NCAA Division I-A Football: crazy statistical analysis

[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:

Code Select Expand


  # 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 .395

I 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.

[ebilmes]

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"

[Josh '99]

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.  :-P

[Rita]

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.

[billhoward]

[quote 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.[/quote]
Cheer for the neutral fan, arms pointing: "Football factory. Potato factory." Score one for the little guy.

[JDeafv]

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?

[jtwcornell91]

Games against non-D1 schools don't count.  Scores from http://prwolfe.bol.ucla.edu/cfootball/scores.htm and team list from http://prwolfe.bol.ucla.edu/cfootball/conferences.htm

[Trotsky]

[quote 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:
[code]
  # 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[/quote]

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?

[ugarte]

Michigan and Wisconsin can be placed in the body of the chart now, right?

[Scersk '97]

[quote 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?[/quote]

http://prwolfe.bol.ucla.edu/cfootball/ratings.htm

184 out of 706.  Poor Principia...

[Dpperk29]

so now does florida come out on top?

[Jacob '06]

[quote Dpperk29]so now does florida come out on top?[/quote]

Boise State all the way!

[ebilmes]

[quote Jacob '06][quote Dpperk29]so now does florida come out on top?[/quote]

Boise State all the way![/quote]

Right, because Boise State is the only undefeated team.

[Trotsky]

[quote Scersk '97][quote 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?[/quote]

http://prwolfe.bol.ucla.edu/cfootball/ratings.htm

184 out of 706.  Poor Principia...[/quote]

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.

[DeltaOne81]

[quote Scersk '97][quote 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?[/quote]

http://prwolfe.bol.ucla.edu/cfootball/ratings.htm

184 out of 706.  Poor Principia...[/quote]

They claim they use Bradley-Terry yet undefeated Boise State is 7th. Explanation?