Optimal Dynamic Clustering Through Relegation and Promotion: How to Design a Competitive Sports League
This paper investigates how the structure of a relegation-promotion system impacts the competitiveness of a sports league. It proposes a rigorous mathematical model of a multi-division hierarchical sports league made up of teams with intrinsic skill levels (ISLs) that change from year to year. Since team skill changes over time, modification in division (or cluster) composition is necessary to optimize competitiveness. This is accomplished through promoting teams with the best records at the end of a season to a higher division and relegating teams with poor records to lower divisions. Such mechanisms are fundamental to the English football league system and the PGA Tour/Nationwide Tour. For reasons discussed in the paper, we use data from the National Basketball Association (in which there is no relegation system) to develop statistical models for year-to-year variability in ISLs and for match outcomes based on the ISLs of the two teams. We then develop a multiple season simulation model to investigate the effect of the number of teams relegated and promoted, the schedule, and the variability of year-to-year ISLs on competitiveness of the divisions. For the NBA data, we find that in a three-division league with ten teams in each division, relegating and promoting three teams at the end of the season results in the most competitive divisions as measured by the long run average within-division ISL standard deviation and the percentage of teams assigned to the correct division. The effect of schedule is minimal.
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Volume (Year): 7 (2011)
Issue (Month): 2 (May)
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Stefan Szymanski & Tommaso M. Valletti, 2005. "Promotion and Relegation in Sporting Contests," Rivista di Politica Economica, SIPI Spa, vol. 95(3), pages 3-39, May-June.
- Roger Noll, 2002. "The Economics of Promotion and Relegation in Sports Leagues: The Cases of English Football," Journal of Sports Economics, , vol. 3(2), pages 169-203, May.
- Andrew S. Zimbalist, 2002. "Competitive Balance in Sports Leagues: An Introduction," Journal of Sports Economics, , vol. 3(2), pages 111-121, May.
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