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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.

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12 Responses to “Ten Thousand 2011 NCAA Tournaments”

  1. DSMok1 Says:

    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?)

  2. Neil Paine Says:

    Not sure, we'll have to see if Doug runs a public P-F-R pool and then probably piggyback off of that.

  3. P Middy Says:

    I like to call it Lost Wages March Sadness, because so many watchable NBA games are not being shown in favor of college "basketball."

  4. AHL Says:

    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 =(

  5. taylor Says:

    DSMok1,

    Could you send me your bracket when you complete it by chance? Thanks

  6. MikeN Says:

    How is this different than just picking the top ratings?

  7. Neil Paine Says:

    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.

  8. dsong Says:

    Ohio St. as the favorite?

    I would lean toward Rock Chalk Nation if I was a betting man. Duke would be my second choice.

  9. Ian Says:

    I'm all for another pool!

  10. Matt Says:

    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.

  11. MikeN Says:

    Texas is a 4 seed rated #4 overall, so I would expect them to be a good pick.

  12. Andrew Says:

    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.