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Sunday, March 14, 2021

NCAA Tournament 2021 Bracket Math for the MDS Model

In an entirely abnormal year, it feels like a fool's errand to try to predict the tournament. This past year has been really hard for most, and none of this feels normal.

But here we are, with the first tournament in 2 years.

With so many uneven schedules, differing numbers of games, and the possibility of teams forfeiting games due to COVID, I'm attempting to anchor on something in the face of larger than normal uncertainty, so I'm adding 2 retrodictive models to my composite this year - which aim more to assess how deserving a team is of its ranking, as opposed to predicting future performance. So my composite will be 6 in total, similar to what FiveThirtyEight does:

  • Predictive
    • 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 overall rating, synthesis of his 3 ratings)
  • Retrodictive

I then use a weighted average of these 6 ratings that reduces outliers by weighting the ratings closer to the median more (higher likelihood this year that this will come in to play due to the retrodictive components). 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
West
1Gonzaga100.00%98.04%83.92%67.54%50.92%37.61%26.56%
16*Appalachian St.100.00%1.96%0.31%0.04%0.00%0.00%0.00%
8Oklahoma100.00%51.33%8.28%3.61%1.33%0.47%0.15%
9Missouri100.00%48.67%7.48%3.16%1.13%0.39%0.12%
5Creighton100.00%72.57%40.20%11.20%5.23%2.34%0.97%
12UC Santa Barbara100.00%27.43%9.09%1.18%0.30%0.07%0.02%
4Virginia100.00%77.04%43.93%12.53%5.96%2.72%1.14%
13Ohio100.00%22.96%6.79%0.74%0.16%0.03%0.01%
6USC100.00%66.93%35.67%16.34%5.19%2.32%0.95%
11*Wichita St.100.00%33.07%12.27%3.69%0.71%0.20%0.05%
3Kansas100.00%82.25%47.78%23.07%7.81%3.69%1.61%
14Eastern Washington100.00%17.75%4.29%0.76%0.08%0.01%0.00%
7Oregon100.00%56.70%21.08%9.84%2.69%1.06%0.38%
10VCU100.00%43.30%13.61%5.47%1.23%0.41%0.12%
2Iowa100.00%89.42%62.79%40.33%17.21%9.81%5.23%
15Grand Canyon100.00%10.58%2.51%0.50%0.05%0.01%0.00%
East
1Michigan100.00%95.84%68.99%48.09%31.23%15.20%8.65%
16*Mt. St. Mary's100.00%4.16%0.52%0.06%0.01%0.00%0.00%
8LSU100.00%52.28%16.41%8.03%3.51%1.02%0.37%
9St. Bonaventure100.00%47.72%14.08%6.58%2.73%0.75%0.25%
5Colorado100.00%69.73%38.57%15.56%7.51%2.48%1.00%
12Georgetown100.00%30.27%10.87%2.50%0.73%0.13%0.03%
4Florida St.100.00%75.55%43.00%17.75%8.74%2.96%1.22%
13UNC Greensboro100.00%24.45%7.56%1.43%0.35%0.05%0.01%
6BYU100.00%61.35%31.75%14.48%6.05%1.91%0.74%
11*UCLA100.00%38.65%15.81%5.51%1.73%0.39%0.11%
3Texas100.00%78.78%46.38%23.22%10.71%3.80%1.63%
14Abilene Christian100.00%21.22%6.06%1.33%0.26%0.03%0.01%
7Connecticut100.00%57.04%23.36%11.47%4.56%1.36%0.50%
10Maryland100.00%42.96%14.89%6.29%2.10%0.51%0.16%
2Alabama100.00%90.72%60.04%37.41%19.76%8.23%4.08%
15Iona100.00%9.28%1.71%0.28%0.03%0.00%0.00%
South
1Baylor100.00%96.03%70.55%51.58%36.11%22.75%12.36%
16Hartford100.00%3.97%0.52%0.07%0.01%0.00%0.00%
8North Carolina100.00%46.92%12.95%6.29%2.82%1.06%0.32%
9Wisconsin100.00%53.08%15.97%8.23%3.94%1.60%0.52%
5Villanova100.00%72.00%40.70%15.21%7.70%3.32%1.17%
12Winthrop100.00%28.00%9.69%1.85%0.54%0.12%0.02%
4Purdue100.00%74.11%41.41%15.36%7.73%3.31%1.15%
13North Texas100.00%25.89%8.20%1.41%0.38%0.08%0.01%
6Texas Tech100.00%61.41%30.92%14.37%5.42%2.15%0.68%
11Utah St.100.00%38.59%15.11%5.39%1.50%0.44%0.10%
3Arkansas100.00%66.26%39.44%20.31%8.65%3.85%1.40%
14Colgate100.00%33.74%14.53%5.20%1.45%0.43%0.10%
7Florida100.00%53.24%19.27%8.49%2.65%0.87%0.23%
10Virginia Tech100.00%46.76%15.61%6.39%1.83%0.55%0.13%
2Ohio St.100.00%90.47%63.08%39.51%19.23%9.77%4.13%
15Oral Roberts100.00%9.53%2.04%0.34%0.03%0.00%0.00%
Midwest
1Illinois100.00%93.56%68.33%48.81%31.63%19.04%9.88%
16Drexel100.00%6.44%1.18%0.22%0.03%0.00%0.00%
8Loyola Chicago100.00%55.38%17.97%9.16%4.00%1.57%0.50%
9Georgia Tech100.00%44.62%12.52%5.73%2.21%0.76%0.21%
5Tennessee100.00%70.70%37.93%14.44%6.51%2.65%0.87%
12Oregon St.100.00%29.30%9.82%2.02%0.52%0.12%0.02%
4Oklahoma St.100.00%78.33%45.89%18.58%8.85%3.82%1.35%
13Liberty100.00%21.67%6.37%1.04%0.21%0.04%0.01%
6San Diego St.100.00%63.92%34.04%15.32%6.47%2.69%0.92%
11Syracuse100.00%36.08%14.43%4.62%1.37%0.40%0.09%
3West Virginia100.00%83.67%47.98%22.68%10.08%4.43%1.60%
14Morehead St.100.00%16.33%3.55%0.56%0.08%0.01%0.00%
7Clemson100.00%50.49%17.27%7.66%2.68%0.93%0.25%
10Rutgers100.00%49.51%16.73%7.34%2.54%0.86%0.23%
2Houston100.00%91.03%64.12%41.49%22.78%12.38%5.70%
15Cleveland St.100.00%8.97%1.89%0.33%0.04%0.00%0.00%
Totals64.0032.0016.008.004.002.001.00

In a testament to KenPom and the larger analytics movement in general, this is the chalkiest set of predictions I've ever put out. There is one predicted upset by seeding in the entire tournament... ironically, Wisconsin (9) over North Carolina (8).

For the rankings, I've included the alt teams as well, because this year is unique due to COVID:

RankTeamRating
1Gonzaga96.80
2Baylor92.91
3Illinois92.00
4Michigan91.49
5Iowa90.17
6Houston89.84
7Alabama88.83
8Ohio St.88.43
9Kansas86.64
10Texas86.40
11Arkansas86.17
12Virginia86.07
13West Virginia86.02
14Creighton85.77
15Florida St.85.76
16USC85.74
17Oklahoma St.85.72
18Villanova85.64
19Purdue85.54
20Colorado85.41
21San Diego St.85.19
22Tennessee84.80
23BYU84.80
24Wisconsin84.66
25Texas Tech84.33
26Loyola Chicago84.26
27Connecticut84.05
28Oregon83.76
29LSU83.75
30North Carolina83.59
31St. Bonaventure82.95
32Clemson82.44
33Georgia Tech82.38
34Rutgers82.27
35Oklahoma82.20
36Florida81.75
37Missouri81.73
38Maryland81.57
39VCU81.41
40UCLA80.77
41Virginia Tech80.62
42Colgate80.31
43Utah St.80.29
44Syracuse80.21
45Michigan St.79.89
46Wichita St.79.63
47Drake78.80
48Georgetown78.20
49Louisville77.92
50Saint Louis77.79
51Winthrop77.51
52UC Santa Barbara77.40
53Ole Miss77.23
54Oregon St.77.20
55Colorado St.76.88
56North Texas76.51
57UNC Greensboro76.11
58Ohio75.74
59Abilene Christian75.26
60Liberty74.79
61Eastern Washington73.73
62Grand Canyon72.75
63Morehead St.72.33
64Cleveland St.71.11
65Drexel70.82
66Iona70.37
67Oral Roberts70.17
68Hartford68.45
69Appalachian St.68.04
70Norfolk St.67.44
71Mt. St. Mary's67.32
72Texas Southern66.66

The inclusion of the retrodictive components could be influencing the chalkiest of the bracket, so I decided to rerun it with only the 4 predictive pieces (FiveThirtyEight, KenPom, Powerrank, Sagarin).

Some slight changes, including some 5 seeds predicted over 4s, and things tighten up elsewhere, which makes more inclined to trust this set of outputs:

SeedTeam1st Round2nd RoundSweet 16Elite 8Final FourChampionshipChampion
West
1Gonzaga100.00%98.37%85.21%69.21%52.74%40.00%28.75%
16*Appalachian St.100.00%1.63%0.25%0.03%0.00%0.00%0.00%
8Oklahoma100.00%54.78%8.60%3.81%1.44%0.54%0.18%
9Missouri100.00%45.22%5.94%2.36%0.79%0.26%0.07%
5Creighton100.00%74.48%42.46%11.62%5.54%2.60%1.10%
12UC Santa Barbara100.00%25.52%8.30%0.97%0.24%0.06%0.01%
4Virginia100.00%75.63%41.96%11.23%5.26%2.43%1.01%
13Ohio100.00%24.37%7.28%0.78%0.18%0.04%0.01%
6USC100.00%68.90%37.47%16.84%5.07%2.30%0.94%
11*Wichita St.100.00%31.10%11.22%3.10%0.52%0.14%0.03%
3Kansas100.00%79.66%45.85%21.36%6.73%3.17%1.35%
14Eastern Washington100.00%20.34%5.46%1.05%0.12%0.02%0.00%
7Oregon100.00%55.91%19.55%9.04%2.25%0.88%0.30%
10VCU100.00%44.09%13.23%5.36%1.12%0.38%0.11%
2Iowa100.00%88.96%64.30%42.60%17.95%10.62%5.79%
15Grand Canyon100.00%11.04%2.92%0.64%0.06%0.01%0.00%
East
1Michigan100.00%96.16%68.29%46.96%30.85%14.34%8.08%
16*Mt. St. Mary's100.00%3.84%0.43%0.05%0.00%0.00%0.00%
8LSU100.00%50.37%15.83%7.62%3.40%0.94%0.33%
9St. Bonaventure100.00%49.63%15.44%7.37%3.26%0.89%0.31%
5Colorado100.00%68.24%38.33%15.96%8.07%2.62%1.08%
12Georgetown100.00%31.76%12.14%3.06%1.00%0.19%0.05%
4Florida St.100.00%75.21%42.02%17.53%8.88%2.89%1.19%
13UNC Greensboro100.00%24.79%7.51%1.46%0.37%0.05%0.01%
6BYU100.00%58.54%31.17%13.89%5.67%1.66%0.62%
11*UCLA100.00%41.46%18.66%6.79%2.24%0.51%0.15%
3Texas100.00%74.44%42.16%20.07%8.79%2.79%1.13%
14Abilene Christian100.00%25.56%8.01%1.93%0.42%0.06%0.01%
7Connecticut100.00%55.83%24.90%13.35%5.65%1.73%0.67%
10Maryland100.00%44.17%17.33%8.29%3.06%0.79%0.27%
2Alabama100.00%90.93%56.39%35.46%18.30%7.09%3.41%
15Iona100.00%9.07%1.38%0.22%0.02%0.00%0.00%
South
1Baylor100.00%96.30%68.63%50.33%35.68%22.45%11.98%
16Hartford100.00%3.70%0.41%0.05%0.01%0.00%0.00%
8North Carolina100.00%46.80%13.82%7.09%3.43%1.37%0.43%
9Wisconsin100.00%53.20%17.14%9.33%4.80%2.07%0.71%
5Villanova100.00%72.90%41.21%15.18%7.81%3.35%1.15%
12Winthrop100.00%27.10%9.10%1.62%0.47%0.10%0.02%
4Purdue100.00%72.04%40.22%14.67%7.49%3.19%1.08%
13North Texas100.00%27.96%9.47%1.73%0.51%0.11%0.02%
6Texas Tech100.00%60.83%32.77%16.11%6.33%2.61%0.85%
11Utah St.100.00%39.17%16.88%6.54%1.94%0.61%0.15%
3Arkansas100.00%62.99%34.75%17.40%6.99%2.94%0.98%
14Colgate100.00%37.01%15.59%5.85%1.67%0.51%0.12%
7Florida100.00%54.84%21.13%9.60%3.08%1.04%0.27%
10Virginia Tech100.00%45.16%15.48%6.30%1.77%0.53%0.12%
2Ohio St.100.00%88.87%60.82%37.73%17.99%8.95%3.63%
15Oral Roberts100.00%11.13%2.57%0.47%0.05%0.01%0.00%
Midwest
1Illinois100.00%93.77%67.71%49.79%32.62%19.93%10.24%
16Drexel100.00%6.23%1.08%0.21%0.03%0.00%0.00%
8Loyola Chicago100.00%56.41%18.91%10.36%4.74%1.96%0.64%
9Georgia Tech100.00%43.59%12.30%5.97%2.36%0.84%0.23%
5Tennessee100.00%70.67%40.52%15.22%6.94%2.86%0.93%
12Oregon St.100.00%29.33%10.80%2.18%0.57%0.13%0.02%
4Oklahoma St.100.00%74.90%41.17%15.04%6.69%2.69%0.85%
13Liberty100.00%25.10%7.51%1.23%0.26%0.05%0.01%
6San Diego St.100.00%58.94%30.55%12.89%5.15%2.04%0.64%
11Syracuse100.00%41.06%17.81%6.05%1.93%0.61%0.15%
3West Virginia100.00%84.64%48.52%22.18%9.62%4.15%1.42%
14Morehead St.100.00%15.36%3.12%0.44%0.06%0.01%0.00%
7Clemson100.00%46.44%14.68%6.36%2.10%0.69%0.17%
10Rutgers100.00%53.56%18.55%8.67%3.14%1.13%0.31%
2Houston100.00%92.32%65.31%43.18%23.76%13.06%5.92%
15Cleveland St.100.00%7.68%1.45%0.24%0.03%0.00%0.00%
Totals64.0032.0016.008.004.002.001.00

RankTeamRating
1Gonzaga96.75
2Baylor92.35
3Illinois91.62
4Michigan90.69
5Iowa90.03
6Houston89.34
7Alabama87.70
8Ohio St.87.51
9Kansas85.67
10Creighton85.63
11Virginia85.35
12Florida St.85.20
13Colorado85.17
14USC85.06
15Wisconsin85.04
16West Virginia85.03
17Villanova85.02
18Purdue84.88
19Texas84.85
20Arkansas84.71
21Texas Tech84.38
22Loyola Chicago84.36
23Connecticut84.32
24Tennessee84.30
25North Carolina83.92
26Oklahoma St.83.90
27BYU83.76
28San Diego St.83.74
29LSU83.02
30St. Bonaventure82.89
31Oregon82.67
32Rutgers82.30
33Maryland82.28
34Georgia Tech82.10
35Oklahoma82.02
36Florida81.56
37Clemson81.05
38UCLA80.75
39VCU80.60
40Syracuse80.58
41Utah St.80.55
42Missouri80.34
43Michigan St.80.10
44Colgate80.09
45Virginia Tech79.87
46Georgetown78.55
47Wichita St.78.19
48Drake77.63
49Saint Louis77.20
50Ole Miss76.89
51North Texas76.74
52Oregon St.76.72
53Winthrop76.52
54UC Santa Barbara76.45
55Louisville76.09
56UNC Greensboro75.70
57Abilene Christian75.69
58Ohio75.66
59Liberty74.53
60Colorado St.74.51
61Eastern Washington74.10
62Grand Canyon72.94
63Morehead St.70.79
64Oral Roberts70.50
65Drexel70.20
66Cleveland St.69.43
67Iona69.05
68Hartford67.43
69Appalachian St.66.96
70Mt. St. Mary's66.01
71Norfolk St.65.87
72Texas Southern64.39

1 comment:

  1. I’ll take that 0.32% chance of UNC winning the natty. It ain’t zero.

    ReplyDelete