NCAA Tournament 2022 Bracket Math for the MDS Model

It has been 8 years since I put out my first NCAA tournament bracket math, and this year's version is more in line with 2014 (and 2019) since last season had a strange retrodictive component due to the unbalanced nature of COVID-impacted schedules.

I've done away with that, and am back to just a composite of 4 different predictive 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)
• Jeff Sagarin (ratings also used in FiveThirtyEight; his Predictor rating)

These are the same 4 as last year, since even though it didn't pick Baylor as the winner, the model was still good enough for certain workplace uses.

I then use a weighted average of these 4 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.

Seed	Team	1st Round	2nd Round	Sweet 16	Elite 8	Final Four	Championship	Champion
	West
1	Gonzaga	100.00%	96.12%	78.33%	61.84%	44.72%	31.40%	21.83%
16	Georgia St.	100.00%	3.88%	0.75%	0.13%	0.02%	0.00%	0.00%
8	Boise St.	100.00%	43.43%	8.01%	3.48%	1.23%	0.40%	0.13%
9	Memphis	100.00%	56.57%	12.91%	6.43%	2.67%	1.04%	0.40%
5	UCONN	100.00%	72.04%	39.64%	12.22%	5.55%	2.38%	1.00%
12	New Mexico St.	100.00%	27.96%	9.22%	1.39%	0.34%	0.08%	0.02%
4	Arkansas	100.00%	69.69%	39.79%	12.58%	5.83%	2.55%	1.10%
13	Vermont	100.00%	30.31%	11.36%	1.94%	0.54%	0.14%	0.03%
6	Alabama	100.00%	60.81%	25.34%	11.33%	3.62%	1.44%	0.56%
11*	Notre Dame	100.00%	39.19%	12.57%	4.35%	1.03%	0.31%	0.09%
3	Texas Tech	100.00%	89.10%	59.72%	34.38%	15.03%	7.92%	4.11%
14	Montana St.	100.00%	10.90%	2.37%	0.38%	0.04%	0.00%	0.00%
7	Michigan St.	100.00%	53.81%	19.35%	7.52%	2.07%	0.71%	0.24%
10	Davidson	100.00%	46.19%	15.11%	5.35%	1.32%	0.41%	0.12%
2	Duke	100.00%	90.77%	63.59%	36.42%	15.96%	8.43%	4.39%
15	CS Fullerton	100.00%	9.23%	1.96%	0.27%	0.02%	0.00%	0.00%
	East
1	Baylor	100.00%	92.54%	64.56%	37.33%	20.26%	9.30%	4.89%
16	Norfolk St.	100.00%	7.46%	1.33%	0.15%	0.02%	0.00%	0.00%
8	North Carolina	100.00%	54.58%	19.60%	7.84%	2.86%	1.07%	0.32%
9	Marquette	100.00%	45.42%	14.52%	5.20%	1.68%	0.43%	0.13%
5	Saint Mary's	100.00%	56.03%	23.03%	9.90%	3.95%	1.28%	0.49%
12*	Indiana	100.00%	43.97%	15.70%	5.86%	2.01%	0.55%	0.18%
4	UCLA	100.00%	87.83%	58.46%	33.23%	17.89%	8.13%	4.24%
13	Akron	100.00%	12.17%	2.81%	0.48%	0.07%	0.01%	0.00%
6	Texas	100.00%	56.54%	26.71%	11.86%	5.36%	1.93%	0.81%
11	Virginia Tech	100.00%	43.46%	17.88%	6.86%	2.67%	0.81%	0.29%
3	Purdue	100.00%	88.57%	53.42%	27.57%	14.48%	6.22%	3.08%
14	Yale	100.00%	11.43%	1.99%	0.27%	0.04%	0.00%	0.00%
7	Murray St.	100.00%	45.33%	13.31%	4.75%	1.58%	0.40%	0.12%
10	San Francisco	100.00%	54.67%	18.14%	7.26%	2.73%	0.80%	0.28%
2	Kentucky	100.00%	90.14%	66.07%	41.00%	24.34%	12.07%	6.82%
15	Saint Peter's	100.00%	9.86%	2.49%	0.42%	0.07%	0.01%	0.00%
	South
1	Arizona	100.00%	93.84%	70.40%	44.36%	27.60%	16.66%	8.66%
16*	Wright St.	100.00%	6.16%	1.19%	0.15%	0.02%	0.00%	0.00%
8	Seton Hall	100.00%	51.30%	14.83%	5.63%	2.08%	0.74%	0.21%
9	TCU	100.00%	48.70%	13.58%	4.99%	1.78%	0.61%	0.16%
5	Houston	100.00%	72.88%	47.20%	24.77%	14.13%	7.79%	3.64%
12	UAB	100.00%	27.12%	11.30%	3.43%	1.16%	0.37%	0.09%
4	Illinois	100.00%	71.58%	33.86%	14.81%	7.11%	3.29%	1.25%
13	Chattanooga	100.00%	28.42%	7.64%	1.86%	0.51%	0.13%	0.03%
6	Colorado St.	100.00%	45.55%	15.95%	5.90%	1.86%	0.63%	0.17%
11	Michigan	100.00%	54.45%	21.20%	8.72%	3.09%	1.17%	0.35%
3	Tennessee	100.00%	89.91%	60.76%	34.49%	17.49%	9.34%	4.20%
14	Longwood	100.00%	10.09%	2.09%	0.30%	0.03%	0.00%	0.00%
7	Ohio St.	100.00%	51.45%	20.54%	8.79%	3.20%	1.24%	0.39%
10	Loyola Chicago	100.00%	48.55%	18.76%	7.77%	2.72%	1.02%	0.31%
2	Villanova	100.00%	88.85%	58.39%	33.65%	17.17%	9.22%	4.17%
15	Delaware	100.00%	11.15%	2.32%	0.38%	0.05%	0.01%	0.00%
	Midwest
1	Kansas	100.00%	94.39%	68.55%	45.41%	28.41%	15.95%	7.96%
16*	Texas Southern	100.00%	5.61%	0.92%	0.12%	0.01%	0.00%	0.00%
8	San Diego St.	100.00%	56.80%	18.71%	8.69%	3.69%	1.32%	0.40%
9	Creighton	100.00%	43.20%	11.82%	4.73%	1.71%	0.51%	0.13%
5	Iowa	100.00%	76.54%	53.83%	27.18%	15.20%	7.48%	3.23%
12	Richmond	100.00%	23.46%	10.01%	2.49%	0.73%	0.17%	0.03%
4	Providence	100.00%	59.77%	23.71%	8.12%	3.18%	1.04%	0.29%
13	South Dakota St.	100.00%	40.23%	12.45%	3.24%	0.99%	0.24%	0.05%
6	LSU	100.00%	63.33%	38.90%	18.17%	8.08%	3.38%	1.22%
11	Iowa St.	100.00%	36.67%	17.81%	6.10%	1.96%	0.58%	0.14%
3	Wisconsin	100.00%	76.23%	37.67%	15.63%	6.14%	2.24%	0.70%
14	Colgate	100.00%	23.77%	5.61%	1.05%	0.18%	0.03%	0.00%
7	USC	100.00%	55.50%	18.91%	8.86%	3.16%	1.04%	0.29%
10	Miami (FL)	100.00%	44.50%	13.14%	5.45%	1.68%	0.47%	0.11%
2	Auburn	100.00%	90.01%	65.46%	44.20%	24.82%	13.30%	6.31%
15	Jacksonville St.	100.00%	9.99%	2.49%	0.53%	0.07%	0.01%	0.00%

I'm not including the COVID contingency teams this year, since I would guess the chances of them coming in to play is vanishingly low. 

Some things immediately stand out:

• Gonzaga is the clear favorite (as they were last year)
• Some very clear 6 over 3 and 5 over 4 upsets to the Sweet 16
• Providence stands out the most - the model really, really thinks they're just lucky
• Some 3 over 2 as well to the Elite 8
• Tennessee a favorite over Villanova, and Texas Tech could take down Coach K
• Kentucky is underseeded - they're #3 in my model, something Tate Frazier has been calling out as our Only Hope to take down Duke
• Houston is too, but they run in to Arizona, the second best team

Full rankings:

Rank	Team	Rating
1	Gonzaga	94.49
2	Arizona	90.00
3	Kentucky	89.54
4	Kansas	89.24
5	Auburn	88.33
6	Baylor	88.16
7	Houston	88.08
8	UCLA	88.00
9	Duke	87.96
10	Texas Tech	87.92
11	Villanova	87.55
12	Tennessee	87.44
13	Purdue	87.06
14	Iowa	86.76
15	Illinois	84.85
16	Arkansas	84.72
17	Texas	84.40
18	UCONN	84.38
19	LSU	84.07
20	Alabama	83.21
21	Memphis	82.95
22	Saint Mary's	82.94
23	Ohio St.	82.15
24	Wisconsin	82.13
25	Virginia Tech	82.11
26	San Diego St.	81.85
27	Michigan	81.77
28	North Carolina	81.65
29	Loyola Chicago	81.64
30	San Francisco	81.60
31	Michigan St.	81.23
32	Indiana	80.83
33	Seton Hall	80.80
34	USC	80.74
35	Providence	80.65
36	Boise St.	80.65
37	TCU	80.34
38	Colorado St.	80.22
39	Marquette	80.05
40	Murray St.	79.96
41	Davidson	79.90
42	UAB	79.59
43	Creighton	79.46
44	Notre Dame	79.38
45	Iowa St.	79.32
46	Miami (FL)	78.81
47	Vermont	77.53
48	South Dakota St.	77.20
49	Chattanooga	76.89
50	Richmond	76.67
51	New Mexico St.	76.24
52	Colgate	72.17
53	Akron	71.72
54	Saint Peter's	71.55
55	Montana St.	70.73
56	Delaware	70.55
57	Jacksonville St.	70.44
58	Yale	70.26
59	Georgia St.	69.87
60	Longwood	69.63
61	CS Fullerton	69.45
62	Wright St.	68.49
63	Norfolk St.	68.03
64	Texas Southern	67.09