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Math Trek

Rankings, Tournaments, and Playoffs

By
4:25pm, December 15, 2006

So many teams and so little room at the top. Which team becomes the national champion in U.S. college football rests on rankings, which reflect the opinions of poll participants (and, nowadays, also computer ratings).

This year, Ohio State plays for the national title in the championship bowl game. And its opponent will be Florida rather than Michigan because the "experts," in their voting, judged that Florida would be the more worthy opponent.

This outcome hasn't pleased everyone, and, as happens nearly every year, many have criticized the vagaries of the ranking system for allowing apparently flawed or unfair outcomes.

Similar problems in determining which team or player deserves a national or year-end championship or how they ought to be seeded for a tournament occur in other sports that also employ elaborate rating schemes to rank teams or players.

In a paper published in a recent issue of SIAM Review, Paul K. Newton and Kamran Aslam of the Univ

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