College Football Bradley-Terry 2010
Posted by jtwcornell91
College Football Bradley-Terry 2010
Posted by: jtwcornell91 (Moderator)
Date: December 03, 2010 02:52PM
Here's what I get when I throw the current results (including Arizona-ASU last night it seems) into my usual scripts. The frequentist/Jeffreys BT is not so enlightening of course:
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The Bayesian version with a regularizing prior looks like this:
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(sorry I didn't go to the trouble of adjusting the colors to match the schools).
And here are the posterior-maximizing ratings, with marginalized one-sigma multiplicative errorbars, in tabular form:
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The Bayesian version with a regularizing prior looks like this:
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(sorry I didn't go to the trouble of adjusting the colors to match the schools).
And here are the posterior-maximizing ratings, with marginalized one-sigma multiplicative errorbars, in tabular form:
Rk Team W- L mle*/err mle/err-mle*err RRWP(mle) 1 Auburn 12- 0 3141.5*/3.1242 1005.5-9814.7 0.9444 2 Oregon 11- 0 1661.4*/3.1403 529.05-5217.4 0.9046 3 TCU 12- 0 1413.0*/2.9875 472.96-4221.3 0.8917 4 Arkansas 10- 2 956.95*/2.2512 425.08-2154.3 0.8552 5 Stanford 11- 1 908.31*/2.4284 374.03-2205.7 0.8498 6 Wisconsin 11- 1 873.04*/2.4287 359.46-2120.4 0.8455 7 LSU 10- 2 834.08*/2.2427 371.90-1870.6 0.8405 8 Michigan St 11- 1 828.80*/2.3413 353.99-1940.5 0.8398 9 Ohio State 12- 1 814.08*/2.3274 349.79-1894.7 0.8378 10 Oklahoma 11- 2 766.68*/2.0691 370.53-1586.4 0.8310 11 Boise St 11- 1 746.20*/2.3849 312.89-1779.6 0.8279 12 Missouri 10- 2 687.05*/2.0830 329.84-1431.1 0.8181 13 Oklahoma St 11- 2 657.27*/2.1036 312.45-1382.6 0.8126 14 Virginia Tech 11- 1 643.55*/2.3448 274.46-1509.0 0.8100 15 Texas A&M 9- 3 582.63*/2.0268 287.46-1180.9 0.7974 16 Nebraska 10- 2 576.38*/2.1263 271.07-1225.5 0.7960 17 Alabama 9- 3 562.54*/2.1164 265.80-1190.6 0.7928 18 Nevada 11- 1 546.96*/2.3939 228.48-1309.4 0.7891 19 South Carolina 9- 3 429.07*/2.0828 206.00-893.68 0.7552 20 Utah 11- 2 410.37*/2.1425 191.54-879.20 0.7486 21 Florida St 9- 3 310.48*/1.9388 160.14-601.98 0.7054 22 Mississippi St 8- 4 292.28*/2.0637 141.63-603.17 0.6955 23 Hawai`i 9- 3 240.45*/2.0212 118.97-485.99 0.6626 24 Notre Dame 8- 5 218.19*/1.8418 118.47-401.86 0.6456 25 North Carolina St 8- 4 205.39*/1.8777 109.38-385.66 0.6349 26 West Virginia 8- 3 204.39*/1.9741 103.54-403.48 0.6340 27 Baylor 7- 5 197.39*/1.9647 100.47-387.81 0.6277 28 Texas Tech 7- 5 196.53*/1.9286 101.91-379.02 0.6270 29 Southern Cal 8- 5 195.97*/1.8752 104.51-367.47 0.6264 30 Air Force 8- 4 192.34*/2.0128 95.562-387.14 0.6231 31 Florida 7- 5 191.38*/1.8922 101.14-362.13 0.6222 32 Tulsa 9- 3 190.43*/1.9825 96.055-377.52 0.6213 33 Michigan 7- 5 190.17*/1.9314 98.460-367.29 0.6210 34 Northern Illinois 10- 2 188.51*/2.0716 90.995-390.52 0.6194 35 Iowa 7- 5 186.39*/1.9222 96.967-358.29 0.6174 36 Penn State 7- 5 181.91*/1.9041 95.538-346.37 0.6129 37 Arizona 7- 5 175.16*/1.8960 92.382-332.10 0.6060 38 Maryland 8- 4 170.54*/1.8775 90.833-320.20 0.6011 39 Kansas St 7- 5 169.95*/1.8966 89.609-322.34 0.6005 40 Illinois 6- 5 167.75*/1.9500 86.027-327.11 0.5981 41 Navy 8- 3 165.33*/1.9585 84.416-323.81 0.5954 42 San Diego St 8- 4 157.55*/2.0546 76.679-323.70 0.5864 43 Miami FL 7- 5 156.18*/1.8874 82.752-294.77 0.5848 44 Central Florida 9- 3 151.91*/1.9460 78.065-295.61 0.5796 45 North Carolina 7- 5 146.85*/1.9040 77.127-279.59 0.5732 46 Washington 6- 6 144.34*/1.8825 76.678-271.72 0.5700 47 Oregon St 6- 6 130.47*/1.9124 68.225-249.52 0.5509 48 Southern Miss 8- 4 129.12*/1.8892 68.347-243.94 0.5489 49 Boston College 7- 5 124.12*/1.8886 65.722-234.41 0.5414 50 Fresno St 7- 4 123.99*/2.0134 61.584-249.65 0.5412 51 Northwestern 7- 5 120.73*/1.9281 62.616-232.77 0.5361 52 Iowa St 5- 7 118.44*/1.8816 62.945-222.84 0.5325 53 Colorado 6- 7 118.10*/1.8359 64.327-216.83 0.5319 54 Arizona St 5- 6 116.84*/1.9811 58.978-231.47 0.5299 55 Clemson 6- 6 116.82*/1.9081 61.225-222.91 0.5298 56 SMU 8- 5 116.81*/1.8504 63.127-216.16 0.5298 57 Georgia 6- 6 115.68*/1.9416 59.583-224.60 0.5280 58 Toledo 9- 4 111.25*/1.9291 57.671-214.61 0.5205 59 Pittsburgh 6- 5 110.70*/1.8782 58.941-207.92 0.5195 60 Brigham Young 7- 6 110.57*/1.9248 57.444-212.82 0.5193 61 South Florida 7- 4 109.61*/1.9149 57.241-209.88 0.5176 62 Tennessee 6- 6 107.05*/1.9737 54.238-211.28 0.5131 63 East Carolina 7- 6 105.15*/1.8272 57.548-192.13 0.5097 64 Texas 6- 7 104.15*/1.8887 55.145-196.71 0.5078 65 Connecticut 7- 4 102.65*/1.9157 53.586-196.65 0.5050 66 California 5- 7 96.526*/1.9170 50.354-185.03 0.4932 67 Miami OH 9- 4 93.706*/1.9446 48.188-182.22 0.4875 68 Temple 8- 4 91.962*/1.9282 47.694-177.32 0.4839 69 Syracuse 6- 5 81.960*/1.8932 43.292-155.16 0.4618 70 Ohio U. 8- 4 80.778*/1.9815 40.766-160.06 0.4590 71 UCLA 5- 7 79.785*/1.8991 42.012-151.52 0.4566 72 Kentucky 6- 6 79.310*/1.9655 40.351-155.88 0.4555 73 Mississippi 5- 7 79.023*/2.0104 39.307-158.87 0.4548 74 Georgia Tech 6- 6 72.637*/1.8791 38.656-136.49 0.4387 75 Minnesota 4- 8 66.833*/1.9797 33.760-132.31 0.4229 76 Louisiana Tech 5- 6 65.547*/2.0179 32.483-132.26 0.4193 77 Kansas 4- 8 64.773*/1.9834 32.658-128.47 0.4170 78 Louisville 6- 6 62.122*/1.8536 33.514-115.15 0.4092 79 Army 6- 5 60.688*/1.9377 31.320-117.60 0.4048 80 Florida Int'l 7- 5 58.045*/1.9226 30.191-111.59 0.3965 81 Purdue 4- 8 57.151*/1.9915 28.698-113.82 0.3936 82 Indiana 5- 7 55.997*/2.0099 27.860-112.55 0.3898 83 Marshall 6- 7 55.032*/1.8647 29.513-102.62 0.3866 84 Cincinnati 4- 7 54.584*/1.9399 28.137-105.89 0.3851 85 Idaho 5- 7 52.270*/1.9680 26.560-102.86 0.3771 86 Houston 5- 7 51.673*/1.9010 27.183-98.228 0.3750 87 Troy 7- 5 50.959*/1.9566 26.044-99.707 0.3725 88 UTEP 6- 6 44.854*/1.9191 23.372-86.080 0.3495 89 Utah St 4- 7 42.326*/2.0824 20.326-88.139 0.3392 90 Rice 5- 8 41.999*/1.8532 22.663-77.831 0.3378 91 Western Michigan 6- 6 41.649*/1.9806 21.029-82.488 0.3364 92 Rutgers 4- 7 38.590*/1.9181 20.119-74.021 0.3231 93 Alabama-Birmingham 5- 8 38.165*/1.8635 20.480-71.121 0.3211 94 Kent St 5- 7 35.131*/1.9291 18.211-67.772 0.3070 95 Colorado St 4- 9 33.863*/2.0106 16.842-68.087 0.3008 96 Wake Forest 3- 9 33.532*/2.0880 16.059-70.015 0.2992 97 Tulane 4- 8 33.221*/1.9041 17.447-63.254 0.2976 98 Virginia 3- 8 31.516*/2.1442 14.698-67.576 0.2889 99 Washington St 2- 9 31.180*/2.2822 13.662-71.159 0.2872 100 Louisiana-Monroe 5- 7 30.984*/2.0286 15.273-62.856 0.2862 101 Duke 3- 9 30.463*/2.0617 14.776-62.805 0.2834 102 Florida Atlantic 5- 7 26.171*/1.9427 13.472-50.841 0.2593 103 Wyoming 3- 9 25.896*/2.1698 11.934-56.190 0.2576 104 Vanderbilt 3-10 25.673*/2.0908 12.279-53.675 0.2563 105 UNLV 3-10 24.743*/2.1671 11.417-53.621 0.2506 106 Arkansas St 5- 8 23.919*/1.9130 12.504-45.757 0.2455 107 Middle Tennessee St 5- 6 22.484*/1.9474 11.546-43.786 0.2363 108 Ball St 4- 7 17.887*/2.0942 8.5411-37.460 0.2040 109 Central Michigan 3- 9 17.259*/2.1525 8.0180-37.150 0.1992 110 Louisiana-Lafayette 4- 9 17.116*/1.9674 8.7001-33.674 0.1981 111 New Mexico St 3-10 16.128*/2.1516 7.4958-34.701 0.1903 112 North Texas 4- 9 15.835*/1.9450 8.1413-30.799 0.1880 113 Bowling Green 3-10 14.222*/2.0942 6.7911-29.783 0.1745 114 Memphis 2-11 11.984*/2.2497 5.3270-26.962 0.1545 115 Eastern Michigan 3-10 11.704*/2.1122 5.5412-24.720 0.1518 116 Western Kentucky 3-10 11.347*/2.0659 5.4926-23.442 0.1484 117 New Mexico 2-11 11.340*/2.3616 4.8016-26.780 0.1483 118 San José St 1-10 9.0151*/3.1825 2.8327-28.690 0.1247 119 Akron 2-10 8.4162*/2.3722 3.5479-19.965 0.1182 120 Buffalo 2-10 7.1598*/2.4282 2.9486-17.385 0.1039
Edited 5 time(s). Last edit at 12/03/2010 03:10PM by CowbellGuy.
Auburn vs Stanford
Posted by: jtwcornell91 (Moderator)
Date: December 03, 2010 03:41PM
With two fictitious games, Auburn is only a 7:2 favorite over Stanford. Of course, that's just a comparison of their most likely ratings; the joint posterior looks like this:
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and the real quantity of interest, the ratio of their ratings, has the following posterior:
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and the real quantity of interest, the ratio of their ratings, has the following posterior:
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Edited 1 time(s). Last edit at 12/03/2010 03:42PM by jtwcornell91.
College Football Bradley-Terry 2010 as of BCS Sunday
Posted by: jtwcornell91 (Moderator)
Date: December 05, 2010 10:26AM
Apparently next weekend's Army-Navy game doesn't count for bowl selection (or at least BCS) purposes, so here are the final "regular season" rankings:
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Rk Team W- L mle*/err mle/err-mle*err RRWP(mle) 1 Auburn 12- 0 3599.1*/3.0979 1161.8-11150. 0.9500 2 Oregon 11- 0 1827.5*/3.1135 586.96-5690.0 0.9105 3 TCU 11- 0 1402.5*/2.9902 469.01-4193.7 0.8899 4 Arkansas 9- 2 972.53*/2.2611 430.11-2199.0 0.8558 5 Stanford 10- 1 927.67*/2.4441 379.56-2267.3 0.8509 6 Oklahoma 11- 2 896.96*/2.0536 436.77-1842.0 0.8473 7 LSU 9- 2 856.77*/2.2514 380.54-1929.0 0.8424 8 Boise St 11- 1 849.89*/2.3935 355.09-2034.2 0.8415 9 Wisconsin 10- 1 848.42*/2.4246 349.92-2057.1 0.8413 10 Virginia Tech 11- 1 799.99*/2.3340 342.75-1867.2 0.8348 11 Michigan St 10- 1 795.02*/2.3407 339.65-1860.9 0.8341 12 Ohio State 11- 1 784.66*/2.3245 337.56-1824.0 0.8326 13 Missouri 9- 2 678.70*/2.0846 325.58-1414.8 0.8155 14 Oklahoma St 10- 2 652.33*/2.1056 309.80-1373.6 0.8107 15 Nevada 11- 1 628.69*/2.3849 263.61-1499.4 0.8061 16 Texas A&M 8- 3 574.49*/2.0332 282.56-1168.0 0.7946 17 Alabama 8- 3 567.84*/2.1238 267.37-1206.0 0.7930 18 Nebraska 9- 3 482.54*/2.0046 240.72-967.29 0.7711 19 South Carolina 8- 4 415.34*/2.0482 202.79-850.68 0.7496 20 Utah 10- 2 413.32*/2.1422 192.94-885.41 0.7489 21 Mississippi St 7- 4 296.33*/2.0682 143.28-612.87 0.6971 22 Florida St 8- 4 283.84*/1.8832 150.72-534.54 0.6901 23 Hawai`i 9- 3 266.94*/2.0163 132.40-538.22 0.6798 24 Notre Dame 7- 5 220.18*/1.8416 119.56-405.50 0.6467 25 West Virginia 8- 3 218.08*/1.9568 111.45-426.73 0.6450 26 Southern Cal 8- 5 216.48*/1.8536 116.79-401.25 0.6438 27 North Carolina St 7- 4 209.07*/1.8831 111.02-393.69 0.6376 28 Baylor 6- 5 197.87*/1.9687 100.50-389.54 0.6278 29 Air Force 7- 4 194.76*/2.0182 96.503-393.07 0.6249 30 Texas Tech 6- 5 194.34*/1.9336 100.51-375.76 0.6245 31 Florida 6- 5 191.45*/1.8896 101.32-361.76 0.6219 32 Tulsa 8- 3 188.32*/1.9817 95.029-373.20 0.6189 33 Michigan 6- 5 185.78*/1.9268 96.418-357.97 0.6164 34 Iowa 6- 5 181.75*/1.9206 94.632-349.06 0.6124 35 Central Florida 9- 3 177.72*/1.9174 92.688-340.76 0.6083 36 Penn State 6- 5 175.33*/1.9012 92.220-333.33 0.6059 37 Arizona 6- 5 174.62*/1.9023 91.795-332.20 0.6051 38 Maryland 7- 4 167.95*/1.8794 89.364-315.64 0.5980 39 Kansas St 6- 5 167.75*/1.8941 88.565-317.73 0.5978 40 Navy 7- 3 163.47*/1.9578 83.496-320.05 0.5930 41 San Diego St 7- 4 158.26*/2.0538 77.059-325.03 0.5870 42 Fresno St 7- 4 157.73*/1.9727 79.959-311.16 0.5864 43 Miami FL 6- 5 155.76*/1.8894 82.438-294.29 0.5840 44 Washington 6- 6 151.26*/1.8584 81.394-281.10 0.5786 45 North Carolina 6- 5 147.74*/1.9087 77.400-281.99 0.5742 46 Northern Illinois 9- 3 140.68*/1.9370 72.626-272.50 0.5650 47 Illinois 5- 6 132.38*/1.8844 70.249-249.46 0.5535 48 Southern Miss 7- 4 130.75*/1.8900 69.180-247.11 0.5512 49 Oregon St 5- 7 127.62*/1.9074 66.906-243.43 0.5466 50 Boston College 6- 5 124.98*/1.8908 66.102-236.32 0.5426 51 Connecticut 7- 4 121.94*/1.8796 64.875-229.21 0.5379 52 Pittsburgh 6- 5 121.14*/1.8466 65.600-223.69 0.5367 53 Colorado 5- 7 118.20*/1.8360 64.377-217.01 0.5320 54 Miami OH 9- 4 118.02*/1.9114 61.747-225.59 0.5317 55 Georgia 5- 6 116.45*/1.9415 59.981-226.09 0.5291 56 Clemson 5- 6 116.42*/1.9065 61.067-221.96 0.5291 57 Arizona St 4- 6 116.26*/1.9890 58.455-231.25 0.5288 58 Northwestern 6- 5 115.88*/1.9224 60.279-222.76 0.5282 59 Iowa St 4- 7 114.14*/1.8805 60.698-214.65 0.5253 60 Brigham Young 6- 6 111.54*/1.9254 57.932-214.76 0.5209 61 Toledo 8- 4 108.79*/1.9252 56.509-209.44 0.5161 62 Tennessee 5- 6 108.05*/1.9733 54.753-213.21 0.5148 63 East Carolina 6- 6 106.43*/1.8311 58.123-194.89 0.5119 64 SMU 7- 6 101.98*/1.8037 56.536-183.94 0.5037 65 Texas 5- 7 101.40*/1.8914 53.613-191.79 0.5027 66 California 4- 7 96.574*/1.9264 50.132-186.04 0.4933 67 Temple 7- 4 93.445*/1.9242 48.563-179.81 0.4870 68 South Florida 6- 5 92.165*/1.8643 49.436-171.82 0.4844 69 Ohio U. 7- 4 83.058*/1.9826 41.894-164.67 0.4644 70 Syracuse 5- 5 82.271*/1.8986 43.333-156.20 0.4626 71 Mississippi 4- 7 81.623*/2.0146 40.515-164.44 0.4611 72 Kentucky 5- 6 79.807*/1.9656 40.602-156.87 0.4568 73 Georgia Tech 5- 6 74.560*/1.8765 39.733-139.92 0.4438 74 UCLA 4- 8 71.880*/1.8735 38.366-134.67 0.4369 75 Louisiana Tech 4- 7 65.419*/2.0033 32.656-131.05 0.4191 76 Minnesota 3- 8 64.519*/1.9654 32.828-126.80 0.4165 77 Kansas 3- 8 64.225*/1.9798 32.440-127.15 0.4156 78 Louisville 5- 6 61.999*/1.8568 33.390-115.12 0.4090 79 Army 5- 5 60.947*/1.9414 31.392-118.32 0.4058 80 Troy 7- 5 57.150*/1.9136 29.865-109.36 0.3938 81 Idaho 5- 7 56.696*/1.9438 29.167-110.21 0.3924 82 Marshall 5- 7 55.563*/1.8654 29.787-103.65 0.3886 83 Purdue 3- 8 54.933*/1.9887 27.622-109.25 0.3865 84 Indiana 4- 7 53.889*/2.0036 26.896-107.97 0.3830 85 Houston 4- 7 51.187*/1.9014 26.921-97.325 0.3736 86 Cincinnati 3- 8 50.387*/1.9191 26.255-96.696 0.3707 87 Florida Int'l 6- 6 45.708*/1.8754 24.373-85.718 0.3531 88 UTEP 5- 6 44.470*/1.9158 23.212-85.196 0.3482 89 Utah St 3- 8 42.966*/2.0821 20.636-89.458 0.3421 90 Rice 4- 8 41.717*/1.8536 22.505-77.327 0.3370 91 Western Michigan 5- 6 41.220*/1.9724 20.898-81.302 0.3348 92 Alabama-Birmingham 4- 8 38.299*/1.8659 20.526-71.462 0.3221 93 Kent St 4- 7 35.766*/1.9305 18.527-69.046 0.3104 94 Rutgers 3- 8 35.631*/1.9048 18.706-67.872 0.3097 95 Colorado St 3- 9 34.910*/2.0141 17.333-70.314 0.3063 96 Wake Forest 2- 9 33.743*/2.0875 16.164-70.439 0.3006 97 Tulane 3- 8 32.997*/1.9062 17.310-62.900 0.2969 98 Virginia 2- 8 31.869*/2.1456 14.853-68.380 0.2911 99 Louisiana-Monroe 4- 7 30.986*/2.0271 15.286-62.812 0.2865 100 Duke 2- 9 30.726*/2.0623 14.899-63.367 0.2851 101 Middle Tennessee St 5- 6 28.519*/1.8834 15.142-53.714 0.2731 102 Washington St 1-10 27.545*/2.2649 12.162-62.386 0.2676 103 Vanderbilt 2-10 26.089*/2.0915 12.473-54.565 0.2591 104 Wyoming 2- 9 25.921*/2.1702 11.944-56.253 0.2581 105 UNLV 2-11 24.162*/2.1471 11.253-51.878 0.2474 106 Arkansas St 4- 8 23.845*/1.9109 12.478-45.567 0.2454 107 Florida Atlantic 4- 8 23.141*/1.9024 12.164-44.024 0.2409 108 Ball St 3- 7 17.629*/2.0860 8.4512-36.775 0.2024 109 Central Michigan 2- 9 17.289*/2.1511 8.0374-37.190 0.1998 110 Louisiana-Lafayette 3- 9 17.186*/1.9665 8.7392-33.797 0.1990 111 New Mexico St 2-10 16.304*/2.1659 7.5276-35.312 0.1921 112 North Texas 3- 9 15.836*/1.9432 8.1495-30.774 0.1883 113 Bowling Green 2-10 14.597*/2.0955 6.9661-30.588 0.1781 114 Memphis 1-11 12.465*/2.2415 5.5608-27.939 0.1593 115 Eastern Michigan 2-10 11.756*/2.1111 5.5686-24.817 0.1526 116 New Mexico 1-11 11.369*/2.3617 4.8138-26.849 0.1489 117 Western Kentucky 2-10 11.250*/2.0606 5.4598-23.182 0.1478 118 Akron 1-10 8.4442*/2.3707 3.5619-20.019 0.1188 119 San José St 0-11 7.9197*/3.1332 2.5277-24.814 0.1129 120 Buffalo 1-10 7.2929*/2.4337 2.9967-17.749 0.1057
Edited 1 time(s). Last edit at 12/05/2010 10:29AM by jtwcornell91.
Oregon vs TCU
Posted by: jtwcornell91 (Moderator)
Date: December 05, 2010 10:40AM
The big question for a rating system this year is whether Oregon or TCU should get the #2 spot. Here's the joint posterior for their ratings:
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and the marginalized posterior for the ratio of their ratings
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According to the posterior, there's a 56.6% likelihood that Oregon is indeed stronger than TCU. (In comparison, the likelihood that Auburn is stronger than Stanford is 82.3%.)
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and the marginalized posterior for the ratio of their ratings
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According to the posterior, there's a 56.6% likelihood that Oregon is indeed stronger than TCU. (In comparison, the likelihood that Auburn is stronger than Stanford is 82.3%.)
Edited 1 time(s). Last edit at 12/05/2010 12:31PM by jtwcornell91.
Re: College Football Bradley-Terry 2010
Posted by: French Rage (---.packetdesign.com)
Date: December 06, 2010 02:50PM
Thanks!
___________________________
03/23/02: Maine 4, Harvard 3
03/28/03: BU 6, Harvard 4
03/26/04: Maine 5, Harvard 4
03/26/05: UNH 3, Harvard 2
03/25/06: Maine 6, Harvard 1
03/23/02: Maine 4, Harvard 3
03/28/03: BU 6, Harvard 4
03/26/04: Maine 5, Harvard 4
03/26/05: UNH 3, Harvard 2
03/25/06: Maine 6, Harvard 1
Re: Oregon vs TCU
Posted by: Roy 82 (128.18.14.---)
Date: December 06, 2010 11:55PM
jtwcornell91
According to the posterior, there's a 56.6% likelihood that Oregon is indeed stronger than TCU.
Posterior? Are you saying that you pulled this out of your
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