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:

Seed	Team	1st Round	2nd Round	Sweet 16	Elite 8	Final Four	Championship	Champion
1	Florida	100.00%	93.20%	69.02%	48.57%	33.71%	21.86%	11.74%
16*	Albany	52.74%	3.76%	0.70%	0.12%	0.02%	0.00%	0.00%
16*	Mount St. Mary's	47.26%	3.04%	0.52%	0.08%	0.01%	0.00%	0.00%
8	Colorado	100.00%	34.82%	7.81%	2.82%	0.98%	0.30%	0.07%
9	Pittsburgh	100.00%	65.18%	21.95%	11.17%	5.55%	2.48%	0.86%
5	VCU	100.00%	68.37%	34.50%	13.09%	6.53%	2.93%	1.02%
12	Stephen F. Austin	100.00%	31.63%	10.35%	2.38%	0.76%	0.21%	0.04%
4	UCLA	100.00%	71.67%	44.01%	19.06%	10.61%	5.37%	2.15%
13	Tulsa	100.00%	28.33%	11.13%	2.71%	0.91%	0.27%	0.06%
6	Ohio St.	100.00%	64.48%	36.59%	17.66%	7.11%	3.16%	1.09%
11	Dayton	100.00%	35.52%	15.17%	5.22%	1.45%	0.45%	0.10%
3	Syracuse	100.00%	74.91%	40.92%	19.55%	7.78%	3.42%	1.17%
14	Western Michigan	100.00%	25.09%	7.32%	1.77%	0.34%	0.07%	0.01%
7	New Mexico	100.00%	56.80%	25.74%	13.50%	5.21%	2.22%	0.73%
10	Stanford	100.00%	43.20%	16.93%	7.76%	2.53%	0.92%	0.25%
2	Kansas	100.00%	84.45%	53.55%	33.62%	16.35%	8.69%	3.68%
15	Eastern Kentucky	100.00%	15.55%	3.78%	0.93%	0.15%	0.03%	0.00%
1	Virginia	100.00%	92.88%	69.39%	43.96%	27.50%	15.43%	7.33%
16	Coastal Carolina	100.00%	7.12%	1.32%	0.17%	0.02%	0.00%	0.00%
8	Memphis	100.00%	50.54%	14.91%	5.66%	2.09%	0.66%	0.17%
9	George Washington	100.00%	49.46%	14.38%	5.39%	1.97%	0.61%	0.15%
5	Cincinnati	100.00%	55.76%	25.65%	10.73%	4.94%	1.97%	0.64%
12	Harvard	100.00%	44.24%	18.03%	6.62%	2.68%	0.93%	0.26%
4	Michigan St.	100.00%	80.87%	50.83%	26.27%	14.81%	7.38%	3.07%
13	Delaware	100.00%	19.13%	5.49%	1.20%	0.29%	0.06%	0.01%
6	North Carolina	100.00%	56.39%	29.11%	13.08%	5.48%	2.20%	0.72%
11	Providence	100.00%	43.61%	19.84%	7.72%	2.79%	0.96%	0.26%
3	Iowa St.	100.00%	71.99%	41.37%	20.47%	9.50%	4.23%	1.55%
14	North Carolina Central	100.00%	28.01%	9.68%	2.74%	0.71%	0.17%	0.03%
7	Connecticut	100.00%	60.00%	26.69%	13.96%	6.02%	2.48%	0.84%
10	Saint Joseph's	100.00%	40.00%	14.26%	6.05%	2.06%	0.66%	0.17%
2	Villanova	100.00%	86.87%	56.16%	35.38%	19.04%	9.86%	4.28%
15	Milwaukee	100.00%	13.13%	2.88%	0.61%	0.10%	0.01%	0.00%
1	Arizona	100.00%	92.10%	64.25%	47.70%	33.29%	17.62%	10.93%
16	Weber St.	100.00%	7.90%	1.30%	0.27%	0.05%	0.00%	0.00%
8	Gonzaga	100.00%	48.18%	16.22%	8.91%	4.42%	1.50%	0.62%
9	Oklahoma St.	100.00%	51.82%	18.22%	10.34%	5.31%	1.88%	0.81%
5	Oklahoma	100.00%	60.26%	31.91%	11.03%	5.18%	1.64%	0.64%
12	North Dakota St.	100.00%	39.74%	17.09%	4.48%	1.66%	0.40%	0.12%
4	San Diego St.	100.00%	70.41%	40.29%	15.06%	7.54%	2.59%	1.08%
13	New Mexico St.	100.00%	29.59%	10.71%	2.22%	0.67%	0.13%	0.03%
6	Baylor	100.00%	57.90%	27.91%	13.31%	5.13%	1.61%	0.62%
11	Nebraska	100.00%	42.10%	17.22%	6.91%	2.19%	0.56%	0.18%
3	Creighton	100.00%	79.69%	48.97%	27.29%	12.62%	4.83%	2.23%
14	Louisiana Lafayette	100.00%	20.31%	5.90%	1.49%	0.28%	0.04%	0.01%
7	Oregon	100.00%	57.78%	26.40%	12.67%	4.80%	1.48%	0.56%
10	BYU	100.00%	42.22%	16.31%	6.61%	2.06%	0.52%	0.16%
2	Wisconsin	100.00%	81.32%	51.88%	30.36%	14.55%	5.80%	2.78%
15	American	100.00%	18.68%	5.41%	1.37%	0.26%	0.04%	0.01%
1	Wichita St.	100.00%	90.83%	57.94%	21.35%	12.45%	6.53%	3.33%
16*	Cal Poly	63.85%	6.86%	1.23%	0.10%	0.02%	0.00%	0.00%
16*	Texas Southern	36.15%	2.31%	0.25%	0.01%	0.00%	0.00%	0.00%
8	Kentucky	100.00%	61.62%	27.44%	8.09%	3.95%	1.71%	0.71%
9	Kansas St.	100.00%	38.38%	13.13%	2.87%	1.08%	0.35%	0.11%
5	Saint Louis	100.00%	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*	Xavier	54.49%	27.13%	5.00%	1.81%	0.70%	0.23%	0.07%
4	Louisville	100.00%	90.10%	77.91%	60.01%	47.26%	35.00%	25.61%
13	Manhattan	100.00%	9.90%	4.09%	1.15%	0.35%	0.09%	0.02%
6	Massachusetts	100.00%	36.79%	13.43%	5.17%	1.12%	0.34%	0.10%
11*	Iowa	46.32%	28.43%	13.35%	6.59%	1.94%	0.80%	0.31%
11*	Tennessee	53.68%	34.79%	17.54%	9.28%	2.99%	1.33%	0.57%
3	Duke	100.00%	78.38%	48.80%	28.62%	10.65%	5.35%	2.60%
14	Mercer	100.00%	21.62%	6.87%	2.01%	0.31%	0.07%	0.02%
7	Texas	100.00%	52.78%	21.09%	8.54%	2.06%	0.71%	0.23%
10	Arizona St.	100.00%	47.22%	17.74%	6.73%	1.51%	0.48%	0.15%
2	Michigan	100.00%	87.19%	58.25%	32.59%	11.83%	5.81%	2.77%
15	Wofford	100.00%	12.81%	2.93%	0.49%	0.04%	0.01%	0.00%

Here are the final ratings as well:

Rank	Team	Rate
1	Louisville	0.945
2	Arizona	0.911
3	Florida	0.910
4	Virginia	0.886
5	Villanova	0.866
6	Wichita St.	0.865
7	Kansas	0.860
8	Michigan St.	0.856
9	Duke	0.853
10	Wisconsin	0.850
11	Michigan	0.848
12	UCLA	0.847
13	Creighton	0.840
14	Iowa St.	0.826
15	Oklahoma St.	0.821
16	Tennessee	0.820
17	VCU	0.814
18	San Diego St.	0.813
19	Pittsburgh	0.812
20	Kentucky	0.812
21	Ohio St.	0.811
22	Gonzaga	0.810
23	Syracuse	0.808
24	Connecticut	0.805
25	New Mexico	0.800
26	Iowa	0.798
27	North Carolina	0.797
28	Cincinnati	0.796
29	Oklahoma	0.793
30	Baylor	0.790
31	Oregon	0.785
32	Harvard	0.756
33	Stanford	0.752
34	Providence	0.752
35	Texas	0.745
36	Saint Louis	0.738
37	Xavier	0.736
38	Saint Joseph's	0.734
39	Nebraska	0.732
40	Kansas St.	0.729
41	BYU	0.728
42	Memphis	0.726
43	Arizona St.	0.723
44	George Washington	0.722
45	North Dakota St.	0.716
46	Massachusetts	0.713
47	Dayton	0.703
48	North Carolina St.	0.700
49	Colorado	0.698
50	Tulsa	0.687
51	Stephen F. Austin	0.669
52	Manhattan	0.655
53	North Carolina Central	0.649
54	New Mexico St.	0.646
55	Mercer	0.616
56	Western Michigan	0.585
57	Delaware	0.585
58	Louisiana Lafayette	0.573
59	American	0.565
60	Eastern Kentucky	0.532
61	Milwaukee	0.494
62	Weber St.	0.466
63	Wofford	0.450
64	Albany	0.438
65	Cal Poly	0.435
66	Mount St. Mary's	0.411
67	Coastal Carolina	0.373
68	Texas Southern	0.304