Tuesday, March 22, 2011

Sweet 16 Odds and Analysis

My personal bracket has been busted, and some of the ratings favorites (Texas, Purdue) didn't fare well either. Fortunately there's still four rounds left to go, and places like Yahoo! have bracket contests for them too (here's the stats bracket for the last four rounds). What? You say you need the odds for the last rounds to fill that out? Here they are:

Rd 3 Rd 4 Rd 5 Rd 6
Ohio St 0.628 0.456 0.278 0.177
Kentucky 0.372 0.228 0.111 0.058
Marquette 0.414 0.113 0.038 0.014
North Carolina 0.586 0.203 0.083 0.037
Duke 0.731 0.49 0.286 0.178
Arizona 0.269 0.115 0.04 0.016
Connecticut 0.456 0.17 0.067 0.029
San Diego St 0.544 0.225 0.098 0.046
Kansas 0.826 0.676 0.462 0.256
Richmond 0.174 0.087 0.028 0.006
VA Commonwealth 0.286 0.04 0.008 0.001
Florida St 0.714 0.197 0.074 0.019
Butler 0.281 0.091 0.025 0.005
Wisconsin 0.719 0.393 0.183 0.075
BYU 0.583 0.32 0.146 0.058
Florida 0.417 0.196 0.075 0.024

Of particular interest here is the improvement of Kansas's odds thanks to weak opponents. From the championship odds below it's easy to see that Kansas is now the favorite to win it all, in large part because they have a 67.6% chance of making the final four.
Remaining Championship Odds
Team Odds
1 Kansas 0.2559
1 Duke 0.1779
1 Ohio St 0.1774
4 Wisconsin 0.075
3 BYU 0.0581
4 Kentucky 0.0575
2 San Diego St 0.0465
2 North Carolina 0.0369
3 Connecticut 0.029
2 Florida 0.0244
10 Florida St 0.0194
5 Arizona 0.0158
11 Marquette 0.0137
12 Richmond 0.006
8 Butler 0.0055
11 VA Commonwealth 0.001

A lot of weird things happened earlier in the tournament (chances VCU makes the sweet 16: 1.26%), and I started wondering if momentum actually played a role in college basketball. I weighted the Power Rankings to give the last 4 weeks 3 times the weight, and the last 2 weeks got 5 times the weight, expecting to see that Louisville/Purdue/Texas would drop significantly. The top 15 shows otherwise though:
Top 15 with Mo'
1 Ohio St
2 Duke
3 Louisville
4 Kansas
5 Notre Dame
6 Kentucky
7 San Diego St
8 Pittsburgh
9 Texas
10 Connecticut
11 Syracuse
12 Purdue
13 Washington
14 North Carolina
15 West Virginia

There were 5 surprise losses in the first round (LV, ND, Pitt, TX, Purdue). Adding up their rankings in the regular rankings they add to 38, and here? 37. Looks like momentum doesn't explain why the ratings have fared poorly so far. I think the real reason that my computer (and other stats ratings) haven't fared well is that sometimes, these things happen.

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