Optimal Dynamic Clustering Through Relegation and Promotion: How to Design a Competitive Sports League
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Martin L Puterman
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 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
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Articles in the same Issue
- Conference Paper
- Uncovering Europe's Best Goalscorers from the 2009-2010 Season
- Dynamic Effort, Sustainability, Myopia, and 110% Effort
- The Intra-Match Home Advantage in Australian Rules Football
- The Relationship between Leader Experience and Team Performance in Cross-Sectional and Longitudinal Designs
- Stratified Odds Ratios for Evaluating NBA Players Based on their Plus/Minus Statistics
- Dependence Relationships between On Field Performance, Wins, and Payroll in Major League Baseball
- Optimal Dynamic Clustering Through Relegation and Promotion: How to Design a Competitive Sports League
- Perception ? Reality: Analyzing Specific Allegations of NBA Referee Bias
- NFL Prediction using Committees of Artificial Neural Networks
- An Alternative to the NFL Draft Pick Value Chart Based upon Player Performance
- Monte Carlo Simulation for High School Football Playoff Seed Projection
- Defining the Performance Coefficient in Golf: A Case Study at the 2009 Masters
- Reconsideration of the Best Batting Order in Baseball: Is the Order to Maximize the Expected Number of Runs Really the Best?
- Never Too Late to Win
- An Extension of the Pythagorean Expectation for Association Football
- Pitcher Accuracy Through Catcher Spotting: Assessing Rater Reliability
- Valuing Nostalgia: The Case of the Topps 1957 Baseball Cards
