## Margin-Aware Bradley-Terry: Yet Another Computer Rating System

[Bumped.  Izzo-Watch done. Back to the wonky stuff. And this is pretty darn wonky, even by my standards. -KJ]

Computer ranking algorithms are a bit of a hobby for me, mostly because the existing ones (at least, those whose formulas I know) are either incredibly complicated, flawed, or both. (And I need something to keep my mind off the Izzo rumors.) Last season I started experimenting with applying the Bradley-Terry method, a well-studied algorithm that (like RPI) cares only about wins and losses but does a much better job of accounting for strength of schedule in realistic ways, to college basketball. This contrasts with the Pomeroy rankings, which ignore wins and losses entirely in favor of point ratio. Both have their strengths and weaknesses; Bradley-Terry can't tell the difference between squeaking past a bubble team and leaving a smoking crater, while Pomeroy can't tell the difference between (31 point win + 1 point loss), (29 point win + 1 point win), and (two 15 point wins). So naturally, I wondered if there's a simple way to account for both in a single system. (The only other system I know of that attempts to do this is Sagarin's, but I don't know how his does it.)

Turns out, there is a simple modification to Bradley-Terry that passes the "sanity check".

Nothing about the Bradley-Terry algorithm requires that the number of wins and losses be an integer. So why not award fractional "victory points" based on the margin of victory? We want the value of an additional point to be greater in close games than in blowouts; the endgame situation isn't much affected if you're up 25 instead of 23, but a 3-point lead instead of a 1-point lead (or a 1-point lead instead of a 1-point deficit) is a much more significant change. In addition, the two teams should be awarded a total of 1 victory point for a game. A simple curve that fits these criteria:

VP = 1 / (1 + exp(-M/k))

where M is the margin of victory and k is a constant chosen to set the balance between wins and points. A win by k points is worth approximately 0.73 "wins" (and a loss by k is worth 0.27), by 2k is worth 0.88, by 3k is worth 0.95, and by 5k is worth 0.993.

(You may be wondering, where's the pace adjustment? Surely a 6-point win in a slow game is "better" than a 6-point win in a fast game, right? I don't believe it is, for one simple reason: Endgame pace and strategy is largely independent of the teams' stylistic preferences and is dictated almost entirely by time and score. If you're down 2 with 10 seconds left, it doesn't really matter whether you're down 42-40 or 102-100. The only case in which this is not true is when a game is such a massive blowout that the scrubs are in, and if it's that big a blowout a few points here or there has little effect.)

Once a team's "record" is calculated by adding up the victory points earned for each game, the Bradley-Terry method is applied without further modification to establish a ranking. But with the records no longer correlating to actual wins, the win probability computation becomes more complicated.

To see how the win probability and expected margin of victory could be calculated from these rankings, I used the pre-tournament data and tried out several values of k. Then I grouped all games played into several bands based on the ratios of the teams' ratings and calculated the favorites' win percentage and average margin in each band to see if a simple pattern emerged. (Actually, I wrote a short script that would spit out the rankings and a summary of the data - average margin and win percentage for each band - to quickly analyze. Poring through 4000+ games manually would be a royal pain.) What I hoped to see is that the win ratio followed a pattern similar to that of the simple Bradley-Terry method (where win ratio = rating ratio) and that the margin also had a simple relationship to the rating ratio.

The results: At a k value of 5, this season there was a solid pattern that held through a very wide range of rating gaps (anything where there were enough games to be even remotely significant). Smaller k values did not produce as clean a fit. Those fits:

Team A win ratio vs. Team B = (Team A rating / Team B rating)^1.5
Team A expected margin of victory vs. Team B = 8.5 ln (Team A rating / Team B rating)
(In other words, if Team A's rating is 4 and Team B's is 1, Team A will win 89% of the time and with an average margin of 11.8.)

Surprisingly, the expected margin of victory actually yields more "victory points" than one would expect given the ratio of the teams' ratings; that is, in the scenario above, if Team A were to win by 11 points their rating would go up and B's would go down despite that being the expected result. I'm not entirely sure I understand why this happens (I suspect it's a function of the awarded victory points decreasing much more sharply in closer games than they would increase in a bigger blowout, just as a favorite winning has less effect on the simple Bradley-Terry ratings than an upset would).

As expected, this method generally produces something between the unmodified Bradley-Terry ratings and Pomeroy's method. Some examples:

• Duke jumps from 5th in BT (and more than a 3:1 underdog to Kansas) to 3rd in MABT and slightly better than a 2:1 underdog to #1 Kansas. Duke was #1 in the pre-tournament Pomeroy rankings. Their chances of beating an average team rise from 96.74% to 98.22% (Pomeroy says 98.48%).
• New Mexico nose-dives from 10th (95.88%) to 28th (93.26%). They sit just outside the top 50 in Pomeroy's final rankings (86.28%).
• Ohio State (Pomeroy #5, 95.91%) jumps from 17th (94.19%) to 9th (96.39%).

A full table of the basic and margin-aware rankings follows. (These are pre-tournament calculations; I haven't rerun the numbers with tournament games included.)

Team BT Rating BT W% v Avg BT Rank MABT Rating MABT W% v Avg MABT Margin v Avg MABT Rank
Kansas 95.302 0.9896 1 22.085 0.9905 26.3 1
Syracuse 43.754 0.9777 3 15.279 0.9835 23.2 2
Duke 29.671 0.9674 5 14.491 0.9822 22.7 3
Kentucky 59.994 0.9836 2 12.070 0.9767 21.2 4
Kansas St. 24.833 0.9613 6 11.382 0.9746 20.7 5
West Virginia 35.488 0.9726 4 11.191 0.9740 20.5 6
Georgetown 20.109 0.9526 11 9.869 0.9688 19.5 7
Villanova 24.332 0.9605 8 9.139 0.9651 18.8 8
Ohio St. 16.217 0.9419 17 8.926 0.9639 18.6 9
Purdue 23.861 0.9598 9 8.872 0.9635 18.6 10
Baylor 19.324 0.9508 12 8.370 0.9603 18.1 11
Brigham Young 16.478 0.9428 16 8.306 0.9599 18.0 12
Wisconsin 13.624 0.9316 21 8.152 0.9588 17.8 13
Temple 24.397 0.9606 7 7.717 0.9554 17.4 14
Texas 13.689 0.9319 20 7.119 0.9500 16.7 15
Maryland 12.948 0.9283 22 6.982 0.9486 16.5 16
Pittsburgh 17.221 0.9451 13 6.772 0.9463 16.3 17
Texas A&M 15.868 0.9407 18 6.648 0.9449 16.1 18
Marquette 11.521 0.9201 27 6.599 0.9443 16.0 19
Notre Dame 10.301 0.9115 30 6.418 0.9421 15.8 20
Michigan St. 11.746 0.9215 26 6.303 0.9406 15.6 21
St. Mary's 11.224 0.9182 28 6.277 0.9402 15.6 22
Tennessee 16.485 0.9428 15 6.202 0.9392 15.5 23
California 8.361 0.8932 42 6.193 0.9391 15.5 24
Missouri 9.690 0.9065 33 6.139 0.9383 15.4 25
Butler 16.707 0.9435 14 5.903 0.9348 15.1 26
Xavier 12.117 0.9238 24 5.813 0.9334 15.0 27
New Mexico 23.245 0.9588 10 5.763 0.9326 14.9 28
Vanderbilt 12.823 0.9277 23 5.624 0.9302 14.7 29
Gonzaga 11.818 0.9220 25 5.602 0.9299 14.6 30
Clemson 9.162 0.9016 37 5.523 0.9285 14.5 31
Louisville 8.917 0.8992 39 5.507 0.9282 14.5 32
Northern Iowa 14.016 0.9334 19 5.365 0.9255 14.3 33
Washington 7.480 0.8821 46 5.062 0.9193 13.8 34
Utah St. 6.532 0.8672 54 5.029 0.9185 13.7 35
Nevada Las Vegas 9.685 0.9064 34 5.012 0.9182 13.7 36
Minnesota 5.881 0.8547 57 4.992 0.9177 13.7 37
Oklahoma St. 9.705 0.9066 32 4.917 0.9160 13.5 38
Connecticut 6.185 0.8608 55 4.917 0.9160 13.5 39
Georgia Tech 7.984 0.8887 44 4.874 0.9150 13.5 40
Texas El Paso 8.721 0.8971 40 4.771 0.9124 13.3 41
Florida St. 10.069 0.9097 31 4.746 0.9118 13.2 42
Mississippi 7.441 0.8815 47 4.665 0.9097 13.1 43
Virginia Tech 9.507 0.9048 36 4.656 0.9095 13.1 44
Florida 7.670 0.8847 45 4.471 0.9043 12.7 45
Mississippi St. 6.585 0.8682 52 4.453 0.9038 12.7 46
Dayton 5.247 0.8399 63 4.380 0.9017 12.6 47
Memphis 5.575 0.8479 61 4.361 0.9011 12.5 48
Wake Forest 8.380 0.8934 41 4.302 0.8992 12.4 49
San Diego St. 9.019 0.9002 38 4.215 0.8964 12.2 50
Seton Hall 8.245 0.8918 43 4.124 0.8933 12.0 51
Arizona St. 6.006 0.8573 56 4.036 0.8902 11.9 52
Richmond 10.471 0.9128 29 3.973 0.8879 11.7 53
Cincinnati 6.541 0.8674 53 3.895 0.8849 11.6 54
Old Dominion 6.894 0.8733 50 3.873 0.8840 11.5 55
Illinois 5.545 0.8472 62 3.809 0.8814 11.4 56
South Florida 6.896 0.8734 49 3.779 0.8802 11.3 57
Siena 6.936 0.8740 48 3.763 0.8795 11.3 58
Miami FL 4.558 0.8201 67 3.627 0.8736 11.0 59
North Carolina 4.738 0.8257 66 3.571 0.8709 10.8 60
Rhode Island 6.797 0.8717 51 3.569 0.8708 10.8 61
St. John's 5.839 0.8538 59 3.392 0.8620 10.4 62
Wichita St. 5.734 0.8515 60 3.342 0.8593 10.3 63
Virginia Commonwealth 3.828 0.7929 75 3.303 0.8572 10.2 64
Alabama 3.819 0.7925 76 3.298 0.8569 10.1 65
North Carolina St. 4.547 0.8197 68 3.169 0.8494 9.8 66
Cornell 9.667 0.9063 35 3.155 0.8486 9.8 67
UAB 5.866 0.8544 58 3.144 0.8479 9.7 68
Murray St. 5.075 0.8354 64 3.137 0.8475 9.7 69
Northwestern 4.073 0.8029 70 3.030 0.8406 9.4 70
Marshall 3.924 0.7969 73 2.927 0.8336 9.1 71
Texas Tech 4.910 0.8308 65 2.826 0.8261 8.8 72
Michigan 2.578 0.7205 98 2.798 0.8239 8.7 73
Iowa St. 3.204 0.7622 87 2.782 0.8227 8.7 74
Portland 3.480 0.7768 83 2.764 0.8213 8.6 75
Tulsa 4.086 0.8034 69 2.754 0.8205 8.6 76
Southern California 3.211 0.7625 86 2.720 0.8177 8.5 77
Virginia 3.045 0.7528 90 2.679 0.8143 8.4 78
Missouri St. 2.991 0.7494 91 2.636 0.8106 8.2 79
Arizona 3.477 0.7766 84 2.586 0.8061 8.1 80
Boston College 3.111 0.7568 89 2.558 0.8036 8.0 81
Georgia 3.295 0.7672 85 2.519 0.8000 7.9 82
Illinois St. 3.677 0.7862 78 2.432 0.7913 7.6 83
Northeastern 2.892 0.7431 93 2.400 0.7880 7.4 84
Nevada 2.956 0.7472 92 2.380 0.7859 7.4 85
South Carolina 3.516 0.7786 81 2.375 0.7854 7.4 86
Kent St. 3.879 0.7950 74 2.359 0.7837 7.3 87
Wofford 3.510 0.7782 82 2.342 0.7819 7.2 88
St. Louis 3.997 0.7999 71 2.339 0.7815 7.2 89
Colorado 2.708 0.7303 95 2.325 0.7800 7.2 90
Providence 2.279 0.6950 104 2.281 0.7750 7.0 91
Charlotte 3.930 0.7972 72 2.265 0.7732 6.9 92
Nebraska 2.476 0.7123 99 2.160 0.7605 6.5 93
Houston 1.985 0.6650 117 2.156 0.7599 6.5 94
Wright St. 2.213 0.6888 107 2.094 0.7519 6.3 95
Ohio 1.877 0.6524 125 2.026 0.7426 6.0 96
Louisiana Tech 3.160 0.7596 88 2.013 0.7407 5.9 97
Southern Mississippi 1.695 0.6289 131 1.998 0.7386 5.9 98
Oklahoma 2.579 0.7206 97 1.936 0.7292 5.6 99
Akron 2.801 0.7369 94 1.901 0.7238 5.5 100
Stanford 1.980 0.6644 119 1.895 0.7229 5.4 101
UCLA 2.251 0.6924 105 1.852 0.7159 5.2 102
Penn St. 1.152 0.5354 159 1.840 0.7140 5.2 103
Washington St. 2.069 0.6742 111 1.837 0.7134 5.2 104
Iona 2.445 0.7097 101 1.830 0.7122 5.1 105
Auburn 1.971 0.6634 121 1.828 0.7120 5.1 106
William & Mary 3.697 0.7871 77 1.799 0.7069 5.0 107
Arkansas 1.993 0.6659 116 1.785 0.7045 4.9 108
Harvard 2.449 0.7101 100 1.781 0.7038 4.9 109
Montana 2.041 0.6712 114 1.779 0.7036 4.9 110
New Mexico St. 3.671 0.7859 79 1.766 0.7012 4.8 111
Bradley 2.403 0.7062 102 1.749 0.6981 4.8 112
IUPUI 2.218 0.6892 106 1.747 0.6979 4.7 113
Sam Houston St. 1.972 0.6636 120 1.736 0.6957 4.7 114
Northern Colorado 2.213 0.6888 108 1.721 0.6931 4.6 115
Oregon 2.370 0.7033 103 1.706 0.6903 4.5 116
Weber St. 2.033 0.6702 115 1.695 0.6882 4.5 117
Oakland 3.583 0.7818 80 1.664 0.6821 4.3 118
Morehead St. 1.946 0.6606 122 1.654 0.6803 4.3 119
Pacific 1.859 0.6503 126 1.634 0.6763 4.2 120
Rutgers 2.638 0.7251 96 1.629 0.6752 4.1 121
Creighton 2.138 0.6813 110 1.625 0.6744 4.1 122
Fairfield 2.068 0.6741 112 1.611 0.6715 4.1 123
Southern Illinois 1.521 0.6033 141 1.605 0.6704 4.0 124
Oregon St. 1.654 0.6232 132 1.601 0.6695 4.0 125
Colorado St. 1.926 0.6582 124 1.546 0.6578 3.7 126
Detroit 1.414 0.5857 147 1.542 0.6569 3.7 127
George Washington 1.801 0.6430 127 1.507 0.6491 3.5 128
Utah 1.723 0.6328 130 1.505 0.6487 3.5 129
Appalachian St. 1.637 0.6208 133 1.496 0.6465 3.4 130
St. Bonaventure 1.595 0.6147 137 1.480 0.6429 3.3 131
Western Kentucky 1.536 0.6057 139 1.466 0.6397 3.3 132
Indiana St. 2.179 0.6854 109 1.461 0.6385 3.2 133
Coastal Carolina 1.739 0.6348 129 1.430 0.6309 3.0 134
Hofstra 1.613 0.6172 136 1.428 0.6304 3.0 135
Niagara 1.232 0.5520 154 1.375 0.6172 2.7 136
Duquesne 1.930 0.6587 123 1.361 0.6136 2.6 137
Southern Methodist 0.880 0.4681 185 1.339 0.6079 2.5 138
Miami OH 1.226 0.5508 155 1.329 0.6050 2.4 139
Western Michigan 1.279 0.5612 151 1.327 0.6046 2.4 140
Wisconsin Milwaukee 1.559 0.6092 138 1.319 0.6024 2.4 141
Oral Roberts 1.414 0.5857 146 1.314 0.6011 2.3 142
Central Florida 1.153 0.5356 158 1.283 0.5924 2.1 143
UC Santa Barbara 2.044 0.6715 113 1.271 0.5890 2.0 144
George Mason 1.526 0.6042 140 1.270 0.5888 2.0 145
Buffalo 1.471 0.5953 143 1.265 0.5874 2.0 146
Western Carolina 1.633 0.6202 134 1.260 0.5859 2.0 147
Drexel 1.313 0.5676 149 1.234 0.5783 1.8 148
Princeton 1.429 0.5884 144 1.225 0.5755 1.7 149
Loyola Marymount 1.366 0.5774 148 1.217 0.5731 1.7 150
Fresno St. 1.054 0.5132 164 1.209 0.5708 1.6 151
Wisconsin Green Bay 1.982 0.6646 118 1.197 0.5670 1.5 152
Iowa 1.089 0.5212 163 1.193 0.5659 1.5 153
Louisiana St. 1.163 0.5376 157 1.193 0.5657 1.5 154
College of Charleston 1.792 0.6419 128 1.181 0.5620 1.4 155
Drake 1.209 0.5473 156 1.180 0.5616 1.4 156
Idaho 1.028 0.5070 168 1.177 0.5610 1.4 157
Indiana 1.000 0.5001 174 1.140 0.5489 1.1 158
Vermont 1.421 0.5870 145 1.129 0.5455 1.0 159
Morgan St. 1.485 0.5975 142 1.123 0.5433 1.0 160
DePaul 0.8978 0.4731 183 1.105 0.5373 0.8 161
Cleveland St. 1.234 0.5524 153 1.096 0.5342 0.8 162
Jacksonville 0.9794 0.4948 177 1.093 0.5334 0.8 163
Boise St. 0.8685 0.4648 187 1.090 0.5322 0.7 164
Belmont 0.9726 0.4931 178 1.089 0.5320 0.7 165
Long Beach St. 1.280 0.5613 150 1.070 0.5253 0.6 166
Texas Christian 1.026 0.5063 169 1.040 0.5148 0.3 167
East Tennessee St. 1.002 0.5004 173 1.034 0.5126 0.3 168
Boston University 1.052 0.5126 166 1.026 0.5095 0.2 169
La Salle 1.052 0.5127 165 1.024 0.5090 0.2 170
Stephen F. Austin 1.024 0.5059 170 1.012 0.5044 0.1 171
Saint Joseph's 1.109 0.5259 161 1.011 0.5043 0.1 172
Middle Tennessee 0.8702 0.4653 186 0.9855 0.4945 -0.1 173
San Jose St. 0.9530 0.4880 180 0.9635 0.4861 -0.3 174
North Texas 1.613 0.6174 135 0.9631 0.4859 -0.3 175
Eastern Michigan 0.7763 0.4370 194 0.9609 0.4850 -0.3 176
Troy 1.265 0.5585 152 0.9540 0.4823 -0.4 177
Rider 1.097 0.5232 162 0.9533 0.4821 -0.4 178
St. Peter's 0.8422 0.4572 189 0.9349 0.4748 -0.6 179
Massachusetts 1.112 0.5264 160 0.9145 0.4665 -0.8 180
Eastern Kentucky 1.032 0.5078 167 0.9071 0.4635 -0.8 181
Lipscomb 0.6334 0.3878 210 0.8890 0.4560 -1.0 182
San Diego 0.6452 0.3922 209 0.8828 0.4534 -1.1 183
Campbell 0.8088 0.4471 192 0.8828 0.4534 -1.1 184
Quinnipiac 0.7348 0.4236 200 0.8827 0.4533 -1.1 185
Denver 0.9812 0.4952 176 0.8782 0.4514 -1.1 186
Bowling Green 0.8960 0.4726 184 0.8682 0.4472 -1.2 187
Stony Brook 0.9339 0.4829 182 0.8609 0.4441 -1.3 188
Davidson 1.018 0.5045 171 0.8551 0.4416 -1.3 189
Robert Morris 1.014 0.5035 172 0.8490 0.4389 -1.4 190
Montana St. 0.7728 0.4359 195 0.8445 0.4369 -1.4 191
Lehigh 0.7255 0.4204 202 0.8409 0.4354 -1.5 192
San Francisco 0.8095 0.4474 191 0.8178 0.4251 -1.7 193
Central Michigan 0.7552 0.4302 198 0.8122 0.4226 -1.8 194
Seattle 0.9361 0.4835 181 0.7997 0.4169 -1.9 195
Arkansas St. 0.6923 0.4091 205 0.7990 0.4166 -1.9 196
Texas A&M Corpus Chris 0.5921 0.3719 212 0.7972 0.4158 -1.9 197
Ball St. 0.8046 0.4459 193 0.7859 0.4106 -2.0 198
Valparaiso 0.8494 0.4593 188 0.7782 0.4070 -2.1 199
The Citadel 0.6731 0.4023 206 0.7690 0.4028 -2.2 200
Portland St. 0.5277 0.3454 216 0.7601 0.3985 -2.3 201
Radford 0.8247 0.4520 190 0.7478 0.3927 -2.5 202
Manhattan 0.4067 0.2891 241 0.7342 0.3861 -2.6 203
Cal St. Fullerton 0.7308 0.4222 201 0.7341 0.3861 -2.6 204
Austin Peay 0.9820 0.4955 175 0.7278 0.3831 -2.7 205
Canisius 0.6578 0.3968 208 0.7215 0.3800 -2.8 206
Texas San Antonio 0.7162 0.4173 203 0.7169 0.3777 -2.8 207
Eastern Illinois 0.9621 0.4903 179 0.7113 0.3750 -2.9 208
Loyola Chicago 0.7703 0.4351 196 0.6984 0.3685 -3.1 209
James Madison 0.5264 0.3449 217 0.6926 0.3656 -3.1 210
Mount St. Mary's 0.4646 0.3172 231 0.6924 0.3655 -3.1 211
Georgia St. 0.4948 0.3310 224 0.6812 0.3599 -3.3 212
NC Wilmington 0.5007 0.3336 222 0.6673 0.3528 -3.4 213
Winthrop 0.7513 0.4290 199 0.6597 0.3489 -3.5 214
Northern Arizona 0.7080 0.4145 204 0.6582 0.3481 -3.6 215
Mercer 0.5091 0.3373 220 0.6548 0.3464 -3.6 216
Hawaii 0.4976 0.3323 223 0.6531 0.3455 -3.6 217
Loyola MD 0.4771 0.3230 230 0.6429 0.3402 -3.8 218
Southeastern Louisiana 0.5592 0.3587 213 0.6405 0.3389 -3.8 219
Maine 0.7623 0.4326 197 0.6383 0.3377 -3.8 220
Florida Atlantic 0.5177 0.3411 218 0.6355 0.3363 -3.9 221
Wyoming 0.5528 0.3560 214 0.6339 0.3354 -3.9 222
Louisiana Lafayette 0.4348 0.3030 235 0.6167 0.3263 -4.1 223
Air Force 0.4855 0.3268 226 0.6072 0.3212 -4.2 224
South Dakota St. 0.4783 0.3236 229 0.6047 0.3198 -4.3 225
Tulane 0.3262 0.2460 256 0.5989 0.3167 -4.4 226
Cal St. Northridge 0.4591 0.3146 232 0.5937 0.3139 -4.4 227
Santa Clara 0.4809 0.3248 228 0.5825 0.3078 -4.6 228
UC Davis 0.5159 0.3403 219 0.5723 0.3021 -4.7 229
East Carolina 0.4191 0.2953 239 0.5704 0.3011 -4.8 230
Evansville 0.4898 0.3288 225 0.5614 0.2961 -4.9 231
South Alabama 0.6715 0.4017 207 0.5539 0.2919 -5.0 232
Towson 0.4265 0.2990 237 0.5419 0.2852 -5.2 233
IUPU Fort Wayne 0.5030 0.3347 221 0.5384 0.2832 -5.3 234
South Dakota 0.6151 0.3808 211 0.5366 0.2822 -5.3 235
Chattanooga 0.4851 0.3267 227 0.5230 0.2744 -5.5 236
Lafayette 0.4047 0.2881 243 0.5173 0.2712 -5.6 237
Texas St. 0.3625 0.2660 247 0.5136 0.2691 -5.7 238
Tennessee Tech 0.5440 0.3523 215 0.5117 0.2680 -5.7 239
UC Riverside 0.4473 0.3090 234 0.5073 0.2654 -5.8 240
Texas Arlington 0.3383 0.2528 252 0.5066 0.2650 -5.8 241
Northern Illinois 0.3616 0.2656 248 0.5045 0.2638 -5.8 242
Furman 0.3548 0.2619 249 0.4942 0.2578 -6.0 243
UC Irvine 0.4264 0.2989 238 0.4928 0.2570 -6.0 244
Cal Poly 0.4519 0.3112 233 0.4873 0.2539 -6.1 245
Illinois Chicago 0.3529 0.2608 250 0.4786 0.2487 -6.3 246
Youngstown St. 0.2694 0.2122 264 0.4759 0.2472 -6.3 247
Samford 0.3082 0.2356 257 0.4563 0.2356 -6.7 248
Rice 0.2619 0.2076 267 0.4502 0.2320 -6.8 249
North Dakota St. 0.2878 0.2235 260 0.4447 0.2287 -6.9 250
Delaware St. 0.4268 0.2991 236 0.4407 0.2264 -7.0 251
Hampton 0.2477 0.1985 272 0.4377 0.2246 -7.0 252
Arkansas Pine Bluff 0.3863 0.2787 244 0.4370 0.2241 -7.0 253
NC Asheville 0.4077 0.2896 240 0.4342 0.2225 -7.1 254
Liberty 0.3680 0.2690 246 0.4273 0.2183 -7.2 255
Delaware 0.3318 0.2492 254 0.4252 0.2171 -7.3 256
Jacksonville St. 0.2441 0.1962 277 0.4212 0.2147 -7.3 257
NC Greensboro 0.3278 0.2469 255 0.4200 0.2140 -7.4 258
South Carolina St. 0.3503 0.2594 251 0.4101 0.2080 -7.6 259
Bucknell 0.2579 0.2050 268 0.4083 0.2069 -7.6 260
Elon 0.2540 0.2026 270 0.4043 0.2045 -7.7 261
New Hampshire 0.2857 0.2222 262 0.4041 0.2044 -7.7 262
Pepperdine 0.2865 0.2227 261 0.4041 0.2044 -7.7 263
Western Illinois 0.2468 0.1980 274 0.4008 0.2024 -7.8 264
Holy Cross 0.1689 0.1445 296 0.3967 0.1999 -7.9 265
North Florida 0.3842 0.2776 245 0.3959 0.1994 -7.9 266
Binghamton 0.3374 0.2523 253 0.3885 0.1949 -8.0 267
Army 0.2682 0.2115 265 0.3833 0.1918 -8.2 268
Tennessee St. 0.2474 0.1983 273 0.3753 0.1870 -8.3 269
Eastern Washington 0.2544 0.2028 269 0.3741 0.1862 -8.4 270
Nicholls St. 0.2439 0.1961 278 0.3720 0.1849 -8.4 271
Texas Southern 0.2343 0.1898 281 0.3663 0.1814 -8.5 272
Jackson St. 0.4061 0.2888 242 0.3640 0.1801 -8.6 273
Sacred Heart 0.2196 0.1800 284 0.3621 0.1789 -8.6 274
Kennesaw St. 0.2433 0.1957 279 0.3613 0.1784 -8.7 275
Arkansas Little Rock 0.2055 0.1705 287 0.3477 0.1702 -9.0 276
Idaho St. 0.2018 0.1679 289 0.3435 0.1676 -9.1 277
Long Island 0.2446 0.1965 276 0.3430 0.1673 -9.1 278
Louisiana Monroe 0.2907 0.2252 259 0.3391 0.1649 -9.2 279
Bethune Cookman 0.2531 0.2020 271 0.3374 0.1639 -9.2 280
Lamar 0.2624 0.2079 266 0.3372 0.1638 -9.2 281
Sacramento St. 0.2340 0.1896 282 0.3331 0.1613 -9.3 282
Yale 0.2057 0.1706 286 0.3296 0.1591 -9.4 283
Missouri Kansas City 0.2425 0.1952 280 0.3291 0.1588 -9.4 284
Cal St. Bakersfield 0.2025 0.1684 288 0.3266 0.1573 -9.5 285
High Point 0.3023 0.2321 258 0.3106 0.1475 -9.9 286
Alabama St. 0.1720 0.1468 294 0.3093 0.1467 -10.0 287
Columbia 0.2126 0.1753 285 0.3074 0.1456 -10.0 288
Navy 0.2461 0.1975 275 0.3066 0.1451 -10.0 289
Charleston Southern 0.2258 0.1842 283 0.3015 0.1420 -10.2 290
Norfolk St. 0.1936 0.1622 290 0.2950 0.1381 -10.4 291
American 0.1753 0.1491 292 0.2945 0.1378 -10.4 292
South Carolina Upstate 0.1504 0.1307 305 0.2937 0.1373 -10.4 293
McNeese St. 0.1500 0.1304 306 0.2841 0.1315 -10.7 294
Monmouth 0.1866 0.1573 291 0.2824 0.1305 -10.7 295
Georgia Southern 0.2759 0.2162 263 0.2801 0.1291 -10.8 296
Colgate 0.1737 0.1480 293 0.2740 0.1254 -11.0 297
Brown 0.1638 0.1407 297 0.2635 0.1192 -11.3 298
Prairie View A&M 0.1636 0.1406 298 0.2580 0.1159 -11.5 299
Southeast Missouri St. 0.1378 0.1211 313 0.2554 0.1143 -11.6 300
North Carolina A&T 0.1192 0.1065 317 0.2524 0.1125 -11.7 301
Florida International 0.1440 0.1259 308 0.2523 0.1125 -11.7 302
Longwood 0.1549 0.1341 303 0.2503 0.1113 -11.8 303
Central Arkansas 0.1003 0.0912 325 0.2473 0.1095 -11.9 304
Albany 0.1057 0.0956 323 0.2440 0.1076 -12.0 305
Florida Gulf Coast 0.1508 0.1311 304 0.2436 0.1073 -12.0 306
Savannah St. 0.1588 0.1370 299 0.2378 0.1039 -12.2 307
Northwestern St. 0.1458 0.1272 307 0.2355 0.1026 -12.3 308
New Orleans 0.1380 0.1213 312 0.2331 0.1011 -12.4 309
Pennsylvania 0.1076 0.0972 321 0.2284 0.0984 -12.6 310
Fordham 0.0870 0.0801 327 0.2250 0.0964 -12.7 311
Centenary 0.1392 0.1222 311 0.2237 0.0957 -12.7 312
Central Connecticut 0.1405 0.1232 309 0.2227 0.0951 -12.8 313
St. Francis PA 0.1702 0.1454 295 0.2189 0.0929 -12.9 314
St. Francis NY 0.1405 0.1232 310 0.2172 0.0919 -13.0 315
Maryland Eastern Shore 0.1570 0.1357 301 0.2157 0.0910 -13.0 316
Fairleigh Dickinson 0.1575 0.1361 300 0.2146 0.0904 -13.1 317
Winston Salem St. 0.1554 0.1345 302 0.2059 0.0854 -13.4 318
Hartford 0.1137 0.1021 318 0.2010 0.0827 -13.6 319
Southern Utah 0.1277 0.1133 315 0.1966 0.0802 -13.8 320
Toledo 0.1054 0.0953 324 0.1943 0.0789 -13.9 321
Virginia Military Inst 0.1367 0.1202 314 0.1889 0.0759 -14.2 322
Houston Baptist 0.1115 0.1003 319 0.1840 0.0732 -14.4 323
Gardner Webb 0.1067 0.0964 322 0.1810 0.0715 -14.5 324
Utah Valley 0.0669 0.0627 330 0.1795 0.0707 -14.6 325
Alabama A&M 0.0734 0.0684 328 0.1768 0.0692 -14.7 326
Florida A&M 0.1222 0.1089 316 0.1723 0.0667 -14.9 327
Presbyterian 0.0662 0.0621 331 0.1605 0.0604 -15.5 328
Mississippi Valley St. 0.0675 0.0632 329 0.1591 0.0596 -15.6 329
Texas Pan American 0.0506 0.0482 337 0.1565 0.0583 -15.8 330
Coppin St. 0.0644 0.0605 332 0.1558 0.0579 -15.8 331
Howard 0.0883 0.0812 326 0.1554 0.0577 -15.8 332
Stetson 0.1084 0.0978 320 0.1443 0.0520 -16.5 333
MD Baltimore County 0.0536 0.0509 336 0.1318 0.0457 -17.2 334
NJ Inst of Technology 0.0483 0.0461 338 0.1250 0.0423 -17.7 335
Marist 0.0306 0.0297 344 0.1198 0.0398 -18.0 336
Dartmouth 0.0638 0.0600 333 0.1189 0.0394 -18.1 337
Wagner 0.0418 0.0401 342 0.1183 0.0391 -18.1 338
Chicago St. 0.0432 0.0415 340 0.1151 0.0376 -18.4 339
North Carolina Central 0.0568 0.0537 334 0.1130 0.0366 -18.5 340
SIU Edwardsville 0.0537 0.0510 335 0.1100 0.0352 -18.8 341
North Dakota 0.0445 0.0426 339 0.1064 0.0335 -19.0 342
Tennessee Martin 0.0419 0.0402 341 0.1014 0.0313 -19.5 343
Grambling 0.0400 0.0385 343 0.0934 0.0277 -20.2 344
Southern 0.0270 0.0263 345 0.0791 0.0218 -21.6 345
Bryant 0.0124 0.0122 346 0.0534 0.0122 -24.9 346
Alcorn St. 0.0119 0.0118 347 0.0362 0.0068 -28.2 347

The "Win % v Avg" columns are the equivalent of Pomeroy's "Pyth" value, and win probability can be calculated from them in exactly the same manner. For MABT, to calculate the expected margin of victory for any game, simply subtract the amounts here. For instance, Duke would be favored over us by 7 points, and we would be favored over Indiana by 14.5.

This method could be applied to any sport; as such, I may try it out for football as well (with a different k value, naturally) next year. Any suggestions for tweaks or clarifications are welcome.

This is a FanPost, written by a member of the TOC community. It does not represent the official positions of The Only Colors, Inc.--largely because we have no official positions.

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