Seed Distributions for March Madness 2014: A Tool for Bracketologists

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Tournament Background

Under the current format of the NCAA Men's Basketball Tournament, 68 teams are selected to compete in a single elimination format1. The Selection Committee seeds each of the teams according to factors such as their regular season records and their performance in their respective conference tournament. The tournament bracket is structured into four regions, each containing 16 teams. Narrowing the field to these 64 teams requires eight teams to participate in four play-in games, termed the First Four.

In the round of 64, each seed No. 1 plays seed No. 16, seed No. 2 plays seed No. 15, and so on, through seed No. 8 who plays seed No. 9. The winner of each game advances in the tournament, with the possible sets of seed match-ups in the round of 32 given by {1,8,9,16}, {2,7,10,15}, {3,6,11,14}, and {4,5,12,13}, corresponding to the four games in each region. The possible sets of seed match-ups in the Sweet Sixteen are given by {1,4,5,8,9,12,13,16} and {2,3,6,7,10,11,14,15}. In the remaining rounds of the tournament (the Elite Eight, the National Semifinals, and the National Championship), the possible sets of seed match-ups include the entire set of 16 seeds.

The winners of each region are designated as the Final Four, where the National Semifinals and National Championship determine the NCAA Men's Basketball Tournament champion over the final weekend of play. While any seed combination reaching the Final Four is possible for these final three games, the probability of each seed combination is not uniformly distributed.

Probabilistic Analysis

Using data from the past 29 tournaments (1985 through 2013), prior seed match-ups and winners can be used to identify a distribution that models the probability of certain seed combinations playing in each round of the tournament. This is accomplished by determining the frequency that each seed reaches a given round, then fitting this data to a truncated geometric distribution2, a nonnegative discrete random variable formed by the number of independent and identically distributed Bernoulli random variables, with success probability p (defined as the probability that the higher seed wins a particular game) that occurs until reaching the first success. Given that the NCAA tournament is single elimination, then a team cannot reach a round unless it has won in all the previous rounds.

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References

1 Jacobson, S. H., King, D. M., 2009, “Seeding in the NCAA Men’s Basketball Tournament: When is a Higher Seed Better?” Journal of Gambling Business and Economics, 3(2), 63-87. Click here for pdf.

2 Jacobson, S. H., Nikolaev, A. G., King, D.M.,  Lee, A. J., 2011, “Seed distributions for the NCAA Men’s Basketball Tournament”, OMEGA, 39(6), 719-724. Click here for pdf.

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Acknowledgements

The authors of this web site would like to thank Douglas King (University of Illinois at Urbana-Champaign), Adrian Lee (CITERI), and Alexander Nikolaev (University of Buffalo), for their comments on this web site.

Web Developers in 2011: Ammar Rizwan and Emon Dai (Students, Department of Computer Science, University of Illinois at Urbana-Champaign)

This is a student project supervised by Professor Sheldon H. Jacobson (Department of Computer Science, University of Illinois at Urbana-Champaign)

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