Seed Distributions for March Madness: A Tool for Bracketologists

Probability Model

To illustrate the results of the seeding distribution analysis, the probability of a particular seed winning the National Championship and the odds against a particular seed winning the National Championship are shown by selecting any seed and clicking Show Results.

Champion Seed Value

Probability:

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Odds:

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Relative Likelihoods

To assess the relative likelihood of two seeds winning the National Championship, pick two seeds and click Show Result to obtain the relative likelihood of one seed winning the National Championship versus the other seed winning the National Championship.

Seed:
Seed:

Conditional Probabilities

One can compute the probability of a seed winning the National Championship given a particular pair of seeds in the National Finals. Pick two seeds to reach the National Finals and click Show Result to obtain the probability that of each of these seeds wins the National Championship given that they reached the National Finals.

Finals: vs

National Champion Distribution

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

Seed National Champions Expected Number of
National Champions
1 22 17.75
2 5 8.75
3 4 4.31
4 1 2.12
5 0 1.05
6 1 0.52
7 1 0.25
8 1 0.13
9 0 0.06
10 0 0.03
11 0 0.015
12 0 0.0074
13 0 0.0036
14 0 0.0018
15 0 0.0009
16 0 0.0004

Using a X2 goodness of fit test, the test statistic value (with 15 degrees of freedom) is 13.16 resulting in a p-value of 0.590, which suggests an excellent fit to the truncated geometric distribution.

National Runner-Up Distribution

Using the analytical approach described in Jacobson et al.2, the following table lists the number of times that each seed was the National Runner-Up since 1985, and the number of times that each seed was expected to have took this distinction.

Seed National Runner-Up Expected Number of
National Runner-Ups
1 12 13.00
2 8 8.17
3 7 5.14
4 2 3.13
5 3 2.03
6 1 1.30
7 0 0.80
8 2 0.51
9 0 0.32
10 0 0.20
11 0 0.13
12 0 0.079
13 0 0.050
14 0 0.031
15 0 0.020
16 0 0.012

Using a X2 goodness of fit test, the test statistic value (with 15 degrees of freedom) is 7.79 resulting in a p-value of 0.93, which suggests an excellent fit to the truncated geometric distribution.

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