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## NCAA Tourney in Monte Carlo

Posted by Sean Forman on March 15, 2010

﻿﻿As I’ve done for the last seven years (2009 post), I’ve relied on a little bit of computer science to fill out my NCAA tourney pool. I have two young kids at home, a baseball site to worry about, and I’ve watched zero NCAA basketball games this year, so using my own scouting and intuition is obviously out.

What I do instead is rely on a rating service and simulation to compute the best (in this case, most likely) bracket to occur. Invariably, this leads to a boring bracket, but you’ll find in the long run that better teams win more games in the NCAA tourney. Doing the simulation also provides some interesting answers to questions like “Which low seeds are most likely to make the Sweet 16?”, and it presents it all in terms of probabilities.

The Method in a Nutshell

I’ve given several talks on this method (slides) if you are interested in a more detailed treatment. First, I use the Sagarin College Basketball Ratings Predictor to determine the relative strength of each team. These are Sagarin’s most accurate ratings for predicting games and inherently take into account things like margin of victory, strength of schedule, game location, etc. I then, essentially, play the 63 games in the tourney (I assume the better play-in team wins) and repeat the process over and over (I stop at 1,000,000 simulations). Along the way, I track who wins each game and summarize the results.

What I Don’t Do

There is no consideration for things like injuries, momentum, location of tourney games, etc. This is purely based on the complete season results for the teams. So if a team lost their star player in the final seconds of the conference championship game to a knee injury, this system won’t take that into account at all. This year Texas has a bad seed due to its poor play down the stretch, but they are rated by Sagarin as the 10th best team. Which team shows up in the tourney is yours to guess, not mine.

The Results

As I said earlier, this system is going to present boring results: no #13 seeds in the Sweet 16 and no #6 seeds in the Final Four. In fact, just using the Sagarin Predictor to create your bracket will give you a similar (but not the same) outcome. For me, the interest is in the probabilities. For example, in 2008, I had Davidson losing in the first round, but they were a 20% shot to make the Sweet 16. Not bad for a #10 seed.

This first chart shows the percentage of times each team lost in a particular round ordered by their Sagarin Predictor rating.

``` When they lost                 1 /     2 /     3 /     4 /     5 /     6 /  Never
1:0:Kansas                0.006 / 0.092 / 0.172 / 0.151 / 0.142 / 0.150 / 0.287 / (287134)
2:1:Duke                  0.004 / 0.162 / 0.135 / 0.122 / 0.135 / 0.159 / 0.283 / (282955)
3:2:Syracuse              0.026 / 0.230 / 0.158 / 0.213 / 0.204 / 0.086 / 0.083 / ( 82758)
4:3:Kentucky              0.034 / 0.371 / 0.253 / 0.133 / 0.121 / 0.051 / 0.037 / ( 36584)
5:4:Wisconsin             0.075 / 0.227 / 0.323 / 0.147 / 0.132 / 0.056 / 0.039 / ( 39485)
6:5:Kansas State          0.024 / 0.411 / 0.178 / 0.174 / 0.130 / 0.048 / 0.036 / ( 35624)
7:6:West Virginia         0.034 / 0.381 / 0.171 / 0.200 / 0.127 / 0.052 / 0.035 / ( 34737)
8:7:Ohio State            0.032 / 0.268 / 0.265 / 0.283 / 0.072 / 0.046 / 0.033 / ( 33419)
9:8:BYU                   0.220 / 0.395 / 0.128 / 0.120 / 0.085 / 0.030 / 0.021 / ( 21141)
10:9:Texas                 0.247 / 0.407 / 0.166 / 0.081 / 0.063 / 0.024 / 0.014 / ( 13703)
11:a:Maryland              0.113 / 0.322 / 0.410 / 0.073 / 0.043 / 0.025 / 0.015 / ( 15465)
12:A:Georgetown            0.081 / 0.309 / 0.300 / 0.217 / 0.050 / 0.027 / 0.016 / ( 15766)
13:b:Baylor                0.090 / 0.277 / 0.275 / 0.247 / 0.059 / 0.034 / 0.017 / ( 17039)
14:B:Villanova             0.023 / 0.287 / 0.295 / 0.275 / 0.065 / 0.037 / 0.018 / ( 18412)
15:c:Purdue                0.210 / 0.309 / 0.357 / 0.056 / 0.036 / 0.020 / 0.010 / ( 10366)
16:C:California            0.363 / 0.515 / 0.055 / 0.032 / 0.020 / 0.011 / 0.005 / (  4968)
17:d:Missouri              0.494 / 0.296 / 0.081 / 0.076 / 0.037 / 0.012 / 0.005 / (  5431)
18:D:Clemson               0.506 / 0.291 / 0.079 / 0.073 / 0.035 / 0.011 / 0.005 / (  4979)
19:e:Xavier-Ohio           0.495 / 0.191 / 0.198 / 0.069 / 0.034 / 0.009 / 0.004 / (  3747)
20:E:Michigan State        0.082 / 0.513 / 0.322 / 0.047 / 0.022 / 0.010 / 0.004 / (  3850)
21:f:Minnesota             0.505 / 0.190 / 0.193 / 0.067 / 0.033 / 0.008 / 0.003 / (  3480)
22:F:Florida State         0.344 / 0.466 / 0.079 / 0.067 / 0.034 / 0.008 / 0.003 / (  3308)
23:g:Marquette             0.484 / 0.176 / 0.212 / 0.083 / 0.033 / 0.009 / 0.003 / (  3109)
24:h:Texas A&M             0.486 / 0.276 / 0.192 / 0.026 / 0.013 / 0.005 / 0.002 / (  1869)
25:G:Tennessee             0.380 / 0.362 / 0.157 / 0.079 / 0.014 / 0.006 / 0.002 / (  2033)
26:H:Washington            0.516 / 0.172 / 0.200 / 0.074 / 0.028 / 0.008 / 0.002 / (  2431)
27:i:Georgia Tech          0.389 / 0.409 / 0.115 / 0.069 / 0.012 / 0.004 / 0.002 / (  1540)
28:I:Utah State            0.514 / 0.267 / 0.179 / 0.023 / 0.011 / 0.005 / 0.001 / (  1434)
29:j:Temple                0.261 / 0.496 / 0.165 / 0.047 / 0.023 / 0.006 / 0.002 / (  1784)
30:J:Vanderbilt            0.320 / 0.323 / 0.250 / 0.069 / 0.030 / 0.006 / 0.002 / (  2120)
31:k:Butler                0.477 / 0.239 / 0.203 / 0.054 / 0.022 / 0.005 / 0.001 / (  1422)
32:K:Pittsburgh            0.098 / 0.528 / 0.264 / 0.073 / 0.029 / 0.006 / 0.002 / (  1741)
33:l:Louisville            0.637 / 0.319 / 0.025 / 0.011 / 0.005 / 0.002 / 0.000 / (   493)
34:L:UTEP                  0.523 / 0.228 / 0.181 / 0.046 / 0.017 / 0.003 / 0.001 / (   956)
35:m:Old Dominion          0.449 / 0.348 / 0.123 / 0.065 / 0.011 / 0.004 / 0.001 / (   924)
36:M:Saint Mary's-Cal.     0.405 / 0.392 / 0.122 / 0.066 / 0.011 / 0.004 / 0.001 / (   903)
40:n:UNLV                  0.465 / 0.480 / 0.037 / 0.012 / 0.004 / 0.001 / 0.000 / (   259)
41:N:New Mexico            0.190 / 0.488 / 0.233 / 0.066 / 0.019 / 0.004 / 0.001 / (   865)
44:o:San Diego State       0.620 / 0.261 / 0.085 / 0.029 / 0.004 / 0.001 / 0.000 / (   252)
45:O:Oklahoma State        0.611 / 0.293 / 0.064 / 0.027 / 0.004 / 0.001 / 0.000 / (   216)
46:p:Notre Dame            0.551 / 0.301 / 0.096 / 0.043 / 0.006 / 0.002 / 0.000 / (   371)
47:P:Wake Forest           0.753 / 0.190 / 0.041 / 0.011 / 0.004 / 0.001 / 0.000 / (   148)
48:q:Northern Iowa         0.535 / 0.423 / 0.030 / 0.009 / 0.003 / 0.001 / 0.000 / (   151)
49:Q:Gonzaga               0.656 / 0.280 / 0.036 / 0.020 / 0.006 / 0.001 / 0.000 / (   214)
50:r:Florida               0.780 / 0.170 / 0.031 / 0.013 / 0.004 / 0.001 / 0.000 / (   145)
55:R:Richmond              0.595 / 0.299 / 0.073 / 0.029 / 0.004 / 0.001 / 0.000 / (   151)
59:s:Murray State          0.680 / 0.210 / 0.091 / 0.015 / 0.004 / 0.000 / 0.000 / (    55)
60:S:Siena                 0.790 / 0.149 / 0.056 / 0.004 / 0.001 / 0.000 / 0.000 / (    39)
70:t:Cornell               0.739 / 0.218 / 0.037 / 0.005 / 0.001 / 0.000 / 0.000 / (    20)
85:T:Houston               0.887 / 0.089 / 0.022 / 0.001 / 0.000 / 0.000 / 0.000 / (     2)
94:u:Wofford               0.925 / 0.059 / 0.015 / 0.001 / 0.000 / 0.000 / 0.000 / (     0)
101:U:Montana               0.810 / 0.165 / 0.023 / 0.002 / 0.000 / 0.000 / 0.000 / (     2)
102:v:Sam Houston State     0.910 / 0.073 / 0.014 / 0.002 / 0.000 / 0.000 / 0.000 / (     0)
105:V:Ohio University       0.919 / 0.069 / 0.011 / 0.001 / 0.000 / 0.000 / 0.000 / (     0)
127:w:New Mexico State      0.918 / 0.076 / 0.007 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
134:W:Oakland-Mich.         0.902 / 0.091 / 0.007 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
144:x:East Tennessee State  0.966 / 0.032 / 0.002 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
146:X:Vermont               0.974 / 0.024 / 0.002 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
149:y:Morgan State          0.966 / 0.032 / 0.002 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
152:Y:UC Santa Barbara      0.968 / 0.030 / 0.003 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
174:z:North Texas           0.976 / 0.023 / 0.001 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
197:Z:Lehigh                0.994 / 0.006 / 0.000 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
200:*:Robert Morris         0.977 / 0.022 / 0.001 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
222:#:Winthrop              0.996 / 0.004 / 0.000 / 0.000 / 0.000 / 0.000 / 0.000 / (     0)
```

The first number by the team name is their overall Sagarin rating (this appears elsewhere) and the second is our unique id for them that you should ignore.

Here is one of the two Montana Championships.

```REGION 3
----------
Kentucky____________
_Kentucky____________
East_Tennessee_State|               |
_Texas_______________
Texas_______________                |               |
_Texas_______________|               |
Wake_Forest_________|                               |
_Texas_______________
Temple______________                                |               |
_Temple______________                |               |
Cornell_____________|               |               |               |
_Wisconsin___________|               |
Wisconsin___________                |                               |
_Wisconsin___________|                               |
Wofford_____________|                                               |
_Montana_____________
Marquette___________                                                |
_Washington__________                                |
Washington__________|               |                               |
_Montana_____________                |
New_Mexico__________                |               |               |
_Montana_____________|               |               |
Montana_____________|                               |               |
_Montana_____________|
Clemson_____________                                |
_Missouri____________                |
Missouri____________|               |               |
_West_Virginia_______|
West_Virginia_______                |
_West_Virginia_______|
Morgan_State________|

FINAL FOUR
----------
Georgetown__________
Butler______________|_Georgetown__________
|_Montana_____________
Montana_____________ _Montana_____________|
Baylor______________|
```

Here are the probabilities of the winners for each game in the bracket.

```First Round Winners

Game  1:Kansas               (  1 - 0.994)
Game  2:UNLV                 ( 40 - 0.535)
Game  3:Michigan State       ( 20 - 0.918)
Game  4:Maryland             ( 11 - 0.887)
Game  5:Tennessee            ( 25 - 0.620)
Game  6:Georgetown           ( 12 - 0.919)
Game  7:Georgia Tech         ( 27 - 0.611)
Game  8:Ohio State           (  8 - 0.968)
Game  9:Syracuse             (  3 - 0.974)
Game 10:Florida State        ( 22 - 0.656)
Game 11:Butler               ( 31 - 0.523)
Game 12:Vanderbilt           ( 30 - 0.680)
Game 13:Xavier-Ohio          ( 19 - 0.505)
Game 14:Pittsburgh           ( 32 - 0.902)
Game 15:BYU                  (  9 - 0.780)
Game 16:Kansas State         (  6 - 0.976)
Game 17:Kentucky             (  4 - 0.966)
Game 18:Texas                ( 10 - 0.753)
Game 19:Temple               ( 29 - 0.739)
Game 20:Wisconsin            (  5 - 0.925)
Game 21:Marquette            ( 23 - 0.516)
Game 22:New Mexico           ( 41 - 0.810)
Game 23:Missouri             ( 17 - 0.506)
Game 24:West Virginia        (  7 - 0.966)
Game 25:Duke                 (  2 - 0.996)
Game 26:California           ( 16 - 0.637)
Game 27:Texas A&M            ( 24 - 0.514)
Game 28:Purdue               ( 15 - 0.790)
Game 29:Old Dominion         ( 35 - 0.551)
Game 30:Baylor               ( 13 - 0.910)
Game 31:Saint Mary's-Cal.    ( 36 - 0.595)
Game 32:Villanova            ( 14 - 0.977)

Into Sweet Sixteen

Game 33:Kansas               (  1 - 0.902)
UNLV                 ( 40 - 0.055)
Northern Iowa        ( 48 - 0.043)
Game 34:Maryland             ( 11 - 0.565)
Michigan State       ( 20 - 0.405)
Houston              ( 85 - 0.023)
Game 35:Georgetown           ( 12 - 0.610)
Tennessee            ( 25 - 0.258)
San Diego State      ( 44 - 0.119)
Game 36:Ohio State           (  8 - 0.700)
Georgia Tech         ( 27 - 0.202)
Oklahoma State       ( 45 - 0.096)
Game 37:Syracuse             (  3 - 0.744)
Florida State        ( 22 - 0.191)
Gonzaga              ( 49 - 0.063)
Game 38:Vanderbilt           ( 30 - 0.357)
Butler               ( 31 - 0.284)
UTEP                 ( 34 - 0.249)
Game 39:Pittsburgh           ( 32 - 0.374)
Xavier-Ohio          ( 19 - 0.314)
Minnesota            ( 21 - 0.305)
Game 40:Kansas State         (  6 - 0.565)
BYU                  (  9 - 0.385)
Florida              ( 50 - 0.049)
Game 41:Kentucky             (  4 - 0.595)
Texas                ( 10 - 0.346)
Wake Forest          ( 47 - 0.057)
Game 42:Wisconsin            (  5 - 0.698)
Temple               ( 29 - 0.243)
Cornell              ( 70 - 0.043)
Game 43:Marquette            ( 23 - 0.340)
New Mexico           ( 41 - 0.322)
Washington           ( 26 - 0.313)
Game 44:West Virginia        (  7 - 0.585)
Missouri             ( 17 - 0.210)
Clemson              ( 18 - 0.203)
Game 45:Duke                 (  2 - 0.834)
California           ( 16 - 0.122)
Louisville           ( 33 - 0.044)
Game 46:Purdue               ( 15 - 0.481)
Texas A&M            ( 24 - 0.238)
Utah State           ( 28 - 0.220)
Game 47:Baylor               ( 13 - 0.633)
Old Dominion         ( 35 - 0.203)
Notre Dame           ( 46 - 0.147)
Game 48:Villanova            ( 14 - 0.690)
Saint Mary's-Cal.    ( 36 - 0.203)
Richmond             ( 55 - 0.106)

Into Elite Eight

Game 49:Kansas               (  1 - 0.730)
Maryland             ( 11 - 0.155)
Michigan State       ( 20 - 0.083)
UNLV                 ( 40 - 0.018)
Game 50:Ohio State           (  8 - 0.434)
Georgetown           ( 12 - 0.310)
Tennessee            ( 25 - 0.101)
Georgia Tech         ( 27 - 0.087)
Game 51:Syracuse             (  3 - 0.586)
Florida State        ( 22 - 0.112)
Vanderbilt           ( 30 - 0.107)
Butler               ( 31 - 0.081)
Game 52:Kansas State         (  6 - 0.387)
BYU                  (  9 - 0.257)
Xavier-Ohio          ( 19 - 0.116)
Minnesota            ( 21 - 0.112)
Game 53:Wisconsin            (  5 - 0.375)
Kentucky             (  4 - 0.342)
Texas                ( 10 - 0.181)
Temple               ( 29 - 0.078)
Game 54:West Virginia        (  7 - 0.414)
Missouri             ( 17 - 0.130)
Marquette            ( 23 - 0.128)
Clemson              ( 18 - 0.124)
Game 55:Duke                 (  2 - 0.699)
Purdue               ( 15 - 0.123)
California           ( 16 - 0.067)
Texas A&M            ( 24 - 0.046)
Game 56:Villanova            ( 14 - 0.395)
Baylor               ( 13 - 0.358)
Saint Mary's-Cal.    ( 36 - 0.081)
Old Dominion         ( 35 - 0.080)

Into Final Four

Game 57:Kansas               (  1 - 0.579)
Ohio State           (  8 - 0.151)
Georgetown           ( 12 - 0.093)
Maryland             ( 11 - 0.083)
Michigan State       ( 20 - 0.035)
Game 58:Syracuse             (  3 - 0.373)
Kansas State         (  6 - 0.213)
BYU                  (  9 - 0.137)
Xavier-Ohio          ( 19 - 0.047)
Florida State        ( 22 - 0.045)
Game 59:Wisconsin            (  5 - 0.228)
West Virginia        (  7 - 0.214)
Kentucky             (  4 - 0.209)
Texas                ( 10 - 0.100)
Missouri             ( 17 - 0.054)
Game 60:Duke                 (  2 - 0.577)
Villanova            ( 14 - 0.120)
Baylor               ( 13 - 0.110)
Purdue               ( 15 - 0.067)
California           ( 16 - 0.035)

Into Championship Game

Game 61:Kansas               (  1 - 0.437)
Syracuse             (  3 - 0.169)
Kansas State         (  6 - 0.083)
Ohio State           (  8 - 0.079)
BYU                  (  9 - 0.051)
Georgetown           ( 12 - 0.043)
Game 62:Duke                 (  2 - 0.442)
Wisconsin            (  5 - 0.096)
Kentucky             (  4 - 0.088)
West Virginia        (  7 - 0.087)
Villanova            ( 14 - 0.055)
Baylor               ( 13 - 0.051)

Champions

Game 63:Kansas               (  1 - 0.287)
Duke                 (  2 - 0.283)
Syracuse             (  3 - 0.083)
Wisconsin            (  5 - 0.039)
Kentucky             (  4 - 0.037)
Kansas State         (  6 - 0.036)
West Virginia        (  7 - 0.035)
```

While the #1 or #2 seeds are the best bets to make the Final Four, the probability of the Final Four being all #1’s or #2’s is actually quite small. Figuring out who not to pick is, of course, the hard part.

Prob. of only #1 or #2 in Final Four =
(.579 + .151) * (..373+.213) * (.214+.209) * (.577+.120) = 12.6%

Some Cinderellas (#6 Seeds or Lower into the Sweet 16)

```# 7-BYU                  (  9 - 0.385)
# 8-Texas                ( 10 - 0.346)
# 6-Xavier-Ohio          ( 19 - 0.314)
#11-Washington           ( 26 - 0.313)
#11-Minnesota            ( 21 - 0.305)
# 6-Tennessee            ( 25 - 0.258)
#12-UTEP                 ( 34 - 0.249)
#12-Utah State           ( 28 - 0.220)
#10-Missouri             ( 17 - 0.210)
# 7-Clemson              ( 18 - 0.203)
#11-Old Dominion         ( 35 - 0.203)
#10-Saint Mary's-Cal.    ( 36 - 0.203)
#10-Georgia Tech         ( 27 - 0.202)
```

In general, #8’s and #9’s are really bad Cinderella picks because (1) they are playing a comparable team in the first round and (2) they are virtually guaranteed to play one of the five best teams in the second round. On the other hand, #6’s and #12’s only have to get past a #4 seed, who has a significant chance of being upset in the first round.

Final Four Teams

The percentage of times each team won the regional:

```Into Final Four

Game 57:Kansas               (  1 - 0.579)
Ohio State           (  8 - 0.151)
Georgetown           ( 12 - 0.093)
Maryland             ( 11 - 0.083)
Michigan State       ( 20 - 0.035)
Game 58:Syracuse             (  3 - 0.373)
Kansas State         (  6 - 0.213)
BYU                  (  9 - 0.137)
Xavier-Ohio          ( 19 - 0.047)
Florida State        ( 22 - 0.045)
Game 59:Wisconsin            (  5 - 0.228)
West Virginia        (  7 - 0.214)
Kentucky             (  4 - 0.209)
Texas                ( 10 - 0.100)
Missouri             ( 17 - 0.054)
Game 60:Duke                 (  2 - 0.577)
Villanova            ( 14 - 0.120)
Baylor               ( 13 - 0.110)
Purdue               ( 15 - 0.067)
California           ( 16 - 0.035)
```

The percentage of times each team was the champion:

```Game 63:Kansas               (  1 - 0.287)
Duke                 (  2 - 0.283)
Syracuse             (  3 - 0.083)
Wisconsin            (  5 - 0.039)
Kentucky             (  4 - 0.037)
Kansas State         (  6 - 0.036)
West Virginia        (  7 - 0.035)
```

Here is my bracket:

```REGION 1
----------
Kansas______________
_Kansas______________
Lehigh______________|               |
_Kansas______________
UNLV________________                |               |
_UNLV________________|               |
Northern_Iowa_______|                               |
_Kansas______________
Michigan_State______                                |               |
_Michigan_State______                |               |
New_Mexico_State____|               |               |               |
_Maryland____________|               |
Maryland____________                |                               |
_Maryland____________|                               |
Houston_____________|                                               |
_Kansas______________
Tennessee___________                                                |
_Tennessee___________                                |
San_Diego_State_____|               |                               |
_Georgetown__________                |
Georgetown__________                |               |               |
_Georgetown__________|               |               |
Ohio_University_____|                               |               |
_Ohio_State__________|
Oklahoma_State______                                |
_Georgia_Tech________                |
Georgia_Tech________|               |               |
_Ohio_State__________|
Ohio_State__________                |
_Ohio_State__________|
UC_Santa_Barbara____|

REGION 2
----------
Syracuse____________
_Syracuse____________
Vermont_____________|               |
_Syracuse____________
Gonzaga_____________                |               |
_Florida_State_______|               |
Florida_State_______|                               |
_Syracuse____________
Butler______________                                |               |
_Butler______________                |               |
UTEP________________|               |               |               |
_Vanderbilt__________|               |
Vanderbilt__________                |                               |
_Vanderbilt__________|                               |
Murray_State________|                                               |
_Syracuse____________
Xavier-Ohio_________                                                |
_Xavier-Ohio_________                                |
Minnesota___________|               |                               |
_Pittsburgh__________                |
Pittsburgh__________                |               |               |
_Pittsburgh__________|               |               |
Oakland-Mich._______|                               |               |
_Kansas_State________|
BYU_________________                                |
_BYU_________________                |
Florida_____________|               |               |
_Kansas_State________|
Kansas_State________                |
_Kansas_State________|
North_Texas_________|

REGION 3
----------
Kentucky____________
_Kentucky____________
East_Tennessee_State|               |
_Kentucky____________
Texas_______________                |               |
_Texas_______________|               |
Wake_Forest_________|                               |
_Wisconsin___________
Temple______________                                |               |
_Temple______________                |               |
Cornell_____________|               |               |               |
_Wisconsin___________|               |
Wisconsin___________                |                               |
_Wisconsin___________|                               |
Wofford_____________|                                               |
_Wisconsin___________
Marquette___________                                                |
_Marquette___________                                |
Washington__________|               |                               |
_Marquette___________                |
New_Mexico__________                |               |               |
_New_Mexico__________|               |               |
Montana_____________|                               |               |
_West_Virginia_______|
Clemson_____________                                |
_Missouri____________                |
Missouri____________|               |               |
_West_Virginia_______|
West_Virginia_______                |
_West_Virginia_______|
Morgan_State________|

REGION 4
----------
Duke________________
_Duke________________
Winthrop____________|               |
_Duke________________
California__________                |               |
_California__________|               |
Louisville__________|                               |
_Duke________________
Texas_A&M___________                                |               |
_Texas_A&M___________                |               |
Utah_State__________|               |               |               |
_Purdue______________|               |
Purdue______________                |                               |
_Purdue______________|                               |
Siena_______________|                                               |
_Duke________________
Notre_Dame__________                                                |
_Old_Dominion________                                |
Old_Dominion________|               |                               |
_Baylor______________                |
Baylor______________                |               |               |
_Baylor______________|               |               |
Sam_Houston_State___|                               |               |
_Villanova___________|
Richmond____________                                |
_Saint_Mary's-Cal.___                |
Saint_Mary's-Cal.___|               |               |
_Villanova___________|
Villanova___________                |
_Villanova___________|
Robert_Morris_______|

FINAL FOUR
----------
Kansas______________
Syracuse____________|_Kansas______________
|_Kansas______________
Wisconsin___________ _Duke________________|
Duke________________|
```

### 9 Responses to “NCAA Tourney in Monte Carlo”

1. Baseball-Reference Blog » Blog Archive » CBB Blog >> NCAA Tourney in Monte Carlo Says:

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2. Zachary Says:

Very helpful, and I’m using it for my bracket. I’m calling a Kansas/BYU and Wisconsin/Duke Final Four, with Kansas beating Duke 71-64 to claim the championship. Minnesota and BYU are my Cinderella darlings. I thought long and hard about Washington, but in the end I decided my initial gut reaction of “Marquette could go deep” was strong enough that the Gophers and Cougars provided enough crystal slippers. I decided to take BYU all the way because Syracuse has looked very shaky of late, and I like the potential return on that investment.

Of course, I’ll probably completely redo my bracket sometime this evening, and make the Catamounts champion.

3. Jared Ras Says:

Stats say that WP is right more often than your gut… I had to read a whole book about it for my college statistics class (“Super Crunchers,” which I’m sure others have read). So, I’ve got one bracket that is identical to yours, even though I doubt my Marquette Golden Eagles will win a single game.

4. Zachary Says:

The numbers like Marquette’s Sweet 16 chances the best in its group, so I feel okay about that. I needed some upsets, though, which is why I hesitated. The one I find most interesting is the the Old Dominion over Notre Dame. 55.1% isn’t huge, but it’s relatively healthy compared to, say, Xavier/Minnesota.

5. LarryinLA Says:

That bracket definitely gives you the highest expected score. However, in a pool with a fair number of participants, it might give you a very poor chance of being at the top. Don’t you need a higher variance strategy to hope to come out on top of the pool? I can’t think of a way to use this information to construct such a strategy though.

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