March 28, 2006: Predictions (final four)

Both of the preliminary games feature one team that is clearly better than the other. But, as always, the final four teams are sufficiently close in talent that anything can happen.

Florida has a 69% chance of knocking off George Mason, but of course that means a 31% chance that they won't. And UCLA has a 55% chance of winning against LSU. This makes for the following odds of championship matchups:

• Florida/UCLA: 38.1% (Florida wins 53.8%)
• Florida/LSU: 30.7% (Florida wins 59.1%)
• UCLA/George Mason: 17.3% (UCLA wins 65.3%)
• LSU/George Mason: 13.9% (LSU wins 60.2%)

Combining the odds of each matchup occurring, along with the odds of each team winning, we estimate that the teams have the following chance of winning the tournament:

• Florida: 38.6%
• UCLA: 28.9%
• LSU: 20.9%
• George Mason: 11.6%

Not that I don't like George Mason. They deserved much better than an 11-seed. But they'll have to overcome 2-1 odds in both upcoming games to win the title. The most likely outcome is Florida winning the first game, which would set up a fairly evenly-matched championship game (whoever wins the Texas/UCLA game).

March 28, 2006: Predictions (fourth round)

Next for the odds of the 8 third-round winners advancing:

``````
FNL4  FNL2 CHAMP
0.658 0.401 0.235 TEXAS
0.711 0.390 0.207 CONNECTICUT
0.521 0.273 0.135 FLORIDA
0.479 0.242 0.115 VILLANOVA
0.516 0.234 0.113 UCLA
0.484 0.212 0.100 MEMPHIS
0.342 0.154 0.066 LOUISIANA ST.
0.289 0.096 0.031 GEORGE MASON
``````
The seeded teams went a combined 0-4, while my predicted winners went a combined 2-2. According to the calculations, the seeds should have won 2.3, while my favorites should have won 2.4.

For the first four rounds, that makes a total of 20 upsets in 60 games according to the seedings, compared with an expectation of 19.5 +/- 3.47. Versus my lines, there were 17 upsets, compared with an expected 18.9 +/- 3.47.

Adding in last season's first two rounds as well, there were 34 upsets (according to the seeds) in 108 games, compared with an expected 33.0 +/- 4.29. Versus my lines, there were 30 upsets, compared with an expected 31.4 +/- 4.29.

It's probably not worth belaboring the point any further. Suffice it to say that, to a very high degree of precision (108 games), tournament games have the same tendency for upsets as regular-season games.

March 28, 2006: Predictions (third round)

Next for the odds of the 16 second-round winners advancing:

``````
ELT8  FNL4  FNL2 CHAMP
0.622 0.461 0.272 0.147 CONNECTICUT
0.743 0.437 0.200 0.105 UCLA
0.721 0.420 0.275 0.172 TEXAS
0.663 0.356 0.195 0.095 VILLANOVA
0.662 0.353 0.222 0.132 DUKE
0.619 0.349 0.195 0.097 FLORIDA
0.629 0.329 0.137 0.066 MEMPHIS
0.378 0.238 0.111 0.047 WASHINGTON
0.545 0.173 0.062 0.020 GEORGE MASON
0.381 0.169 0.075 0.028 GEORGETOWN
0.455 0.128 0.041 0.011 WICHITA ST.
0.338 0.127 0.059 0.026 LOUISIANA ST.
0.337 0.126 0.049 0.016 BOSTON COLLEGE
0.279 0.100 0.043 0.017 WEST VIRGINIA
0.257 0.086 0.020 0.006 GONZAGA
``````
The seeded teams went a combined 6-2, while my predicted winners went a combined 7-1. According to the calculations, the seeds should have won 5.1, while my favorites should have won 5.2.

For the first three rounds, that makes a total of 16 upsets in 56 games according to the seedings, compared with an expectation of 17.8 +/- 3.33. Versus my lines, there were 15 upsets, compared with an expected 17.3 +/- 3.33.

Adding in last season's first two rounds as well, there were 30 upsets (according to the seeds) in 104 games, compared with an expected 31.3 +/- 4.18. Versus my lines, there were 28 upsets, compared with an expected 29.8 +/- 4.18.

March 28, 2006: Predictions (second round)

Next for the odds of the 32 first-round winners advancing:

``````
SWT16  ELT8  FNL4  FNL2 CHAMP
0.790 0.594 0.355 0.232 0.141 TEXAS
0.812 0.561 0.331 0.214 0.128 DUKE
0.788 0.588 0.360 0.181 0.098 UCLA
0.707 0.497 0.266 0.156 0.082 NORTH CAROLINA
0.672 0.485 0.283 0.152 0.078 VILLANOVA
0.745 0.471 0.303 0.190 0.109 CONNECTICUT
0.752 0.454 0.265 0.138 0.069 FLORIDA
0.720 0.403 0.219 0.096 0.046 MEMPHIS
0.618 0.338 0.179 0.076 0.035 PITTSBURGH
0.788 0.281 0.109 0.049 0.019 WEST VIRGINIA
0.720 0.277 0.114 0.042 0.015 BOSTON COLLEGE
0.555 0.270 0.137 0.061 0.026 OHIO ST.
0.589 0.239 0.105 0.052 0.023 LOUISIANA ST.
0.583 0.227 0.083 0.034 0.012 TENNESSEE
0.506 0.221 0.115 0.058 0.026 ILLINOIS
0.494 0.213 0.109 0.054 0.024 WASHINGTON
0.445 0.193 0.087 0.034 0.013 GEORGETOWN
0.328 0.184 0.075 0.028 0.010 ARIZONA
0.545 0.182 0.069 0.019 0.006 INDIANA
0.382 0.165 0.069 0.022 0.008 BRADLEY
0.293 0.145 0.048 0.018 0.006 GEORGE MASON
0.455 0.135 0.045 0.011 0.003 GONZAGA
0.411 0.134 0.048 0.019 0.007 TEXAS A&M
0.417 0.131 0.038 0.013 0.004 WICHITA ST.
0.210 0.097 0.029 0.010 0.003 N.C. STATE
0.255 0.095 0.038 0.014 0.005 KENTUCKY
0.212 0.094 0.029 0.006 0.002 ALABAMA
0.280 0.093 0.031 0.007 0.002 BUCKNELL
0.248 0.084 0.027 0.007 0.002 WIS.-MILWAUKEE
0.188 0.066 0.018 0.006 0.002 GEORGE WASHINGTON
0.280 0.054 0.012 0.002 0.000 MONTANA
0.212 0.028 0.004 0.001 0.000 NORTHWESTERN ST.
``````
The seeded teams went a combined 11-5, while my predicted winners went a combined 10-6. According to the calculations, the seeds should have won 10.8, while my favorites should have won 10.9.

For the first two rounds, that makes a total of 14 upsets in 48 games, both by the seedings and by my lines. The expected number of upsets is 14.9 +/- 3.05 and 14.5 +/- 3.05, respectively.

Including last season, there were 28 upsets (according to the seeds) in 96 games, compared with an expected 28.4 +/- 4.18. Versus my lines, there were 27 upsets, compared with an expected 27.0 +/- 4.18.

March 28, 2006: Predictions (zero/first rounds)

Below are the odds of each of the 64 teams advancing to each round in the tournament (again, calculated based on pre-tournament rankings):

``````
FIRST SECND SWT16  ELT8  FNL4  FNL2 CHAMP
1.000 0.976 0.789 0.589 0.357 0.231 0.141 DUKE
1.000 0.934 0.735 0.504 0.328 0.212 0.120 CONNECTICUT
1.000 0.907 0.733 0.546 0.334 0.219 0.135 TEXAS
1.000 0.964 0.698 0.514 0.324 0.176 0.090 VILLANOVA
1.000 0.925 0.654 0.481 0.250 0.115 0.057 UCLA
1.000 0.891 0.659 0.499 0.283 0.174 0.093 NORTH CAROLINA
1.000 0.798 0.570 0.340 0.189 0.092 0.043 FLORIDA
1.000 0.836 0.529 0.250 0.146 0.062 0.029 MEMPHIS
1.000 0.753 0.522 0.355 0.247 0.135 0.079 KANSAS
1.000 0.856 0.516 0.289 0.149 0.067 0.028 OHIO ST.
1.000 0.821 0.488 0.193 0.081 0.037 0.016 IOWA
1.000 0.716 0.467 0.188 0.071 0.031 0.011 TENNESSEE
1.000 0.698 0.425 0.163 0.069 0.032 0.013 LOUISIANA ST.
1.000 0.703 0.413 0.184 0.096 0.049 0.021 ILLINOIS
1.000 0.647 0.412 0.164 0.075 0.028 0.010 BOSTON COLLEGE
1.000 0.722 0.385 0.162 0.080 0.039 0.016 WASHINGTON
1.000 0.574 0.329 0.125 0.042 0.012 0.004 INDIANA
1.000 0.755 0.321 0.175 0.099 0.041 0.018 PITTSBURGH
1.000 0.676 0.318 0.103 0.039 0.012 0.003 NEVADA
1.000 0.660 0.315 0.124 0.063 0.022 0.009 ARKANSAS
1.000 0.590 0.296 0.102 0.037 0.015 0.005 WEST VIRGINIA
1.000 0.592 0.290 0.093 0.033 0.013 0.005 TEXAS A&M
1.000 0.575 0.278 0.136 0.061 0.023 0.008 GEORGETOWN
1.000 0.609 0.274 0.083 0.023 0.008 0.002 WICHITA ST.
1.000 0.539 0.256 0.085 0.024 0.006 0.002 GONZAGA
1.000 0.622 0.231 0.133 0.048 0.014 0.005 MARQUETTE
1.000 0.426 0.213 0.067 0.018 0.004 0.001 SAN DIEGO ST.
1.000 0.564 0.211 0.085 0.032 0.010 0.003 OKLAHOMA
1.000 0.461 0.201 0.060 0.015 0.003 0.001 XAVIER
1.000 0.425 0.176 0.074 0.028 0.009 0.003 N. IOWA
1.000 0.353 0.174 0.047 0.015 0.004 0.001 PACIFIC
1.000 0.410 0.171 0.046 0.013 0.004 0.001 S. ILLINOIS
1.000 0.600 0.167 0.071 0.028 0.011 0.003 KENTUCKY
1.000 0.516 0.164 0.088 0.029 0.011 0.003 MICHIGAN ST.
1.000 0.408 0.163 0.040 0.011 0.003 0.001 SYRACUSE
1.000 0.520 0.158 0.083 0.034 0.011 0.003 ARIZONA
1.000 0.484 0.147 0.077 0.025 0.009 0.003 GEORGE MASON
1.000 0.480 0.139 0.070 0.028 0.009 0.002 WISCONSIN
1.000 0.436 0.139 0.048 0.015 0.004 0.001 WIS.-MILWAUKEE
1.000 0.391 0.136 0.030 0.006 0.001 0.000 SETON HALL
1.000 0.302 0.122 0.027 0.007 0.002 0.000 IONA
1.000 0.284 0.122 0.026 0.005 0.001 0.000 WINTHROP
1.000 0.545 0.121 0.053 0.016 0.006 0.002 N.C.-WILMINGTON
1.000 0.502 0.119 0.050 0.015 0.005 0.001 N.C. STATE
1.000 0.498 0.117 0.049 0.015 0.005 0.001 CALIFORNIA
1.000 0.297 0.114 0.030 0.010 0.003 0.001 AIR FORCE
1.000 0.340 0.112 0.028 0.010 0.002 0.001 BUCKNELL
1.000 0.247 0.109 0.046 0.020 0.006 0.002 BRADLEY
1.000 0.378 0.101 0.046 0.012 0.002 0.001 ALABAMA
1.000 0.324 0.097 0.018 0.004 0.001 0.000 MONTANA
1.000 0.455 0.087 0.035 0.009 0.003 0.001 GEORGE WASHINGTON
1.000 0.278 0.087 0.020 0.006 0.002 0.000 UTAH ST.
1.000 0.400 0.082 0.027 0.008 0.002 0.001 ALA.-BIRMINGHAM
1.000 0.202 0.080 0.023 0.006 0.001 0.000 SOUTH ALABAMA
1.000 0.245 0.048 0.014 0.004 0.001 0.000 KENT ST.
1.000 0.179 0.045 0.006 0.001 0.000 0.000 NORTHWESTERN ST.
1.000 0.164 0.044 0.007 0.002 0.000 0.000 ORAL ROBERTS
1.000 0.144 0.031 0.006 0.001 0.000 0.000 DAVIDSON
1.000 0.109 0.030 0.009 0.001 0.000 0.000 MURRAY ST.
1.000 0.093 0.030 0.008 0.001 0.000 0.000 PENN
1.000 0.066 0.016 0.003 0.000 0.000 0.000 ALBANY, N.Y.
1.000 0.075 0.014 0.003 0.000 0.000 0.000 BELMONT
0.705 0.032 0.004 0.001 0.000 0.000 0.000 MONMOUTH, N.J.
1.000 0.024 0.003 0.000 0.000 0.000 0.000 SOUTHERN U.
0.295 0.004 0.000 0.000 0.000 0.000 0.000 HAMPTON
``````
As with last season, I'll keep two score tallies. One is based on the seedings, the other based on my predictive rankings. The seeded teams went a combined 23-9, while my predicted winners went a combined 24-8. This is actually better than the favorites would have been expected to perform, according to the rankings -- the calculations would expect 22.3-9.7 and 22.6-9.4, respectively.

Combined with last season, seeded favorites have gone 47-17, compared with a prediction of 18.2 +/- 3.3 upsets. My ranking favorites have gone 48-16, compared with a prediction of 17.0 +/- 3.3 upsets.

March 27, 2006: Selections

Obviously I'm a bit late writing this column this season, but I should make my customary comments (especially with the heat the selection committee took for certain at-large teams). So I'm writing this as objectively as possible, based on my rankings before any NCAA or NIT games were played.

First off, let's critique the selections. First off, there were 31 automatic bids. I'll list them here with important stats taken from my ranking page:

``````
STANDARD   PREDICTIVE     RPI
RNK RATING  RNK RATING  RNK RATING SD CREC TEAM
1  4.523    2  1.752    1 0.6841  1 14-2 DUKE
4  4.150    9  1.376    4 0.6507  1 13-1 MEMPHIS
6  4.121   53  0.810   10 0.6253  3 14-0 GONZAGA
9  4.003    8  1.441   15 0.6130  3 10-6 FLORIDA
10  3.996    7  1.457    9 0.6273  2 14-4 UCLA
15  3.854   15  1.254    7 0.6312  3 11-5 IOWA
17  3.840    4  1.687   20 0.6057  4 14-3 KANSAS
19  3.748   38  0.924   19 0.6064  5 13-3 NEVADA
22  3.652   60  0.757   42 0.5866  9 14-0 BUCKNELL
24  3.612   48  0.843   17 0.6107  5  7-9 SYRACUSE
40  3.447   37  0.929   28 0.5982  9 15-3 N.C.-WILMINGTON
46  3.387   42  0.878   29 0.5980 11 12-6 S. ILLINOIS
52  3.308   57  0.765   55 0.5752 11 13-3 SAN DIEGO ST.
56  3.236   63  0.739   64 0.5656 13 13-5 IONA
60  3.201   75  0.634   48 0.5804 12 15-3 KENT ST.
63  3.169   93  0.467   61 0.5684 12 12-2 MONTANA
64  3.168  116  0.336   60 0.5684 14 15-1 NORTHWESTERN ST.
67  3.149   67  0.711   77 0.5523 14  8-8 XAVIER
70  3.123   55  0.783   52 0.5774 11 12-4 WIS.-MILWAUKEE
71  3.119   80  0.607   66 0.5640 14 12-3 SOUTH ALABAMA
74  3.086   62  0.757   88 0.5455 13 12-2 PACIFIC
88  2.965  103  0.398   65 0.5644 14 17-3 MURRAY ST.
94  2.923   85  0.568   73 0.5577 15 13-3 WINTHROP
103  2.829   97  0.451   98 0.5390 15 12-2 PENN
119  2.690  102  0.399  130 0.5185 16 13-3 ORAL ROBERTS
125  2.654  126  0.276   94 0.5410 15 10-5 DAVIDSON
140  2.561  130  0.204  119 0.5228 16 13-3 ALBANY, N.Y.
160  2.375  176 -0.104  144 0.5097 17 12-6 MONMOUTH, N.J.
165  2.365  159  0.016  115 0.5271 15 15-5 BELMONT
180  2.250  196 -0.226  132 0.5164 16 15-3 SOUTHERN U.
293  1.267  270 -0.642  284 0.4280 18 10-8 HAMPTON
``````

So, that's 31 out of 65 teams. Now let's look at the teams that would be considered locks for historical reasons (RPI top-32, or RPI top-50 with 20 wins in a major conference).

``````
STANDARD   PREDICTIVE     RPI
RNK RATING  RNK RATING  RNK RATING SD CREC TEAM
2  4.376    3  1.714    3 0.6509  1 14-2 CONNECTICUT
3  4.309    6  1.581    2 0.6662  1 14-2 VILLANOVA
5  4.131    1  1.776    8 0.6299  2 13-4 TEXAS
7  4.052   11  1.337    5 0.6400  2 12-4 OHIO ST.
8  4.023   52  0.817   37 0.5918  8 16-0 GEORGE WASHINGTON
11  3.981   10  1.358   14 0.6202  4 11-5 ILLINOIS
12  3.926    5  1.632   12 0.6222  3 11-5 NORTH CAROLINA
13  3.910   19  1.134   22 0.6020  4 11-5 BOSTON COLLEGE
14  3.870   12  1.325   11 0.6230  5 10-6 PITTSBURGH
16  3.841   18  1.139    6 0.6329  2 12-4 TENNESSEE
18  3.772   14  1.259   13 0.6216  4 14-2 LOUISIANA ST.
20  3.735   13  1.289   35 0.5922  5 13-5 WASHINGTON
21  3.686   17  1.155   36 0.5920  7 10-6 GEORGETOWN
23  3.625   20  1.105   38 0.5918  6 11-5 WEST VIRGINIA
25  3.589   45  0.851   27 0.5983  7 14-4 WICHITA ST.
26  3.578   36  0.943   16 0.6118  6 11-5 OKLAHOMA
27  3.571   21  1.076   44 0.5847 12 10-6 TEXAS A&M
29  3.556   16  1.169   45 0.5829  8 10-6 ARKANSAS
30  3.549   65  0.717   30 0.5971 XX 14-4 HOFSTRA
31  3.543   25  1.011   18 0.6085  6  8-8 MICHIGAN ST.
32  3.524   58  0.762   32 0.5943  9 12-2 ALA.-BIRMINGHAM
33  3.513   22  1.062   21 0.6030 XX 12-6 MISSOURI ST.
34  3.506   23  1.024   31 0.5962  7 10-6 MARQUETTE
35  3.499   33  0.966   25 0.5990 10 11-7 N. IOWA
37  3.471   26  1.008   24 0.5992  8 11-7 ARIZONA
38  3.455   24  1.016   41 0.5890  8  9-7 KENTUCKY
41  3.441   32  0.970   26 0.5984 11 15-3 GEORGE MASON
49  3.366   34  0.959   23 0.6000  9  9-7 WISCONSIN
``````

So that's 26 of 28 "locks" that made the tournament. The teams left out were Missouri State and Hofstra. Missouri State's omission is especially curious. They finished tied for second in their conference, and were the top-ranked MVC team in the RPI rankings. Most likely, it was "MVC fatigue"; Wichita State and Bradley were also selected as at-large bids, and the commmittee probably felt that the MVC didn't deserve a fourth bid. Of course, any objective measurement ranked Missouri State ahead of Bradley (and Missouri State also had a better conference record), so this still is a very curious choice.

The other omission was Hofstra, a team ranked #30 in the RPI, as well as #30 in my win-loss ranking. The only reason to leave out Hofstra is their poor score-based (predictive) ranking, which is a fair enough excuse. But, if we're leaving out teams we suspect aren't good (despite a good record), UAB would have been an equally good team to leave out, and they were given a 9-seed for having finished second in a supposedly major conference (never mind that CAA was stronger than CUSA this year). More likely, the committee didn't want to take more than two CAA teams.

It's probably worth noting that this is the second straight year in which two "historical locks" have been omitted, and both years, both teams left out were from mid-major conferences...

OK, now for the teams on the bubble. This means teams in the RPI top 68, preferably at least at .500 in conference play.

``````
STANDARD   PREDICTIVE     RPI
RNK RATING  RNK RATING  RNK RATING SD CREC TEAM
28  3.565   39  0.908   51 0.5790 10 10-6 N.C. STATE
36  3.472   31  0.971   63 0.5658 XX  9-7 FLORIDA ST.
39  3.448   35  0.951   34 0.5932  6  9-7 INDIANA
42  3.439   50  0.824   50 0.5791 13 12-4 AIR FORCE
43  3.435   64  0.720   59 0.5716 XX  9-7 COLORADO
44  3.433   40  0.902   57 0.5739  7 12-6 CALIFORNIA
45  3.412   44  0.858   47 0.5807 XX  8-8 MICHIGAN
47  3.383   41  0.879   40 0.5895 XX  8-8 CINCINNATI
48  3.371   61  0.757   39 0.5906 XX 12-6 CREIGHTON
50  3.363   54  0.799   49 0.5799 XX  8-8 MARYLAND
51  3.331   27  1.003   33 0.5934 13 11-7 BRADLEY
53  3.278   83  0.575   58 0.5725 10  9-7 SETON HALL
54  3.246   68  0.700   46 0.5815 12 11-5 UTAH ST.
57  3.226   66  0.713   56 0.5748 10 10-6 ALABAMA
58  3.225   29  0.993   43 0.5862 XX  9-7 ST. JOSEPH'S
61  3.194   91  0.472   67 0.5638 XX 12-4 BRIGHAM YOUNG
62  3.193   96  0.457   54 0.5766 XX 12-2 W. KENTUCKY
73  3.103   81  0.598   53 0.5773 XX  9-5 HOUSTON
84  2.995   86  0.517   68 0.5620 XX 11-5 LOUISIANA TECH
``````

Needless to say, we've got some very curious selections here. First the good — the bottom six teams in my rankings were all left out. Also, all teams exactly .500 were left out. And we can understand Florida State's omission due to a poor RPI. (FSU ranked #31 in my "improved RPI", once again demonstrating that the NCAA really needs a new official ranking system, but this can't be blamed on the committee.)

This leaves the selections of Seton Hall, Utah State, and Alabama, while Colorado and Creighton were left out. Creighton was apparently a MVC team that "had" to be left out (along with Missouri State). As for Colorado, this is another inexplicable omission; the Buffalos were probably dumped due to the combination of poor RPI and predictive ranking.

So putting all the selections and seedings together, what do we get? In terms of the tangible rankings, the selections are best modeled with 53% win-loss ranking, 31% RPI ranking, and 16% predictive ranking. So certainly it's nice to see that the committee's primary decision-making procedure mimics a statistically-sound ranking based on wins and losses only, but it's also disturbing to see that the RPI accounts for about 1/3 of the selection process.