# 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 set of four seeds reaching the Final Four is shown by selecting any four seeds and clicking Show Results.

Odds:

?

## Relative Likelihoods

To assess the relative likelihood of two sets of four seeds reaching the Final Four, pick two sets of four seeds and click Show Result to obtain the relative likelihood of one set of four seeds reaching the Final Four versus the other set of four seeds reaching the Final Four.

Set of Seeds A:
Set of Seeds B:

## Final Four 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 Final Four since 1985, and the number of times that each seed was expected to have appeared.

Seed Final Four Appearances Expected Number of
Final Four Appearances
1 62 52.2
2 32 34.8
3 17 23.1
4 15 15.4
5 9 10.3
6 3 6.8
7 3 4.5
8 6 3.0
9 2 2.0
10 1 1.3
11 6 0.90
12 0 0.60
13 0 0.40
14 0 0.26
15 0 0.18
16 0 0.12

Using a X2 goodness of fit test, the test statistic value (with 15 degrees of freedom) is 40.27 resulting in a p-value of 0.0008, which suggests a poor fit to the truncated geometric distribution. In further analyzing the data, this is because No. 11 seeds has been overly represented in the Final Four, contributing over 70 percent of the test-statistic value.

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