Ten Thousand 2011 NCAA Tournaments
Posted by Neil Paine on March 14, 2011
Using Ken Pomeroy's ratings and the log5 formula, I set up a Monte Carlo Simulation and ran the 2011 NCAA Tournament 10,000 times. Here was the most likely bracket:
East
Ohio St. | ||||
Ohio St. | ||||
Texas-San Antonio | Ohio St. | |||
George Mason | ||||
George Mason | ||||
Villanova | Ohio St. | |||
West Virginia | ||||
West Virginia | ||||
Clemson | ||||
Kentucky | Kentucky | |||
Kentucky | ||||
Princeton | Ohio St. | |||
Xavier | ||||
Marquette | ||||
Marquette | Syracuse | |||
Syracuse | ||||
Syracuse | ||||
Indiana State | ||||
Washington | Syracuse | |||
Washington | ||||
Georgia | ||||
North Carolina | North Carolina | |||
North Carolina | ||||
Long Island U |
West
Duke | ||||
Duke | ||||
Hampton | Duke | |||
Michigan | ||||
Michigan | ||||
Tennessee | Duke | |||
Arizona | ||||
Arizona | ||||
Memphis | ||||
Texas | Texas | |||
Texas | ||||
Oakland | ||||
Cincinnati | Duke | |||
Cincinnati | ||||
Missouri | Connecticut | |||
Connecticut | ||||
Connecticut | ||||
Bucknell | ||||
Temple | San Diego St. | |||
Temple | ||||
Penn State | ||||
San Diego St. | San Diego St. | |||
San Diego St. | ||||
Northern Colorado |
Southwest
Kansas | ||||
Kansas | ||||
Boston University | Kansas | |||
Nevada Las Vegas | ||||
Illinois | ||||
Illinois | Kansas | |||
Vanderbilt | ||||
Vanderbilt | ||||
Richmond | ||||
Louisville | Louisville | |||
Louisville | ||||
Morehead State | ||||
Georgetown | Kansas | |||
Georgetown | ||||
Southern California | Purdue | |||
Purdue | ||||
Purdue | ||||
Saint Peter's | ||||
Texas A&M | Purdue | |||
Texas A&M | ||||
Florida State | ||||
Notre Dame | Notre Dame | |||
Notre Dame | ||||
Akron |
Southeast
Pittsburgh | ||||
Pittsburgh | ||||
UNC Asheville | Pittsburgh | |||
Butler | ||||
Old Dominion | ||||
Old Dominion | Pittsburgh | |||
Kansas State | ||||
Utah State | ||||
Utah State | ||||
Wisconsin | Wisconsin | |||
Wisconsin | ||||
Belmont | ||||
St. John's | Pittsburgh | |||
Gonzaga | ||||
Gonzaga | BYU | |||
BYU | ||||
BYU | ||||
Wofford | ||||
UCLA | BYU | |||
Michigan State | ||||
Michigan State | ||||
Florida | Florida | |||
Florida | ||||
UC Santa Barbara |
Final Four
Ohio St. | ||
Ohio St. | ||
Duke | ||
Ohio St. | ||
Kansas | National Champions | |
Kansas | ||
Pittsburgh |
In 10,000 simulations, here were the # of times each team reached each round:
Team | Round 1 | Round 2 | Sweet 16 | Elite 8 | Final Four | Chmp. Game | Champions |
---|---|---|---|---|---|---|---|
Ohio St. | 10000 | 9929 | 8509 | 6336 | 4920 | 3246 | 2305 |
Duke | 10000 | 9846 | 8520 | 5690 | 4185 | 2334 | 1523 |
Kansas | 10000 | 9737 | 7386 | 5338 | 3551 | 2390 | 1215 |
Pittsburgh | 10000 | 9560 | 7794 | 4872 | 3302 | 1718 | 769 |
Texas | 10000 | 8780 | 6987 | 3273 | 2031 | 1004 | 580 |
San Diego St. | 10000 | 9303 | 7130 | 4795 | 2041 | 953 | 516 |
Purdue | 10000 | 9258 | 6957 | 4262 | 2132 | 1230 | 501 |
Notre Dame | 10000 | 9238 | 6804 | 3689 | 1761 | 985 | 340 |
Kentucky | 10000 | 8946 | 6172 | 2282 | 1362 | 635 | 329 |
Brigham Young | 10000 | 8686 | 5698 | 3583 | 1690 | 710 | 249 |
Louisville | 10000 | 8812 | 6166 | 2598 | 1301 | 678 | 244 |
Syracuse | 10000 | 9059 | 6259 | 3570 | 1295 | 515 | 244 |
Wisconsin | 10000 | 6199 | 3965 | 2064 | 1290 | 621 | 242 |
North Carolina | 10000 | 9069 | 5260 | 2833 | 923 | 364 | 153 |
Florida | 10000 | 8880 | 5819 | 2970 | 1212 | 437 | 125 |
Washington | 10000 | 7307 | 3800 | 1989 | 646 | 243 | 96 |
Connecticut | 10000 | 8408 | 4958 | 2220 | 669 | 209 | 78 |
Utah St. | 10000 | 5958 | 2601 | 1107 | 584 | 217 | 73 |
Belmont | 10000 | 3801 | 2006 | 821 | 428 | 159 | 49 |
Gonzaga | 10000 | 5294 | 2227 | 1115 | 384 | 115 | 35 |
Cincinnati | 10000 | 5677 | 2814 | 1180 | 320 | 86 | 32 |
Illinois | 10000 | 5215 | 1396 | 658 | 261 | 128 | 31 |
Nevada Las Vegas | 10000 | 4785 | 1203 | 540 | 202 | 81 | 27 |
West Virginia | 10000 | 5797 | 2206 | 531 | 218 | 72 | 26 |
St. John's | 10000 | 4706 | 1793 | 847 | 267 | 86 | 24 |
Arizona | 10000 | 7803 | 2322 | 576 | 214 | 57 | 23 |
Michigan St. | 10000 | 5431 | 2260 | 842 | 252 | 68 | 15 |
Georgetown | 10000 | 6157 | 1967 | 722 | 215 | 67 | 15 |
Vanderbilt | 10000 | 5526 | 2087 | 542 | 186 | 66 | 15 |
Kansas St. | 10000 | 4042 | 1428 | 512 | 226 | 60 | 13 |
Marquette | 10000 | 5272 | 1949 | 752 | 159 | 38 | 13 |
Florida St. | 10000 | 4995 | 1576 | 523 | 121 | 36 | 13 |
George Mason | 10000 | 5065 | 760 | 292 | 114 | 31 | 13 |
Missouri | 10000 | 4323 | 1902 | 653 | 171 | 43 | 11 |
Texas A&M | 10000 | 5005 | 1479 | 487 | 125 | 43 | 8 |
Clemson | 6566 | 3097 | 1129 | 245 | 97 | 31 | 8 |
Penn St. | 10000 | 4957 | 1372 | 545 | 108 | 24 | 7 |
Xavier | 10000 | 4728 | 1606 | 560 | 117 | 24 | 6 |
Old Dominion | 10000 | 5187 | 1109 | 332 | 116 | 24 | 6 |
Villanova | 10000 | 4935 | 724 | 251 | 90 | 24 | 6 |
Michigan | 10000 | 5706 | 909 | 252 | 76 | 19 | 6 |
Temple | 10000 | 5043 | 1373 | 541 | 136 | 29 | 5 |
UCLA | 10000 | 4569 | 1704 | 563 | 143 | 31 | 3 |
Richmond | 10000 | 4474 | 1471 | 301 | 75 | 20 | 2 |
Southern California | 7112 | 3112 | 826 | 271 | 63 | 16 | 2 |
Georgia | 10000 | 2693 | 826 | 263 | 42 | 7 | 2 |
Butler | 10000 | 4813 | 1022 | 283 | 99 | 14 | 1 |
Tennessee | 10000 | 4294 | 553 | 132 | 28 | 4 | 1 |
UAB | 3434 | 1106 | 258 | 43 | 14 | 5 | 0 |
Oakland | 10000 | 1220 | 455 | 53 | 14 | 2 | 0 |
Memphis | 10000 | 2197 | 236 | 22 | 4 | 1 | 0 |
Wofford | 10000 | 1314 | 282 | 59 | 5 | 0 | 0 |
Morehead St. | 10000 | 1188 | 276 | 23 | 2 | 0 | 0 |
Northern Colorado | 10000 | 697 | 125 | 18 | 2 | 0 | 0 |
Akron | 10000 | 762 | 141 | 16 | 2 | 0 | 0 |
Virginia Commonwealth | 2888 | 731 | 98 | 16 | 2 | 0 | 0 |
Bucknell | 10000 | 1592 | 326 | 48 | 1 | 0 | 0 |
UC Santa Barbara | 10000 | 1120 | 217 | 21 | 1 | 0 | 0 |
Princeton | 10000 | 1054 | 235 | 20 | 1 | 0 | 0 |
Indiana St. | 10000 | 941 | 186 | 19 | 1 | 0 | 0 |
St. Peter's | 10000 | 742 | 152 | 14 | 1 | 0 | 0 |
Long Island | 10000 | 931 | 114 | 14 | 1 | 0 | 0 |
NC Asheville | 6900 | 365 | 69 | 9 | 1 | 0 | 0 |
Hampton | 10000 | 154 | 18 | 2 | 0 | 0 | 0 |
Boston University | 10000 | 263 | 15 | 0 | 0 | 0 | 0 |
Arkansas Little Rock | 3100 | 75 | 6 | 0 | 0 | 0 | 0 |
Texas San Antonio | 7340 | 63 | 6 | 0 | 0 | 0 | 0 |
Alabama St. | 2660 | 8 | 1 | 0 | 0 | 0 | 0 |
Now, the usual caveat is this: I recognize that the odds of four #1 seeds reaching the Final Four is low (2008 is the only time it happened in the 64-team era). We know one or more of these top seeds will likely fall before it's all said and done. The problem is that we can't say with any certainty which #1 seed will fall, and the same goes with many of the upsets we see in the tourney. Whether they play "giant killers" or not, the best option if you're going for pure accuracy is to hedge your bets and pick all four #1 seeds, because it's the most likely outcome.
Of course, caveat #2 is that playing in a pool requires the winner to take a risky strategy to differentiate him or herself from the rest of the participants. Especially in a big pool, you have to make the picks the competition isn't making if you want to win it all. Players who successfully balance accuracy & uniqueness are the ones who have the greatest probability of winning their pool.
March 14th, 2011 at 8:51 am
I'll put a post up on this. The correct way to pick in a *large* group would be to pick based on the highest value of ActualOdds+(ActualOdds-ChosenbyGroupOdds). So if Pitt wins 7% of the time, but is picked only 3% of the time by the group, the value of that choice to you would be .07+(.07-.03)=.11. Compare that value to all of the options....
Duke would have been the pick last year.
Incidentally, are you guys here at BBRef running a bracket challenge like last year? I *should* have won it last year, I maintain, only I found a flaw in my math right after my picks were locked in. My revised methodology would have won it by quite a ways. :-) (Don't all of us stat guys say that?)
March 14th, 2011 at 8:58 am
Not sure, we'll have to see if Doug runs a public P-F-R pool and then probably piggyback off of that.
March 14th, 2011 at 11:05 am
I like to call it
Lost WagesMarch Sadness, because so many watchable NBA games are not being shown in favor of college "basketball."March 14th, 2011 at 11:39 am
The interesting outlier here is Texas, who's the 4 see in in Duke's bracket, yet they come out winning the championship more often than expected.
Probably because of my sad sack Arizona, who'll probably be 5-12'd this year =(
March 14th, 2011 at 2:35 pm
DSMok1,
Could you send me your bracket when you complete it by chance? Thanks
March 14th, 2011 at 6:02 pm
How is this different than just picking the top ratings?
March 14th, 2011 at 6:11 pm
In terms of the likeliest picks, it isn't. But the frequency table tells you how often you can expect each outcome to happen. Like AHL noticed in #4, somebody like Texas is a good value pick because they won the title in more sims than you'd expect from their seeding. Just eyeballing the ratings and making picks that way, you wouldn't pick up on something like that.
March 14th, 2011 at 6:21 pm
Ohio St. as the favorite?
I would lean toward Rock Chalk Nation if I was a betting man. Duke would be my second choice.
March 14th, 2011 at 8:58 pm
I'm all for another pool!
March 15th, 2011 at 9:14 am
According to Pomeroy, Texas should have been a 1 seed, so that's why they're winning a lot in the sim.
Also, although Florida is highly overseeded, they are in a very weak bracket. The took BYU to overtime last year in the tourney and now the teams are essentially the same except BYU is missing Davies, so Florida may actually be a value pick there to get to the elite 8.
March 17th, 2011 at 2:22 am
Texas is a 4 seed rated #4 overall, so I would expect them to be a good pick.
March 19th, 2011 at 12:09 am
How is the required number of simulations for a MC sim. determined? I've tried to find info on this but have struggled to find anything. Obviously if you run the 10,000 simulations again and the percentages change significantly it would be an insufficient number, but could someone point me to a method that doesn't involve trial and error? Any help much appreciated.