Journal of Sports Economics, , vol. 2(2), pages 145-167, May.
    4. 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.
    5. R. Alan Bowman & James Lambrinos & Thomas Ashman, 2018. "Prospective measures of competitive balance application to money lines in the national hockey league," Applied Economics, Taylor & Francis Journals, vol. 50(46), pages 4925-4936, October.
    6. Jean-pascal Gayant & Nicolas Le Pape, 2012. "How to account for changes in the size of Sports Leagues? The Iso Competitive Balance Curves," Economics Bulletin, AccessEcon, vol. 32(2), pages 1715-1723.
    7. M. Kevin McGee, 2016. "Two universal, probabilistic measures of competitive imbalance," Applied Economics, Taylor & Francis Journals, vol. 48(31), pages 2883-2894, July.
    8. Antonio Ávila-Cano & Francisco Triguero-Ruiz, 2018. "The distribution of soccer leagues scores that generates the minimum of competitive balance: Truncated-Cascade Distribution," Working Papers 2018-04, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    9. Joshua Utt & Rodney Fort, 2002. "Pitfalls to Measuring Competitive Balance With Gini Coefficients," Journal of Sports Economics, , vol. 3(4), pages 367-373, November.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. R. Alan Bowman & Thomas Ashman & James Lambrinos, 2013. "Prospective measures of competitive balance: application to money lines in major league baseball," Applied Economics, Taylor & Francis Journals, vol. 45(29), pages 4071-4081, October.
    15. Wladimir Andreff, 2015. "Disequilibrium Sports Economics: Competitive Imbalance and Budget Constraints," Post-Print hal-01305633, HAL.
    16. Martin Schmidt, 2001. "Competition in Major League Baseball: the impact expansion," Applied Economics Letters, Taylor & Francis Journals, vol. 8(1), pages 21-26.
    17. Szpiro, George G., 1987. "Hirschman versus Herfindahl: Some topological properties for the use of concentration indexes," Mathematical Social Sciences, Elsevier, vol. 14(3), pages 299-302, December.
    18. John Considine & Liam Gallagher, 2018. "Competitive balance in a quasi-double knockout tournament," Applied Economics, Taylor & Francis Journals, vol. 50(18), pages 2048-2055, April.
    19. Brad R. Humphreys, 2002. "Alternative Measures of Competitive Balance in Sports Leagues," Journal of Sports Economics, , vol. 3(2), pages 133-148, May.
    20. R. Alan Bowman & James Lambrinos & Thomas Ashman, 2013. "Competitive Balance in the Eyes of the Sports Fan," Journal of Sports Economics, , vol. 14(5), pages 498-520, October.
    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. Dubois, Marc, 2022. "Dominance criteria on grids for measuring competitive balance in sports leagues," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 1-10.
    2. Antonio Avila‐Cano & Francisco Triguero‐Ruiz, 2023. "On the control of competitive balance in the major European football leagues," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(2), pages 1254-1263, March.
    3. Triguero-Ruiz, Francisco & Avila-Cano, Antonio & Trujillo Aranda, Francisco, 2023. "Measuring the diversification of energy sources: The energy mix," Renewable Energy, Elsevier, vol. 216(C).
    4. 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.
    5. 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.
    6. Francisco Triguero‐Ruiz & Antonio Avila‐Cano, 2023. "On competitive balance in the group stage of the UEFA Champions League," Scottish Journal of Political Economy, Scottish Economic Society, vol. 70(3), pages 231-248, July.
    7. Nicolas Scelles & Aurélien François, 2021. "Does a country’s income inequality affect its citizens’ quest for equality in leisure? Evidence from European men’s football," Economics and Business Letters, Oviedo University Press, vol. 10(2), pages 133-139.
    8. Marco Di Domizio & Raul Caruso & Bernd Frick, 2020. "Intelligenza Collettiva E Valore Di Mercato Dei Calciatori: Il Caso Transfermarkt," Rivista di Diritto ed Economia dello Sport, Centro di diritto e business dello Sport, vol. 16(2), pages 155-172, novembre.

    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. Antonio Ávila-Cano & Francisco Triguero-Ruiz, 2018. "The distribution of soccer leagues scores that generates the minimum of competitive balance: Truncated-Cascade Distribution," Working Papers 2018-04, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    3. 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.
    4. 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.
    5. Dubois, Marc, 2022. "Dominance criteria on grids for measuring competitive balance in sports leagues," Mathematical Social Sciences, Elsevier, vol. 115(C), pages 1-10.
    6. 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.
    7. R. Alan Bowman & James Lambrinos & Thomas Ashman, 2013. "Competitive Balance in the Eyes of the Sports Fan," Journal of Sports Economics, , vol. 14(5), pages 498-520, October.
    8. 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.
    9. Robert J. Lemke & Matthew Leonard & Kelebogile Tlhokwane, 2010. "Estimating Attendance at Major League Baseball Games for the 2007 Season," Journal of Sports Economics, , vol. 11(3), pages 316-348, June.
    10. 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.
    11. 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.
    12. 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.
    13. Allen R. Sanderson & John J. Siegfried, 2003. "Thinking about Competitive Balance," Journal of Sports Economics, , vol. 4(4), pages 255-279, November.
    14. 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.
    15. Tony Caporale & Trevor Collier, 2015. "Are We Getting Better or Are They Getting Worse? Draft Position, Strength of Schedule, and Competitive Balance in the National Football League," Journal of Labor Research, Springer, vol. 36(3), pages 291-300, September.
    16. 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.
    17. 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.
    18. John R. Crooker & Aju J. Fenn, 2007. "Sports Leagues and Parity When League Parity Generates Fan Enthusiasm," Journal of Sports Economics, , vol. 8(2), pages 139-164, May.
    19. 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.
    20. András Gyimesi, 2020. "League Ranking Mobility Affects Attendance: Evidence From European Soccer Leagues," Journal of Sports Economics, , vol. 21(8), pages 808-828, December.

    More about this item

    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:taf:applec:v:51:y:2019:i:7:p:698-710. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RAEC20 .

    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.