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 eight seeds reaching the Elite Eight is shown by selecting any eight seeds and clicking Show Results.

Elite Eight Seed Combination

Odds:

?

Relative Likelihoods

To assess the relative likelihood of two sets of eight
seeds reaching the Elite Eight, pick two sets of eight seeds and click Show Result to obtain
the relative likelihood of one set of eight seeds reaching the Elite Eight versus the other set of eight seeds reaching the Elite Eight.

Elite Eight 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 Elite Eight since 1985,
and the number of times that each seed was expected to have appeared.

Seed

Elite Eight Appearances

Expected Number of Elite Eight Appearances

1

103

92.6

2

69

66.9

3

40

38.6

4

25

37.7

5

12

15.3

6

17

22.2

7

10

12.8

8

9

6.2

9

5

2.5

10

9

7.4

11

10

4.3

12

2

1.0

13

0

0.4

14

0

2.5

15

1

1.4

16

0

0.2

Since not all sixteen seeds have the opportunity to play each other up until this point in the tournament,
the Elite Eight teams must be broken up into two sets of eight seeds each:

Set 1: 1,4,5,8,9,12,13,16 Set 2: 2,3,6,7,10,11,14,15

Using a X^{2} goodness of fit test, the test statistic value
(with 7 degrees of freedom) for Set 1 is 11.3 resulting in a p-value of 0.127, which suggests a good fit to the truncated
geometric distribution, while the test statistic value (with 7 degrees of freedom) for Set 2 is 12.6 resulting in a p-value of 0.082,
which suggests an adequate fit to the truncated geometric distribution.