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Professors Develop “Math Madness” to Select and Seed NCAA Basketball Tournament Teams

If you’re a fan of National Collegiate Athletic Association (NCAA) Division I basketball, you’ve probably eagerly awaited the annual tournament famously known as “March Madness’ or the “Big Dance”. 

You’ve also probably wondered how the rotating 10-person selection committee evaluates and chooses the 36 at-large teams that compete in the 68-team tournament bracket. The 36 at-large teams are comprised of those teams that did not automatically qualify for the tournament by winning their conference championship.

Exactly how the committee choses those at-large selections has never been a transparent process and since it is human beings making the team selections, biases can also play into the selection procedure.

However, SDSU management information systems professor and department chair, Dr. Bruce Reinig, and his colleague, Dr. Ira Horowitz of the University of Florida, recently published research which demonstrated the use of a mathematical algorithm that automatically and objectively selects and seeds at-large teams.

The algorithm is based on the following seven team-performance metrics:

  • Associated Press (AP) poll numbers
  • USA Today coach’s poll numbers
    Basketball fans at a game

    Program developed at SDSU can predict the NCAA Basketball Tournament at-large seeds with near-perfect accuracy.


  • Winning percentage
  • Rating percentage index (RPI)
  • Strength of schedule
  • Wins against teams in the basketball power index (BPI) top 50 (also known as quality wins)
  • Losses to teams not in the BPI top 50 (also known as non-quality losses)

When the professors used the algorithm to determine the outcome of the at-large selections prior to the committee’s announcement in 2017, they found they matched 37 of 38 teams selected for the tournament (the selection committee chose Marquette, where the algorithm targeted Illinois State).

Reinig and Horowitz submitted their mathematical programming approach and research findings to the INFORMS journal Interfaces for publication. Their research was accepted and will be published in the spring of 2018.

The algorithm was applied again in 2018 prior to Selection Sunday. But this time, the professors found their approach matched 33 out of 36 of the committee’s at large selections and there was a notable change in the selection committee process that may have accounted for the difference this year. That change was the introductions of “quadrants” which classifies a team’s wins and losses by home games, away games and neutral games and the RPI ranking of each opponent into four separate categories. 

“We would have had Oklahoma State, Baylor and Louisville in the Big Dance, whereas the selection committee went with UCLA, Missouri and Arizona State,” said Reinig. “I’m curious to learn what led to their decision especially with the new quadrant system since Oklahoma State beat number-one seed Kansas twice during the regular season this year.”

But the professors’ research isn’t over. “We will examine how best to incorporate quadrants into the algorithm,” said Reinig. “One nice aspect to our approach is the ease in which we are able to add new variables to the existing decision making process.”