NCAA Tournament 2017 Bracket Math for the MDS Model

This year I've done something a little different. After correctly picking the champion last year, I haven't kept up the MDS Model throughout this season, and so I've generated a new set of rankings similar to what I used to sportsbet in Las Vegas. 

I'm taking a composite of 6 different models, similar to what FiveThirtyEight does: 

• FiveThirtyEight (so I'm including a composite of a composite)
• KenPom (who's ratings are also included in FiveThirtyEight, so they're counted twice)
• Powerrank (created and maintained by Ed Feng)
• Preseason Polls (has shown to be a predictor of tournament success)
• Massey Composite (another composite, this time spanning 68 rating systems)
• Prediction Machine (the only component that is a simulator)

I then use a weighted average of these 6 ratings that reduces outliers by weighting the ratings closer to the median higher. This smooths out the final Aggregate ratings that I then use to project the tournament.

Note: For simplicity, I've taken the highest rated team in each play-in game and included them (sorry Mt St Mary's/UC Davis/Providence/Wake Forest).

Seed	Team	1st Round	2nd Round	Sweet 16	Elite 8	Final Four	Championship	Champion
	East
1	Villanova	100.00%	98.43%	69.85%	45.68%	29.02%	18.08%	11.08%
16*	New Orleans	100.00%	1.57%	0.10%	0.00%	0.00%	0.00%	0.00%
8	Wisconsin	100.00%	73.55%	25.80%	12.89%	6.18%	2.89%	1.31%
9	Virginia Tech	100.00%	26.45%	4.25%	1.16%	0.29%	0.07%	0.02%
5	Virginia	100.00%	81.47%	51.23%	23.55%	12.74%	6.73%	3.47%
12	UNC Wilmington	100.00%	18.53%	5.60%	0.94%	0.21%	0.04%	0.01%
4	Florida	100.00%	80.77%	39.34%	15.27%	7.15%	3.25%	1.44%
13	East Tennessee St.	100.00%	19.23%	3.82%	0.50%	0.09%	0.02%	0.00%
6	SMU	100.00%	72.88%	42.17%	19.91%	8.37%	3.90%	1.77%
11*	USC	100.00%	27.12%	9.60%	2.50%	0.54%	0.13%	0.03%
3	Baylor	100.00%	83.50%	44.93%	20.16%	8.00%	3.54%	1.52%
14	New Mexico St.	100.00%	16.50%	3.30%	0.49%	0.06%	0.01%	0.00%
7	South Carolina	100.00%	51.85%	13.27%	4.83%	1.23%	0.36%	0.10%
10	Marquette	100.00%	48.15%	11.66%	4.05%	0.97%	0.27%	0.07%
2	Duke	100.00%	95.65%	74.33%	47.98%	25.14%	14.31%	7.98%
15	Troy	100.00%	4.35%	0.75%	0.07%	0.00%	0.00%	0.00%
	West
1	Gonzaga	100.00%	96.68%	76.81%	50.88%	34.58%	19.71%	11.73%
16	South Dakota St.	100.00%	3.32%	0.52%	0.05%	0.00%	0.00%	0.00%
8	Northwestern	100.00%	44.79%	9.24%	3.05%	1.03%	0.25%	0.07%
9	Vanderbilt	100.00%	55.21%	13.43%	5.06%	1.96%	0.56%	0.17%
5	Notre Dame	100.00%	69.95%	29.46%	10.47%	4.80%	1.67%	0.62%
12	Princeton	100.00%	30.05%	7.43%	1.46%	0.39%	0.07%	0.01%
4	West Virginia	100.00%	86.48%	59.35%	28.51%	16.89%	8.08%	4.07%
13	Bucknell	100.00%	13.52%	3.77%	0.53%	0.11%	0.01%	0.00%
6	Maryland	100.00%	46.52%	22.88%	8.66%	2.73%	0.83%	0.27%
11	Xavier	100.00%	53.48%	28.06%	11.54%	3.99%	1.33%	0.47%
3	Florida St.	100.00%	83.66%	45.87%	20.30%	7.61%	2.75%	1.06%
14	Florida Gulf Coast	100.00%	16.34%	3.19%	0.43%	0.05%	0.00%	0.00%
7	Saint Mary's	100.00%	68.55%	34.42%	20.65%	9.02%	3.82%	1.71%
10	VCU	100.00%	31.45%	10.23%	4.21%	1.12%	0.28%	0.08%
2	Arizona	100.00%	94.18%	54.80%	34.15%	15.72%	7.03%	3.32%
15	North Dakota	100.00%	5.82%	0.54%	0.06%	0.00%	0.00%	0.00%
	Midwest
1	Kansas	100.00%	97.10%	69.44%	44.80%	26.96%	15.31%	8.18%
16*	North Carolina Central	100.00%	2.90%	0.27%	0.02%	0.00%	0.00%	0.00%
8	Miami FL	100.00%	49.20%	14.73%	6.26%	2.37%	0.83%	0.26%
9	Michigan St.	100.00%	50.80%	15.56%	6.73%	2.60%	0.92%	0.30%
5	Iowa St.	100.00%	74.06%	38.61%	16.74%	7.82%	3.40%	1.36%
12	Nevada	100.00%	25.94%	7.51%	1.62%	0.38%	0.08%	0.02%
4	Purdue	100.00%	79.90%	48.02%	22.71%	11.52%	5.46%	2.40%
13	Vermont	100.00%	20.10%	5.86%	1.12%	0.24%	0.04%	0.01%
6	Creighton	100.00%	54.47%	23.44%	9.64%	3.82%	1.46%	0.51%
11	Rhode Island	100.00%	45.53%	17.74%	6.55%	2.32%	0.79%	0.25%
3	Oregon	100.00%	89.06%	56.74%	29.93%	15.30%	7.61%	3.52%
14	Iona	100.00%	10.94%	2.08%	0.27%	0.03%	0.00%	0.00%
7	Michigan	100.00%	55.53%	21.00%	9.57%	3.86%	1.51%	0.54%
10	Oklahoma St.	100.00%	44.47%	14.62%	5.88%	2.07%	0.70%	0.22%
2	Louisville	100.00%	96.63%	64.11%	38.15%	20.70%	10.93%	5.40%
15	Jacksonville St.	100.00%	3.37%	0.27%	0.02%	0.00%	0.00%	0.00%
	South
1	North Carolina	100.00%	97.34%	75.80%	56.47%	32.44%	18.68%	9.93%
16	Texas Southern	100.00%	2.66%	0.33%	0.04%	0.00%	0.00%	0.00%
8	Arkansas	100.00%	49.42%	11.69%	5.42%	1.54%	0.44%	0.11%
9	Seton Hall	100.00%	50.58%	12.18%	5.71%	1.65%	0.48%	0.12%
5	Minnesota	100.00%	51.72%	20.74%	5.29%	1.33%	0.33%	0.07%
12	Middle Tennessee	100.00%	48.28%	18.61%	4.51%	1.07%	0.26%	0.05%
4	Butler	100.00%	83.67%	55.88%	22.00%	8.68%	3.43%	1.21%
13	Winthrop	100.00%	16.33%	4.77%	0.56%	0.06%	0.01%	0.00%
6	Cincinnati	100.00%	62.96%	31.03%	12.26%	5.63%	2.39%	0.91%
11*	Kansas St.	100.00%	37.04%	13.75%	3.83%	1.30%	0.39%	0.10%
3	UCLA	100.00%	91.27%	54.05%	23.70%	11.89%	5.57%	2.36%
14	Kent St.	100.00%	8.73%	1.17%	0.08%	0.01%	0.00%	0.00%
7	Dayton	100.00%	30.13%	7.27%	2.57%	0.83%	0.24%	0.06%
10	Wichita St.	100.00%	69.87%	29.15%	16.14%	8.27%	3.97%	1.73%
2	Kentucky	100.00%	95.66%	63.11%	41.35%	25.30%	14.77%	7.98%
15	Northern Kentucky	100.00%	4.34%	0.46%	0.05%	0.00%	0.00%	0.00%
	Totals	64.00	32.00	16.00	8.00	4.00	2.00	1.00

I'll include the final ratings as well at the bottom of this post, but here are the top 10 teams:

Rank	Team	Rating
1	Villanova	93.45
2	Gonzaga	92.79
3	Kentucky	91.68
4	Kansas	91.47
5	Duke	91.44
6	North Carolina	91.38
7	Louisville	90.03
8	Virginia	89.95
9	West Virginia	89.50
10	Oregon	88.91

Note that Gonzaga has the highest win probability in the tournament, yet is actually ranked behind Villanova by almost a full point. The lower probability for Villanova is due to the extremely difficult path the committee put them through, including having to potentially face Wisconsin (#14), Virginia (#8), and Duke (#5) just to get to the Final Four.

Here is the how the bracket flows if you take the highest probable team in each round:

A word of caution though about going straight chalk: in most pools you want to gauge "contrarian" picks relative to the overall pool. That's the reason my model won my pool last year; it had Villanova winning it all when most no one else did. The same goes for my cousin 2 years ago. He simply took my model, substituted Duke for Kentucky as his champion, and won my pool. 

I would use the win probabilities as a jumping off point to gauge more "likely" upsets and make picks that way that make sense. For example, (12) MTSU over (5) Minnesota at 48.28% is more likely than most brackets probably are picking that game. (6) SMU's chances to advance to the Sweet 16 (42.17%) are extremely close to (3) Baylor's (44.93%), which illustrates another opportunity where value probably lies.

Here are the full ratings for all 68 teams:

Rank	Team	Rating
1	Villanova	93.45
2	Gonzaga	92.79
3	Kentucky	91.68
4	Kansas	91.47
5	Duke	91.44
6	North Carolina	91.38
7	Louisville	90.03
8	Virginia	89.95
9	West Virginia	89.50
10	Oregon	88.91
11	Arizona	88.38
12	Purdue	88.07
13	Wichita St.	87.94
14	Wisconsin	87.74
15	SMU	87.71
16	UCLA	87.54
17	Saint Mary's	87.52
18	Florida	87.32
19	Baylor	86.84
20	Iowa St.	86.64
21	Cincinnati	85.94
22	Florida St.	85.19
23	Michigan	85.00
24	Butler	84.88
25	Creighton	84.72
26	Notre Dame	84.71
27	Xavier	84.06
28	Michigan St.	83.68
29	Miami FL	83.40
30	Rhode Island	83.15
31	Oklahoma St.	83.06
32	Maryland	82.85
33	Vanderbilt	82.12
34	Kansas St.	81.33
35	South Carolina	81.12
36	VCU	80.78
37	Seton Hall	80.77
38	Dayton	80.68
39	Arkansas	80.57
40	Marquette	80.47
41	Northwestern	80.29
42	Wake Forest	80.25
43	USC	79.22
44	Minnesota	79.12
45	Virginia Tech	78.96
46	Providence	78.93
47	Middle Tennessee	78.52
48	Nevada	77.64
49	UNC Wilmington	77.46
50	Princeton	77.41
51	Vermont	76.38
52	East Tennessee St.	75.19
53	Bucknell	74.12
54	New Mexico St.	73.26
55	Iona	71.75
56	Florida Gulf Coast	71.51
57	Winthrop	71.20
58	Kent St.	68.60
59	Northern Kentucky	67.80
60	Troy	67.57
61	South Dakota St.	67.19
62	North Dakota	66.48
63	North Carolina Central	65.03
64	Jacksonville St.	64.51
65	Texas Southern	64.43
66	New Orleans	63.45
67	UC Davis	62.96
68	Mount St. Mary's	61.67