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 losing in the National Championship game are shown by selecting any seed and clicking Show Results.
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.
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.
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 | 24 | 19.3 |
| 2 | 5 | 9.5 |
| 3 | 4 | 4.7 |
| 4 | 2 | 2.3 |
| 5 | 0 | 1.1 |
| 6 | 1 | 0.56 |
| 7 | 1 | 0.28 |
| 8 | 1 | 0.14 |
| 9 | 0 | 0.07 |
| 10 | 0 | 0.03 |
| 11 | 0 | 0.02 |
| 12 | 0 | 0.01 |
| 13 | 0 | 0.004 |
| 14 | 0 | 0.004 |
| 15 | 0 | 0.001 |
| 16 | 0 | 0.0005 |
Using a X2 goodness of fit test, the test statistic value (with 15 degrees of freedom) is 12.4 resulting in a p-value of 0.65, which suggests an excellent fit to the truncated geometric 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 | 13 | 13.3 |
| 2 | 8 | 8.7 |
| 3 | 7 | 5.6 |
| 4 | 2 | 3.7 |
| 5 | 4 | 2.4 |
| 6 | 1 | 1.5 |
| 7 | 0 | 1.0 |
| 8 | 3 | 0.7 |
| 9 | 0 | 0.4 |
| 10 | 0 | 0.3 |
| 11 | 0 | 0.2 |
| 12 | 0 | 0.1 |
| 13 | 0 | 0.08 |
| 14 | 0 | 0.05 |
| 15 | 0 | 0.03 |
| 16 | 0 | 0.02 |
Using a X2 goodness of fit test, the test statistic value (with 15 degrees of freedom) is 13.1 resulting in a p-value of 0.60, which suggests an excellent fit to the truncated geometric distribution.
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