References
- Agresti, A. (2013). Categorical data analysis (3rd ed.). Wiley.
- Ávila-Cano, A., & Triguero-Ruiz, F. (2018). The distribution of soccer leagues scores that generates the minimum of competitive balance: Truncated-Cascade distribution. Málaga Economic Theory Research Center Working Papers, No. 2018-04.
- Bajo, O., & Salas, R. (2002). Inequality foundations of concentration measures: An application to the Hannah-Kay indices. Spanish Economic Review, 4(4), 311–316. https://doi.org/https://doi.org/10.1007/s101080200053
- Bradley, R. A., & Terry, M. E. (1952). Rank analysis of incomplete block designs: I. The method of paired comparisons. Biometrika, 39(3/4), 324–345. https://doi.org/https://doi.org/10.1093/biomet/39.3-4.324
- Brandes, L., & Franck, E. (2007). Who made who? An empirical analysis of competitive balance in European soccer leagues. Eastern Economic Journal, 33(3), 379–403. https://doi.org/https://doi.org/10.1057/eej.2007.32
- Clarke, S. R. (1993). Computer forecasting of Australian Rules football for a daily newspaper. Journal of the Operational Research Society, 44(8), 753–759. https://doi.org/https://doi.org/10.1057/jors.1993.134
- del Corral, J., García-Unanue, J., & Herencia-Quintanar, F. (2016). Are NBA policies that promote long-term competitive balance effective? What is the price? The Open Sports Sciences Journal, 9(1), 81–93. https://doi.org/https://doi.org/10.2174/1875399X01609010081
- Depken, C. A. (1999). Free-agency and the competitiveness of Major League Baseball. Review of Industrial Organization, 14(3), 205–217. https://doi.org/https://doi.org/10.1023/A:1007788303098
- Eckard, E. W. (2017). The uncertainty-of-outcome hypothesis and the industrial organization of sports leagues: Evidence from U.S. college football. Journal of Sports Economics, 18(3), 298–317. https://doi.org/https://doi.org/10.1177/1527002515576002
- Fenn, A. J., von Allmen, P., Brook, S., & Preissing, T. J. (2005). The influence of structural changes and international players on competitive balance in the NHL. Atlantic Economic Journal, 33(2), 215–224. https://doi.org/https://doi.org/10.1007/s11293-005-3763-0
- Fort, R., & Maxcy, J. (2003). Comment on “Competitive balance in sports leagues: An introduction”. Journal of Sports Economics, 4(2), 154–160. https://doi.org/https://doi.org/10.1177/1527002503004002005
- Fort, R., & Quirk, J. (1997). Introducing a competitive economic environment into professional sports. In W. Hendricks (Ed.), Advances in the economics of sports (Vol. 2, pp. 3–26). JAI Press.
- Friesl, M., Lenten, L. J. A., Libich, J., & Stehlík, P. (2017). In search of goals: Increasing ice hockey’s attractiveness by a sides swap. Journal of the Operational Research Society, 68(9), 1006–1018. https://doi.org/https://doi.org/10.1057/s41274-017-0243-2
- Gasparetto, T., & Barajas, A. (2016). Playoffs or just league: A debate in Brazilian football. The Open Sports Sciences Journal, 9(1), 94–103. https://doi.org/https://doi.org/10.2174/1875399X01609010094
- Gayant, J.-P., & Le Pape, N. (2015). The metrics of competitive imbalance. In W. Andreff (Ed.), Disequilibrium sports economics: Competitive imbalance and budget constraints (pp. 104–130). Edward Elgar.
- Goossens, D. R., Beliën, J., & Spieksma, F. C. R. (2012). Comparing league formats with respect to match importance in Belgian football. Annals of Operations Research, 194(1), 223–240. https://doi.org/https://doi.org/10.1007/s10479-010-0764-4
- Hall, M., & Tideman, N. (1967). Measures of concentration. Journal of the American Statistical Association, 62(317), 162–168. https://doi.org/https://doi.org/10.1080/01621459.1967.10482897
- Horowitz, I. (1997). The increasing competitive balance in Major League Baseball. Review of Industrial Organization, 12(3), 373–387. https://doi.org/https://doi.org/10.1023/A:1007799730191
- Howarth, A., & Robinson, T. A. (2008). The impact of the salary cap in the European rugby Super League. International Journal of Business and Management, 3(6), 3–7.
- Humphreys, B. R. (2019). A practical guide to measuring competitive balance. In J. García (Ed.), Sports (and) economics (pp. 75–103). FUNCAS Social and Economic Studies, Funcas.
- Humphreys, B. R., & Watanabe, N. M. (2012). Competitive balance. In L. H. Kahane and S. Shmanske (Eds.), The Oxford handbook of sports economics, Volume 1: The economics of sports (pp. 18–37). Oxford University Press.
- Jane, W.-J. (2014). The relationship between outcome uncertainties and match attendance: New evidence in the National Basketball Association. Review of Industrial Organization, 45(2), 177–200. https://doi.org/https://doi.org/10.1007/s11151-014-9436-x
- Jane, W.-J. (2016). The effect of star quality on attendance demand: The case of the National Basketball Association. Journal of Sports Economics, 17(4), 396–417. https://doi.org/https://doi.org/10.1177/1527002514530405
- Kendall, G., & Lenten, L. J. A. (2017). When sports rules go awry. European Journal of Operational Research, 257(2), 377–394. https://doi.org/https://doi.org/10.1016/j.ejor.2016.06.050
- King, N. (2011). The use of win percentages for competitive balance measures: An investigation of how well win percentages measure team ability and the implications for competitive balance analysis. [MCom thesis]. University of Otago.
- King, N., Owen, P. D., & Audas, R. (2012). Playoff uncertainty, match uncertainty and attendance at Australian National Rugby League matches. Economic Record, 88(281), 262–277. https://doi.org/https://doi.org/10.1111/j.1475-4932.2011.00778.x
- Larsen, A., Fenn, A. J., & Spenner, E. L. (2006). The impact of free agency and the salary cap on competitive balance in the National Football League. Journal of Sports Economics, 7(4), 374–390. https://doi.org/https://doi.org/10.1177/1527002505279345
- Lee, Y. H., Kim, Y., & Kim, S. (2019a). A bias-corrected estimator of competitive balance in sports leagues. Journal of Sports Economics, 20(4), 479–508. https://doi.org/https://doi.org/10.1177/1527002518777974
- Lee, Y. H., Kim, Y., & Kim, S. (2019b). Competitive balance with unbalanced schedules. Journal of Quantitative Analysis in Sports, 15(3), 239–260. https://doi.org/https://doi.org/10.1515/jqas-2017-0100
- Lenten, L. J. A. (2008). Unbalanced schedules and the estimation of competitive balance in the Scottish Premier League. Scottish Journal of Political Economy, 55(4), 488–508. https://doi.org/https://doi.org/10.1111/j.1467-9485.2008.00463.x
- Lenten, L. J. A. (2009). Towards a new dynamic measure of competitive balance: A study applied to Australia’s two major professional ‘football’ leagues. Economic Analysis and Policy, 39(3), 407–428. https://doi.org/https://doi.org/10.1016/S0313-5926(09)50036-7
- Lenten, L. J. A. (2015). Measurement of competitive balance in conference and divisional tournament design. Journal of Sports Economics, 16(1), 3–25. https://doi.org/https://doi.org/10.1177/1527002512471538
- Lenten, L. J. A. (2017). A formal test for asymmetry in the uncertainty of outcome hypothesis. Journal of Sports Economics, 18(3), 253–270. https://doi.org/https://doi.org/10.1177/1527002514567921
- Manasis, V., Ntzoufras, I., & Reade, J. (2015). Measuring competitive balance and uncertainty of outcome hypothesis in European football. arXiv preprint arXiv:1507.00634.
- Marchi, M., & Albert, J. (2014). Analyzing baseball data with R. CRC Press.
- Martinez, M., & Willner, J. (2017). Competitive balance and consumer demand in the English Football League. Applied Finance and Accounting, 3(2), 49–60. https://doi.org/https://doi.org/10.11114/afa.v3i2.2411
- McGee, M. K. (2016). Two universal, probabilistic measures of competitive imbalance. Applied Economics, 48(31), 2883–2894. https://doi.org/https://doi.org/10.1080/00036846.2015.1130792
- Michie, J., & Oughton, C. (2004). Competitive balance in football: Trends and effects. The Sports Nexus.
- Michie, J., & Oughton, C. (2005). Competitive balance in football: An update. The Sports Nexus.
- Mills, B., & Fort, R. (2014). League-level attendance and outcome uncertainty in U.S. pro sports leagues. Economic Inquiry, 52(1), 205–218. https://doi.org/https://doi.org/10.1111/ecin.12037
- Neale, W. C. (1964). The peculiar economics of professional sports. The Quarterly Journal of Economics, 78(1), 1–14. https://doi.org/https://doi.org/10.2307/1880543
- Noll, R. G. (1988). Professional basketball. Stanford University. Studies in Industrial Economics Paper, 144.
- Owen, D. (2014). Measurement of competitive balance and uncertainty of outcome. In J. Goddard and P. Sloane (Eds.), Handbook on the economics of professional football (pp. 41–59). Edward Elgar.
- Owen, P. D. (2010). Limitations of the relative standard deviation of win percentages for measuring competitive balance in sports leagues. Economics Letters, 109(1), 38–41. https://doi.org/https://doi.org/10.1016/j.econlet.2010.07.012
- Owen, P. D., & King, N. (2015). Competitive balance measures in sports leagues: The effects of variation in season length. Economic Inquiry, 53(1), 731–744. https://doi.org/https://doi.org/10.1111/ecin.12102
- Owen, P. D., Ryan, M., & Weatherston, C. R. (2007). Measuring competitive balance in professional team sports using the Herfindahl-Hirschman index. Review of Industrial Organization, 31(4), 289–302. https://doi.org/https://doi.org/10.1007/s11151-008-9157-0
- Pawlowski, T., Breuer, C., & Hovemann, A. (2010). Top clubs’ performance and the competitive situation in European domestic football competitions. Journal of Sports Economics, 11(2), 186–202. https://doi.org/https://doi.org/10.1177/1527002510363100
- R Core Team. (2018). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/.
- Rao, P. V., & Kupper, L. L. (1967). Ties in paired-comparison experiments: A generalization of the Bradley-Terry model. Journal of the American Statistical Association, 62(317), 194–204. https://doi.org/https://doi.org/10.1080/01621459.1967.10482901
- Rottenberg, S. (1956). The baseball players' labor market. Journal of Political Economy, 64(3), 242–258. https://doi.org/https://doi.org/10.1086/257790
- Scarf, P., Yusof, M. M., & Bilbao, M. (2009). A numerical study of designs for sporting contests. European Journal of Operational Research, 198(1), 190–198. https://doi.org/https://doi.org/10.1016/j.ejor.2008.07.029
- Scully, G. W. (1989). The business of Major League Baseball. University of Chicago Press.
- Szymanski, S. (2003). The economic design of sporting contests. Journal of Economic Literature, 41(4), 1137–1187. https://doi.org/https://doi.org/10.1257/jel.41.4.1137
- Tainsky, S., Xu, J., & Yang, Q. (2017). Competitive balance and the participation–spectatorship gap in Chinese table tennis. Applied Economics, 49(3), 263–272. https://doi.org/https://doi.org/10.1080/00036846.2016.1197363
- Totty, E. S., & Owens, M. F. (2011). Salary caps and competitive balance in professional sports leagues. Journal for Economic Educators, 11(2), 46–56.
- Triguero Ruiz, F., & Avila-Cano, A. (2019). The distance to competitive balance: A cardinal measure. Applied Economics, 51(7), 698–710. https://doi.org/https://doi.org/10.1080/00036846.2018.1512743
- Utt, J., & Fort, R. (2002). Pitfalls to measuring competitive balance with Gini coefficients. Journal of Sports Economics, 3(4), 367–373. https://doi.org/https://doi.org/10.1177/152700250200300406
- Van Scyoc, L., & McGee, M. K. (2016). Testing for competitive balance. Empirical Economics, 50(3), 1029–1043. https://doi.org/https://doi.org/10.1007/s00181-015-0968-1
- Vaziri, B., Dabadghao, S., Yih, Y., & Morin, T. L. (2018). Properties of sports ranking methods. Journal of the Operational Research Society, 69(5), 776–787. https://doi.org/https://doi.org/10.1057/s41274-017-0266-8
- Wright, M. B. (2014). OR analysis of sporting rules – A survey. European Journal of Operational Research, 232(1), 1–8. https://doi.org/https://doi.org/10.1016/j.ejor.2013.03.043