College Football Bradley-Terry 2010

[jtwcornell91]

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:

Code Select Expand


 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


[jtwcornell91]

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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[jtwcornell91]

 -- moved topic --

[jtwcornell91]

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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Code Select Expand


 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


[jtwcornell91]

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:
[clear]

[clear]
and the marginalized posterior for the ratio of their ratings
[clear]

[clear]
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%.)

[French Rage]

Thanks!

::banana::::rock::::thud::::woot::

[Roy 82]

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 ::moon::