Monday, March 14, 2016

NCAA tournament projections - 2016

Selection Sunday is like the Christmas Day of College Basketball Fans.  After a lot of speculating, we finally get to see where our favorite teams landed or do some statistical estimation regarding roads to the Final Four.  With the bracket set yesterday, we can finally do some math!

Thanks to Ken Pomeroy we can compute a win probability for any match-up based on the teams' respective Pythagorean win percentage.  In turn, using the probabilities from previous rounds, we can estimate the likelihood of a team advancing to any round once the tourney schedule is set.  In theory this allows us to see the most likely winners in each slot of a potentially completed bracket.

Instead of titling by the ridiculously misleading regions, I'll just describe them by where they appear on the standard bracket (top left, top right, bottom left, bottom right) and list the probability of the team reaching the various rounds of the tournament.  I advanced the favorite in each of the play-in games, but will update as that changes.  Finally, use the BOLD to track the teams with the highest win probability of reaching each position:

TOP RIGHT Pyth Round 1 Sweet 16 Elite 8 Final 4 Finals Champs
Kansas 1 0.9503 96.9% 75.5% 57.4% 37.3% 26.0% 15.4%
Austin Peay 16 0.3819 3.1% 0.3% 0.0% 0.0% 0.0% 0.0%
Colorado 8 0.7788 34.9% 6.2% 2.3% 0.6% 0.2% 0.0%
Connecticut 9 0.8677 65.1% 18.0% 9.5% 3.8% 1.7% 0.6%
Maryland 5 0.8725 72.6% 39.9% 13.4% 5.4% 2.5% 0.9%
South Dakota St. 12 0.7209 27.4% 8.8% 1.5% 0.3% 0.1% 0.0%
California 4 0.8767 68.8% 39.3% 13.5% 5.6% 2.6% 0.9%
Hawaii 13 0.7635 31.2% 12.0% 2.4% 0.6% 0.2% 0.0%
Arizona 6 0.8927 90.8% 48.8% 21.6% 9.0% 4.6% 1.8%
Wichita St 11 0.4579 9.2% 1.2% 0.1% 0.0% 0.0% 0.0%
Miami FL 3 0.8971 86.7% 47.5% 21.6% 9.2% 4.8% 1.9%
Buffalo 14 0.5727 13.3% 2.4% 0.3% 0.0% 0.0% 0.0%
Iowa 7 0.8832 76.2% 29.9% 14.5% 5.8% 2.8% 1.0%
Temple 10 0.703 23.8% 4.5% 1.0% 0.2% 0.0% 0.0%
Villanova 2 0.9352 89.9% 63.3% 40.5% 22.1% 14.0% 7.3%
UNC Asheville 15 0.6194 10.1% 2.4% 0.4% 0.1% 0.0% 0.0%

Unsurprisingly, the overall number 1 seed is the favorite (15% probability), which isn't far off from the implied probability under the 1:5 odds posted on a popular Vegas book.  Indeed, this method tends to yield boring picks, like often picking the higher seed.  However, it seems like there are some interesting "underdogs" to pick to the sweet 16 this year in Maryland and Arizona.

BOTTOM LEFT Pyth Round 1 Sweet 16 Elite 8 Final 4 Finals Champ
Oregon 1 0.9123 96.6% 65.7% 41.9% 23.9% 11.0% 4.9%
Holy Cross 16 0.2702 3.4% 0.2% 0.0% 0.0% 0.0% 0.0%
Saint Joseph's 8 0.8159 45.5% 14.6% 6.3% 2.3% 0.6% 0.2%
Cinncinati 9 0.8414 54.5% 19.5% 9.3% 3.8% 1.2% 0.4%
Baylor 5 0.8705 60.7% 33.5% 15.3% 7.1% 2.6% 0.9%
Yale 12 0.8132 39.3% 17.6% 6.3% 2.3% 0.6% 0.2%
Duke 4 0.8752 72.3% 39.9% 18.7% 8.9% 3.3% 1.2%
UNC Wilmington 13 0.729 27.7% 9.0% 2.3% 0.6% 0.1% 0.0%
Texas 6 0.8487 68.1% 31.7% 13.6% 5.9% 1.9% 0.6%
Northern Iowa 11 0.724 31.9% 9.6% 2.6% 0.7% 0.1% 0.0%
Texas A&M 3 0.8923 83.6% 54.2% 28.2% 14.9% 6.1% 2.4%
Green Bay 14 0.619 16.4% 4.5% 0.9% 0.2% 0.0% 0.0%
Oregon St. 7 0.7691 41.3% 11.8% 4.2% 1.3% 0.3% 0.1%
VCU 10 0.8259 58.7% 20.9% 9.1% 3.6% 1.0% 0.3%
Oklahoma 2 0.9199 83.8% 61.6% 39.8% 24.1% 11.7% 5.5%
Cal St. Bakersfield 15 0.6902 16.2% 5.7% 1.6% 0.4% 0.1% 0.0%

To comment on interesting upsets, it looks like VCU should beat Oregon state this year.  If you're the type of person who always picks a 5-12 upset, Yale seems the better bet to upset (~40% win probability, UPDATE, they just beat Baylor...statistics, baby!).  Finally, while Texas A&M would have been a nice sleeper here, the stronger Oklahoma looks poised to make a run to the final 4, provided they can edge out Oregon what looks to be a coin flip of a game (UPDATE: Holy Cross Victory makes slightly easier path for Oregon, giving them a small edge now over Oklahoma).

Team Pyth Round 1 Sweet 16 Elite 8 Final 4 Finals Champ
North Carolina 1 0.9407 94.7% 75.9% 48.0% 32.1% 17.5% 10.2%
Florida Gulf Coast 16 0.4686 5.3% 1.0% 0.1% 0.0% 0.0% 0.0%
USC 8 0.7946 49.3% 11.3% 3.5% 1.2% 0.3% 0.1%
Providence 9 0.7991 50.7% 11.8% 3.7% 1.3% 0.3% 0.1%
Indiana 5 0.8959 81.9% 40.0% 17.4% 9.2% 3.7% 1.6%
Chattanooga 12 0.6557 18.1% 3.5% 0.6% 0.1% 0.0% 0.0%
Kentucky 4 0.9198 83.2% 51.9% 25.9% 15.4% 7.2% 3.7%
Stony Brook 13 0.6979 16.8% 4.6% 0.9% 0.2% 0.0% 0.0%
Notre Dame 6 0.8131 55.4% 17.9% 7.3% 2.1% 0.5% 0.2%
Michigan 11 0.7778 44.6% 12.4% 4.5% 1.1% 0.2% 0.1%
West Virginia 3 0.9236 70.1% 52.8% 34.4% 17.5% 8.4% 4.4%
Stephen F. Austin 14 0.8378 29.9% 17.0% 7.6% 2.4% 0.7% 0.2%
Wisconsin 7 0.839 56.2% 24.6% 10.2% 3.2% 1.0% 0.3%
Pittsburgh 10 0.8024 43.8% 16.7% 6.0% 1.6% 0.4% 0.1%
Xavier 2 0.8946 86.4% 55.7% 29.5% 12.5% 5.0% 2.2%
Weber State 15 0.5717 13.6% 3.0% 0.5% 0.1% 0.0% 0.0%

With the exception of West Virginia to the Elite 8, there's not much excitement here.

BOTTOM RIGHT Pyth Round 1 Sweet 16 Elite 8 Final 4 Finals Champ
Virginia 1 0.9482 97.0% 78.5% 54.9% 34.5% 21.6% 13.3%
Hampton 16 0.3639 3.0% 0.4% 0.0% 0.0% 0.0% 0.0%
Texas Tech 8 0.8096 49.5% 10.4% 3.7% 1.1% 0.3% 0.1%
Butler 9 0.8129 50.5% 10.8% 3.9% 1.2% 0.4% 0.1%
Purdue 5 0.9078 71.4% 43.1% 18.3% 8.9% 4.3% 2.0%
Arkansas Little Rock 12 0.7978 28.6% 11.2% 2.7% 0.8% 0.2% 0.1%
Iowa State 4 0.8919 75.2% 39.0% 15.1% 6.7% 2.9% 1.3%
Iona 13 0.731 24.8% 6.7% 1.3% 0.3% 0.1% 0.0%
Seton Hall 6 0.8674 51.4% 30.2% 11.1% 3.9% 1.5% 0.6%
Gonzaga 11 0.8609 48.6% 27.9% 9.9% 3.4% 1.3% 0.5%
Utah 3 0.8547 75.2% 36.1% 12.5% 4.2% 1.5% 0.5%
Fresno State 14 0.6595 24.8% 5.8% 0.9% 0.1% 0.0% 0.0%
Dayton 7 0.7806 45.3% 9.7% 3.7% 0.9% 0.2% 0.1%
Syracuse 10 0.8111 54.7% 13.3% 5.7% 1.5% 0.5% 0.1%
Michigan State 2 0.945 92.2% 74.9% 55.8% 32.3% 19.7% 11.9%
Middle Tennessee 15 0.5926 7.8% 2.1% 0.4% 0.1% 0.0% 0.0%

Looks like Virginia is the favorite to match-up against Kansas in the finals, and we have two interesting picks in Syracuse over Dayton in the opening round and Purdue to advance to the sweet 16 (over Iowa State).

To summarize, the expected "upsets" in the opening round are all 9 seeds and two 10 seeds (Syracuse and VCU), which is pretty conservative as we're simply selecting the favorite (highest probability).  Into the sweet 16, we expect Maryland, Arizona, and Purdue to win over the respective 3 and 4 seeds they're likely to match up against.  West Virginia is the only surprise to the elite 8, and Oklahoma is the only possible surprise to the final 4.  Bear in mind these overview estimates don't consider potential home court advantage or match-up issues, so if you have an inkling about a team because they are close to home or match up well, you are wise to deviate at your own discretion.

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