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 |