NCAA Division I-A Football: crazy statistical analysis
Posted by jtwcornell91
NCAA Division I-A Football: crazy statistical analysis
Posted by: jtwcornell91 (Moderator)
Date: December 24, 2006 04:26PM
I finally got around to doing a Bradley-Terry (aka KRACH) analysis of the Division I-A football silliness. I knew that Ohio State and Boise State, being undefeated, would have "infinite" BT ratings that couldn't be compared to each other, and that Michigan, having only lost to OSU, would have an "infinite" rating that's infinitely worse than OSU and incomparible with BSU. I didn't realize that Wisconsin had only lost to Michigan, and is therefore infinitely worse than OSU and Michigan but incomparible with BSU and infinitely beter than everybody else. This complicates things, since it means Michigan and BSU actually have the same RRWP if we do the usual of assigning a .500 HHWP to BSU with the three teams with whom they're incomparible. The situation is nicely illustrated by the following chart (numbers shown are projected round-robin winning percentages):
"Everybody else" fits on a traditional Bradley-Terry scale:
"Everybody else" fits on a traditional Bradley-Terry scale:
# Team BT RRWP W- L W/L SOS RPI 5 Florida 79836 .948 11- 1 11.00 7258 .680 6 LSU 33011 .928 10- 2 5.000 6602 .623 7 Auburn 27231 .922 10- 2 5.000 5446 .611 8 Southern Cal 24329 .919 10- 2 5.000 4866 .649 9 Arkansas 21699 .915 9- 3 3.000 7233 .599 10 Notre Dame 19169 .911 10- 2 5.000 3834 .611 11 Tennessee 14154 .899 9- 3 3.000 4718 .607 12 California 9701 .883 8- 3 2.667 3638 .602 13 Oregon St 7104 .868 8- 4 2.000 3552 .592 14 Louisville 5505 .854 11- 1 11.00 500.4 .636 15 Penn State 4542 .843 7- 4 1.750 2595 .571 16 UCLA 3744 .831 7- 5 1.400 2675 .571 17 Oregon 2886 .814 6- 5 1.200 2405 .551 18 Arizona 2562 .806 5- 6 .8333 3075 .553 19 Georgia 2494 .804 7- 4 1.750 1425 .548 20 Arizona St 2453 .803 6- 5 1.200 2045 .533 21 Washington St 2315 .799 6- 6 1.000 2315 .525 22 South Carolina 2145 .793 6- 5 1.200 1788 .570 23 West Virginia 1976 .787 9- 2 4.500 439.1 .615 24 Rutgers 1816 .781 9- 2 4.500 403.6 .608 25 Kentucky 1688 .775 6- 5 1.200 1406 .562 26 Oklahoma 1638 .773 11- 2 5.500 297.7 .599 27 Wake Forest 1539 .768 10- 2 5.000 307.8 .576 28 Virginia Tech 1456 .764 9- 2 4.500 323.5 .599 29 Washington 1152 .744 5- 7 .7143 1613 .520 30 Georgia Tech 854.2 .719 8- 4 2.000 427.1 .561 31 Boston College 795.9 .712 8- 3 2.667 298.5 .583 32 Hawai`i 727.4 .704 9- 3 3.000 242.5 .532 33 Brigham Young 669.8 .697 10- 2 5.000 134.0 .566 34 Texas 666.0 .696 8- 3 2.667 249.8 .602 35 Clemson 630.8 .691 8- 4 2.000 315.4 .542 36 Cincinnati 572.2 .682 6- 5 1.200 476.8 .575 37 Alabama 538.5 .676 6- 6 1.000 538.5 .498 38 Maryland 486.3 .666 7- 4 1.750 277.9 .557 39 Minnesota 421.8 .652 5- 6 .8333 506.2 .545 40 Purdue 376.4 .640 7- 5 1.400 268.9 .524 41 South Florida 375.5 .640 7- 4 1.750 214.6 .526 42 Texas A&M 366.8 .638 8- 3 2.667 137.6 .569 43 Nebraska 355.9 .634 8- 4 2.000 178.0 .571 44 Navy 258.7 .601 8- 3 2.667 97.00 .494 45 TCU 225.6 .586 9- 2 4.500 50.14 .538 46 Missouri 198.6 .571 7- 4 1.750 113.5 .551 47 Vanderbilt 160.7 .547 3- 8 .3750 428.4 .467 48 Indiana 153.8 .542 5- 6 .8333 184.5 .525 49 Iowa 138.8 .530 5- 6 .8333 166.6 .514 50 Houston 138.1 .530 9- 3 3.000 46.02 .541 51 Florida St 137.9 .530 6- 6 1.000 137.9 .528 52 Mississippi 136.7 .529 3- 8 .3750 364.6 .469 53 San José St 123.2 .516 7- 4 1.750 70.41 .476 54 Pittsburgh 123.0 .516 5- 6 .8333 147.5 .503 55 Texas Tech 119.7 .513 6- 5 1.200 99.76 .529 56 Nevada 116.1 .509 8- 4 2.000 58.07 .485 57 Miami FL 114.3 .507 5- 6 .8333 137.2 .496 58 Central Michigan 108.0 .501 9- 4 2.250 48.01 .529 59 Tulsa 103.8 .496 7- 4 1.750 59.30 .533 60 Stanford 97.58 .489 1-11 .0909 1073 .450 61 Kansas St 92.27 .482 6- 5 1.200 76.89 .507 62 Connecticut 89.49 .478 3- 8 .3750 238.6 .497 63 Oklahoma St 86.93 .475 5- 6 .8333 104.3 .529 64 Rice 86.28 .474 7- 5 1.400 61.63 .510 65 Southern Miss 84.97 .472 7- 5 1.400 60.70 .523 66 Syracuse 71.91 .452 4- 8 .5000 143.8 .480 67 Utah 68.11 .445 6- 5 1.200 56.76 .502 68 East Carolina 65.24 .440 7- 5 1.400 46.60 .491 69 Northwestern 56.87 .423 4- 7 .5714 99.53 .478 70 Michigan St 56.66 .423 4- 8 .5000 113.3 .466 71 Western Michigan 54.26 .417 8- 4 2.000 27.13 .489 72 Mississippi St 51.53 .411 2- 9 .2222 231.9 .454 73 Virginia 50.02 .407 5- 7 .7143 70.03 .462 74 Ohio U. 48.90 .405 8- 4 2.000 24.45 .499 75 Kansas 46.74 .399 5- 6 .8333 56.08 .463 76 Wyoming 40.70 .382 6- 6 1.000 40.70 .475 77 Middle Tennessee St 40.39 .381 6- 5 1.200 33.66 .494 78 New Mexico 40.01 .380 6- 5 1.200 33.34 .478 79 Baylor 34.62 .363 3- 8 .3750 92.31 .459 80 SMU 24.53 .322 5- 6 .8333 29.44 .461 81 Northern Illinois 23.84 .319 6- 5 1.200 19.87 .471 82 Tulane 22.76 .313 4- 8 .5000 45.52 .453 83 Troy 21.66 .308 6- 5 1.200 18.05 .451 84 Air Force 21.41 .306 4- 8 .5000 42.82 .461 85 Iowa St 19.28 .295 3- 8 .3750 51.42 .435 86 Marshall 17.84 .286 4- 7 .5714 31.23 .435 87 Ball St 17.37 .283 5- 6 .8333 20.85 .461 88 North Carolina St 17.04 .281 2- 9 .2222 76.69 .442 89 North Carolina 16.89 .280 2- 9 .2222 76.02 .449 90 UTEP 16.49 .277 5- 7 .7143 23.09 .425 91 Colorado 15.47 .270 2- 9 .2222 69.59 .415 92 Central Florida 14.67 .264 3- 8 .3750 39.13 .431 93 Illinois 13.95 .259 1-10 .1000 139.5 .435 94 Fresno St 13.62 .256 4- 8 .5000 27.24 .438 95 San Diego St 13.09 .252 3- 8 .3750 34.90 .441 96 Arkansas St 11.61 .240 6- 6 1.000 11.61 .419 97 Louisiana-Lafayette 10.38 .228 5- 6 .8333 12.45 .441 98 Colorado St 10.15 .226 3- 8 .3750 27.05 .406 99 Alabama-Birmingham 9.757 .222 3- 9 .3333 29.27 .398 100 Akron 9.259 .217 5- 7 .7143 12.96 .427 101 Florida Atlantic 8.982 .214 4- 7 .5714 15.72 .413 102 Army 8.802 .212 2- 9 .2222 39.61 .417 103 Toledo 8.671 .210 4- 7 .5714 15.17 .413 104 Idaho 8.275 .206 3- 8 .3750 22.07 .419 105 Kent St 8.141 .204 6- 6 1.000 8.141 .411 106 Louisiana-Monroe 4.818 .158 3- 8 .3750 12.85 .390 107 UNLV 3.399 .131 1-10 .1000 33.99 .384 108 New Mexico St 3.141 .126 2- 8 .2500 12.56 .391 109 Memphis 2.808 .118 1-10 .1000 28.08 .365 110 North Texas 2.632 .114 3- 9 .3333 7.895 .371 111 Miami OH 2.605 .113 2-10 .2000 13.02 .372 112 Louisiana Tech 2.461 .109 2-10 .2000 12.30 .403 113 Bowling Green 2.296 .105 4- 8 .5000 4.593 .395 114 Buffalo 1.801 .091 2-10 .2000 9.005 .405 115 Utah St 1.420 .079 1-11 .0909 15.62 .396 116 Eastern Michigan 1.345 .076 1-11 .0909 14.79 .364 117 Temple 1.255 .073 1-11 .0909 13.81 .395I have some ideas for a Bayesian approach where results modify a prior reflecting ignorance about the strengths of the teams; these may get tested depending on how my vacation goes.
Edited 1 time(s). Last edit at 12/24/2006 04:27PM by jtwcornell91.
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: ebilmes (---.hsd1.fl.comcast.net)
Date: December 24, 2006 05:30PM
Wow. Guess JTW didn't have a lot of last-minute shopping to do.
Thanks for this analysis, though: it gives those of us who think it should be OSU-Michigan in the title game another reason to consider ourselves right.
I also like the "Hawai'i"
Thanks for this analysis, though: it gives those of us who think it should be OSU-Michigan in the title game another reason to consider ourselves right.
I also like the "Hawai'i"
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: Josh '99 (---.nyc.res.rr.com)
Date: December 27, 2006 12:37AM
Neat. Thanks, John.
And it's also another reason for those of us who think it should be Boise against Ohio State to believe WE'RE right.
And it's also another reason for those of us who think it should be Boise against Ohio State to believe WE'RE right.
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: Rita (---.agry.purdue.edu)
Date: January 02, 2007 10:11AM
Yeah Boise State!! It was very nice to see BSU take down Oklahoma, especially after listening to the pundits on espn radio saying that they didn't have a shot to win and their best chance was to lose by 10 points or less.
Some very gutsy calls that paid off big.
Some very gutsy calls that paid off big.
Edited 1 time(s). Last edit at 01/02/2007 12:42PM by Rita.
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: billhoward (---.hsd1.nj.comcast.net)
Date: January 02, 2007 10:17AM
Cheer for the neutral fan, arms pointing: "Football factory. Potato factory." Score one for the little guy.Rita
Yeah Boise State!! It was very nice to see BSU take down Oklahoma, especially after listening to the pundits on espn radio not saying that they didn't have a shot to win and their best chance was to lose by 10 points or less. Some very gutsy calls that paid off big.
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: JDeafv (---.twcny.res.rr.com)
Date: January 07, 2007 01:56AM
What database did you use for the results to all D-1 college football games? Also, how do games against non D-1 schools factor into the calc?
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: jtwcornell91 (Moderator)
Date: January 07, 2007 10:08AM
Games against non-D1 schools don't count. Scores from [prwolfe.bol.ucla.edu] and team list from [prwolfe.bol.ucla.edu]
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: Trotsky (---.ashbva.adelphia.net)
Date: January 07, 2007 01:46PM
jtwcornell91
I finally got around to doing a Bradley-Terry (aka KRACH) analysis of the Division I-A football silliness. I knew that Ohio State and Boise State, being undefeated, would have "infinite" BT ratings that couldn't be compared to each other, and that Michigan, having only lost to OSU, would have an "infinite" rating that's infinitely worse than OSU and incomparible with BSU. I didn't realize that Wisconsin had only lost to Michigan, and is therefore infinitely worse than OSU and Michigan but incomparible with BSU and infinitely beter than everybody else. This complicates things, since it means Michigan and BSU actually have the same RRWP if we do the usual of assigning a .500 HHWP to BSU with the three teams with whom they're incomparible. The situation is nicely illustrated by the following chart (numbers shown are projected round-robin winning percentages):
"Everybody else" fits on a traditional Bradley-Terry scale:
# Team BT RRWP W- L W/L SOS RPI 5 Florida 79836 .948 11- 1 11.00 7258 .680 6 LSU 33011 .928 10- 2 5.000 6602 .623
Screw these teams, where does Cornell finish? There are some IA-IAA match-ups. Doesn't that broaden the set of teams enough to allow us to determine whether Cornell is, say, 307th or 319th?
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: ugarte (38.136.14.---)
Date: January 08, 2007 09:43AM
Michigan and Wisconsin can be placed in the body of the chart now, right?
___________________________
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Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: Scersk '97 (---.dsl.chcgil.sbcglobal.net)
Date: January 08, 2007 06:52PM
Trotsky
Screw these teams, where does Cornell finish? There are some IA-IAA match-ups. Doesn't that broaden the set of teams enough to allow us to determine whether Cornell is, say, 307th or 319th?
[prwolfe.bol.ucla.edu]
184 out of 706. Poor Principia...
Edited 1 time(s). Last edit at 01/08/2007 06:53PM by Scersk '97.
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: Dpperk29 (---.twcny.res.rr.com)
Date: January 09, 2007 12:13AM
so now does florida come out on top?
___________________________
"That damn bell at Clarkson." -Ken Dryden in reference to his hatred for the Clarkson Bell.
"That damn bell at Clarkson." -Ken Dryden in reference to his hatred for the Clarkson Bell.
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: Jacob '06 (---.caltech.edu)
Date: January 09, 2007 12:21AM
Dpperk29
so now does florida come out on top?
Boise State all the way!
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: ebilmes (---.37.10.97.adsl.snet.net)
Date: January 10, 2007 11:51AM
Jacob '06Dpperk29
so now does florida come out on top?
Boise State all the way!
Right, because Boise State is the only undefeated team.
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: Trotsky (---.raytheon.com)
Date: January 11, 2007 11:31AM
Scersk '97Trotsky
Screw these teams, where does Cornell finish? There are some IA-IAA match-ups. Doesn't that broaden the set of teams enough to allow us to determine whether Cornell is, say, 307th or 319th?
[prwolfe.bol.ucla.edu]
184 out of 706. Poor Principia...
Interesting. Several D-II conferences rank above I-AA. The Ivies are the 16th-strongest conference, so I guess when we hit about 75 bowl game (in, say, 2012), Ivies will start to get bids.
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: DeltaOne81 (---.raytheon.com)
Date: January 11, 2007 11:37AM
Scersk '97Trotsky
Screw these teams, where does Cornell finish? There are some IA-IAA match-ups. Doesn't that broaden the set of teams enough to allow us to determine whether Cornell is, say, 307th or 319th?
[prwolfe.bol.ucla.edu]
184 out of 706. Poor Principia...
They claim they use Bradley-Terry yet undefeated Boise State is 7th. Explanation?
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: KeithK (---.dsl.snfc21.pacbell.net)
Date: January 11, 2007 01:12PM
One way to get around the infinite rating issue is to add a fictitious team to the rankings who has played and tied all teams. This gives everyone a non-zero and non-perfect winning percentage. I can easily imagine Boise State's SoS factors driving them to 7th if this were done.DeltaOne81Scersk '97Trotsky
Screw these teams, where does Cornell finish? There are some IA-IAA match-ups. Doesn't that broaden the set of teams enough to allow us to determine whether Cornell is, say, 307th or 319th?
[prwolfe.bol.ucla.edu]
184 out of 706. Poor Principia...
They claim they use Bradley-Terry yet undefeated Boise State is 7th. Explanation?
Re: NCAA Division I-A Football: crazy statistical analysis
Posted by: jtwcornell91 (Moderator)
Date: January 18, 2007 02:33PM
I never managed to write it all up, but if you look at things from a Bayesian point of view, the usual Bradley-Terry (complete with undefined ML estimates) arises from the choice of a Jeffreys prior on each team's rating (uniform in the logarithm). If you use a prior which is instead uniform in the HHWP of each team vs the "fictitious team" with a rating of 100, the MLE automatically exists, and looks like the thing Ken used to do, only you get two games against the fictitious team: one win and one loss. The pre-bowl rankings look like this (the first column is the rating, the second is the common log of the rating divided by 100, the next two--identical because of an internal check I never got around to putting out--are the one-sigma errorbar on that logarithm, holding all the other ratings fixed at their maximum-likelihood values, and the last one is the one-sigma errorbar after marginalizing over all the other ratings):
Ohio State 2450 3.199 .8043 .8043 .8615 Michigan 1510 2.715 .6218 .6218 .6973 Florida 1506 2.712 .5775 .5775 .6483 Boise St 1125 2.420 .7939 .7939 .8362 Louisville 912.2 2.211 .5798 .5798 .6324 Southern Cal 879.6 2.174 .4893 .4893 .5527 LSU 785.6 2.061 .5329 .5329 .6030 Wisconsin 726.7 1.983 .6377 .6377 .7000 Auburn 712.7 1.964 .5374 .5374 .6045 Notre Dame 682.7 1.921 .5359 .5359 .5834 Arkansas 572.1 1.744 .5086 .5086 .5812 Tennessee 530.2 1.668 .4882 .4882 .5552 West Virginia 518.2 1.645 .5219 .5219 .5798 Rutgers 501.6 1.613 .5257 .5257 .5858 Oklahoma 494.2 1.598 .4894 .4894 .5406 California 469.5 1.547 .4638 .4638 .5330 Wake Forest 452.7 1.510 .5075 .5075 .5643 Virginia Tech 442.1 1.486 .5124 .5124 .5665 Oregon St 371.4 1.312 .4458 .4458 .5217 Texas 349.3 1.251 .4999 .4999 .5542 Brigham Young 332.5 1.202 .5094 .5094 .5574 Boston College 315.1 1.148 .4811 .4811 .5373 Penn State 278.3 1.023 .5283 .5283 .5915 UCLA 260.8 .9587 .4259 .4259 .4945 Texas A&M 255.5 .9380 .4804 .4804 .5367 Georgia 247.9 .9079 .4895 .4895 .5474 Georgia Tech 247.0 .9041 .4584 .4584 .5135 TCU 241.2 .8805 .5174 .5174 .5694 Nebraska 236.6 .8612 .4573 .4573 .5127 Hawai`i 225.1 .8112 .5056 .5056 .5582 South Carolina 219.6 .7868 .4680 .4680 .5280 Oregon 218.3 .7807 .4469 .4469 .5193 Clemson 216.4 .7718 .4618 .4618 .5182 Maryland 215.1 .7658 .4616 .4616 .5190 Kentucky 211.8 .7503 .4818 .4818 .5385 Cincinnati 208.1 .7327 .4867 .4867 .5447 Arizona St 192.4 .6545 .4463 .4463 .5176 Houston 191.0 .6472 .4498 .4498 .5033 Arizona 187.6 .6294 .4434 .4434 .5138 South Florida 186.1 .6209 .4876 .4876 .5435 Missouri 176.9 .5705 .4465 .4465 .4970 Navy 176.8 .5697 .5225 .5225 .5599 Washington St 169.5 .5279 .4388 .4388 .5069 Central Michigan 162.5 .4858 .4664 .4664 .5179 Purdue 155.9 .4438 .4439 .4439 .5065 Tulsa 140.2 .3377 .4530 .4530 .5041 Minnesota 139.0 .3293 .4870 .4870 .5451 Washington 129.1 .2556 .4344 .4344 .5032 Texas Tech 128.9 .2537 .4489 .4489 .5005 Southern Miss 125.6 .2275 .4545 .4545 .5110 Florida St 121.9 .1983 .4403 .4403 .4910 Alabama 120.8 .1889 .5084 .5084 .5614 Nevada 118.0 .1654 .4805 .4805 .5370 Rice 116.8 .1553 .4275 .4275 .4754 Ohio U. 115.3 .1422 .4639 .4639 .5159 Kansas St 114.2 .1328 .4541 .4541 .5059 Indiana 113.9 .1300 .4679 .4679 .5254 Western Michigan 111.7 .1110 .4390 .4390 .4927 Iowa 107.2 .0697 .4712 .4712 .5275 San José St 105.0 .0484 .4876 .4876 .5476 Oklahoma St 104.1 .0401 .4404 .4404 .4948 East Carolina 102.2 .0220 .4320 .4320 .4838 Utah 99.99 - 0 .4794 .4794 .5392 Pittsburgh 99.14 - 0 .4569 .4569 .5085 Miami FL 93.33 -.0691 .4901 .4901 .5414 Middle Tennessee St 91.71 -.0866 .4857 .4857 .5371 New Mexico 80.18 -.2208 .4527 .4527 .5122 Northern Illinois 73.70 -.3052 .4772 .4772 .5357 Wyoming 73.32 -.3104 .4452 .4452 .5032 Kansas 71.34 -.3377 .4417 .4417 .4939 Troy 66.56 -.4071 .4579 .4579 .5117 Connecticut 66.52 -.4077 .4857 .4857 .5356 Virginia 66.21 -.4124 .4320 .4320 .4830 Syracuse 65.57 -.4221 .4647 .4647 .5148 Northwestern 62.58 -.4687 .5104 .5104 .5648 SMU 58.92 -.5290 .4329 .4329 .4859 Mississippi 58.33 -.5391 .5105 .5105 .5627 Michigan St 57.47 -.5539 .4799 .4799 .5349 Ball St 57.15 -.5595 .4661 .4661 .5254 Vanderbilt 54.21 -.6122 .5487 .5487 .6010 Baylor 48.82 -.7170 .4782 .4782 .5278 Louisiana-Lafayette 47.25 -.7497 .4802 .4802 .5375 Air Force 47.22 -.7504 .4628 .4628 .5224 Tulane 47.08 -.7533 .4431 .4431 .4974 Arkansas St 46.81 -.7591 .4394 .4394 .4975 Marshall 44.49 -.8100 .4602 .4602 .5156 UTEP 43.99 -.8211 .4250 .4250 .4777 Kent St 42.68 -.8514 .4389 .4389 .5013 Akron 41.25 -.8854 .4391 .4391 .4954 Mississippi St 40.49 -.9041 .5366 .5366 .5844 Iowa St 38.95 -.9429 .4872 .4872 .5347 Fresno St 38.85 -.9455 .4789 .4789 .5454 Florida Atlantic 36.38 -1.011 .4675 .4675 .5267 Central Florida 35.16 -1.045 .4831 .4831 .5366 Toledo 35.01 -1.050 .4432 .4432 .4996 San Diego St 34.05 -1.077 .4804 .4804 .5419 North Carolina St 33.19 -1.103 .5116 .5116 .5584 North Carolina 32.55 -1.122 .5615 .5615 .6131 Stanford 32.44 -1.126 .5845 .5845 .6324 Idaho 29.48 -1.221 .5049 .5049 .5727 Colorado 29.41 -1.224 .5117 .5117 .5590 Colorado St 28.36 -1.260 .4708 .4708 .5334 Alabama-Birmingham 26.71 -1.320 .4609 .4609 .5158 Army 25.71 -1.358 .5033 .5033 .5414 Louisiana-Monroe 24.80 -1.394 .4945 .4945 .5537 Illinois 23.17 -1.462 .5895 .5895 .6387 Bowling Green 21.29 -1.547 .4799 .4799 .5505 New Mexico St 18.11 -1.709 .5346 .5346 .6047 North Texas 17.72 -1.730 .4744 .4744 .5316 Miami OH 16.24 -1.818 .4960 .4960 .5558 Louisiana Tech 16.20 -1.820 .5306 .5306 .5979 Buffalo 15.85 -1.842 .5203 .5203 .5889 UNLV 13.55 -1.999 .5799 .5799 .6345 Memphis 12.52 -2.078 .5771 .5771 .6250 Temple 12.31 -2.095 .5938 .5938 .6462 Utah St 11.07 -2.200 .5954 .5954 .6640 Eastern Michigan 10.54 -2.250 .5672 .5672 .6153 Duke 8.795 -2.431 .7844 .7844 .8234 Florida Int'l 3.891 -3.246 .7636 .7636 .8061Note (for those of you who got this far) that that errorbar is not actually what you really want; what's interesting is the distribution of the ratio of two teams' ratings, marginalizing ober all the others'.
Edited 1 time(s). Last edit at 05/09/2007 07:47AM by jtwcornell91.
Post-bowl followup
Posted by: jtwcornell91 (Moderator)
Date: January 18, 2007 02:40PM
And here's "everybody else":
# Team BT RRWP W- L W/L SOS RPI 2 Florida 106464 .975 12- 1 12.00 8872 .698 3 Ohio State 63212 .965 12- 1 12.00 5268 .642 4 LSU 29549 .945 11- 2 5.500 5372 .633 5 Michigan 24880 .940 11- 2 5.500 4524 .651 6 Wisconsin 24871 .939 11- 1 11.00 2261 .597 7 Auburn 22963 .937 11- 2 5.500 4175 .620 8 Southern Cal 16721 .925 11- 2 5.500 3040 .654 9 Arkansas 12523 .914 9- 4 2.250 5566 .597 10 Louisville 8539 .896 12- 1 12.00 711.6 .652 11 Notre Dame 6750 .884 10- 3 3.333 2025 .595 12 Tennessee 6615 .883 9- 4 2.250 2940 .597 13 California 4221 .858 9- 3 3.000 1407 .603 14 Penn State 4095 .856 8- 4 2.000 2047 .573 15 Oregon St 3118 .838 9- 4 2.250 1386 .596 16 West Virginia 2999 .836 10- 2 5.000 599.8 .627 17 Georgia 2840 .832 8- 4 2.000 1420 .568 18 Rutgers 2301 .817 10- 2 5.000 460.3 .611 19 South Carolina 2012 .807 7- 5 1.400 1437 .581 20 Kentucky 1989 .806 7- 5 1.400 1421 .578 21 Wake Forest 1477 .783 10- 3 3.333 443.1 .573 22 Oklahoma 1277 .771 11- 3 3.667 348.3 .593 23 Virginia Tech 1250 .769 9- 3 3.000 416.8 .584 24 Arizona 1156 .762 5- 6 .8333 1387 .550 25 Brigham Young 1049 .754 11- 2 5.500 190.8 .572 26 Boston College 1043 .753 9- 3 3.000 347.6 .591 27 UCLA 1027 .752 7- 6 1.167 879.9 .552 28 Oregon 968.7 .747 6- 6 1.000 968.7 .544 29 Washington St 923.9 .743 6- 6 1.000 923.9 .521 30 Georgia Tech 771.7 .726 8- 5 1.600 482.3 .555 31 Texas 759.6 .725 9- 3 3.000 253.2 .591 32 Arizona St 742.1 .723 6- 6 1.000 742.1 .525 33 Hawai`i 721.2 .720 10- 3 3.333 216.4 .539 34 Cincinnati 670.7 .713 7- 5 1.400 479.1 .582 35 Maryland 666.0 .712 8- 4 2.000 333.0 .563 36 Clemson 610.2 .704 8- 5 1.600 381.4 .530 37 Washington 506.1 .686 5- 7 .7143 708.5 .515 38 South Florida 461.2 .676 8- 4 2.000 230.6 .541 39 Texas A&M 392.2 .660 8- 4 2.000 196.1 .558 40 Nebraska 386.3 .658 8- 5 1.600 241.4 .563 41 TCU 299.9 .631 10- 2 5.000 59.98 .547 42 Florida St 255.5 .614 7- 6 1.167 219.0 .538 43 Alabama 196.6 .584 6- 7 .8571 229.3 .486 44 Purdue 194.4 .583 7- 6 1.167 166.6 .513 45 Missouri 193.9 .583 7- 5 1.400 138.5 .532 46 Navy 178.8 .573 8- 4 2.000 89.40 .486 47 Texas Tech 176.0 .572 7- 5 1.400 125.7 .531 48 Miami FL 171.4 .568 6- 6 1.000 171.4 .508 49 Minnesota 152.8 .555 5- 7 .7143 213.9 .524 50 Houston 136.3 .542 9- 4 2.250 60.56 .531 51 Oklahoma St 135.1 .541 6- 6 1.000 135.1 .527 52 Central Michigan 122.7 .529 10- 4 2.500 49.09 .531 53 Pittsburgh 120.9 .527 5- 6 .8333 145.0 .508 54 San José St 107.9 .513 8- 4 2.000 53.93 .489 55 Kansas St 102.1 .507 6- 6 1.000 102.1 .506 56 Vanderbilt 101.7 .506 3- 8 .3750 271.2 .463 57 Utah 100.9 .505 7- 5 1.400 72.08 .516 58 Indiana 98.13 .502 5- 6 .8333 117.8 .508 59 Mississippi 97.73 .501 3- 8 .3750 260.6 .465 60 Southern Miss 90.32 .492 8- 5 1.600 56.45 .524 61 Iowa 83.43 .482 5- 7 .7143 116.8 .500 62 Connecticut 80.98 .478 3- 8 .3750 215.9 .498 63 Tulsa 73.07 .466 7- 5 1.400 52.19 .513 64 Nevada 68.07 .457 8- 5 1.600 42.55 .476 65 Syracuse 66.02 .453 4- 8 .5000 132.0 .482 66 Rice 58.73 .438 7- 6 1.167 50.34 .491 67 Stanford 55.85 .432 1-11 .0909 614.4 .444 68 East Carolina 55.21 .431 7- 6 1.167 47.32 .481 69 Virginia 55.00 .430 5- 7 .7143 77.00 .458 70 Kansas 52.46 .424 5- 6 .8333 62.95 .455 71 Western Michigan 48.68 .415 8- 5 1.600 30.42 .481 72 Wyoming 44.02 .403 6- 6 1.000 44.02 .477 73 Baylor 40.22 .391 3- 8 .3750 107.3 .456 74 Middle Tennessee St 40.06 .391 6- 6 1.000 40.06 .495 75 Mississippi St 39.54 .389 2- 9 .2222 178.0 .458 76 New Mexico 37.35 .382 6- 6 1.000 37.35 .474 77 Troy 37.19 .382 7- 5 1.400 26.57 .465 78 Michigan St 37.02 .381 4- 8 .5000 74.03 .453 79 Northwestern 35.68 .377 4- 7 .5714 62.45 .466 80 Ohio U. 35.66 .377 8- 5 1.600 22.29 .486 81 SMU 22.66 .322 5- 6 .8333 27.19 .452 82 Air Force 22.29 .320 4- 8 .5000 44.58 .455 83 Tulane 20.01 .307 4- 8 .5000 40.02 .448 84 Iowa St 19.47 .304 3- 8 .3750 51.91 .425 85 Northern Illinois 19.16 .302 6- 6 1.000 19.16 .465 86 North Carolina 18.93 .301 2- 9 .2222 85.20 .440 87 North Carolina St 18.01 .295 2- 9 .2222 81.06 .438 88 Marshall 16.72 .287 4- 7 .5714 29.26 .430 89 Colorado 16.59 .286 2- 9 .2222 74.67 .407 90 UTEP 15.16 .276 5- 7 .7143 21.22 .417 91 Ball St 14.68 .272 5- 6 .8333 17.61 .450 92 San Diego St 13.48 .263 3- 8 .3750 35.96 .445 93 Central Florida 13.43 .262 3- 8 .3750 35.81 .429 94 Arkansas St 13.12 .260 6- 6 1.000 13.12 .420 95 Louisiana-Lafayette 12.03 .250 5- 6 .8333 14.44 .437 96 Fresno St 11.41 .245 4- 8 .5000 22.81 .438 97 Florida Atlantic 10.73 .238 4- 7 .5714 18.78 .413 98 Colorado St 10.13 .232 3- 8 .3750 27.01 .405 99 Illinois 9.561 .227 1-10 .1000 95.61 .426 100 Alabama-Birmingham 9.353 .224 3- 9 .3333 28.06 .396 101 Army 8.460 .214 2- 9 .2222 38.07 .407 102 Akron 8.449 .214 5- 7 .7143 11.83 .426 103 Toledo 7.880 .207 4- 7 .5714 13.79 .408 104 Kent St 7.023 .197 6- 6 1.000 7.023 .402 105 Idaho 6.684 .192 3- 8 .3750 17.82 .421 106 Louisiana-Monroe 5.564 .176 3- 8 .3750 14.84 .389 107 UNLV 3.449 .137 1-10 .1000 34.49 .384 108 North Texas 2.793 .122 3- 9 .3333 8.380 .369 109 New Mexico St 2.691 .120 2- 8 .2500 10.76 .390 110 Memphis 2.667 .119 1-10 .1000 26.67 .356 111 Miami OH 2.206 .107 2-10 .2000 11.03 .365 112 Louisiana Tech 2.181 .106 2-10 .2000 10.90 .398 113 Bowling Green 1.993 .101 4- 8 .5000 3.987 .389 114 Buffalo 1.546 .087 2-10 .2000 7.729 .403 115 Utah St 1.233 .076 1-11 .0909 13.56 .398 116 Eastern Michigan 1.177 .074 1-11 .0909 12.94 .354 117 Temple 1.071 .070 1-11 .0909 11.79 .387
Edited 1 time(s). Last edit at 01/18/2007 02:41PM by jtwcornell91.
Re: Post-bowl followup
Posted by: jtwcornell91 (Moderator)
Date: January 18, 2007 02:43PM
And with the regularizing prior:
Florida 2253 3.115 .5771 .5771 .6380 Boise St 1610 2.779 .7847 .7847 .8221 Ohio State 1467 2.685 .6223 .6223 .6717 Louisville 1245 2.522 .5744 .5744 .6249 Southern Cal 1050 2.351 .4880 .4880 .5428 LSU 1033 2.335 .5272 .5272 .5856 Michigan 995.0 2.298 .5244 .5244 .5828 Auburn 903.9 2.202 .5352 .5352 .5910 Wisconsin 874.4 2.168 .6136 .6136 .6643 West Virginia 669.4 1.901 .5169 .5169 .5716 Rutgers 595.0 1.783 .5265 .5265 .5806 Notre Dame 534.5 1.676 .4886 .4886 .5333 Arkansas 533.8 1.675 .4854 .4854 .5461 California 508.5 1.626 .4564 .4564 .5141 Tennessee 467.0 1.541 .4578 .4578 .5137 Oklahoma 438.2 1.477 .4601 .4601 .5085 Oregon St 418.3 1.431 .4411 .4411 .5049 Wake Forest 412.7 1.417 .4726 .4726 .5241 Brigham Young 404.7 1.398 .5017 .5017 .5469 Boston College 372.6 1.315 .4631 .4631 .5123 Virginia Tech 360.0 1.281 .4627 .4627 .5122 Texas 359.1 1.278 .4785 .4785 .5253 Georgia 340.7 1.226 .4762 .4762 .5288 Penn State 329.4 1.192 .4972 .4972 .5500 Kentucky 285.3 1.048 .4669 .4669 .5183 TCU 281.4 1.035 .5115 .5115 .5565 South Carolina 274.4 1.010 .4520 .4520 .5048 Hawai`i 271.4 .9985 .4970 .4970 .5445 Maryland 258.4 .9493 .4457 .4457 .4959 Cincinnati 246.7 .9029 .4671 .4671 .5199 Georgia Tech 230.6 .8356 .4328 .4328 .4839 South Florida 229.5 .8307 .4794 .4794 .5309 Texas A&M 224.3 .8079 .4497 .4497 .4989 Nebraska 219.3 .7853 .4392 .4392 .4882 UCLA 210.6 .7450 .4069 .4069 .4647 Clemson 193.9 .6620 .4360 .4360 .4861 Oregon 189.9 .6415 .4305 .4305 .4933 Arizona 188.3 .6330 .4496 .4496 .5129 Central Michigan 179.8 .5868 .4551 .4551 .5002 Washington St 167.5 .5158 .4426 .4426 .5031 Houston 166.4 .5094 .4212 .4212 .4702 Arizona St 163.3 .4904 .4294 .4294 .4918 Florida St 154.7 .4361 .4237 .4237 .4688 Missouri 153.9 .4310 .4250 .4250 .4708 Texas Tech 148.9 .3984 .4303 .4303 .4764 Navy 147.1 .3860 .4874 .4874 .5238 Southern Miss 136.7 .3126 .4367 .4367 .4866 Purdue 132.7 .2832 .4271 .4271 .4789 Washington 127.0 .2387 .4342 .4342 .4960 San José St 125.0 .2233 .4746 .4746 .5285 Utah 124.6 .2196 .4612 .4612 .5136 Oklahoma St 120.0 .1822 .4171 .4171 .4662 Miami FL 117.7 .1626 .4592 .4592 .5045 Tulsa 111.9 .1124 .4280 .4280 .4753 Minnesota 109.8 .0936 .4633 .4633 .5102 Kansas St 108.3 .0802 .4425 .4425 .4899 Pittsburgh 105.5 .0533 .4661 .4661 .5142 Indiana 103.8 .0376 .4642 .4642 .5150 Alabama 102.9 .0282 .4841 .4841 .5302 Nevada 100.5 0 .4502 .4502 .5022 Western Michigan 99.06 - 0 .4212 .4212 .4711 Ohio U. 94.83 -.0530 .4382 .4382 .4864 Rice 93.43 -.0679 .4054 .4054 .4522 Iowa 91.03 -.0939 .4513 .4513 .5005 East Carolina 89.32 -.1130 .4145 .4145 .4639 Middle Tennessee St 85.53 -.1564 .4648 .4648 .5129 Troy 82.49 -.1925 .4386 .4386 .4874 Wyoming 77.11 -.2600 .4501 .4501 .5040 New Mexico 72.55 -.3208 .4336 .4336 .4899 Kansas 71.02 -.3422 .4413 .4413 .4904 Connecticut 68.64 -.3763 .4905 .4905 .5371 Virginia 68.02 -.3854 .4320 .4320 .4793 Syracuse 68.01 -.3855 .4714 .4714 .5182 Northern Illinois 63.96 -.4469 .4587 .4587 .5114 Mississippi 59.99 -.5110 .5151 .5151 .5623 Northwestern 58.38 -.5382 .5092 .5092 .5574 Vanderbilt 56.10 -.5781 .5546 .5546 .6010 SMU 56.03 -.5792 .4304 .4304 .4814 Michigan St 54.00 -.6162 .4760 .4760 .5262 Ball St 53.62 -.6233 .4645 .4645 .5198 Baylor 49.42 -.7047 .4793 .4793 .5250 Arkansas St 47.99 -.7343 .4420 .4420 .4976 Air Force 47.70 -.7402 .4627 .4627 .5178 Louisiana-Lafayette 47.64 -.7415 .4795 .4795 .5340 Tulane 45.37 -.7903 .4427 .4427 .4951 Marshall 43.45 -.8335 .4610 .4610 .5145 Mississippi St 42.61 -.8530 .5456 .5456 .5893 UTEP 42.14 -.8643 .4225 .4225 .4739 Akron 40.44 -.9053 .4412 .4412 .4957 Kent St 39.99 -.9166 .4355 .4355 .4962 Fresno St 39.50 -.9288 .4803 .4803 .5434 Iowa St 37.91 -.9699 .4854 .4854 .5309 Florida Atlantic 37.52 -.9803 .4685 .4685 .5243 San Diego St 35.54 -1.034 .4847 .4847 .5430 Central Florida 34.42 -1.067 .4839 .4839 .5360 Toledo 33.86 -1.083 .4442 .4442 .4985 North Carolina St 33.81 -1.085 .5129 .5129 .5565 North Carolina 33.23 -1.102 .5601 .5601 .6078 Stanford 31.42 -1.158 .5827 .5827 .6258 Idaho 29.94 -1.206 .5068 .5068 .5712 Colorado 29.22 -1.230 .5112 .5112 .5564 Colorado St 28.91 -1.241 .4720 .4720 .5313 Alabama-Birmingham 26.57 -1.325 .4617 .4617 .5155 Louisiana-Monroe 25.31 -1.374 .4950 .4950 .5517 Army 24.86 -1.392 .5014 .5014 .5388 Illinois 21.92 -1.518 .5890 .5890 .6342 Bowling Green 20.48 -1.586 .4796 .4796 .5483 New Mexico St 18.20 -1.703 .5346 .5346 .6027 North Texas 17.80 -1.726 .4735 .4735 .5288 Louisiana Tech 16.31 -1.813 .5298 .5298 .5945 Miami OH 15.39 -1.871 .4949 .4949 .5528 Buffalo 15.18 -1.885 .5211 .5211 .5879 UNLV 13.83 -1.978 .5813 .5813 .6331 Memphis 12.17 -2.106 .5756 .5756 .6219 Temple 11.71 -2.145 .5927 .5927 .6433 Utah St 11.44 -2.168 .5983 .5983 .6648 Eastern Michigan 9.941 -2.309 .5658 .5658 .6120 Duke 8.956 -2.413 .7843 .7843 .8208 Florida Int'l 3.979 -3.224 .7652 .7652 .8070
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