March 14, 2010

NCAA Tourney Odds

Filed under: Uncategorized — wwinston @ 8:10 pm

Using the well-known and highly respected  Sagarin Ratings (found at http://www.usatoday.com/sports/sagarin/bkt0910.htm)

I have “simulated” the NCAA Men’s tourney 5000 times. For each team, the table below gives the chance of the team winning 0, 1, 2, 3, 4, 5, or 6 games.

For example, we see Kansas has a 31.9% chance of winning the tournment (winning 6 games ), a 44.6% chance of making the final game (winning 5 or 6 games) and a 60% Chance (winning 4, 5, or 6 games) of making the final 4. See below the table (or Chapter 43 of my book Mathletics) for how I ran the simulation. The table makes it clear that Kansas has by far the best chance of winning the tourney. There is around a 38% chance that a non 1 seed wins the tourney.

Team 0 1 2 3 4 5 6
Kansas 0.004 0.117 0.141 0.138 0.154 0.127 0.319
Duke 0.009 0.223 0.215 0.177 0.135 0.119 0.121
Syracuse 0.033 0.239 0.175 0.194 0.180 0.070 0.108
Kentucky 0.031 0.299 0.208 0.172 0.130 0.087 0.074
West Va. 0.044 0.304 0.192 0.202 0.114 0.079 0.067
Kan St 0.044 0.371 0.198 0.176 0.130 0.037 0.043
Villanova 0.029 0.310 0.259 0.211 0.094 0.060 0.037
Baylor 0.110 0.287 0.286 0.170 0.079 0.042 0.026
Georgetown 0.102 0.346 0.238 0.211 0.052 0.031 0.020
Ohio St 0.086 0.321 0.268 0.229 0.053 0.026 0.018
Purdue 0.267 0.297 0.261 0.083 0.050 0.027 0.015
Wisconsin 0.180 0.350 0.276 0.099 0.052 0.027 0.015
BYU  0.293 0.377 0.125 0.102 0.067 0.020 0.015
Temple 0.315 0.310 0.228 0.078 0.041 0.018 0.010
Maryland 0.142 0.335 0.397 0.059 0.041 0.016 0.010
Texas 0.339 0.410 0.118 0.066 0.038 0.021 0.009
Pitt 0.165 0.386 0.268 0.107 0.053 0.012 0.009
Texas A & M 0.389 0.299 0.194 0.063 0.033 0.013 0.008
Butler 0.443 0.239 0.203 0.065 0.033 0.009 0.008
New Mexico 0.174 0.386 0.269 0.107 0.040 0.017 0.007
Xavier 0.373 0.275 0.209 0.086 0.041 0.009 0.006
Marquette 0.421 0.262 0.195 0.076 0.027 0.014 0.005
Mich St 0.187 0.412 0.320 0.047 0.020 0.008 0.005
Tennesee 0.406 0.317 0.140 0.103 0.021 0.009 0.005
Vandy 0.333 0.325 0.223 0.070 0.035 0.008 0.005
Missouri 0.481 0.332 0.093 0.059 0.020 0.010 0.004
Georgia Tech 0.486 0.308 0.123 0.065 0.011 0.003 0.003
Clemson 0.519 0.324 0.073 0.052 0.019 0.010 0.003
Fla. St. 0.449 0.393 0.081 0.047 0.023 0.005 0.002
Saint Mary’s 0.469 0.349 0.108 0.052 0.016 0.005 0.002
Notre Dame 0.488 0.319 0.121 0.053 0.011 0.005 0.002
Cal 0.459 0.406 0.080 0.032 0.017 0.005 0.002
San Diego St 0.594 0.250 0.094 0.050 0.008 0.002 0.002
Okla St. 0.514 0.302 0.111 0.058 0.011 0.003 0.001
Richmond 0.531 0.315 0.094 0.041 0.014 0.004 0.001
UTEP 0.557 0.212 0.165 0.041 0.017 0.005 0.001
Utah  St 0.611 0.239 0.111 0.025 0.010 0.003 0.001
N Iowa 0.469 0.462 0.038 0.019 0.007 0.004 0.001
UNLV 0.531 0.418 0.031 0.013 0.005 0.002 0.001
Gonzaga 0.551 0.339 0.059 0.034 0.013 0.003 0.001
Louisville 0.541 0.362 0.058 0.025 0.009 0.004 0.001
Washington 0.579 0.215 0.142 0.042 0.015 0.005 0.001
Minn 0.627 0.207 0.119 0.034 0.011 0.002 0.001
Florida 0.707 0.211 0.048 0.024 0.007 0.002 0.001
Old Dominion 0.512 0.303 0.112 0.051 0.016 0.005 0.001
Wake 0.661 0.264 0.046 0.019 0.007 0.002 0.000
Murray St. 0.667 0.223 0.089 0.015 0.004 0.001 0.000
Cornell 0.685 0.203 0.082 0.021 0.006 0.003 0.000
Siena 0.733 0.165 0.081 0.015 0.005 0.002 0.000
New Mex St 0.813 0.146 0.039 0.001 0.001 0.000 0.000
Wofford 0.820 0.136 0.040 0.003 0.001 0.000 0.000
Montana 0.826 0.136 0.034 0.004 0.000 0.000 0.000
Oakland 0.835 0.131 0.029 0.004 0.001 0.000 0.000
Houston 0.858 0.107 0.033 0.001 0.001 0.000 0.000
Sam Houston 0.890 0.090 0.017 0.003 0.000 0.000 0.000
Ohio 0.898 0.087 0.012 0.002 0.000 0.000 0.000
UC Santa Barbara 0.914 0.070 0.014 0.002 0.000 0.000 0.000
Morgan St, 0.956 0.040 0.003 0.001 0.000 0.000 0.000
North Tex 0.956 0.040 0.004 0.000 0.000 0.000 0.000
Vermont 0.967 0.029 0.004 0.000 0.000 0.000 0.000
East Tenn. St. 0.969 0.028 0.003 0.000 0.000 0.000 0.000
Robert Morris 0.971 0.027 0.002 0.000 0.000 0.000 0.000
Play In Game 0.991 0.009 0.000 0.000 0.000 0.000 0.000
Lehigh 0.996 0.003 0.000 0.000 0.000 0.000 0.000

We assumed that the outcome of each game follows a normal random variable with mean margin = Sagarin rating of higher rated team- Sagarin rating of lower rated team and standard deviation 10 points. Then we used the simulation add-in @RISK to play out the tournament 5000 times.

If you want to see the chance a team wins at least a certain number of games look below. So 6 column is chance team wins tourney, 5 column is chance team makes it to final game, 4 column is chance team makes it to Final4, 3 Column is chance team makes it to Regional Final or beyond, 2 Column is chance team makes it to Sweet Sixteen or beyond, and 1 column is chance team wins their opening game.

 

Team 1 2 3 4 5 6
Kansas 0.996 0.879 0.738 0.600 0.446 0.319
Duke 0.991 0.767 0.552 0.375 0.240 0.121
Syracuse 0.967 0.728 0.552 0.358 0.178 0.108
Kentucky 0.969 0.671 0.463 0.291 0.161 0.074
West Va. 0.956 0.653 0.461 0.259 0.146 0.067
Kan St 0.956 0.585 0.387 0.211 0.081 0.043
Villanova 0.971 0.662 0.402 0.191 0.097 0.037
Baylor 0.890 0.603 0.317 0.147 0.068 0.026
Georgetown 0.898 0.552 0.314 0.103 0.051 0.020
Ohio St 0.914 0.594 0.325 0.096 0.043 0.018
Purdue 0.733 0.436 0.176 0.092 0.042 0.015
Wisconsin 0.820 0.470 0.194 0.094 0.042 0.015
BYU  0.707 0.329 0.204 0.102 0.035 0.015
Temple 0.685 0.374 0.147 0.069 0.028 0.010
Maryland 0.858 0.523 0.126 0.067 0.026 0.010
Texas 0.661 0.251 0.134 0.068 0.030 0.009
Pitt 0.835 0.448 0.180 0.073 0.021 0.009
Texas A & M 0.611 0.312 0.118 0.054 0.021 0.008
Butler 0.557 0.318 0.115 0.050 0.017 0.008
New Mexico 0.826 0.440 0.171 0.064 0.024 0.007
Xavier 0.627 0.352 0.143 0.057 0.016 0.006
Marquette 0.579 0.318 0.123 0.047 0.019 0.005
Mich St 0.813 0.401 0.080 0.033 0.013 0.005
Tennesee 0.594 0.277 0.137 0.035 0.013 0.005
Vandy 0.667 0.342 0.118 0.048 0.013 0.005
Missouri 0.519 0.187 0.094 0.034 0.014 0.004
Georgia Tech 0.514 0.206 0.083 0.018 0.007 0.003
Clemson 0.481 0.157 0.084 0.033 0.013 0.003
Fla. St. 0.551 0.158 0.077 0.030 0.007 0.002
Saint Mary’s 0.531 0.183 0.075 0.023 0.007 0.002
Notre Dame 0.512 0.192 0.071 0.019 0.007 0.002
San Diego St 0.406 0.156 0.063 0.012 0.004 0.002
Cal 0.541 0.135 0.055 0.024 0.007 0.002
Okla St. 0.486 0.185 0.073 0.015 0.004 0.001
UTEP 0.443 0.230 0.065 0.024 0.007 0.001
Utah  St 0.389 0.151 0.039 0.015 0.004 0.001
Richmond 0.469 0.154 0.060 0.019 0.005 0.001
UNLV 0.469 0.051 0.021 0.007 0.003 0.001
N Iowa 0.531 0.069 0.031 0.012 0.005 0.001
Gonzaga 0.449 0.110 0.051 0.017 0.004 0.001
Minn 0.373 0.166 0.047 0.014 0.003 0.001
Florida 0.293 0.082 0.034 0.010 0.003 0.001
Washington 0.421 0.205 0.063 0.021 0.006 0.001
Lousiville 0.459 0.097 0.039 0.014 0.005 0.001
Old Dominion 0.488 0.185 0.073 0.021 0.006 0.001
Murray St. 0.333 0.110 0.020 0.006 0.001 0.000
Wake 0.339 0.075 0.029 0.010 0.003 0.000
Cornell 0.315 0.112 0.030 0.009 0.003 0.000
Lehigh 0.004 0.000 0.000 0.000 0.000 0.000
New Mex St 0.187 0.041 0.002 0.001 0.000 0.000
Houston 0.142 0.035 0.002 0.001 0.000 0.000
Ohio 0.102 0.015 0.002 0.000 0.000 0.000
UC Santa Barbara 0.086 0.016 0.002 0.000 0.000 0.000
Vermont 0.033 0.004 0.000 0.000 0.000 0.000
Oakland 0.165 0.034 0.004 0.001 0.000 0.000
North Tex 0.044 0.004 0.000 0.000 0.000 0.000
East Tenn. St. 0.031 0.003 0.000 0.000 0.000 0.000
Wofford 0.180 0.044 0.004 0.001 0.000 0.000
Montana 0.174 0.037 0.004 0.000 0.000 0.000
Morgan St, 0.044 0.003 0.001 0.000 0.000 0.000
Winthrop 0.009 0.000 0.000 0.000 0.000 0.000
Siena 0.267 0.102 0.021 0.006 0.002 0.000
Robert Morris 0.029 0.002 0.000 0.000 0.000 0.000
Sam Houston 0.110 0.020 0.003 0.000 0.000 0.000

9 Comments »

  1. Professor Winston,

    Thanks for the post. I would assume based on the numbers (primarily Purdue), you don’t take into account late season injuries. With the injury to Robbie Hummel, I think Purdue’s chances of advancing past the 3rd round (even advancing past A&M) seems unlikely. Would be curious how you would factor such a variable in.

    -Jim Brown

    Comment by Jim Brown — March 14, 2010 @ 9:00 pm

  2. You are right. The injury is partially accounted for in their rating. I guess I would reduce their rating by say 3 or 4 points and rerun it

    Comment by wwinston — March 14, 2010 @ 9:54 pm

  3. This table would be a lot more useful if instead of listing the probability the team would win that exact number of games, you listed the chance the team would win that number of games or better.

    Comment by ahoy — March 14, 2010 @ 10:38 pm

  4. Thanks. I added it.

    Comment by wwinston — March 14, 2010 @ 11:41 pm

  5. 2 Questions:

    1. I know you are close with Sagarin, so I assume you know the method. The chess rating takes into account W/L record, while the Point rating supposedly gives the best predictive value. Why then are we using a combined metric as opposed to solely the Point rating?

    2. It is assumed that the NCAA tournament games are played on neutral courts, but some of the teams are located fairly close to the game locations or might be in the future rounds. Historically, has there been a “near-court advantage?”

    Comment by Mike — March 15, 2010 @ 12:59 pm

  6. [...] best (or second best) conference has six teams! How can they only be expected to win 7 or 8 games? Wayne Winston had a nicely formatted chart that used the Sagarin Ratings to project out win probabilities for [...]

    Pingback by NCAA Conference Win Totals | Miracle Covers — March 17, 2010 @ 1:21 am

  7. As a previous commentor pointed out, it would be better if these calculations used the Sagarin “PURE POINTS” or “PREDICTOR” values rather than the overall rating. Sagarin describes the “PREDICTOR” rating as the best predictor of future games The overall rating is his way of making the ratings more “polictically correct” and similar to the RPI. It combines the PREDICTOR rating with another rating called ELOC CHESS which only looks at wins and losses and ignores margin of victory.

    Thanks.

    Comment by Russ — March 21, 2010 @ 9:45 pm

  8. [...] Ditto from above, except its not a Duke grad student and he’s using the Sagarin ratings instead of Pomeroy. [Wayne Winston] [...]

    Pingback by Important links for stats nerds — April 25, 2010 @ 12:50 pm

  9. [...] the NCAA tourney there has been a slew of posts (see mathletics, Trick, and Punk Rock OR) using mathematical and statistical modeling to make predictions of the [...]

    Pingback by A Random Forest» Blog Archive » Pythagorean Part 1: Introduction to the "Pythagorean Theorem". — July 19, 2010 @ 2:29 am

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