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.

Final Four Seed Combination

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.

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

60

51.5

2

32

33.6

3

17

21.9

4

13

14.3

5

7

9.3

6

3

6.1

7

3

4.0

8

6

2.6

9

1

1.7

10

1

1.1

11

5

0.72

12

0

0.47

13

0

0.31

14

0

0.20

15

0

0.13

16

0

0.08

Using a X^{2 }goodness of fit test, the test statistic value (with 15 degrees of freedom)
is 36.6 resulting in a p-value of 0.001, 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 nearly three-quarters of the test-statistic value.