NCAA Tournament 2023 Bracket Math for the MDS Model

Going in to last year's tournament, UNC had a 0.32% chance of winning it all. Going in to the Final Four, 10%. And at halftime of the title game, 83%. I mean, look at this:

But more importantly, look at this:

Time marches onward, so let's get to this year's bracket. As in 2022 and in 2021, I'm using 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)

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
	South
1	Alabama	100.00%	95.81%	68.43%	51.03%	33.77%	22.22%	13.12%
16*	TX A&M-CC	100.00%	4.19%	0.51%	0.08%	0.01%	0.00%	0.00%
8	Maryland	100.00%	49.85%	15.45%	8.38%	3.72%	1.64%	0.61%
9	West Virginia	100.00%	50.15%	15.61%	8.48%	3.79%	1.67%	0.63%
5	San Diego St.	100.00%	69.09%	42.48%	16.15%	7.62%	3.56%	1.42%
12	Charleston	100.00%	30.91%	13.07%	2.84%	0.82%	0.23%	0.05%
4	Virginia	100.00%	68.18%	34.15%	11.15%	4.62%	1.89%	0.65%
13	Furman	100.00%	31.82%	10.30%	1.89%	0.47%	0.11%	0.02%
6	Creighton	100.00%	66.80%	38.14%	20.06%	9.36%	4.79%	2.12%
11	NC State	100.00%	33.20%	13.56%	4.91%	1.52%	0.53%	0.15%
3	Baylor	100.00%	81.06%	44.03%	22.60%	10.27%	5.13%	2.20%
14	UCSB	100.00%	18.94%	4.27%	0.89%	0.15%	0.03%	0.00%
7	Missouri	100.00%	40.74%	13.62%	5.01%	1.52%	0.51%	0.14%
10	Utah St.	100.00%	59.26%	24.71%	11.28%	4.34%	1.85%	0.67%
2	Arizona	100.00%	86.40%	58.14%	34.54%	17.89%	10.10%	5.00%
15	Princeton	100.00%	13.60%	3.54%	0.72%	0.11%	0.02%	0.00%
	East
1	Purdue	100.00%	97.38%	62.64%	36.65%	23.25%	12.40%	6.30%
16*	Texas Southern	100.00%	2.62%	0.15%	0.01%	0.00%	0.00%	0.00%
8	Memphis	100.00%	54.68%	21.40%	9.94%	5.10%	2.07%	0.86%
9	FAU	100.00%	45.32%	15.80%	6.63%	3.10%	1.14%	0.39%
5	Duke	100.00%	67.42%	31.05%	13.72%	7.20%	3.05%	1.21%
12	Oral Roberts	100.00%	32.58%	9.81%	2.72%	0.96%	0.25%	0.06%
4	Tennessee	100.00%	83.18%	54.23%	29.34%	18.26%	9.51%	4.71%
13	La.-Lafayette	100.00%	16.82%	4.90%	0.98%	0.26%	0.05%	0.01%
6	Kentucky	100.00%	56.85%	31.98%	15.75%	6.55%	2.61%	0.97%
11	Providence	100.00%	43.15%	21.46%	9.13%	3.21%	1.08%	0.34%
3	Kansas St.	100.00%	78.72%	41.56%	20.40%	8.45%	3.35%	1.25%
14	Montana St.	100.00%	21.28%	5.00%	1.06%	0.17%	0.03%	0.00%
7	Michigan St.	100.00%	52.51%	23.59%	11.68%	4.46%	1.63%	0.56%
10	USC	100.00%	47.49%	20.23%	9.51%	3.42%	1.17%	0.37%
2	Marquette	100.00%	83.42%	51.95%	31.44%	15.45%	7.29%	3.26%
15	Vermont	100.00%	16.58%	4.23%	1.04%	0.17%	0.03%	0.00%
	Midwest
1	Houston	100.00%	94.99%	70.61%	54.43%	36.82%	22.97%	14.54%
16	Northern Kentucky	100.00%	5.01%	0.81%	0.15%	0.02%	0.00%	0.00%
8	Iowa	100.00%	48.06%	13.35%	7.05%	2.96%	1.07%	0.40%
9	Auburn	100.00%	51.94%	15.23%	8.34%	3.65%	1.39%	0.54%
5	Miami (FL)	100.00%	59.46%	29.55%	9.02%	3.61%	1.24%	0.44%
12	Drake	100.00%	40.54%	16.37%	3.78%	1.19%	0.31%	0.08%
4	Indiana	100.00%	64.96%	38.57%	13.65%	6.20%	2.46%	1.00%
13	Kent St.	100.00%	35.04%	15.51%	3.57%	1.12%	0.29%	0.08%
6	Iowa St.	100.00%	60.25%	31.69%	13.65%	5.40%	2.12%	0.85%
11*	Mississippi St.	100.00%	39.75%	17.05%	5.72%	1.75%	0.52%	0.16%
3	Xavier	100.00%	84.17%	47.98%	22.03%	9.32%	3.92%	1.69%
14	Kennesaw St.	100.00%	15.83%	3.28%	0.47%	0.06%	0.01%	0.00%
7	Texas A&M	100.00%	56.22%	22.63%	11.58%	4.56%	1.78%	0.71%
10	Penn St.	100.00%	43.78%	15.21%	6.85%	2.32%	0.77%	0.27%
2	Texas	100.00%	88.06%	59.35%	39.05%	20.93%	11.29%	6.20%
15	Colgate	100.00%	11.94%	2.80%	0.64%	0.10%	0.01%	0.00%
	West
1	Kansas	100.00%	94.58%	59.26%	32.56%	16.92%	8.65%	4.53%
16	Howard	100.00%	5.42%	0.54%	0.04%	0.00%	0.00%	0.00%
8	Arkansas	100.00%	52.67%	21.79%	9.54%	3.89%	1.56%	0.64%
9	Illinois	100.00%	47.33%	18.41%	7.59%	2.90%	1.09%	0.42%
5	St. Mary's	100.00%	67.10%	31.41%	15.25%	6.91%	3.08%	1.41%
12	VCU	100.00%	32.90%	10.17%	3.24%	0.95%	0.27%	0.08%
4	Connecticut	100.00%	78.93%	51.20%	29.77%	16.30%	8.79%	4.85%
13	Iona	100.00%	21.07%	7.22%	2.02%	0.51%	0.13%	0.03%
6	TCU	100.00%	63.51%	26.95%	11.44%	4.88%	1.97%	0.82%
11*	Nevada	100.00%	36.49%	11.11%	3.35%	1.01%	0.29%	0.08%
3	Gonzaga	100.00%	86.14%	58.21%	32.14%	17.92%	9.53%	5.19%
14	Grand Canyon	100.00%	13.86%	3.73%	0.68%	0.12%	0.02%	0.00%
7	Northwestern	100.00%	47.80%	14.76%	5.44%	1.89%	0.62%	0.21%
10	Boise St.	100.00%	52.20%	17.07%	6.64%	2.43%	0.84%	0.30%
2	UCLA	100.00%	92.52%	66.71%	40.11%	23.36%	12.99%	7.40%
15	UNC Asheville	100.00%	7.48%	1.47%	0.19%	0.02%	0.00%	0.00%

Some notes:

• Sweet 16 and on are all chalk, except for UCLA to the Final Four
• Houston and Alabama get very clear paths to the Final Four at #1 and #2 overall
• The Midwest region catches none of the breaks. 4 top 10 teams are here... and #10 is Kansas
• #3 UCLA (2 seed), #4 Connecticut (4 seed), #6 Gonzaga (3 seed), #10 Kansas (1 seed)
• Similarly, the East region also has strong teams, that are just slightly less good than Purdue
• #7 Purdue (1 seed), #8 Tennessee (4 seed), #11 Marquette (2 seed)
• Rutgers got hosed. Bracket Matrix had them as far more likely to get in than Nevada, and I have them at a rating of 83.5, above 12 at-large bids:
• Boise St.
• Miami (FL)
• USC
• Penn St.
• Providence
• Northwestern
• NC State
• Mississippi St.
• Missouri
• Nevada
• Arizona St.
• Pittsburgh

Full rankings:

Rank	Seed	Team	Rating
1	1	Houston	93.26
2	1	Alabama	92.76
3	2	UCLA	90.91
4	4	Connecticut	90.27
5	2	Texas	90.18
6	3	Gonzaga	90.01
7	1	Purdue	89.77
8	4	Tennessee	89.32
9	2	Arizona	89.30
10	1	Kansas	89.25
11	2	Marquette	87.56
12	6	Creighton	87.41
13	3	Baylor	86.96
14	5	St. Mary's	86.85
15	3	Xavier	85.94
16	5	San Diego St.	85.83
17	5	Duke	85.79
18	8	Memphis	85.38
19	6	TCU	85.31
20	8	Arkansas	85.19
21	4	Indiana	85.07
22	6	Iowa St.	84.90
23	9	West Virginia	84.90
24	6	Kentucky	84.85
25	8	Maryland	84.84
26	7	Texas A&M	84.83
27	3	Kansas St.	84.79
28	9	Auburn	84.47
29	10	Utah St.	84.34
30	9	Illinois	84.26
31	8	Iowa	83.79
32	9	FAU	83.75
33	4	Virginia	83.73
34	7	Michigan St.	83.61
35	10	Boise St.	83.10
36	5	Miami (FL)	83.09
37	10	USC	82.74
38	10	Penn St.	82.64
39	11	Providence	82.44
40	7	Northwestern	82.33
41	11	NC State	81.35
42	11	Mississippi St.	81.28
43	7	Missouri	81.07
44	12	VCU	80.67
45	11	Nevada	80.49
46	11	Arizona St.	80.02
47	12	Drake	79.75
48	13	Kent St.	79.71
49	12	Oral Roberts	79.49
50	11	Pittsburgh	79.44
51	13	Iona	79.05
52	12	Charleston	78.87
53	13	Furman	77.14
54	13	La.-Lafayette	75.92
55	14	Grand Canyon	74.85
56	14	UCSB	74.68
57	15	Vermont	74.02
58	15	Princeton	73.97
59	15	Colgate	73.75
60	14	Montana St.	73.68
61	14	Kennesaw St.	71.97
62	15	UNC Asheville	70.80
63	16	Northern Kentucky	70.32
64	16	TX A&M-CC	68.65
65	16	Howard	66.85
66	16	SE Missouri St.	64.79
67	16	Texas Southern	62.72
68	16	Fairleigh Dickinson	60.38