Optimal dynamic clustering through relegation and promotion: How to design a competitive sports league

Abstract

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. © 2011 American Statistical Association. All rights reserved.