Sunday, March 15, 2015

NCAA tourney odds - 2015

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 today, 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 ESPN bracket (top left, top right, bottom left, bottom right) and list the probability of the team reaching the various rounds of the tournament.  I'll also BOLD the team with the highest win probability of reaching each position so the reader can easily see the most likely outcome:

TOP RIGHT Pyth Round 1 Sweet 16 Elite 8 Final 4 Finals Champs
Kentucky 1 0.9787 97.5% 89.3% 81.1% 67.6% 45.7% 33.5%
Manhattan 16 0.5411 2.5% 0.6% 0.1% 0.0% 0.0% 0.0%
Cincinnati 8 0.8242 56.6% 6.2% 3.2% 1.1% 0.2% 0.1%
Purdue 9 0.7825 43.4% 3.9% 1.7% 0.5% 0.1% 0.0%
West Virginia 5 0.8539 62.8% 37.1% 6.1% 2.4% 0.6% 0.2%
Buffalo 12 0.7759 37.2% 17.2% 1.9% 0.5% 0.1% 0.0%
Maryland 4 0.8289 61.8% 31.0% 4.5% 1.6% 0.3% 0.1%
Valparaiso 13 0.7499 38.2% 14.7% 1.5% 0.4% 0.1% 0.0%
Butler 6 0.8624 47.8% 20.5% 8.7% 1.8% 0.4% 0.1%
Texas 11 0.8725 52.2% 23.4% 10.4% 2.3% 0.6% 0.2%
Notre Dame 3 0.9127 87.5% 53.8% 29.4% 8.3% 2.8% 1.1%
Northeastern 14 0.598 12.5% 2.3% 0.4% 0.0% 0.0% 0.0%
Wichita State 7 0.9044 73.2% 39.3% 21.0% 5.6% 1.8% 0.7%
Indiana 10 0.7762 26.8% 8.5% 2.6% 0.4% 0.1% 0.0%
Kansas 2 0.9111 83.6% 48.6% 26.9% 7.5% 2.5% 1.0%
New Mexico State 15 0.6674 16.4% 3.7% 0.8% 0.1% 0.0% 0.0%

BOTTOM RIGHT Pyth Round 1 Sweet 16 Elite 8 Final 4 Finals Champ
Wisconsin 1 0.9615 95.6% 81.9% 64.5% 36.3% 17.4% 10.5%
Coastal Carolina 16 0.5371 4.4% 1.0% 0.2% 0.0% 0.0% 0.0%
Oregon 8 0.7972 47.3% 7.8% 3.0% 0.6% 0.1% 0.0%
Oklahoma State 9 0.8141 52.7% 9.4% 3.9% 0.8% 0.1% 0.0%
Arkansas 5 0.8416 73.1% 31.7% 7.8% 1.9% 0.4% 0.1%
Wofford 12 0.6617 26.9% 6.2% 0.8% 0.1% 0.0% 0.0%
North Carolina 4 0.9019 79.3% 54.3% 18.8% 6.5% 1.9% 0.7%
Harvard 13 0.7059 20.7% 7.8% 1.1% 0.1% 0.0% 0.0%
Xavier 6 0.8518 52.4% 23.4% 5.2% 1.5% 0.3% 0.1%
BYU 11 0.8395 47.6% 20.3% 4.2% 1.1% 0.2% 0.1%
Baylor 3 0.9038 77.3% 48.7% 15.0% 5.8% 1.7% 0.6%
Georgia State 14 0.7344 22.7% 7.6% 1.0% 0.2% 0.0% 0.0%
VCU 17 0.7499 31.3% 3.4% 1.1% 0.2% 0.0% 0.0%
Ohio State 10 0.868 68.7% 13.6% 6.7% 2.1% 0.5% 0.1%
Arizona 2 0.9674 97.7% 82.7% 66.8% 42.7% 22.1% 14.2%
Texas Southern 15 0.4111 2.3% 0.3% 0.0% 0.0% 0.0% 0.0%

TOP LEFT Pyth Round 1 Sweet 16 Elite 8 Final 4 Finals Champ
Villanova 1 0.9571 96.7% 81.5% 60.2% 35.8% 23.0% 10.0%
Lafayette 16 0.4285 3.3% 0.5% 0.0% 0.0% 0.0% 0.0%
North Carolina State 8 0.8111 51.7% 9.5% 3.5% 0.8% 0.2% 0.0%
LSU 9 0.8006 48.3% 8.5% 3.0% 0.7% 0.2% 0.0%
Northern Iowa 5 0.908 84.9% 54.2% 20.6% 8.4% 3.8% 1.0%
Wyoming 12 0.6373 15.1% 3.9% 0.5% 0.1% 0.0% 0.0%
Louisville 4 0.8756 78.7% 37.3% 11.7% 3.9% 1.5% 0.3%
UC Irvine 13 0.6559 21.3% 4.6% 0.6% 0.1% 0.0% 0.0%
Providence 6 0.8458 56.9% 22.1% 5.8% 1.7% 0.5% 0.1%
Dayton 11 0.8057 43.1% 14.2% 3.1% 0.7% 0.2% 0.0%
Oklahoma 3 0.915 89.1% 61.3% 24.3% 10.4% 4.9% 1.4%
Albany 14 0.5686 10.9% 2.3% 0.2% 0.0% 0.0% 0.0%
Michigan State 7 0.8786 61.7% 16.5% 8.0% 2.7% 1.0% 0.2%
Georgia 10 0.8178 38.3% 7.4% 2.7% 0.7% 0.2% 0.0%
Virginia 2 0.9587 95.3% 75.4% 55.8% 33.8% 22.0% 9.7%
Belmont 15 0.5363 4.7% 0.8% 0.1% 0.0% 0.0% 0.0%


BOTTOM LEFT Pyth Round 1 Sweet 16 Elite 8 Final 4 Finals Champ
Duke 1 0.9395 93.3% 71.0% 45.2% 26.3% 12.6% 4.5%
North Florida 12 0.5258 6.7% 1.2% 0.2% 0.0% 0.0% 0.0%
San Diego State 8 0.8468 57.7% 17.3% 6.9% 2.4% 0.6% 0.1%
St. John's 9 0.8019 42.3% 10.4% 3.4% 0.9% 0.2% 0.0%
Utah 5 0.9275 74.0% 52.0% 27.7% 14.8% 6.4% 2.0%
Stephen F. Austin 12 0.8183 26.0% 12.2% 3.7% 1.1% 0.2% 0.0%
Georgetown 4 0.867 83.6% 33.7% 12.8% 4.8% 1.4% 0.3%
Eastern Washington 13 0.5618 16.4% 2.1% 0.2% 0.0% 0.0% 0.0%
SMU 6 0.8734 62.5% 29.7% 11.0% 4.3% 1.3% 0.3%
UCLA 11 0.8056 37.5% 13.6% 3.6% 1.0% 0.2% 0.0%
Iowa State 3 0.9047 86.5% 53.9% 23.8% 11.0% 4.0% 1.0%
UAB 14 0.5979 13.5% 2.8% 0.3% 0.0% 0.0% 0.0%
Iowa 7 0.8594 55.3% 16.7% 7.6% 2.7% 0.8% 0.1%
Davidson 10 0.8319 44.7% 11.8% 4.8% 1.5% 0.4% 0.1%
Gonzaga 2 0.944 93.8% 70.5% 48.7% 29.0% 14.5% 5.4%
North Dakota St. 15 0.5258 6.2% 1.0% 0.1% 0.0% 0.0% 0.0%
With so many games, we expect to see some "unlikely" winners into the round of 32, but as the tourney progresses, these unexpected winners will eventually fall out.  Looking into the latter rounds, it seems that Kentucky, with the overall 1 seed, has a gaudy 1 in 3 chance of winning the tourney.  

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