Selection Sunday is like the Christmas Day of College Basketball Fans. After a lot of speculating, we finally get to see where our favorite teams landed or do some statistical estimation regarding roads to the Final Four. With the bracket set today, we can finally do some math!
Thanks to
Ken Pomeroy we can compute a win probability for any match-up based on the teams' respective Pythagorean win percentage. In turn, using the probabilities from previous rounds, we can estimate the likelihood of a team advancing to any round once the tourney schedule is set. In theory this allows us to see the most likely winners in each slot of a potentially completed bracket.
Instead of titling by the ridiculously misleading regions, I'll just describe them by where they appear on the standard ESPN bracket (top left, top right, bottom left, bottom right) and list the probability of the team reaching the various rounds of the tournament. I'll also BOLD the team with the highest win probability of reaching each position so the reader can easily see the most likely outcome:
| TOP RIGHT |
Pyth |
Round 1 |
Sweet 16 |
Elite 8 |
Final 4 |
Finals |
Champs |
| Kentucky 1 |
0.9787 |
97.5% |
89.3% |
81.1% |
67.6% |
45.7% |
33.5% |
| Manhattan 16 |
0.5411 |
2.5% |
0.6% |
0.1% |
0.0% |
0.0% |
0.0% |
| Cincinnati 8 |
0.8242 |
56.6% |
6.2% |
3.2% |
1.1% |
0.2% |
0.1% |
| Purdue 9 |
0.7825 |
43.4% |
3.9% |
1.7% |
0.5% |
0.1% |
0.0% |
| West Virginia 5 |
0.8539 |
62.8% |
37.1% |
6.1% |
2.4% |
0.6% |
0.2% |
| Buffalo 12 |
0.7759 |
37.2% |
17.2% |
1.9% |
0.5% |
0.1% |
0.0% |
| Maryland 4 |
0.8289 |
61.8% |
31.0% |
4.5% |
1.6% |
0.3% |
0.1% |
| Valparaiso 13 |
0.7499 |
38.2% |
14.7% |
1.5% |
0.4% |
0.1% |
0.0% |
| Butler 6 |
0.8624 |
47.8% |
20.5% |
8.7% |
1.8% |
0.4% |
0.1% |
| Texas 11 |
0.8725 |
52.2% |
23.4% |
10.4% |
2.3% |
0.6% |
0.2% |
| Notre Dame 3 |
0.9127 |
87.5% |
53.8% |
29.4% |
8.3% |
2.8% |
1.1% |
| Northeastern 14 |
0.598 |
12.5% |
2.3% |
0.4% |
0.0% |
0.0% |
0.0% |
| Wichita State 7 |
0.9044 |
73.2% |
39.3% |
21.0% |
5.6% |
1.8% |
0.7% |
| Indiana 10 |
0.7762 |
26.8% |
8.5% |
2.6% |
0.4% |
0.1% |
0.0% |
| Kansas 2 |
0.9111 |
83.6% |
48.6% |
26.9% |
7.5% |
2.5% |
1.0% |
| New Mexico State 15 |
0.6674 |
16.4% |
3.7% |
0.8% |
0.1% |
0.0% |
0.0% |
| BOTTOM RIGHT |
Pyth |
Round 1 |
Sweet 16 |
Elite 8 |
Final 4 |
Finals |
Champ |
| Wisconsin 1 |
0.9615 |
95.6% |
81.9% |
64.5% |
36.3% |
17.4% |
10.5% |
| Coastal Carolina 16 |
0.5371 |
4.4% |
1.0% |
0.2% |
0.0% |
0.0% |
0.0% |
| Oregon 8 |
0.7972 |
47.3% |
7.8% |
3.0% |
0.6% |
0.1% |
0.0% |
| Oklahoma State 9 |
0.8141 |
52.7% |
9.4% |
3.9% |
0.8% |
0.1% |
0.0% |
| Arkansas 5 |
0.8416 |
73.1% |
31.7% |
7.8% |
1.9% |
0.4% |
0.1% |
| Wofford 12 |
0.6617 |
26.9% |
6.2% |
0.8% |
0.1% |
0.0% |
0.0% |
| North Carolina 4 |
0.9019 |
79.3% |
54.3% |
18.8% |
6.5% |
1.9% |
0.7% |
| Harvard 13 |
0.7059 |
20.7% |
7.8% |
1.1% |
0.1% |
0.0% |
0.0% |
| Xavier 6 |
0.8518 |
52.4% |
23.4% |
5.2% |
1.5% |
0.3% |
0.1% |
| BYU 11 |
0.8395 |
47.6% |
20.3% |
4.2% |
1.1% |
0.2% |
0.1% |
| Baylor 3 |
0.9038 |
77.3% |
48.7% |
15.0% |
5.8% |
1.7% |
0.6% |
| Georgia State 14 |
0.7344 |
22.7% |
7.6% |
1.0% |
0.2% |
0.0% |
0.0% |
| VCU 17 |
0.7499 |
31.3% |
3.4% |
1.1% |
0.2% |
0.0% |
0.0% |
| Ohio State 10 |
0.868 |
68.7% |
13.6% |
6.7% |
2.1% |
0.5% |
0.1% |
| Arizona 2 |
0.9674 |
97.7% |
82.7% |
66.8% |
42.7% |
22.1% |
14.2% |
| Texas Southern 15 |
0.4111 |
2.3% |
0.3% |
0.0% |
0.0% |
0.0% |
0.0% |
| TOP LEFT |
Pyth |
Round 1 |
Sweet 16 |
Elite 8 |
Final 4 |
Finals |
Champ |
| Villanova 1 |
0.9571 |
96.7% |
81.5% |
60.2% |
35.8% |
23.0% |
10.0% |
| Lafayette 16 |
0.4285 |
3.3% |
0.5% |
0.0% |
0.0% |
0.0% |
0.0% |
| North Carolina State 8 |
0.8111 |
51.7% |
9.5% |
3.5% |
0.8% |
0.2% |
0.0% |
| LSU 9 |
0.8006 |
48.3% |
8.5% |
3.0% |
0.7% |
0.2% |
0.0% |
| Northern Iowa 5 |
0.908 |
84.9% |
54.2% |
20.6% |
8.4% |
3.8% |
1.0% |
| Wyoming 12 |
0.6373 |
15.1% |
3.9% |
0.5% |
0.1% |
0.0% |
0.0% |
| Louisville 4 |
0.8756 |
78.7% |
37.3% |
11.7% |
3.9% |
1.5% |
0.3% |
| UC Irvine 13 |
0.6559 |
21.3% |
4.6% |
0.6% |
0.1% |
0.0% |
0.0% |
| Providence 6 |
0.8458 |
56.9% |
22.1% |
5.8% |
1.7% |
0.5% |
0.1% |
| Dayton 11 |
0.8057 |
43.1% |
14.2% |
3.1% |
0.7% |
0.2% |
0.0% |
| Oklahoma 3 |
0.915 |
89.1% |
61.3% |
24.3% |
10.4% |
4.9% |
1.4% |
| Albany 14 |
0.5686 |
10.9% |
2.3% |
0.2% |
0.0% |
0.0% |
0.0% |
| Michigan State 7 |
0.8786 |
61.7% |
16.5% |
8.0% |
2.7% |
1.0% |
0.2% |
| Georgia 10 |
0.8178 |
38.3% |
7.4% |
2.7% |
0.7% |
0.2% |
0.0% |
| Virginia 2 |
0.9587 |
95.3% |
75.4% |
55.8% |
33.8% |
22.0% |
9.7% |
| Belmont 15 |
0.5363 |
4.7% |
0.8% |
0.1% |
0.0% |
0.0% |
0.0% |
| BOTTOM LEFT |
Pyth |
Round 1 |
Sweet 16 |
Elite 8 |
Final 4 |
Finals |
Champ |
| Duke 1 |
0.9395 |
93.3% |
71.0% |
45.2% |
26.3% |
12.6% |
4.5% |
| North Florida 12 |
0.5258 |
6.7% |
1.2% |
0.2% |
0.0% |
0.0% |
0.0% |
| San Diego State 8 |
0.8468 |
57.7% |
17.3% |
6.9% |
2.4% |
0.6% |
0.1% |
| St. John's 9 |
0.8019 |
42.3% |
10.4% |
3.4% |
0.9% |
0.2% |
0.0% |
| Utah 5 |
0.9275 |
74.0% |
52.0% |
27.7% |
14.8% |
6.4% |
2.0% |
| Stephen F. Austin 12 |
0.8183 |
26.0% |
12.2% |
3.7% |
1.1% |
0.2% |
0.0% |
| Georgetown 4 |
0.867 |
83.6% |
33.7% |
12.8% |
4.8% |
1.4% |
0.3% |
| Eastern Washington 13 |
0.5618 |
16.4% |
2.1% |
0.2% |
0.0% |
0.0% |
0.0% |
| SMU 6 |
0.8734 |
62.5% |
29.7% |
11.0% |
4.3% |
1.3% |
0.3% |
| UCLA 11 |
0.8056 |
37.5% |
13.6% |
3.6% |
1.0% |
0.2% |
0.0% |
| Iowa State 3 |
0.9047 |
86.5% |
53.9% |
23.8% |
11.0% |
4.0% |
1.0% |
| UAB 14 |
0.5979 |
13.5% |
2.8% |
0.3% |
0.0% |
0.0% |
0.0% |
| Iowa 7 |
0.8594 |
55.3% |
16.7% |
7.6% |
2.7% |
0.8% |
0.1% |
| Davidson 10 |
0.8319 |
44.7% |
11.8% |
4.8% |
1.5% |
0.4% |
0.1% |
| Gonzaga 2 |
0.944 |
93.8% |
70.5% |
48.7% |
29.0% |
14.5% |
5.4% |
| North Dakota St. 15 |
0.5258 |
6.2% |
1.0% |
0.1% |
0.0% |
0.0% |
0.0% |
With so many games, we expect to see some "unlikely" winners into the round of 32, but as the tourney progresses, these unexpected winners will eventually fall out. Looking into the latter rounds, it seems that Kentucky, with the overall 1 seed, has a gaudy 1 in 3 chance of winning the tourney.
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