A Statistical Analysis of the 'Fairness' of the NCAA Basketball Tournaments

• Activity Number: 263
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Sports
• Author(s): Tracy Morris*+ and Minzhe Wu
• Companies: University of Central Oklahoma and University of Central Oklahoma
• Keywords: tournament design ; basketball ; sports statistics ; probability ; simulation

Abstract

The "fairness" of tournament designs is of crucial importance in competitive sports. For example, in a previous paper, Morris and Bokhari (2012) showed that in certain situations it is more advantageous to be seeded 10, 11, or 12 than 8 or 9. The objective of this research was to examine the "fairness" (meaning higher-ranked teams should perform better, on average, than lower-ranked teams) of the NCAA basketball tournaments relative to other tournament variations, such as reseeding and round robin designs. Data was collected from mcubed.net (http://mcubed.net/ncaab) concerning seed and game outcome (win or loss) for both the men's and women's tournaments dating back to the beginning of each tournament (1939 for the men's and 1982 for the women's). This data was used to develop a model for estimating the probabilities of any given seed beating any other seed. These estimated probabilities were then used to simulate the outcomes of other tournament designs.