Seed Distributions for March Madness: A Tool for Bracketologists

Probability Model

To illustrate the results of the seeding distribution analysis, the odds against a particular pair of seeds reaching the National Finals is shown by selecting any two seeds and clicking Show Results.

National Finals Seed Combination

    

Odds:


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Relative Likelihoods

To assess the relative likelihood of two pairs of two seeds reaching the National Finals, pick two pairs of two seeds and click Show Result to obtain the relative likelihood of one pair of two seeds reaching the National Finals versus the other pair of two seeds reaching the National Finals.

Pair of Seeds A:
Pair of Seeds B:

National Final Conditional Probabilities

One can determine the probability of a pair of seeds reaching the National Finals given a set of four seeds in the Final Four. Pick four seeds to reach the Final Four and click Show Result to obtain the probability for all possible pairs of seeds (up to four) reaching the National Finals given this set of Final Four seeds.

Final Four

Region 1 vs Region 4

Region 2 vs Region 3

Championship Game Seed Distribution

Using the analytical approach described in Jacobson et al.2, the following table lists the number of times that each seed reached the National Finals game since 1985, and the number of times that each seed was expected to have appeared.

Seed National Finals Game Appearances Expected National Finals Game Appearances
1 37 31.4
2 13 18.0
3 11 10.4
4 3 6.0
5 3 3.4
6 2 2.0
7 1 1.1
8 4 0.7
9 0 0.2
10 0 0.2
11 0 0.1
12 0 0.07
13 0 0.04
14 0 0.02
15 0 0.01
16 0 0.01

Using a X2 goodness of fit test, the test statistic value (with 15 degrees of freedom) is 22.0 resulting in a p-value of 0.11, which suggests a good fit to the truncated geometric distribution. 

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