It's that time again: Raymond comes up with an absurd, arbitrary criterion for filling out his NCAA bracket.

This time, I studied all the games played in the NCAA men's basketball tournament since 1985 and computed how many of the games were won by the favorite and how many were upsets, broken down by the numerical difference between the seeding of the two teams.

Seed
Difference
Winner Upset
Rate
FavoriteUnderdog
1 121 105 46%
2 14 18 56%
3 110 76 41%
4 55 23 29%
5 113 45 28%
6 9 2 18%
7 100 42 30%
8 114 40 26%
9 81 19 19%
10 3 2 40%
11 86 15 15%
12 3 0 0%
13 84 4 5%
14 0 0 N/A
15 88 0 0%

I found it interesting that when the teams are seeded N and N+2, you get an upset more than half the time!

If the probability of the favorite winning is p and I choose the favorite with probability q, then the prediction would be correct pq + (1−p)(1−q) = (2p−1)q + (1−p) of the time. If you hold p constant, then this is maximized when q = 0 if p < ½, or when q = 1 if p > ½. (If p = ½, then it doesn't matter what you pick for q.)

Therefore, to maximize the number of correct predictions, I should always choose the favorite, unless the two teams are seeded N and N+2, in which case I always choose the underdog. But that makes for a boring bracket. Consequently, I went for the suboptimal algorithm of choosing q = p. Here is the result:

Update:

• Correct predictions are in green.
• Incorrect predictions are in red.
• (!) marks upsets correctly predicted.
• (*) marks upsets predicted but did not take place.
• (x) marks actual upsets not predicted.

#### Opening Round Game

16Mount St. Marys Mount St. Marys
16Coppin St.

#### East bracket

1North Carolina North Carolina North Carolina North Carolina Louisville
16Mount St. Marys
8Indiana Arkansas (!)
9Arkansas
5Notre Dame Notre Dame Washington St.
12George Mason
4Washington St. Washington St.
13Winthrop
6Oklahoma Oklahoma Louisville Louisville (!)
11St. Joes
3Louisville Louisville
14Boise St.
7Butler South Alabama (*) Tennessee
10South Alabama
2Tennessee Tennessee
15American

#### Midwest bracket

1Kansas Kansas Kansas Kansas Gonzaga
16Portland St.
8UNLV UNLV
9Kent St.
5Clemson Villanova (!) Villanova
12Villanova
4Vanderbilt Siena (!)
13Siena
6USC Kansas St. (!) Wisconsin Gonzaga
11Kansas St.
3Wisconsin Wisconsin
14Cal St. Fullerton
7Gonzaga Gonzaga (x) Gonzaga
10Davidson
2Georgetown UMBC (*)
15UMBC

#### South bracket

1Memphis Memphis Oregon Michigan St. Michigan St.
16Texas Arlington
8Mississippi St. Oregon (x)
9Oregon
5Michigan St. Michigan St. Michigan St. (!)
12Temple
4Pittsburgh Pittsburgh
13Oral Roberts
6Marquette Marquette Stanford Stanford (*)
11Kentucky
3Stanford Stanford
14Cornel
7Miami Fla Miami Fla Texas
10St. Marys
2Texas Texas
15Austin Peay

#### West bracket

1UCLA UCLA UCLA UCLA Xavier
16Miss Valley St.
8BYU Texas A&M (!)
9Texas A&M
5Drake Drake (x) Drake
12W. Kentucky
4Connecticut San Diego (!)
13San Diego
6Purdue Purdue Xavier Xavier
11Baylor
3Xavier Xavier
14Georgia
7West Virginia West Virginia Duke
10Arizona
2Duke Duke
15Belmont

#### Finals

3Louisville Michigan St. Michigan St.
5Michigan St.
7Gonzaga Xavier
3Xavier