Using Mathematical Programming to Select and Seed Teams for the NCAA Tournament

We develop a mathematical programming model to select, rank, and seed 68 teams for the National Collegiate Athletic Association (NCAA) Men’s Basketball Tournament. The selections and seeding are the responsibility of a 10-person selection committee, which chooses from 351 Division I college basketball teams and considers many team-performance attributes. Our approach yields a logically consistent initial starting point based on finding dominant relationships among the teams, and the minimax objective function. We first apply the procedure to data for each of the five tournaments from 2012 to 2016 and show that our rankings align well with those of the respective committees. We then implement the procedure and obtain a set of recommendations for the 2017 NCAA tournament’s committee, prior to the announcement of its selections. Our model’s recommendations closely align with those of the committee, thus supporting our contention that the approach provides a viable, readily implemented, and easily understood basis for both informing the committee’s decisions and encouraging its members to articulate their reasons for choosing otherwise. The approach requires no training data from prior seasons or previous recommendations, and can be expanded to other applications where decision makers are tasked with selecting and ranking a set of entities that has quantifiable performance attributes.