Tuesday, March 14, 2017

NCAA Tournament 2017 Bracket Math for the MDS Model

This year I've done something a little different. After correctly picking the champion last year, I haven't kept up the MDS Model throughout this season, and so I've generated a new set of rankings similar to what I used to sportsbet in Las Vegas. 

I'm taking a composite of 6 different 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)
  • Preseason Polls (has shown to be a predictor of tournament success)
  • Massey Composite (another composite, this time spanning 68 rating systems)
  • Prediction Machine (the only component that is a simulator)
I then use a weighted average of these 6 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 (sorry Mt St Mary's/UC Davis/Providence/Wake Forest).


SeedTeam1st Round2nd RoundSweet 16Elite 8Final FourChampionshipChampion
East
1Villanova100.00%98.43%69.85%45.68%29.02%18.08%11.08%
16*New Orleans100.00%1.57%0.10%0.00%0.00%0.00%0.00%
8Wisconsin100.00%73.55%25.80%12.89%6.18%2.89%1.31%
9Virginia Tech100.00%26.45%4.25%1.16%0.29%0.07%0.02%
5Virginia100.00%81.47%51.23%23.55%12.74%6.73%3.47%
12UNC Wilmington100.00%18.53%5.60%0.94%0.21%0.04%0.01%
4Florida100.00%80.77%39.34%15.27%7.15%3.25%1.44%
13East Tennessee St.100.00%19.23%3.82%0.50%0.09%0.02%0.00%
6SMU100.00%72.88%42.17%19.91%8.37%3.90%1.77%
11*USC100.00%27.12%9.60%2.50%0.54%0.13%0.03%
3Baylor100.00%83.50%44.93%20.16%8.00%3.54%1.52%
14New Mexico St.100.00%16.50%3.30%0.49%0.06%0.01%0.00%
7South Carolina100.00%51.85%13.27%4.83%1.23%0.36%0.10%
10Marquette100.00%48.15%11.66%4.05%0.97%0.27%0.07%
2Duke100.00%95.65%74.33%47.98%25.14%14.31%7.98%
15Troy100.00%4.35%0.75%0.07%0.00%0.00%0.00%
West
1Gonzaga100.00%96.68%76.81%50.88%34.58%19.71%11.73%
16South Dakota St.100.00%3.32%0.52%0.05%0.00%0.00%0.00%
8Northwestern100.00%44.79%9.24%3.05%1.03%0.25%0.07%
9Vanderbilt100.00%55.21%13.43%5.06%1.96%0.56%0.17%
5Notre Dame100.00%69.95%29.46%10.47%4.80%1.67%0.62%
12Princeton100.00%30.05%7.43%1.46%0.39%0.07%0.01%
4West Virginia100.00%86.48%59.35%28.51%16.89%8.08%4.07%
13Bucknell100.00%13.52%3.77%0.53%0.11%0.01%0.00%
6Maryland100.00%46.52%22.88%8.66%2.73%0.83%0.27%
11Xavier100.00%53.48%28.06%11.54%3.99%1.33%0.47%
3Florida St.100.00%83.66%45.87%20.30%7.61%2.75%1.06%
14Florida Gulf Coast100.00%16.34%3.19%0.43%0.05%0.00%0.00%
7Saint Mary's100.00%68.55%34.42%20.65%9.02%3.82%1.71%
10VCU100.00%31.45%10.23%4.21%1.12%0.28%0.08%
2Arizona100.00%94.18%54.80%34.15%15.72%7.03%3.32%
15North Dakota100.00%5.82%0.54%0.06%0.00%0.00%0.00%
Midwest
1Kansas100.00%97.10%69.44%44.80%26.96%15.31%8.18%
16*North Carolina Central100.00%2.90%0.27%0.02%0.00%0.00%0.00%
8Miami FL100.00%49.20%14.73%6.26%2.37%0.83%0.26%
9Michigan St.100.00%50.80%15.56%6.73%2.60%0.92%0.30%
5Iowa St.100.00%74.06%38.61%16.74%7.82%3.40%1.36%
12Nevada100.00%25.94%7.51%1.62%0.38%0.08%0.02%
4Purdue100.00%79.90%48.02%22.71%11.52%5.46%2.40%
13Vermont100.00%20.10%5.86%1.12%0.24%0.04%0.01%
6Creighton100.00%54.47%23.44%9.64%3.82%1.46%0.51%
11Rhode Island100.00%45.53%17.74%6.55%2.32%0.79%0.25%
3Oregon100.00%89.06%56.74%29.93%15.30%7.61%3.52%
14Iona100.00%10.94%2.08%0.27%0.03%0.00%0.00%
7Michigan100.00%55.53%21.00%9.57%3.86%1.51%0.54%
10Oklahoma St.100.00%44.47%14.62%5.88%2.07%0.70%0.22%
2Louisville100.00%96.63%64.11%38.15%20.70%10.93%5.40%
15Jacksonville St.100.00%3.37%0.27%0.02%0.00%0.00%0.00%
South
1North Carolina100.00%97.34%75.80%56.47%32.44%18.68%9.93%
16Texas Southern100.00%2.66%0.33%0.04%0.00%0.00%0.00%
8Arkansas100.00%49.42%11.69%5.42%1.54%0.44%0.11%
9Seton Hall100.00%50.58%12.18%5.71%1.65%0.48%0.12%
5Minnesota100.00%51.72%20.74%5.29%1.33%0.33%0.07%
12Middle Tennessee100.00%48.28%18.61%4.51%1.07%0.26%0.05%
4Butler100.00%83.67%55.88%22.00%8.68%3.43%1.21%
13Winthrop100.00%16.33%4.77%0.56%0.06%0.01%0.00%
6Cincinnati100.00%62.96%31.03%12.26%5.63%2.39%0.91%
11*Kansas St.100.00%37.04%13.75%3.83%1.30%0.39%0.10%
3UCLA100.00%91.27%54.05%23.70%11.89%5.57%2.36%
14Kent St.100.00%8.73%1.17%0.08%0.01%0.00%0.00%
7Dayton100.00%30.13%7.27%2.57%0.83%0.24%0.06%
10Wichita St.100.00%69.87%29.15%16.14%8.27%3.97%1.73%
2Kentucky100.00%95.66%63.11%41.35%25.30%14.77%7.98%
15Northern Kentucky100.00%4.34%0.46%0.05%0.00%0.00%0.00%
Totals64.0032.0016.008.004.002.001.00

I'll include the final ratings as well at the bottom of this post, but here are the top 10 teams:


RankTeamRating
1Villanova93.45
2Gonzaga92.79
3Kentucky91.68
4Kansas91.47
5Duke91.44
6North Carolina91.38
7Louisville90.03
8Virginia89.95
9West Virginia89.50
10Oregon88.91
Note that Gonzaga has the highest win probability in the tournament, yet is actually ranked behind Villanova by almost a full point. The lower probability for Villanova is due to the extremely difficult path the committee put them through, including having to potentially face Wisconsin (#14), Virginia (#8), and Duke (#5) just to get to the Final Four.

Here is the how the bracket flows if you take the highest probable team in each round:

A word of caution though about going straight chalk: in most pools you want to gauge "contrarian" picks relative to the overall pool. That's the reason my model won my pool last year; it had Villanova winning it all when most no one else did. The same goes for my cousin 2 years ago. He simply took my model, substituted Duke for Kentucky as his champion, and won my pool. 

I would use the win probabilities as a jumping off point to gauge more "likely" upsets and make picks that way that make sense. For example, (12) MTSU over (5) Minnesota at 48.28% is more likely than most brackets probably are picking that game. (6) SMU's chances to advance to the Sweet 16 (42.17%) are extremely close to (3) Baylor's (44.93%), which illustrates another opportunity where value probably lies.

Here are the full ratings for all 68 teams:


RankTeamRating
1Villanova93.45
2Gonzaga92.79
3Kentucky91.68
4Kansas91.47
5Duke91.44
6North Carolina91.38
7Louisville90.03
8Virginia89.95
9West Virginia89.50
10Oregon88.91
11Arizona88.38
12Purdue88.07
13Wichita St.87.94
14Wisconsin87.74
15SMU87.71
16UCLA87.54
17Saint Mary's87.52
18Florida87.32
19Baylor86.84
20Iowa St.86.64
21Cincinnati85.94
22Florida St.85.19
23Michigan85.00
24Butler84.88
25Creighton84.72
26Notre Dame84.71
27Xavier84.06
28Michigan St.83.68
29Miami FL83.40
30Rhode Island83.15
31Oklahoma St.83.06
32Maryland82.85
33Vanderbilt82.12
34Kansas St.81.33
35South Carolina81.12
36VCU80.78
37Seton Hall80.77
38Dayton80.68
39Arkansas80.57
40Marquette80.47
41Northwestern80.29
42Wake Forest80.25
43USC79.22
44Minnesota79.12
45Virginia Tech78.96
46Providence78.93
47Middle Tennessee78.52
48Nevada77.64
49UNC Wilmington77.46
50Princeton77.41
51Vermont76.38
52East Tennessee St.75.19
53Bucknell74.12
54New Mexico St.73.26
55Iona71.75
56Florida Gulf Coast71.51
57Winthrop71.20
58Kent St.68.60
59Northern Kentucky67.80
60Troy67.57
61South Dakota St.67.19
62North Dakota66.48
63North Carolina Central65.03
64Jacksonville St.64.51
65Texas Southern64.43
66New Orleans63.45
67UC Davis62.96
68Mount St. Mary's61.67

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