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Monday, March 14, 2016

NCAA Tournament 2016 Bracket Math for the MDS Model

As always, here are the picks by the MDS Model for this year's NCAA tournament, as well as the win probabilities (using Log5). 





Round-by-round probabilities:

SeedTeam1st Round2nd RoundSweet 16Elite 8Final FourChampionshipChampion
West
1Oregon100.00%98.39%65.20%40.63%24.58%11.36%5.18%
16*Holy Cross30.32%0.26%0.00%0.00%0.00%0.00%0.00%
16*Southern University69.68%1.35%0.05%0.00%0.00%0.00%0.00%
8Saint Joseph100.00%45.03%14.56%6.37%2.65%0.76%0.21%
9Cincinnati100.00%54.97%20.18%9.78%4.53%1.49%0.48%
5Baylor100.00%64.81%30.08%12.26%5.59%1.81%0.57%
12Yale100.00%35.19%11.64%3.20%1.01%0.21%0.04%
4Duke100.00%83.02%53.56%26.93%14.88%6.11%2.46%
13North Carolina-Wilmington100.00%16.98%4.71%0.83%0.17%0.02%0.00%
6Texas100.00%70.36%27.90%10.10%3.45%0.88%0.22%
11Northern Iowa100.00%29.64%6.83%1.35%0.25%0.03%0.00%
3Texas A&M100.00%93.88%64.45%31.80%15.01%5.53%1.99%
14Green Bay100.00%6.12%0.83%0.05%0.00%0.00%0.00%
7Oregon State100.00%30.28%8.45%2.94%0.79%0.15%0.03%
10Virginia Commonwealth100.00%69.72%31.67%17.19%7.77%2.72%0.93%
2Oklahoma100.00%93.11%59.04%36.47%19.31%8.15%3.38%
15Cal State Bakersfield100.00%6.89%0.84%0.10%0.01%0.00%0.00%
South
1Kansas100.00%98.36%73.00%52.56%29.76%19.86%10.98%
16Austin Peay100.00%1.64%0.08%0.00%0.00%0.00%0.00%
8Colorado100.00%31.57%5.61%1.96%0.43%0.13%0.03%
9Connecticut100.00%68.43%21.31%11.30%4.17%1.95%0.69%
5Maryland100.00%77.22%42.17%15.21%5.55%2.57%0.89%
12South Dakota State100.00%22.78%6.38%0.96%0.15%0.03%0.00%
4California100.00%80.86%46.49%17.34%6.54%3.11%1.12%
13Hawaii100.00%19.14%4.96%0.65%0.09%0.02%0.00%
6Arizona100.00%53.24%26.91%9.68%4.10%2.01%0.75%
11Wichita State100.00%46.76%22.23%7.39%2.91%1.33%0.46%
3Miami (FL)100.00%88.02%49.10%19.51%9.05%4.81%1.99%
14Buffalo100.00%11.98%1.76%0.17%0.02%0.00%0.00%
7Iowa100.00%82.06%24.07%11.20%4.46%2.06%0.72%
10Temple100.00%17.94%1.76%0.29%0.04%0.01%0.00%
2Villanova100.00%95.70%73.51%51.69%32.73%22.89%13.47%
15UNC Asheville100.00%4.30%0.67%0.07%0.01%0.00%0.00%
Midwest
1Virginia100.00%99.08%82.19%53.20%31.68%19.09%11.27%
16Hampton100.00%0.92%0.04%0.00%0.00%0.00%0.00%
8Texas Tech100.00%43.12%6.72%1.77%0.41%0.09%0.02%
9Butler100.00%56.88%11.05%3.49%0.97%0.26%0.07%
5Purdue100.00%88.00%63.28%30.82%16.22%8.58%4.44%
12Arkansas-Little Rock100.00%12.00%3.42%0.46%0.07%0.01%0.00%
4Iowa State100.00%81.10%30.62%9.96%3.61%1.28%0.44%
13Iona100.00%18.90%2.68%0.30%0.04%0.00%0.00%
6Seton Hall100.00%48.85%23.13%6.20%1.68%0.49%0.14%
11Gonzaga100.00%51.15%24.76%6.84%1.91%0.58%0.17%
3Utah100.00%84.64%49.04%16.36%5.55%2.04%0.73%
14Fresno State100.00%15.36%3.07%0.29%0.03%0.00%0.00%
7Dayton100.00%58.69%15.43%7.99%2.50%0.85%0.28%
10Syracuse100.00%41.31%8.54%3.69%0.91%0.24%0.06%
2Michigan State100.00%94.78%75.11%58.47%34.42%21.45%13.10%
15Middle Tennessee100.00%5.22%0.92%0.16%0.01%0.00%0.00%
East
1North Carolina100.00%97.62%79.20%46.66%28.62%14.57%8.00%
16*Florida Gulf Coast74.22%2.12%0.24%0.01%0.00%0.00%0.00%
16*Fairleigh Dickinson25.78%0.26%0.01%0.00%0.00%0.00%0.00%
8USC100.00%60.37%13.88%4.04%1.27%0.29%0.08%
9Providence100.00%39.63%6.67%1.44%0.34%0.06%0.01%
5Indiana100.00%86.21%38.46%16.74%8.07%3.05%1.27%
12Chattanooga100.00%13.79%1.85%0.23%0.03%0.00%0.00%
12null0.00%0.00%0.00%0.00%0.00%0.00%0.00%
4Kentucky100.00%87.33%56.67%30.37%17.78%8.53%4.44%
13Stony Brook100.00%12.67%3.02%0.50%0.09%0.01%0.00%
6Notre Dame100.00%55.83%16.61%6.17%1.66%0.40%0.11%
11*Michigan59.86%28.79%8.16%2.89%0.73%0.17%0.04%
11*Tulsa40.14%15.38%3.33%0.90%0.17%0.03%0.01%
3West Virginia100.00%85.48%66.46%42.94%22.76%11.09%5.86%
14Stephen F. Austin100.00%14.52%5.44%1.34%0.23%0.03%0.01%
7Wisconsin100.00%47.71%16.98%6.01%1.70%0.43%0.12%
10Pittsburgh100.00%52.29%19.65%7.33%2.20%0.59%0.18%
2Xavier100.00%94.55%62.82%32.37%14.34%5.78%2.55%
15Weber State100.00%5.45%0.56%0.04%0.00%0.00%0.00%
Totals64.0032.0016.008.004.002.001.00

There is a lot more parity this year: the top 4 most likely winners win the title 39.75% of the time, whereas last year Kentucky ALONE had a 41.77% chance to win it all (the top 4 (Kentucky, Wisconsin, Virginia, Arizona) amounted to almost 75%). 

Take a look at this year's top 10 before the tournament:


Pyth
1Villanova0.957
2Michigan State0.955
3Virginia0.952
4Kansas0.951
5Louisville0.948
6North Carolina0.943
7West Virginia0.938
8Kentucky0.936
9Purdue0.935
10Oregon0.928

Compared to last year's:


Pyth
1Kentucky0.989
2Wisconsin0.978
3Arizona0.977
4Virginia0.977
5Villanova0.970
6Duke0.961
7Gonzaga0.959
8Utah0.958
9North Carolina0.945
10Baylor0.941

Last year there were 8 teams better ratings-wise than this year's #1 team.

Also, I checked. UNC's chances of winning it all are indeed calculated correctly; the totals at the bottom sum exactly as they should. That is 8% to 6 decimal places: 0.08000273131. 

You can't write this stuff.

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