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Ranking Sports Teams: A Customizable Quadratic Assignment Approach

Department of Industrial Engineering, University of Arkansas, 4207 Bell Engineering Center, Fayetteville, Arkansas 72701
Department of Operations, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106
Department of Industrial Engineering, University of Arkansas, 4207 Bell Engineering Center, Fayetteville, Arkansas 72701
cassady{at}uark.edu
lisa.maillart{at}case.edu
ssalman{at}uark.edu

Ranking sports teams in the absence of full round-robin tournaments is big business, especially for NCAA Division I-A college football. The Bowl Championship Series awards millions of dollars each year to the conferences whose teams are awarded bids. We formulated the sports-team-ranking problem as a customizable quadratic-assignment problem. Decision makers can tailor our model to suit their personal definitions of the degree of victory for each game played and the relative distance between ranking positions. We developed a parameter-section procedure for determining these customized values and executed it using the 2004 college football season. Because the problem size is so large, we developed a heuristic solution procedure based on a genetic algorithm and local search techniques. This heuristic performs well on a special problem instance in which we can easily identify the optimal ranking. To examine the behavior of our approach, we implemented the heuristic for the 1999 through 2004 college football seasons. We concluded that our approach works best when the margin of victory of individual games is not considered, the location of games is considered, and the date of games is considered. Finally, we evaluated how our approach would have weighed in on several recent controversies in NCAA Division I-A college football and found that our approach generally agrees with traditional schools of thought regarding these controversies.

Key Words: programming: quadratic; recreation and sports