THE BLOG
05/14/2010 05:12 am ET Updated May 25, 2011

NCAA Predictions via Simulation

Using the well-known and highly respected Sagarin Ratings 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 tournament (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 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
Gtown 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
Wisc 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
Tex 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 Mex 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
Ga. 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
St. Mary's 0.469 0.349 0.108 0.052 0.016 0.005 0.002
N 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
SD State 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
Wash 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 Dom 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
N 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
SamHous 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
UCSB 0.914 0.070 0.014 0.002 0.000 0.000 0.000
MorganSt. 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
E Tenn St. 0.969 0.028 0.003 0.000 0.000 0.000 0.000
RobMorris 0.971 0.027 0.002 0.000 0.000 0.000 0.000
Play In 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.

Hope this helps you win your pool!