Tuesday, March 18, 2014

Bracket Math for the Aggregate Model

In all its glory, the Aggregate Model is finished for the NCAA Tournament. It is actually fairly similar to Nate Silver's composite (but was created independently, and in my case, originally implemented for college football). Mine is a central mean (calculated the same way as Jeff Sagarin's) of the following models:

KenPom
Kenneth Massey
Sagarin's Predictor
Statfox
Dokter Entropy
Sonny Moore

These were chosen based on personal preference and their performance throughout the season (per the Prediction Tracker). So far in 2013-14, this Aggregate Model has picked 74.35% outright winners for NCAAB.



Here's the predicted bracket:


Unfortunately, it's pretty chalky, except for the predicted national champion of Louisville. The full round-by-round probabilities are as follows:


SeedTeam1st Round2nd RoundSweet 16Elite 8Final FourChampionshipChampion
1Florida100.00%93.20%69.02%48.57%33.71%21.86%11.74%
16*Albany52.74%3.76%0.70%0.12%0.02%0.00%0.00%
16*Mount St. Mary's47.26%3.04%0.52%0.08%0.01%0.00%0.00%
8Colorado100.00%34.82%7.81%2.82%0.98%0.30%0.07%
9Pittsburgh100.00%65.18%21.95%11.17%5.55%2.48%0.86%
5VCU100.00%68.37%34.50%13.09%6.53%2.93%1.02%
12Stephen F. Austin100.00%31.63%10.35%2.38%0.76%0.21%0.04%
4UCLA100.00%71.67%44.01%19.06%10.61%5.37%2.15%
13Tulsa100.00%28.33%11.13%2.71%0.91%0.27%0.06%
6Ohio St.100.00%64.48%36.59%17.66%7.11%3.16%1.09%
11Dayton100.00%35.52%15.17%5.22%1.45%0.45%0.10%
3Syracuse100.00%74.91%40.92%19.55%7.78%3.42%1.17%
14Western Michigan100.00%25.09%7.32%1.77%0.34%0.07%0.01%
7New Mexico100.00%56.80%25.74%13.50%5.21%2.22%0.73%
10Stanford100.00%43.20%16.93%7.76%2.53%0.92%0.25%
2Kansas100.00%84.45%53.55%33.62%16.35%8.69%3.68%
15Eastern Kentucky100.00%15.55%3.78%0.93%0.15%0.03%0.00%
1Virginia100.00%92.88%69.39%43.96%27.50%15.43%7.33%
16Coastal Carolina100.00%7.12%1.32%0.17%0.02%0.00%0.00%
8Memphis100.00%50.54%14.91%5.66%2.09%0.66%0.17%
9George Washington100.00%49.46%14.38%5.39%1.97%0.61%0.15%
5Cincinnati100.00%55.76%25.65%10.73%4.94%1.97%0.64%
12Harvard100.00%44.24%18.03%6.62%2.68%0.93%0.26%
4Michigan St.100.00%80.87%50.83%26.27%14.81%7.38%3.07%
13Delaware100.00%19.13%5.49%1.20%0.29%0.06%0.01%
6North Carolina100.00%56.39%29.11%13.08%5.48%2.20%0.72%
11Providence100.00%43.61%19.84%7.72%2.79%0.96%0.26%
3Iowa St.100.00%71.99%41.37%20.47%9.50%4.23%1.55%
14North Carolina Central100.00%28.01%9.68%2.74%0.71%0.17%0.03%
7Connecticut100.00%60.00%26.69%13.96%6.02%2.48%0.84%
10Saint Joseph's100.00%40.00%14.26%6.05%2.06%0.66%0.17%
2Villanova100.00%86.87%56.16%35.38%19.04%9.86%4.28%
15Milwaukee100.00%13.13%2.88%0.61%0.10%0.01%0.00%
1Arizona100.00%92.10%64.25%47.70%33.29%17.62%10.93%
16Weber St.100.00%7.90%1.30%0.27%0.05%0.00%0.00%
8Gonzaga100.00%48.18%16.22%8.91%4.42%1.50%0.62%
9Oklahoma St.100.00%51.82%18.22%10.34%5.31%1.88%0.81%
5Oklahoma100.00%60.26%31.91%11.03%5.18%1.64%0.64%
12North Dakota St.100.00%39.74%17.09%4.48%1.66%0.40%0.12%
4San Diego St.100.00%70.41%40.29%15.06%7.54%2.59%1.08%
13New Mexico St.100.00%29.59%10.71%2.22%0.67%0.13%0.03%
6Baylor100.00%57.90%27.91%13.31%5.13%1.61%0.62%
11Nebraska100.00%42.10%17.22%6.91%2.19%0.56%0.18%
3Creighton100.00%79.69%48.97%27.29%12.62%4.83%2.23%
14Louisiana Lafayette100.00%20.31%5.90%1.49%0.28%0.04%0.01%
7Oregon100.00%57.78%26.40%12.67%4.80%1.48%0.56%
10BYU100.00%42.22%16.31%6.61%2.06%0.52%0.16%
2Wisconsin100.00%81.32%51.88%30.36%14.55%5.80%2.78%
15American100.00%18.68%5.41%1.37%0.26%0.04%0.01%
1Wichita St.100.00%90.83%57.94%21.35%12.45%6.53%3.33%
16*Cal Poly63.85%6.86%1.23%0.10%0.02%0.00%0.00%
16*Texas Southern36.15%2.31%0.25%0.01%0.00%0.00%0.00%
8Kentucky100.00%61.62%27.44%8.09%3.95%1.71%0.71%
9Kansas St.100.00%38.38%13.13%2.87%1.08%0.35%0.11%
5Saint Louis100.00%52.24%9.67%3.52%1.36%0.46%0.15%
12*North Carolina St.45.51%20.62%3.33%1.08%0.37%0.11%0.03%
12*Xavier54.49%27.13%5.00%1.81%0.70%0.23%0.07%
4Louisville100.00%90.10%77.91%60.01%47.26%35.00%25.61%
13Manhattan100.00%9.90%4.09%1.15%0.35%0.09%0.02%
6Massachusetts100.00%36.79%13.43%5.17%1.12%0.34%0.10%
11*Iowa46.32%28.43%13.35%6.59%1.94%0.80%0.31%
11*Tennessee53.68%34.79%17.54%9.28%2.99%1.33%0.57%
3Duke100.00%78.38%48.80%28.62%10.65%5.35%2.60%
14Mercer100.00%21.62%6.87%2.01%0.31%0.07%0.02%
7Texas100.00%52.78%21.09%8.54%2.06%0.71%0.23%
10Arizona St.100.00%47.22%17.74%6.73%1.51%0.48%0.15%
2Michigan100.00%87.19%58.25%32.59%11.83%5.81%2.77%
15Wofford100.00%12.81%2.93%0.49%0.04%0.01%0.00%

Here are the final ratings as well:


RankTeamRate
1Louisville0.945
2Arizona0.911
3Florida0.910
4Virginia0.886
5Villanova0.866
6Wichita St.0.865
7Kansas0.860
8Michigan St.0.856
9Duke0.853
10Wisconsin0.850
11Michigan0.848
12UCLA0.847
13Creighton0.840
14Iowa St.0.826
15Oklahoma St.0.821
16Tennessee0.820
17VCU0.814
18San Diego St.0.813
19Pittsburgh0.812
20Kentucky0.812
21Ohio St.0.811
22Gonzaga0.810
23Syracuse0.808
24Connecticut0.805
25New Mexico0.800
26Iowa0.798
27North Carolina0.797
28Cincinnati0.796
29Oklahoma0.793
30Baylor0.790
31Oregon0.785
32Harvard0.756
33Stanford0.752
34Providence0.752
35Texas0.745
36Saint Louis0.738
37Xavier0.736
38Saint Joseph's0.734
39Nebraska0.732
40Kansas St.0.729
41BYU0.728
42Memphis0.726
43Arizona St.0.723
44George Washington0.722
45North Dakota St.0.716
46Massachusetts0.713
47Dayton0.703
48North Carolina St.0.700
49Colorado0.698
50Tulsa0.687
51Stephen F. Austin0.669
52Manhattan0.655
53North Carolina Central0.649
54New Mexico St.0.646
55Mercer0.616
56Western Michigan0.585
57Delaware0.585
58Louisiana Lafayette0.573
59American0.565
60Eastern Kentucky0.532
61Milwaukee0.494
62Weber St.0.466
63Wofford0.450
64Albany0.438
65Cal Poly0.435
66Mount St. Mary's0.411
67Coastal Carolina0.373
68Texas Southern0.304

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