{"id":386,"date":"2011-03-16T15:51:40","date_gmt":"2011-03-16T20:51:40","guid":{"rendered":"http:\/\/godismyjudgeok.com\/DStats\/?p=386"},"modified":"2013-10-11T09:32:06","modified_gmt":"2013-10-11T14:32:06","slug":"ncaa-tourney-bayesian-power-ratings","status":"publish","type":"post","link":"http:\/\/godismyjudgeok.com\/DStats\/2011\/ncaa-basketball\/ncaa-tourney-bayesian-power-ratings\/","title":{"rendered":"NCAA Tourney Bayesian Ratings and Odds"},"content":{"rendered":"

Okay, ready for the tournament?<\/p>\n

I’ve put together some adjustments based on the work I teased yesterday<\/a>.\u00a0 The theory behind the adjustments may be found on STATS @ MTSU<\/a> and Dr. Winner @ Florida<\/a>.\u00a0 Basically, I’m adjusting for teams that raise their game to a higher level against good foes (or vise-versa).\u00a0 For instance, Long Island plays much better against good teams–probably because they got bored against the bad teams\/pulled their starters.\u00a0 Now, we can’t just take a simple linear regression; the slope doesn’t continue infinitely.\u00a0 So I construct the Prediction Interval to estimate the mean and standard deviation at any point along the regression line, and regress based on the REGRESSED standard deviation<\/a> of the team’s adjusted efficiency differentials.<\/p>\n

For example, let’s see what Hampton looks like.\u00a0 They raise their game more than just about anyone in the field; they’ve played a very easy schedule.\u00a0 Here’s what their regressed curves look like:<\/p>\n

\"Hampton's<\/a>

Hampton's Regressed Efficiency Differential Curve<\/p><\/div>\n

To simplify the math, I presumed that all games in the tournament were against +25 level foes: I estimate that this is “the best” that each team can play with it all on the line.\u00a0 Of course, a few teams have played worse with it all on the line (see Duke).<\/p>\n

To incorporate this into the Bayesian ratings, I simply took the latest Bayesian rating and added in the projected differential at +25, minus the average efficiency differential for the team.<\/p>\n

Next, I set about estimating the standard deviation for each team.\u00a0 We can easily calculate the team’s standard deviation of performances; I estimated that the standard deviation of the Bayesian efficiency was 1 less than that.\u00a0 Next, I looked at the standard deviation of the curve above at the +25 mark.\u00a0 I decided the best way to combine the two was to take the geometric mean of the Bayesian-based Stdev and the stdev of the non-regressed efficiency differential curve.\u00a0 I’m not totally sure how to do this here, so this is my best guess; I’m a little over my head mathematically.\u00a0 Anyway, the results look about right intuitively.<\/p>\n

So now we’ve got a new “Tourmament Power Rating” and a standard deviation… so it’s easy to calculate odds for each game.<\/p>\n

First, here’s the ratings in tabular form:<\/p>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
O<\/th>Sd<\/th>Re<\/th>Team<\/th>Conf<\/th>W-L<\/th>Bayesian<\/th>Rk<\/th>25Delta<\/th>Tourney<\/th>Rk<\/th>Stdev<\/th>\n<\/tr>\n<\/thead>\n
1<\/td>1<\/td>E<\/td>Ohio St.<\/td>B10<\/td>32-2<\/td>33.47<\/td>1<\/td>-0.22<\/td>33.25<\/td>1<\/td>14.81<\/td>\n<\/tr>\n
2<\/td>16<\/td>E<\/td>Alabama St.<\/td>SWAC<\/td>17-17<\/td>-13.90<\/td>299<\/td>-0.77<\/td>-14.66<\/td>68<\/td>16.34<\/td>\n<\/tr>\n
2<\/td>16<\/td>E<\/td>Texas San Antonio<\/td>Slnd<\/td>19-13<\/td>-6.58<\/td>232<\/td>4.22<\/td>-2.36<\/td>66<\/td>10.69<\/td>\n<\/tr>\n
3<\/td>9<\/td>E<\/td>Villanova<\/td>BE<\/td>21-11<\/td>18.90<\/td>25<\/td>-1.14<\/td>17.76<\/td>37<\/td>15.51<\/td>\n<\/tr>\n
4<\/td>8<\/td>E<\/td>George Mason<\/td>CAA<\/td>26-6<\/td>15.62<\/td>44<\/td>-1.16<\/td>14.46<\/td>46<\/td>15.71<\/td>\n<\/tr>\n
5<\/td>5<\/td>E<\/td>West Virginia<\/td>BE<\/td>20-11<\/td>21.74<\/td>16<\/td>0.08<\/td>21.82<\/td>18<\/td>14.12<\/td>\n<\/tr>\n
6<\/td>12<\/td>E<\/td>Clemson<\/td>ACC<\/td>22-11<\/td>20.68<\/td>19<\/td>1.94<\/td>22.62<\/td>17<\/td>13.05<\/td>\n<\/tr>\n
6<\/td>12<\/td>E<\/td>UAB<\/td>CUSA<\/td>22-9<\/td>12.13<\/td>65<\/td>-0.95<\/td>11.18<\/td>50<\/td>14.09<\/td>\n<\/tr>\n
7<\/td>13<\/td>E<\/td>Princeton<\/td>Ivy<\/td>25-6<\/td>6.12<\/td>100<\/td>0.54<\/td>6.66<\/td>55<\/td>13.87<\/td>\n<\/tr>\n
8<\/td>4<\/td>E<\/td>Kentucky<\/td>SEC<\/td>25-8<\/td>27.05<\/td>6<\/td>-0.20<\/td>26.85<\/td>6<\/td>14.35<\/td>\n<\/tr>\n
9<\/td>3<\/td>E<\/td>Syracuse<\/td>BE<\/td>26-7<\/td>25.52<\/td>9<\/td>-0.35<\/td>25.17<\/td>11<\/td>17.45<\/td>\n<\/tr>\n
10<\/td>14<\/td>E<\/td>Indiana St.<\/td>MVC<\/td>20-13<\/td>5.52<\/td>104<\/td>-0.88<\/td>4.64<\/td>58<\/td>16.16<\/td>\n<\/tr>\n
11<\/td>11<\/td>E<\/td>Marquette<\/td>BE<\/td>20-14<\/td>18.70<\/td>28<\/td>0.97<\/td>19.67<\/td>24<\/td>13.97<\/td>\n<\/tr>\n
12<\/td>6<\/td>E<\/td>Xavier<\/td>A10<\/td>24-7<\/td>18.76<\/td>27<\/td>2.80<\/td>21.57<\/td>20<\/td>17.24<\/td>\n<\/tr>\n
13<\/td>7<\/td>E<\/td>Washington<\/td>P10<\/td>23-10<\/td>22.82<\/td>15<\/td>-2.36<\/td>20.46<\/td>23<\/td>15.76<\/td>\n<\/tr>\n
14<\/td>10<\/td>E<\/td>Georgia<\/td>SEC<\/td>21-11<\/td>13.09<\/td>61<\/td>1.87<\/td>14.96<\/td>45<\/td>14.89<\/td>\n<\/tr>\n
15<\/td>15<\/td>E<\/td>Long Island<\/td>NEC<\/td>27-5<\/td>1.30<\/td>148<\/td>2.98<\/td>4.28<\/td>59<\/td>13.05<\/td>\n<\/tr>\n
16<\/td>2<\/td>E<\/td>North Carolina<\/td>ACC<\/td>26-7<\/td>23.04<\/td>14<\/td>0.26<\/td>23.30<\/td>15<\/td>15.95<\/td>\n<\/tr>\n
19<\/td>1<\/td>W<\/td>Duke<\/td>ACC<\/td>30-4<\/td>32.26<\/td>2<\/td>-3.06<\/td>29.20<\/td>3<\/td>12.23<\/td>\n<\/tr>\n
20<\/td>16<\/td>W<\/td>Hampton<\/td>MEAC<\/td>24-8<\/td>-5.84<\/td>224<\/td>9.84<\/td>4.00<\/td>60<\/td>12.99<\/td>\n<\/tr>\n
21<\/td>9<\/td>W<\/td>Tennessee<\/td>SEC<\/td>19-14<\/td>15.58<\/td>46<\/td>3.21<\/td>18.79<\/td>28<\/td>13.65<\/td>\n<\/tr>\n
22<\/td>8<\/td>W<\/td>Michigan<\/td>B10<\/td>20-13<\/td>16.25<\/td>42<\/td>1.53<\/td>17.78<\/td>36<\/td>13.71<\/td>\n<\/tr>\n
23<\/td>5<\/td>W<\/td>Arizona<\/td>P10<\/td>27-7<\/td>18.43<\/td>33<\/td>-3.17<\/td>15.26<\/td>44<\/td>13.94<\/td>\n<\/tr>\n
24<\/td>12<\/td>W<\/td>Memphis<\/td>CUSA<\/td>25-9<\/td>10.05<\/td>73<\/td>-0.34<\/td>9.72<\/td>53<\/td>15.05<\/td>\n<\/tr>\n
25<\/td>13<\/td>W<\/td>Oakland<\/td>Sum<\/td>25-9<\/td>10.75<\/td>70<\/td>-0.43<\/td>10.32<\/td>51<\/td>12.65<\/td>\n<\/tr>\n
26<\/td>4<\/td>W<\/td>Texas<\/td>B12<\/td>27-7<\/td>27.42<\/td>4<\/td>1.30<\/td>28.72<\/td>4<\/td>14.29<\/td>\n<\/tr>\n
27<\/td>3<\/td>W<\/td>Connecticut<\/td>BE<\/td>26-9<\/td>21.70<\/td>17<\/td>1.64<\/td>23.35<\/td>14<\/td>13.34<\/td>\n<\/tr>\n
28<\/td>14<\/td>W<\/td>Bucknell<\/td>Pat<\/td>25-8<\/td>4.40<\/td>115<\/td>1.10<\/td>5.50<\/td>57<\/td>14.78<\/td>\n<\/tr>\n
29<\/td>11<\/td>W<\/td>Missouri<\/td>B12<\/td>23-10<\/td>18.20<\/td>35<\/td>0.68<\/td>18.88<\/td>27<\/td>14.36<\/td>\n<\/tr>\n
30<\/td>6<\/td>W<\/td>Cincinnati<\/td>BE<\/td>25-8<\/td>18.47<\/td>31<\/td>-0.42<\/td>18.05<\/td>35<\/td>17.60<\/td>\n<\/tr>\n
31<\/td>7<\/td>W<\/td>Temple<\/td>A10<\/td>25-7<\/td>17.29<\/td>37<\/td>0.77<\/td>18.06<\/td>34<\/td>13.40<\/td>\n<\/tr>\n
32<\/td>10<\/td>W<\/td>Penn St.<\/td>B10<\/td>19-14<\/td>15.58<\/td>45<\/td>1.38<\/td>16.96<\/td>40<\/td>17.06<\/td>\n<\/tr>\n
33<\/td>15<\/td>W<\/td>Northern Colorado<\/td>BSky<\/td>21-10<\/td>2.87<\/td>128<\/td>-2.70<\/td>0.17<\/td>62<\/td>12.14<\/td>\n<\/tr>\n
34<\/td>2<\/td>W<\/td>San Diego St.<\/td>MWC<\/td>32-2<\/td>24.10<\/td>12<\/td>2.61<\/td>26.72<\/td>7<\/td>14.10<\/td>\n<\/tr>\n
36<\/td>1<\/td>SW<\/td>Kansas<\/td>B12<\/td>32-2<\/td>31.42<\/td>3<\/td>-1.42<\/td>30.00<\/td>2<\/td>15.24<\/td>\n<\/tr>\n
37<\/td>16<\/td>SW<\/td>Boston University<\/td>AE<\/td>21-13<\/td>-0.25<\/td>160<\/td>-0.77<\/td>-1.02<\/td>64<\/td>14.23<\/td>\n<\/tr>\n
38<\/td>9<\/td>SW<\/td>Illinois<\/td>B10<\/td>19-13<\/td>20.18<\/td>21<\/td>0.41<\/td>20.59<\/td>22<\/td>12.90<\/td>\n<\/tr>\n
39<\/td>8<\/td>SW<\/td>Nevada Las Vegas<\/td>MWC<\/td>24-8<\/td>19.37<\/td>24<\/td>-0.84<\/td>18.53<\/td>29<\/td>14.53<\/td>\n<\/tr>\n
40<\/td>5<\/td>SW<\/td>Vanderbilt<\/td>SEC<\/td>23-10<\/td>18.58<\/td>30<\/td>-0.12<\/td>18.45<\/td>30<\/td>13.52<\/td>\n<\/tr>\n
41<\/td>12<\/td>SW<\/td>Richmond<\/td>A10<\/td>27-7<\/td>15.10<\/td>49<\/td>-0.81<\/td>14.29<\/td>47<\/td>15.02<\/td>\n<\/tr>\n
42<\/td>13<\/td>SW<\/td>Morehead St.<\/td>OVC<\/td>24-9<\/td>5.97<\/td>102<\/td>4.12<\/td>10.09<\/td>52<\/td>15.10<\/td>\n<\/tr>\n
43<\/td>4<\/td>SW<\/td>Louisville<\/td>BE<\/td>25-9<\/td>24.14<\/td>11<\/td>0.27<\/td>24.41<\/td>13<\/td>14.67<\/td>\n<\/tr>\n
44<\/td>3<\/td>SW<\/td>Purdue<\/td>B10<\/td>25-7<\/td>25.79<\/td>8<\/td>0.40<\/td>26.19<\/td>8<\/td>14.51<\/td>\n<\/tr>\n
45<\/td>14<\/td>SW<\/td>St. Peter's<\/td>MAAC<\/td>20-13<\/td>2.57<\/td>131<\/td>-1.67<\/td>0.90<\/td>61<\/td>16.04<\/td>\n<\/tr>\n
46<\/td>11<\/td>SW<\/td>Southern California<\/td>P10<\/td>19-14<\/td>15.40<\/td>47<\/td>2.68<\/td>18.08<\/td>33<\/td>16.55<\/td>\n<\/tr>\n
46<\/td>11<\/td>SW<\/td>Virginia Commonwealth<\/td>CAA<\/td>23-11<\/td>9.32<\/td>76<\/td>3.74<\/td>13.06<\/td>49<\/td>14.06<\/td>\n<\/tr>\n
47<\/td>6<\/td>SW<\/td>Georgetown<\/td>BE<\/td>21-10<\/td>19.52<\/td>22<\/td>-0.45<\/td>19.07<\/td>26<\/td>15.06<\/td>\n<\/tr>\n
48<\/td>7<\/td>SW<\/td>Texas A&M<\/td>B12<\/td>24-8<\/td>17.34<\/td>36<\/td>0.00<\/td>17.34<\/td>39<\/td>12.76<\/td>\n<\/tr>\n
49<\/td>10<\/td>SW<\/td>Florida St.<\/td>ACC<\/td>21-10<\/td>16.66<\/td>39<\/td>-1.16<\/td>15.50<\/td>43<\/td>10.01<\/td>\n<\/tr>\n
50<\/td>15<\/td>SW<\/td>Akron<\/td>MAC<\/td>23-12<\/td>4.81<\/td>112<\/td>-4.81<\/td>0.00<\/td>63<\/td>15.78<\/td>\n<\/tr>\n
51<\/td>2<\/td>SW<\/td>Notre Dame<\/td>BE<\/td>26-6<\/td>25.37<\/td>10<\/td>0.21<\/td>25.58<\/td>10<\/td>16.26<\/td>\n<\/tr>\n
53<\/td>1<\/td>SE<\/td>Pittsburgh<\/td>BE<\/td>27-5<\/td>27.26<\/td>5<\/td>-0.35<\/td>26.92<\/td>5<\/td>12.13<\/td>\n<\/tr>\n
54<\/td>16<\/td>SE<\/td>Arkansas Little Rock<\/td>SB<\/td>19-17<\/td>-5.36<\/td>220<\/td>-8.35<\/td>-13.70<\/td>67<\/td>14.98<\/td>\n<\/tr>\n
54<\/td>16<\/td>SE<\/td>NC Asheville<\/td>BSth<\/td>20-13<\/td>-0.93<\/td>167<\/td>-0.53<\/td>-1.46<\/td>65<\/td>17.12<\/td>\n<\/tr>\n
55<\/td>9<\/td>SE<\/td>Old Dominion<\/td>CAA<\/td>27-6<\/td>14.92<\/td>50<\/td>-0.91<\/td>14.01<\/td>48<\/td>13.56<\/td>\n<\/tr>\n
56<\/td>8<\/td>SE<\/td>Butler<\/td>Horz<\/td>23-9<\/td>16.32<\/td>41<\/td>3.03<\/td>19.35<\/td>25<\/td>17.75<\/td>\n<\/tr>\n
57<\/td>5<\/td>SE<\/td>Kansas St.<\/td>B12<\/td>22-10<\/td>19.41<\/td>23<\/td>1.50<\/td>20.91<\/td>21<\/td>14.77<\/td>\n<\/tr>\n
58<\/td>12<\/td>SE<\/td>Utah St.<\/td>WAC<\/td>30-3<\/td>20.35<\/td>20<\/td>1.44<\/td>21.79<\/td>19<\/td>15.45<\/td>\n<\/tr>\n
59<\/td>13<\/td>SE<\/td>Belmont<\/td>ASun<\/td>30-4<\/td>18.60<\/td>29<\/td>-2.68<\/td>15.92<\/td>42<\/td>16.76<\/td>\n<\/tr>\n
60<\/td>4<\/td>SE<\/td>Wisconsin<\/td>B10<\/td>23-8<\/td>26.79<\/td>7<\/td>-0.64<\/td>26.15<\/td>9<\/td>16.88<\/td>\n<\/tr>\n
61<\/td>3<\/td>SE<\/td>Brigham Young<\/td>MWC<\/td>30-4<\/td>23.40<\/td>13<\/td>1.35<\/td>24.75<\/td>12<\/td>15.71<\/td>\n<\/tr>\n
62<\/td>14<\/td>SE<\/td>Wofford<\/td>SC<\/td>21-12<\/td>8.09<\/td>87<\/td>-1.26<\/td>6.84<\/td>54<\/td>17.07<\/td>\n<\/tr>\n
63<\/td>11<\/td>SE<\/td>Gonzaga<\/td>WCC<\/td>24-9<\/td>18.46<\/td>32<\/td>-2.22<\/td>16.24<\/td>41<\/td>14.68<\/td>\n<\/tr>\n
64<\/td>6<\/td>SE<\/td>St. John's<\/td>BE<\/td>21-11<\/td>16.66<\/td>40<\/td>1.76<\/td>18.42<\/td>31<\/td>17.79<\/td>\n<\/tr>\n
65<\/td>7<\/td>SE<\/td>UCLA<\/td>P10<\/td>22-10<\/td>14.61<\/td>52<\/td>3.58<\/td>18.18<\/td>32<\/td>14.67<\/td>\n<\/tr>\n
66<\/td>10<\/td>SE<\/td>Michigan St.<\/td>B10<\/td>19-14<\/td>17.09<\/td>38<\/td>0.46<\/td>17.55<\/td>38<\/td>16.02<\/td>\n<\/tr>\n
67<\/td>15<\/td>SE<\/td>UC Santa Barbara<\/td>BW<\/td>18-13<\/td>2.19<\/td>137<\/td>3.56<\/td>5.74<\/td>56<\/td>14.84<\/td>\n<\/tr>\n
68<\/td>2<\/td>SE<\/td>Florida<\/td>SEC<\/td>26-7<\/td>21.50<\/td>18<\/td>1.74<\/td>23.24<\/td>16<\/td>16.39<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

A few notes:<\/p>\n

    \n
  • Teams to watch out for: Clemson, Utah St., Marquette, Missouri, Illinois, and Texas.<\/li>\n
  • Overseeded teams: Arizona, George Mason, ODU, Cincinnati, Texas A&M, and Vanderbilt.<\/li>\n
  • Hampton raises its game a lot, but it’s still not good.\u00a0 San Diego does quite a bit also, and they are good.<\/li>\n
  • Duke and Arizona got their great efficiencies by beating up on the little guys.<\/li>\n<\/ul>\n

    And here are my directly calculated odds for each team to reach each level in the tournament:<\/p>\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
    O<\/th>Sd<\/th>Re<\/th>Team<\/th>64<\/th>32<\/th>16<\/th>Elite 8<\/th>Final 4<\/th>Final<\/th>Champ<\/th>1 in<\/th>\n<\/tr>\n<\/thead>\n
    1<\/td>1<\/td>E<\/td>Ohio St.<\/td>100<\/td>99.74<\/td>86.265<\/td>61.971<\/td>46.4918<\/td>31.0991<\/td>21.39532<\/td>4.67<\/td>\n<\/tr>\n
    8<\/td>4<\/td>E<\/td>Kentucky<\/td>100<\/td>92.37<\/td>59.225<\/td>22.991<\/td>13.9956<\/td>6.9810<\/td>3.68788<\/td>27.1<\/td>\n<\/tr>\n
    9<\/td>3<\/td>E<\/td>Syracuse<\/td>100<\/td>88.90<\/td>53.936<\/td>32.034<\/td>12.4445<\/td>5.6966<\/td>2.76581<\/td>36.2<\/td>\n<\/tr>\n
    16<\/td>2<\/td>E<\/td>North Carolina<\/td>100<\/td>90.42<\/td>56.027<\/td>28.646<\/td>9.7302<\/td>3.9611<\/td>1.73444<\/td>57.7<\/td>\n<\/tr>\n
    12<\/td>6<\/td>E<\/td>Xavier<\/td>100<\/td>54.82<\/td>25.495<\/td>13.004<\/td>4.0086<\/td>1.4810<\/td>0.59137<\/td>169<\/td>\n<\/tr>\n
    13<\/td>7<\/td>E<\/td>Washington<\/td>100<\/td>64.00<\/td>30.138<\/td>13.348<\/td>3.6887<\/td>1.2382<\/td>0.45524<\/td>220<\/td>\n<\/tr>\n
    5<\/td>5<\/td>E<\/td>West Virginia<\/td>100<\/td>53.59<\/td>21.430<\/td>5.842<\/td>2.8131<\/td>1.0161<\/td>0.40160<\/td>249<\/td>\n<\/tr>\n
    6<\/td>12<\/td>E<\/td>Clemson<\/td>80.0<\/td>41.91<\/td>17.492<\/td>4.957<\/td>2.4906<\/td>0.9413<\/td>0.38895<\/td>257<\/td>\n<\/tr>\n
    11<\/td>11<\/td>E<\/td>Marquette<\/td>100<\/td>45.18<\/td>18.821<\/td>8.684<\/td>2.1555<\/td>0.6591<\/td>0.22431<\/td>446<\/td>\n<\/tr>\n
    3<\/td>9<\/td>E<\/td>Villanova<\/td>100<\/td>58.36<\/td>9.079<\/td>2.929<\/td>1.1236<\/td>0.3055<\/td>0.09283<\/td>1077<\/td>\n<\/tr>\n
    14<\/td>10<\/td>E<\/td>Georgia<\/td>100<\/td>36.00<\/td>12.259<\/td>3.833<\/td>0.6438<\/td>0.1347<\/td>0.03235<\/td>3091<\/td>\n<\/tr>\n
    4<\/td>8<\/td>E<\/td>George Mason<\/td>100<\/td>41.64<\/td>4.636<\/td>1.161<\/td>0.3592<\/td>0.0741<\/td>0.01750<\/td>5714<\/td>\n<\/tr>\n
    6<\/td>12<\/td>E<\/td>UAB<\/td>20.0<\/td>4.50<\/td>0.778<\/td>0.081<\/td>0.0187<\/td>0.0026<\/td>0.00042<\/td>236328<\/td>\n<\/tr>\n
    10<\/td>14<\/td>E<\/td>Indiana St.<\/td>100<\/td>11.10<\/td>1.748<\/td>0.273<\/td>0.0163<\/td>0.0012<\/td>0.00011<\/td>872170<\/td>\n<\/tr>\n
    7<\/td>13<\/td>E<\/td>Princeton<\/td>100<\/td>7.63<\/td>1.075<\/td>0.067<\/td>0.0101<\/td>0.0008<\/td>0.00008<\/td>1261187<\/td>\n<\/tr>\n
    15<\/td>15<\/td>E<\/td>Long Island<\/td>100<\/td>9.58<\/td>1.576<\/td>0.178<\/td>0.0073<\/td>0.0004<\/td>0.00003<\/td>3684929<\/td>\n<\/tr>\n
    2<\/td>16<\/td>E<\/td>Texas San Antonio<\/td>81.4<\/td>0.24<\/td>0.017<\/td>0.000<\/td>0.0000<\/td>0.0000<\/td>0.00000<\/td>32042448855<\/td>\n<\/tr>\n
    2<\/td>16<\/td>E<\/td>Alabama St.<\/td>18.6<\/td>0.02<\/td>0.001<\/td>0.000<\/td>0.0000<\/td>0.0000<\/td>0.00000<\/td>92485855933097<\/td>\n<\/tr>\n
    19<\/td>1<\/td>W<\/td>Duke<\/td>100<\/td>97.71<\/td>78.072<\/td>46.442<\/td>30.5745<\/td>16.0242<\/td>9.54891<\/td>10.47<\/td>\n<\/tr>\n
    26<\/td>4<\/td>W<\/td>Texas<\/td>100<\/td>91.36<\/td>78.143<\/td>42.890<\/td>27.2983<\/td>13.9476<\/td>8.05711<\/td>12.41<\/td>\n<\/tr>\n
    34<\/td>2<\/td>W<\/td>San Diego St.<\/td>100<\/td>97.82<\/td>71.862<\/td>46.694<\/td>21.8962<\/td>10.0679<\/td>5.28571<\/td>18.92<\/td>\n<\/tr>\n
    27<\/td>3<\/td>W<\/td>Connecticut<\/td>100<\/td>89.76<\/td>56.499<\/td>26.854<\/td>10.0105<\/td>3.7336<\/td>1.61838<\/td>61.8<\/td>\n<\/tr>\n
    29<\/td>11<\/td>W<\/td>Missouri<\/td>100<\/td>52.07<\/td>21.844<\/td>7.877<\/td>2.1044<\/td>0.5794<\/td>0.18736<\/td>534<\/td>\n<\/tr>\n
    30<\/td>6<\/td>W<\/td>Cincinnati<\/td>100<\/td>47.93<\/td>19.623<\/td>6.978<\/td>1.9010<\/td>0.5275<\/td>0.16976<\/td>589<\/td>\n<\/tr>\n
    21<\/td>9<\/td>W<\/td>Tennessee<\/td>100<\/td>52.95<\/td>11.970<\/td>3.939<\/td>1.4547<\/td>0.3916<\/td>0.12428<\/td>805<\/td>\n<\/tr>\n
    31<\/td>7<\/td>W<\/td>Temple<\/td>100<\/td>52.85<\/td>14.729<\/td>6.102<\/td>1.4727<\/td>0.3715<\/td>0.11084<\/td>902<\/td>\n<\/tr>\n
    32<\/td>10<\/td>W<\/td>Penn St.<\/td>100<\/td>47.15<\/td>13.184<\/td>5.253<\/td>1.2949<\/td>0.3283<\/td>0.09705<\/td>1030<\/td>\n<\/tr>\n
    22<\/td>8<\/td>W<\/td>Michigan<\/td>100<\/td>47.05<\/td>9.633<\/td>2.951<\/td>1.0136<\/td>0.2518<\/td>0.07393<\/td>1353<\/td>\n<\/tr>\n
    23<\/td>5<\/td>W<\/td>Arizona<\/td>100<\/td>64.88<\/td>13.699<\/td>2.793<\/td>0.7924<\/td>0.1598<\/td>0.03829<\/td>2612<\/td>\n<\/tr>\n
    24<\/td>12<\/td>W<\/td>Memphis<\/td>100<\/td>35.12<\/td>4.599<\/td>0.562<\/td>0.1012<\/td>0.0126<\/td>0.00188<\/td>53133<\/td>\n<\/tr>\n
    25<\/td>13<\/td>W<\/td>Oakland<\/td>100<\/td>8.64<\/td>3.560<\/td>0.396<\/td>0.0681<\/td>0.0079<\/td>0.00111<\/td>89988<\/td>\n<\/tr>\n
    28<\/td>14<\/td>W<\/td>Bucknell<\/td>100<\/td>10.24<\/td>2.034<\/td>0.226<\/td>0.0148<\/td>0.0012<\/td>0.00011<\/td>935504<\/td>\n<\/tr>\n
    20<\/td>16<\/td>W<\/td>Hampton<\/td>100<\/td>2.29<\/td>0.325<\/td>0.027<\/td>0.0023<\/td>0.0001<\/td>0.00001<\/td>11921993<\/td>\n<\/tr>\n
    33<\/td>15<\/td>W<\/td>Northern Colorado<\/td>100<\/td>2.18<\/td>0.225<\/td>0.015<\/td>0.0003<\/td>0.0000<\/td>0.00000<\/td>283924556<\/td>\n<\/tr>\n
    36<\/td>1<\/td>SW<\/td>Kansas<\/td>100<\/td>98.23<\/td>74.808<\/td>53.807<\/td>34.8755<\/td>22.7012<\/td>12.19612<\/td>8.20<\/td>\n<\/tr>\n
    44<\/td>3<\/td>SW<\/td>Purdue<\/td>100<\/td>95.09<\/td>67.158<\/td>39.793<\/td>19.9643<\/td>11.1169<\/td>4.85640<\/td>20.6<\/td>\n<\/tr>\n
    51<\/td>2<\/td>SW<\/td>Notre Dame<\/td>100<\/td>94.48<\/td>69.823<\/td>38.343<\/td>18.6570<\/td>10.0540<\/td>4.27609<\/td>23.4<\/td>\n<\/tr>\n
    43<\/td>4<\/td>SW<\/td>Louisville<\/td>100<\/td>83.20<\/td>58.053<\/td>24.605<\/td>12.5245<\/td>6.3875<\/td>2.49977<\/td>40.0<\/td>\n<\/tr>\n
    38<\/td>9<\/td>SW<\/td>Illinois<\/td>100<\/td>55.97<\/td>14.822<\/td>7.233<\/td>2.9317<\/td>1.1871<\/td>0.34145<\/td>293<\/td>\n<\/tr>\n
    47<\/td>6<\/td>SW<\/td>Georgetown<\/td>100<\/td>57.52<\/td>19.716<\/td>8.116<\/td>2.6492<\/td>0.9904<\/td>0.26462<\/td>378<\/td>\n<\/tr>\n
    40<\/td>5<\/td>SW<\/td>Vanderbilt<\/td>100<\/td>61.46<\/td>24.637<\/td>6.773<\/td>2.3841<\/td>0.8385<\/td>0.20407<\/td>490<\/td>\n<\/tr>\n
    39<\/td>8<\/td>SW<\/td>Nevada Las Vegas<\/td>100<\/td>44.03<\/td>10.247<\/td>4.454<\/td>1.5950<\/td>0.5713<\/td>0.14397<\/td>695<\/td>\n<\/tr>\n
    48<\/td>7<\/td>SW<\/td>Texas A&M<\/td>100<\/td>56.37<\/td>18.024<\/td>5.986<\/td>1.6408<\/td>0.5253<\/td>0.11272<\/td>887<\/td>\n<\/tr>\n
    46<\/td>11<\/td>SW<\/td>Southern California<\/td>62.8<\/td>29.83<\/td>9.794<\/td>3.835<\/td>1.1966<\/td>0.4269<\/td>0.10962<\/td>912<\/td>\n<\/tr>\n
    41<\/td>12<\/td>SW<\/td>Richmond<\/td>100<\/td>38.54<\/td>11.894<\/td>2.391<\/td>0.6306<\/td>0.1666<\/td>0.02921<\/td>3424<\/td>\n<\/tr>\n
    49<\/td>10<\/td>SW<\/td>Florida St.<\/td>100<\/td>43.63<\/td>11.510<\/td>3.122<\/td>0.6739<\/td>0.1744<\/td>0.02766<\/td>3615<\/td>\n<\/tr>\n
    46<\/td>11<\/td>SW<\/td>Virginia Commonwealth<\/td>37.2<\/td>12.65<\/td>2.646<\/td>0.700<\/td>0.1366<\/td>0.0317<\/td>0.00470<\/td>21274<\/td>\n<\/tr>\n
    42<\/td>13<\/td>SW<\/td>Morehead St.<\/td>100<\/td>16.80<\/td>5.415<\/td>0.729<\/td>0.1338<\/td>0.0247<\/td>0.00283<\/td>35298<\/td>\n<\/tr>\n
    45<\/td>14<\/td>SW<\/td>St. Peter's<\/td>100<\/td>4.91<\/td>0.686<\/td>0.059<\/td>0.0035<\/td>0.0003<\/td>0.00001<\/td>9254589<\/td>\n<\/tr>\n
    50<\/td>15<\/td>SW<\/td>Akron<\/td>100<\/td>5.52<\/td>0.643<\/td>0.045<\/td>0.0023<\/td>0.0002<\/td>0.00001<\/td>18342534<\/td>\n<\/tr>\n
    37<\/td>16<\/td>SW<\/td>Boston University<\/td>100<\/td>1.77<\/td>0.123<\/td>0.009<\/td>0.0004<\/td>0.0000<\/td>0.00000<\/td>187954430<\/td>\n<\/tr>\n
    53<\/td>1<\/td>SE<\/td>Pittsburgh<\/td>100<\/td>97.80<\/td>72.996<\/td>44.334<\/td>28.3021<\/td>14.8112<\/td>6.69897<\/td>14.93<\/td>\n<\/tr>\n
    61<\/td>3<\/td>SE<\/td>Brigham Young<\/td>100<\/td>86.25<\/td>58.306<\/td>35.203<\/td>17.6695<\/td>8.2399<\/td>3.32266<\/td>30.1<\/td>\n<\/tr>\n
    60<\/td>4<\/td>SE<\/td>Wisconsin<\/td>100<\/td>72.83<\/td>44.945<\/td>24.059<\/td>14.5186<\/td>7.2797<\/td>3.20779<\/td>31.2<\/td>\n<\/tr>\n
    68<\/td>2<\/td>SE<\/td>Florida<\/td>100<\/td>86.84<\/td>54.880<\/td>29.759<\/td>13.8063<\/td>5.9385<\/td>2.19205<\/td>45.6<\/td>\n<\/tr>\n
    58<\/td>12<\/td>SE<\/td>Utah St.<\/td>100<\/td>52.33<\/td>24.144<\/td>10.166<\/td>5.0966<\/td>1.9999<\/td>0.66136<\/td>151<\/td>\n<\/tr>\n
    57<\/td>5<\/td>SE<\/td>Kansas St.<\/td>100<\/td>47.67<\/td>20.953<\/td>8.289<\/td>3.9709<\/td>1.4627<\/td>0.44823<\/td>223<\/td>\n<\/tr>\n
    56<\/td>8<\/td>SE<\/td>Butler<\/td>100<\/td>63.22<\/td>20.357<\/td>8.492<\/td>3.7786<\/td>1.3035<\/td>0.37840<\/td>264<\/td>\n<\/tr>\n
    64<\/td>6<\/td>SE<\/td>St. John's<\/td>100<\/td>55.32<\/td>22.533<\/td>10.194<\/td>3.6046<\/td>1.1722<\/td>0.31870<\/td>314<\/td>\n<\/tr>\n
    65<\/td>7<\/td>SE<\/td>UCLA<\/td>100<\/td>51.64<\/td>22.153<\/td>9.283<\/td>3.0833<\/td>0.9352<\/td>0.22991<\/td>435<\/td>\n<\/tr>\n
    66<\/td>10<\/td>SE<\/td>Michigan St.<\/td>100<\/td>48.36<\/td>20.196<\/td>8.230<\/td>2.6733<\/td>0.7939<\/td>0.19261<\/td>519<\/td>\n<\/tr>\n
    63<\/td>11<\/td>SE<\/td>Gonzaga<\/td>100<\/td>44.68<\/td>15.533<\/td>6.112<\/td>1.7531<\/td>0.4568<\/td>0.09473<\/td>1056<\/td>\n<\/tr>\n
    59<\/td>13<\/td>SE<\/td>Belmont<\/td>100<\/td>27.17<\/td>9.958<\/td>2.871<\/td>1.0459<\/td>0.2797<\/td>0.06073<\/td>1647<\/td>\n<\/tr>\n
    55<\/td>9<\/td>SE<\/td>Old Dominion<\/td>100<\/td>36.78<\/td>6.360<\/td>1.769<\/td>0.5415<\/td>0.1124<\/td>0.01790<\/td>5585<\/td>\n<\/tr>\n
    62<\/td>14<\/td>SE<\/td>Wofford<\/td>100<\/td>13.75<\/td>3.628<\/td>0.759<\/td>0.1046<\/td>0.0128<\/td>0.00118<\/td>84838<\/td>\n<\/tr>\n
    67<\/td>15<\/td>SE<\/td>UC Santa Barbara<\/td>100<\/td>13.16<\/td>2.771<\/td>0.460<\/td>0.0494<\/td>0.0046<\/td>0.00031<\/td>320919<\/td>\n<\/tr>\n
    54<\/td>16<\/td>SE<\/td>NC Asheville<\/td>77.7<\/td>2.17<\/td>0.286<\/td>0.021<\/td>0.0018<\/td>0.0001<\/td>0.00000<\/td>33535383<\/td>\n<\/tr>\n
    54<\/td>16<\/td>SE<\/td>Arkansas Little Rock<\/td>22.3<\/td>0.03<\/td>0.001<\/td>0.000<\/td>0.0000<\/td>0.0000<\/td>0.00000<\/td>57507213911169<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n

    That’s a bit hard to follow, so perhaps a pretty chart would be easier:<\/p>\n

    \"\"<\/a>

    Tourney Flow 2011<\/p><\/div>\n

    This helps us visualize which parts of the bracket are harder and which are easier.\u00a0 In particular, Pitt’s bracket is really weak.\u00a0 Ohio State is a solid favorite.<\/p>\n

    EDIT: Spreadsheets NOW AVAILABLE:<\/p>\n