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The middle-seed anomaly: why does it occur in some sports tournaments but not others?

Dale Zimmerman and Hong Beng Lim


Previously published statistical analyses of NCAA Division I Men’s Tournament (“March Madness”) game outcomes have revealed that the relationship between tournament seed and the time-aggregated number of third-round (“Sweet 16”) appearances for the middle half of the seeds exhibits a statistically and practically significant departure from monotonicity. In particular, the 8- and 9-seeds combined appear less often than any one of seeds 10–12. In this article, we show that a similar “middle-seed anomaly” also occurs in the NCAA Division I Women’s Tournament but does not occur in two other major sports tournaments that are similar in structure to March Madness. We offer explanations for the presence of a middle-seed anomaly in the NCAA basketball tournaments, and its absence in the others, that are based on the combined effects of the functional form of the relationship between team strength and seed specific to each tournament, the degree of parity among teams, and certain elements of tournament structure. Although these explanations account for the existence of middle-seed anomalies in the NCAA basketball tournaments, their larger-than-expected magnitudes, which arise mainly from the overperformance of seeds 10–12 in the second round, remain enigmatic.

Corresponding author: Dale Zimmerman, University of Iowa, Iowa City, USA, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.


Baumann, R., V. A. Matheson, and C. A. Howe. 2010. “Anomalies in Tournament Design: The Madness of March Madness.” Journal of Quantitative Analysis in Sports 6: 1–9. Search in Google Scholar

Bradley, R. A., and M. E. Terry. 1952. “Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons.” Biometrika 39: 324–45. Search in Google Scholar

Clay, D. C., A. S. Bro, and N. J. Clay. 2015. “Geospatial Determinants of Game Outcomes in NCAA Men’s Basketball.” The International Journal of Sport and Society 4: 71–81. Search in Google Scholar

Doyel, G. 2009. Eight, Nine, Futility Time: Cowboys, Saints will Learn Sunday. Also available at Search in Google Scholar

Dykstra, R., and H. El Barmi. 2006. “Chi-bar-square Distributions.” In Encyclopedia of Statistical Sciences, edited by S. Kotz, C. B. Read, N. Balakrishnan, B. Vidakovic, and N. L. Johnson, 2nd ed. Hoboken, NJ: Wiley. Search in Google Scholar

El Barmi, H., and M. Johnson. 2006. “A Unified Approach to Testing for and against a Set of Linear Inequality Constraints in the Product Multinomial Setting.” Journal of Multivariate Analysis 97: 1894–912. Search in Google Scholar

Giknis, F. 2016. Is Parity Still an Issue for Women’s NCAA Basketball? Search in Google Scholar

Glickman, M. E., and H. S. Stern. 2017. “Estimating Team Strength in the NFL.” In Handbook of Statistical Methods and Analyses in Sports, edited by J. Albert, M. E. Glickman, T. B. Swartz, and R. H. Koning, 113–35. Boca Raton, FL: CRC Press. Search in Google Scholar

Harville, D. A., and M. H. Smith. 1994. “The Home-Court Advantage: how Large Is it and Does it Vary from Team to Team?” The American Statistician 48: 22–8. Search in Google Scholar

Morris, T. L., and F. H. Bohkari. 2012. “The Dreaded Middle Seeds — Are They the Worst Seeds in the NCAA Basketball Tournament?” Journal of Quantitative Analysis in Sports 8: 1–13. Search in Google Scholar

Pollard, R., and G. Pollard. 2005. “Long-term Trends in Professional Sports in Nortmh Aerica and England (1876–2003).” Journal of Sports Sciences 23: 337–50. Search in Google Scholar

Reinig, B. A., and I. Horowitz. 2019. “Analyzing the Impact of the NCAA Selection Committee’s New Quadrant System.” Journal of Sports Analytics 5: 325–33. Search in Google Scholar

Stefani, R. T. 1978. “Improved Least Squares Football, Basketball, and Soccer Predictions.” IEEE Transactions on Systems, Man, and Cybernetics 10: 116–23. Search in Google Scholar

Swartz, T. B., and A. Arce. 2014. “New Insights Involving the Home Team Advantage.” International Journal of Sports Science & Coaching 9: 681–92. Search in Google Scholar

Zimmerman, D. L., N. D. Zimmerman, and J. T. Zimmerman. 2020. “March Madness “Anomalies”: Are They Real, and if So, Can They Be Explained?” The American Statistician, Search in Google Scholar

Received: 2020-06-04
Revised: 2021-04-19
Accepted: 2021-04-21
Published Online: 2021-05-07
Published in Print: 2021-09-27

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