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Tuesday, March 14, 2023

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:
  • 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

SeedTeam1st Round2nd RoundSweet 16Elite 8Final FourChampionshipChampion
South
1Alabama100.00%95.81%68.43%51.03%33.77%22.22%13.12%
16*TX A&M-CC100.00%4.19%0.51%0.08%0.01%0.00%0.00%
8Maryland100.00%49.85%15.45%8.38%3.72%1.64%0.61%
9West Virginia100.00%50.15%15.61%8.48%3.79%1.67%0.63%
5San Diego St.100.00%69.09%42.48%16.15%7.62%3.56%1.42%
12Charleston100.00%30.91%13.07%2.84%0.82%0.23%0.05%
4Virginia100.00%68.18%34.15%11.15%4.62%1.89%0.65%
13Furman100.00%31.82%10.30%1.89%0.47%0.11%0.02%
6Creighton100.00%66.80%38.14%20.06%9.36%4.79%2.12%
11NC State100.00%33.20%13.56%4.91%1.52%0.53%0.15%
3Baylor100.00%81.06%44.03%22.60%10.27%5.13%2.20%
14UCSB100.00%18.94%4.27%0.89%0.15%0.03%0.00%
7Missouri100.00%40.74%13.62%5.01%1.52%0.51%0.14%
10Utah St.100.00%59.26%24.71%11.28%4.34%1.85%0.67%
2Arizona100.00%86.40%58.14%34.54%17.89%10.10%5.00%
15Princeton100.00%13.60%3.54%0.72%0.11%0.02%0.00%
East
1Purdue100.00%97.38%62.64%36.65%23.25%12.40%6.30%
16*Texas Southern100.00%2.62%0.15%0.01%0.00%0.00%0.00%
8Memphis100.00%54.68%21.40%9.94%5.10%2.07%0.86%
9FAU100.00%45.32%15.80%6.63%3.10%1.14%0.39%
5Duke100.00%67.42%31.05%13.72%7.20%3.05%1.21%
12Oral Roberts100.00%32.58%9.81%2.72%0.96%0.25%0.06%
4Tennessee100.00%83.18%54.23%29.34%18.26%9.51%4.71%
13La.-Lafayette100.00%16.82%4.90%0.98%0.26%0.05%0.01%
6Kentucky100.00%56.85%31.98%15.75%6.55%2.61%0.97%
11Providence100.00%43.15%21.46%9.13%3.21%1.08%0.34%
3Kansas St.100.00%78.72%41.56%20.40%8.45%3.35%1.25%
14Montana St.100.00%21.28%5.00%1.06%0.17%0.03%0.00%
7Michigan St.100.00%52.51%23.59%11.68%4.46%1.63%0.56%
10USC100.00%47.49%20.23%9.51%3.42%1.17%0.37%
2Marquette100.00%83.42%51.95%31.44%15.45%7.29%3.26%
15Vermont100.00%16.58%4.23%1.04%0.17%0.03%0.00%
Midwest
1Houston100.00%94.99%70.61%54.43%36.82%22.97%14.54%
16Northern Kentucky100.00%5.01%0.81%0.15%0.02%0.00%0.00%
8Iowa100.00%48.06%13.35%7.05%2.96%1.07%0.40%
9Auburn100.00%51.94%15.23%8.34%3.65%1.39%0.54%
5Miami (FL)100.00%59.46%29.55%9.02%3.61%1.24%0.44%
12Drake100.00%40.54%16.37%3.78%1.19%0.31%0.08%
4Indiana100.00%64.96%38.57%13.65%6.20%2.46%1.00%
13Kent St.100.00%35.04%15.51%3.57%1.12%0.29%0.08%
6Iowa 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%
3Xavier100.00%84.17%47.98%22.03%9.32%3.92%1.69%
14Kennesaw St.100.00%15.83%3.28%0.47%0.06%0.01%0.00%
7Texas A&M100.00%56.22%22.63%11.58%4.56%1.78%0.71%
10Penn St.100.00%43.78%15.21%6.85%2.32%0.77%0.27%
2Texas100.00%88.06%59.35%39.05%20.93%11.29%6.20%
15Colgate100.00%11.94%2.80%0.64%0.10%0.01%0.00%
West
1Kansas100.00%94.58%59.26%32.56%16.92%8.65%4.53%
16Howard100.00%5.42%0.54%0.04%0.00%0.00%0.00%
8Arkansas100.00%52.67%21.79%9.54%3.89%1.56%0.64%
9Illinois100.00%47.33%18.41%7.59%2.90%1.09%0.42%
5St. Mary's100.00%67.10%31.41%15.25%6.91%3.08%1.41%
12VCU100.00%32.90%10.17%3.24%0.95%0.27%0.08%
4Connecticut100.00%78.93%51.20%29.77%16.30%8.79%4.85%
13Iona100.00%21.07%7.22%2.02%0.51%0.13%0.03%
6TCU100.00%63.51%26.95%11.44%4.88%1.97%0.82%
11*Nevada100.00%36.49%11.11%3.35%1.01%0.29%0.08%
3Gonzaga100.00%86.14%58.21%32.14%17.92%9.53%5.19%
14Grand Canyon100.00%13.86%3.73%0.68%0.12%0.02%0.00%
7Northwestern100.00%47.80%14.76%5.44%1.89%0.62%0.21%
10Boise St.100.00%52.20%17.07%6.64%2.43%0.84%0.30%
2UCLA100.00%92.52%66.71%40.11%23.36%12.99%7.40%
15UNC Asheville100.00%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:

RankSeedTeamRating
11Houston93.26
21Alabama92.76
32UCLA90.91
44Connecticut90.27
52Texas90.18
63Gonzaga90.01
71Purdue89.77
84Tennessee89.32
92Arizona89.30
101Kansas89.25
112Marquette87.56
126Creighton87.41
133Baylor86.96
145St. Mary's86.85
153Xavier85.94
165San Diego St.85.83
175Duke85.79
188Memphis85.38
196TCU85.31
208Arkansas85.19
214Indiana85.07
226Iowa St.84.90
239West Virginia84.90
246Kentucky84.85
258Maryland84.84
267Texas A&M84.83
273Kansas St.84.79
289Auburn84.47
2910Utah St.84.34
309Illinois84.26
318Iowa83.79
329FAU83.75
334Virginia83.73
347Michigan St.83.61
3510Boise St.83.10
365Miami (FL)83.09
3710USC82.74
3810Penn St.82.64
3911Providence82.44
407Northwestern82.33
4111NC State81.35
4211Mississippi St.81.28
437Missouri81.07
4412VCU80.67
4511Nevada80.49
4611Arizona St.80.02
4712Drake79.75
4813Kent St.79.71
4912Oral Roberts79.49
5011Pittsburgh79.44
5113Iona79.05
5212Charleston78.87
5313Furman77.14
5413La.-Lafayette75.92
5514Grand Canyon74.85
5614UCSB74.68
5715Vermont74.02
5815Princeton73.97
5915Colgate73.75
6014Montana St.73.68
6114Kennesaw St.71.97
6215UNC Asheville70.80
6316Northern Kentucky70.32
6416TX A&M-CC68.65
6516Howard66.85
6616SE Missouri St.64.79
6716Texas Southern62.72
6816Fairleigh Dickinson60.38

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