Sunday, March 15, 2015

NCAA Tournament Bracket Math for the MDS Model

Quick turnaround this year:

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


Note: The winning score prediction was gathered from Massey Ratings.


Round-by-round win probabilities:

SeedTeam1st Round2nd RoundSweet 16Elite 8Final FourChampionshipChampion
Midwest
1Kentucky100.00%99.19%92.69%87.49%78.53%55.48%41.77%
16*Manhattan81.98%0.67%0.08%0.01%0.00%0.00%0.00%
16*Hampton18.02%0.18%0.02%0.00%0.00%0.00%0.00%
8Cincinnati100.00%67.69%5.66%3.38%1.46%0.27%0.06%
9Purdue100.00%32.31%1.57%0.66%0.18%0.02%0.00%
5West Virginia100.00%66.78%41.74%4.30%1.74%0.30%0.06%
12Buffalo100.00%33.22%15.31%0.91%0.23%0.02%0.00%
4Maryland100.00%73.06%35.78%2.99%1.02%0.14%0.02%
13Valparaiso100.00%26.94%7.17%0.26%0.04%0.00%0.00%
6Butler100.00%45.98%24.31%10.72%1.57%0.31%0.07%
11Texas100.00%54.02%30.59%14.68%2.39%0.54%0.14%
3Notre Dame100.00%88.13%43.70%20.01%3.07%0.65%0.16%
14Northeastern100.00%11.87%1.39%0.15%0.01%0.00%0.00%
7Wichita State100.00%69.03%34.72%19.07%3.31%0.80%0.23%
10Indiana100.00%30.97%10.13%3.60%0.36%0.05%0.01%
2Kansas100.00%89.41%53.47%31.52%6.08%1.65%0.52%
15New Mexico State100.00%10.59%1.68%0.25%0.01%0.00%0.00%
West
1Wisconsin100.00%98.47%89.75%69.40%42.08%18.63%11.43%
16Coastal Carolina100.00%1.53%0.22%0.01%0.00%0.00%0.00%
8Oregon100.00%39.88%3.23%0.75%0.10%0.01%0.00%
9Oklahoma State100.00%60.12%6.80%2.07%0.37%0.04%0.01%
5Arkansas100.00%86.91%29.01%5.26%1.15%0.17%0.04%
12Wofford100.00%13.09%1.11%0.04%0.00%0.00%0.00%
4North Carolina100.00%88.73%66.46%22.20%8.80%2.38%0.93%
13Harvard100.00%11.27%3.42%0.27%0.02%0.00%0.00%
6Xavier100.00%59.35%22.52%4.51%0.97%0.16%0.04%
11*Brigham Young52.55%21.36%6.47%0.97%0.16%0.02%0.00%
11*Ole Miss47.45%18.14%5.50%0.82%0.13%0.02%0.00%
3Baylor100.00%86.59%48.83%16.31%5.73%1.48%0.55%
14Georgia State100.00%13.41%22.18%1.77%0.16%0.01%0.00%
7Virginia Commonwealth100.00%34.60%5.31%2.53%0.55%0.09%0.02%
10Ohio State100.00%65.40%16.56%10.21%3.37%0.82%0.29%
2Arizona100.00%99.62%78.13%63.72%36.55%15.94%9.66%
15Texas Southern100.00%0.38%0.01%0.00%0.00%0.00%0.00%
East
1Villanova100.00%97.50%83.64%64.72%34.25%20.98%7.68%
16Lafayette100.00%2.50%0.35%0.03%0.00%0.00%0.00%
8North Carolina State100.00%63.56%11.65%4.83%1.00%0.25%0.03%
9LSU100.00%36.44%4.36%1.28%0.18%0.03%0.00%
5Northern Iowa100.00%89.50%38.17%9.34%2.10%0.57%0.07%
12Wyoming100.00%10.50%1.04%0.05%0.00%0.00%0.00%
4Louisville100.00%89.69%58.66%19.61%6.10%2.27%0.42%
13UC Irvine100.00%10.31%2.13%0.14%0.01%0.00%0.00%
6Providence100.00%65.79%21.08%3.49%0.83%0.19%0.02%
11*Boise State48.42%16.57%3.39%0.33%0.05%0.01%0.00%
11*Dayton51.58%18.39%3.76%0.37%0.05%0.01%0.00%
3Oklahoma100.00%96.91%57.68%17.27%6.90%2.78%0.57%
14Albany100.00%3.09%17.85%0.29%0.01%0.00%0.00%
7Michigan State100.00%72.47%16.25%9.92%3.69%1.38%0.26%
10Georgia100.00%27.53%2.89%1.21%0.24%0.05%0.00%
2Virginia100.00%98.49%80.75%67.47%44.64%30.28%13.05%
15Belmont100.00%1.51%0.11%0.02%0.00%0.00%0.00%
South
1Duke100.00%98.05%81.28%48.64%29.55%13.58%4.26%
16*Robert Morris66.52%1.30%0.12%0.00%0.00%0.00%0.00%
16*North Florida33.48%0.99%0.09%0.00%0.00%0.00%0.00%
8San Diego State100.00%59.90%12.06%3.41%0.98%0.18%0.02%
9St. John100.00%40.10%6.55%1.40%0.30%0.04%0.00%
5Utah100.00%88.63%66.28%36.15%21.39%9.49%2.85%
12Stephen F. Austin100.00%11.37%3.43%0.54%0.09%0.01%0.00%
4Georgetown100.00%90.14%29.67%9.82%3.61%0.89%0.13%
13Eastern Washington100.00%9.86%0.62%0.04%0.00%0.00%0.00%
6Southern Methodist100.00%75.47%36.62%12.87%4.12%1.04%0.16%
11UCLA100.00%24.53%6.23%1.00%0.14%0.01%0.00%
3Iowa State100.00%90.65%55.69%22.28%8.21%2.42%0.45%
14UAB100.00%9.35%1.46%0.11%0.01%0.00%0.00%
7Iowa100.00%66.39%16.68%7.25%1.99%0.43%0.06%
10Davidson100.00%33.61%5.07%1.45%0.24%0.03%0.00%
2Gonzaga100.00%98.11%78.11%55.04%29.38%13.11%3.96%
15North Dakota State100.00%1.89%0.14%0.01%0.00%0.00%0.00%

It's unlikely anyone stops Kentucky from going undefeated. I have Kentucky's Pyth rating at 0.989, which is extremely high (KenPom has them at 0.979), and yet I still only (yeah, only) have them winning the title 41.77% of the time. This is very, very high (for example, compared to the most likely champion by MDS last year, Arizona, which only had odds of 23.63% to win it all), and yet they're STILL overvauled by the sportsbooks, where you can get them at 1/1 odds (which implies 50%).

I have a few value bets for winning it all:
TeamImplied OddsMDS OddsValue
Virginia5.56%13.05%7.49%
Arizona7.69%9.66%1.97%
Utah1.79%2.85%1.06%


So UNC is at 66.46% to make the second weekend (Los Angeles), and 8.80% to make the Final Four (Indianapolis).

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