[OT] Bradley-Terry for football?
Posted by David Harding '72
[OT] Bradley-Terry for football?
Posted by: David Harding '72 (---.client.comcast.net)
Date: January 01, 2004 10:45PM
A month ago the question was raised of applying the Bradley-Terry rating system to football. t[elf.elynah.com]
[q](BTW, does anyone know of a machine-readable archive of college football scores, à la USCHO, from which one could construct Bradley-Terry ratings for I-A gridiron? It might provide an interesting counterpoint to BCS.)[/q]
Just curious. Did anyone do anything? Do any of the BCS components do anything similar?
[q](BTW, does anyone know of a machine-readable archive of college football scores, à la USCHO, from which one could construct Bradley-Terry ratings for I-A gridiron? It might provide an interesting counterpoint to BCS.)[/q]
Just curious. Did anyone do anything? Do any of the BCS components do anything similar?
Re: [OT] Bradley-Terry for football?
Posted by: jtwcornell91 (---.tnt12.nyc9.da.uu.net)
Date: January 02, 2004 02:31AM
[board.uscho.com]
It includes all pre-bowl results but no bowl results. I'll add in the bowls soon after the LSU-OU game is played. (I'll probably try it with and without my idea of weighting bowl results double.)
It includes all pre-bowl results but no bowl results. I'll add in the bowls soon after the LSU-OU game is played. (I'll probably try it with and without my idea of weighting bowl results double.)
Re: [OT] Bradley-Terry for football?
Posted by: jtwcornell91 (---.tnt12.nyc9.da.uu.net)
Date: January 02, 2004 02:37AM
Here's the whole thing, along with the (traditional 25/50/25 weighting) RPI:
# Team _BT__ RRWP W- L _W/L_ _SOS_ RPI 1 LSU 5074 .945 11- 1 11.00 461.3 .628 2 Oklahoma 4405 .938 12- 1 12.00 367.1 .643 3 Miami OH 2755 .911 12- 1 12.00 229.6 .601 4 Ohio St 2183 .895 10- 2 5.000 436.7 .634 5 Texas 2114 .892 10- 2 5.000 422.7 .605 6 Michigan 1873 .883 10- 2 5.000 374.7 .609 7 Southern Cal 1795 .879 11- 1 11.00 163.2 .615 8 Georgia 1630 .871 10- 3 3.333 488.9 .600 9 Florida St 1563 .868 10- 2 5.000 312.6 .619 10 Miami FL 1428 .860 10- 2 5.000 285.6 .619 11 Tennessee 1402 .858 10- 2 5.000 280.5 .589 12 Iowa 1316 .853 9- 3 3.000 438.5 .586 13 Kansas St 1096 .835 9- 3 3.000 365.4 .607 14 Florida 1067 .833 7- 4 1.750 609.6 .598 15 Purdue 1029 .829 9- 3 3.000 343.1 .570 16 Oklahoma St 966.4 .823 8- 3 2.667 362.4 .567 17 Bowling Green 963.3 .822 8- 3 2.667 361.2 .596 18 Nebraska 704.0 .789 9- 3 3.000 234.7 .577 19 Mississippi 691.5 .787 9- 3 3.000 230.5 .554 20 Utah 559.3 .762 9- 2 4.500 124.3 .576 21 Boise St 540.6 .758 11- 1 11.00 49.14 .548 22 Arkansas 519.4 .753 8- 4 2.000 259.7 .570 23 Maryland 505.4 .750 8- 3 2.667 189.5 .575 24 Washington St 495.8 .747 9- 3 3.000 165.3 .572 25 TCU 483.3 .744 11- 1 11.00 43.93 .564 26 Auburn 410.4 .724 6- 5 1.200 342.0 .545 27 Minnesota 406.3 .722 9- 3 3.000 135.4 .535 28 Michigan St 368.8 .710 8- 4 2.000 184.4 .545 29 Texas Tech 365.2 .709 7- 5 1.400 260.9 .536 30 Clemson 360.2 .707 7- 4 1.750 205.8 .550 31 Oregon 319.8 .691 8- 4 2.000 159.9 .555 32 North Carolina St 285.3 .676 6- 5 1.200 237.7 .555 33 Missouri 280.7 .674 7- 4 1.750 160.4 .522 34 Wisconsin 258.8 .663 7- 5 1.400 184.8 .541 35 Northern Illinois 256.5 .661 9- 2 4.500 57.01 .506 36 Southern Miss 235.0 .649 9- 3 3.000 78.35 .566 37 New Mexico 210.5 .634 7- 4 1.750 120.3 .526 38 West Virginia 210.3 .634 8- 4 2.000 105.2 .535 39 California 202.4 .629 7- 6 1.167 173.5 .535 40 Colorado St 201.2 .628 6- 5 1.200 167.7 .541 41 Virginia 195.2 .624 7- 5 1.400 139.4 .528 42 Pittsburgh 191.4 .621 8- 4 2.000 95.70 .545 43 Notre Dame 190.8 .620 5- 7 .7143 267.1 .562 44 Virginia Tech 190.7 .620 7- 4 1.750 109.0 .544 45 Georgia Tech 182.9 .615 6- 6 1.000 182.9 .506 46 Oregon St 181.3 .613 6- 5 1.200 151.1 .536 47 Northwestern 179.6 .612 6- 6 1.000 179.6 .518 48 Colorado 179.5 .612 5- 7 .7143 251.2 .528 49 UCLA 150.1 .587 6- 6 1.000 150.1 .508 50 Boston College 127.6 .564 7- 5 1.400 91.13 .525 51 South Carolina 126.2 .563 5- 7 .7143 176.7 .517 52 Washington 121.8 .558 6- 6 1.000 121.8 .511 53 Air Force 121.2 .557 6- 5 1.200 101.0 .508 54 UNLV 114.5 .549 6- 6 1.000 114.5 .512 55 Fresno St 114.4 .549 7- 5 1.400 81.69 .517 56 Kansas 113.9 .548 5- 6 .8333 136.7 .481 57 Texas A&M 105.9 .538 4- 8 .5000 211.8 .519 58 Wake Forest 101.7 .533 5- 7 .7143 142.4 .495 59 Connecticut 92.63 .520 8- 3 2.667 34.74 .493 60 Toledo 83.48 .505 7- 4 1.750 47.70 .508 61 Louisville 83.01 .505 9- 3 3.000 27.67 .497 62 Brigham Young 82.42 .504 4- 8 .5000 164.8 .491 63 Alabama 80.42 .500 4- 9 .4444 180.9 .528 64 San Diego St 79.01 .498 4- 6 .6667 118.5 .478 65 Syracuse 78.87 .498 6- 6 1.000 78.87 .501 66 Navy 78.03 .496 7- 3 2.333 33.44 .478 67 Stanford 76.56 .494 4- 7 .5714 134.0 .478 68 North Texas 75.89 .493 9- 3 3.000 25.30 .498 69 Tulsa 73.31 .488 7- 4 1.750 41.89 .495 70 Hawai`i 71.97 .486 7- 5 1.400 51.40 .495 71 Memphis 66.70 .476 7- 4 1.750 38.12 .513 72 Arizona St 57.92 .457 4- 7 .5714 101.4 .468 73 South Florida 57.26 .456 5- 4 1.250 45.81 .498 74 Marshall 56.16 .453 7- 4 1.750 32.09 .515 75 Duke 53.79 .448 3- 8 .3750 143.4 .468 76 Houston 50.30 .440 7- 5 1.400 35.93 .501 77 Rutgers 46.29 .429 5- 7 .7143 64.81 .479 78 Nevada 42.92 .420 5- 6 .8333 51.51 .476 79 Wyoming 42.68 .419 3- 8 .3750 113.8 .460 80 Louisiana Tech 32.39 .388 5- 7 .7143 45.35 .485 81 Alabama-Birmingham 32.04 .386 5- 7 .7143 44.86 .475 82 Arizona 23.38 .353 2-10 .2000 116.9 .467 83 Troy St 22.95 .351 4- 6 .6667 34.43 .480 84 Rice 19.35 .334 5- 7 .7143 27.08 .438 85 Tulane 17.84 .327 4- 7 .5714 31.21 .467 86 Baylor 17.59 .325 2- 9 .2222 79.17 .444 87 Cincinnati 17.02 .322 4- 7 .5714 29.79 .466 88 North Carolina 14.29 .307 2-10 .2000 71.47 .408 89 Penn St 13.08 .299 3- 9 .3333 39.23 .461 90 Western Michigan 9.077 .270 4- 7 .5714 15.88 .449 91 Mississippi St 7.929 .261 2-10 .2000 39.65 .434 92 Ball St 4.722 .226 3- 8 .3750 12.59 .451 93 Kentucky 4.456 .223 3- 8 .3750 11.88 .407 94 Vanderbilt 4.399 .222 1-10 .1000 43.99 .428 95 Temple 2.591 .192 1-10 .1000 25.91 .403 96 Kent St 2.409 .189 4- 7 .5714 4.215 .431 97 Middle Tennessee St 2.328 .187 4- 7 .5714 4.074 .405 98 Louisiana-Lafayette 2.052 .181 3- 8 .3750 5.471 .414 99 Akron 1.923 .177 5- 5 1.000 1.923 .430 100 Iowa St 1.715 .172 1-10 .1000 17.15 .453 101 Arkansas St 1.200 .156 3- 7 .4286 2.800 .389 102 Utah St 1.151 .154 3- 9 .3333 3.453 .379 103 Idaho .9703 .147 3- 7 .4286 2.264 .389 104 Eastern Michigan .6235 .131 2- 8 .2500 2.494 .399 105 New Mexico St .5032 .123 2- 9 .2222 2.264 .369 106 Louisiana-Monroe .2464 .102 1- 9 .1111 2.218 .350 107 Central Michigan .2085 .098 1- 9 .1111 1.877 .381 108 Central Florida .1507 .091 2- 9 .2222 .6782 .358 109 Buffalo .0949 .082 1-10 .1000 .9491 .389 110 Ohio U. .0868 .080 1-10 .1000 .8680 .340 111 San José St 0 .034 2- 8 .2500 0 .386 112 East Carolina 0 .030 1-11 .0909 0 .377 113 Indiana 0 .030 1-10 .1000 0 .407 114 UTEP 0 .026 1-10 .1000 0 .348 115 Illinois 0 .022 0-11 0 0 .408 116 Army 0 .022 0-13 0 0 .361 117 SMU 0 .017 0-12 0 0 .348
Re: [OT] Bradley-Terry for football?
Posted by: Greg Berge (64.49.66.---)
Date: January 02, 2004 08:49AM
I haven't read through the notes on the site so forgive a dumb question. Are the SOS for the bottom 7 teams zero because they played no D-1A opponents?
No, wait, two of them are Big 10 schools. What gives?
Post Edited (01-02-04 08:50)
No, wait, two of them are Big 10 schools. What gives?
Post Edited (01-02-04 08:50)
Re: [OT] Bradley-Terry for football?
Posted by: jtwcornell91 (---.tnt12.nyc9.da.uu.net)
Date: January 02, 2004 10:45AM
Greg Berge '85 wrote:
I haven't read through the notes on the site so forgive a dumb question. Are the SOS for the bottom 7 teams zero because they played no D-1A opponents?
No, wait, two of them are Big 10 schools. What gives?
The bottom 7 teams have a rating of 0 because they either are winless or have only beaten other teams with 0 ratings. (In fact, not all the "0" BT rating entries are equivalent; the ratios of these teams' ratings are in various cases finite, zero, infinite, or undefined, which is reflected somewhat in their differing RRWPs.) So the explanation of the BT rating as "win-loss ratio times weighted average of opponents' ratings" breaks down a bit. In partcular, that explanation hides the fact that the weighting factor depends on a team's own rating. When the team has a "zero rating" (which in this case actually means it's zero compared to the top 110 teams), this weighting factor causes the games against other teams with zero ratings to overwhelm those against teams with finite ratings.
As an example, consider Indiana and Illinois. Indiana played and lost 10 games against the top 110 teams (call them "the pack"
and played and won one game against Illinois. Indiana's rating is zero compared to anyone's in the pack but infinite compared to Illinois's. So if we look at the average which defines Indiana's strength of schedule, it looks like this
Mich Ill
------------ + ... + ---------
Mich + Ind Ill + Ind
----------------------------------
1 1
------------ + ... + ---------
Mich + Ind Ill + Ind
where the "..." represents the corresponding terms for Indiana against the other 9 teams they've played from the pack, which will behave the same way as the Michigan term. Now, Indiana's rating is zero compared to Michigan's, so Mich + Ind = Michand likewise Illinois's rating is zero compared to Indiana's, so
Ill + Ind = Indwhich makes the strength of schedule for Indiana
Mich Ill Ill
------ + ... + ----- 1 + ... + -----
Mich Ind Ind
------------------------ = ------------------------
1 1 1 1
------ + ... + ----- ------ + ... + -----
Mich Ind Mich Ind
Now, in the numerator of the last expression, Illinois's rating divided by Indiana's is zero, while the 9 terms represented by the "..." are each in turn equal to 1 for the same reason Michigan's term is. In denominator, if Indiana's rating is zero compared to that of Michigan or any other team in the pack, then one over (e.g.) Michigan's rating has to be zero compared to one over Indiana's. So the strength of schedule for Indiana is equal to
10
----------- = 10 * Ind
1 / Ind
so Indiana's average opponent is 10 times as strong as Indiana, but 10 times zero is still zero.Of course, the easier way to see that their SOS has to be zero is that their winning ratio is non-zero because of the game over Illinois, so their SOS must be zero (compared to ratings in the pack) to for their rating to come out to zero (which we know it has to because they have lost to every non-winless team they've played).
Illinois's SOS doesn't "have to" be zero, since their winning ratio is zero, but it turns out that it is, because it's dominated by the game against Indiana.
Well, you asked...
Re: [OT] Bradley-Terry for football?
Posted by: atb9 (---.nycap.rr.com)
Date: January 02, 2004 11:50AM
UConn is a great story! Wow.
Re: [OT] Bradley-Terry for football?
Posted by: David Harding '72 (---.client.comcast.net)
Date: January 02, 2004 10:04PM
Thanks, John. It gives a very interesting perspective.
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