KRACH 19 Nov 2009 - Addresses most of the problems from last week
I put a bit of effort in cleaning up my code to address some of the problems from last week:
- Undefeated and winless teams: I added the fictitious tie. Now there's a path from every team to every other team. While this is a hack, it's reasonable and about as far as I really care to go with it. I also calculated the round-robin winning percentage (RRWP) and KRACH strength of schedule (SOS). These are useful metrics for comparing teams that don't line up very well, as per John Whelan's KRACH site. Now the undefeated and winless teams can be compared with multiple data elements.
- Rasmus: Open source: The original Pairwise and KRACH code was freely given to me years ago by John Whelan. This code is my own, based only on the information given in his KRACH site; given that, I'm comfortable sharing my code, so long as the user gives due credit to John and Ken Butler.
- joeyb: Undefeated teams will always rate better than teams with losses: To investigate this, I created a fictitious team that was 10-0 with wins against only the bottom ten teams. It rated out at #37, well below several 1- and 2-loss teams.
- SpartanDan: Top teams are ranked backwards: You are correct, sir. I mistakenly assumed that a larger deviation from predicted meant a less accurate KRACH. This has been fixed, as in 1) above, with the RRWP, SOS and fictitious tie.
- Seth9: The rating doesn't apply to college football: You may be right on this. It's still curious, and now trivial, for me to crunch the numbers. EDIT: But is this any less applicable than any of the computer ratings used in the BCS? And it certainly does not have the bias and politicking associated with opinion polls.
Again, this rating includes all D-IA games through 15 November 2009:
Team | BlogPoll | BCS | Rank | KRACH | RRWP | Record Rank | W | L | T | Win % | SOS Rank | SOS |
Alabama | 1 | 2 | 1 | 50.413 | 0.953 | 1 | 10 | 0 | 0 | 1.000 | 10 | 2.401 |
Florida | 3 | 1 | 2 | 43.477 | 0.946 | 1 | 9 | 0 | 0 | 1.000 | 15 | 2.288 |
Cincinnati | 5 | 5 | 3 | 36.050 | 0.937 | 1 | 9 | 0 | 0 | 1.000 | 23 | 1.897 |
TCU | 4 | 4 | 4 | 29.380 | 0.926 | 1 | 9 | 0 | 0 | 1.000 | 35 | 1.546 |
Texas | 2 | 3 | 5 | 26.406 | 0.920 | 1 | 10 | 0 | 0 | 1.000 | 52 | 1.257 |
Boise State | 6 | 6 | 6 | 21.243 | 0.906 | 1 | 9 | 0 | 0 | 1.000 | 59 | 1.118 |
Georgia Tech | 7 | 7 | 7 | 13.464 | 0.870 | 2 | 9 | 1 | 0 | 0.900 | 18 | 2.126 |
LSU | 11 | 8 | 8 | 9.599 | 0.837 | 5 | 8 | 2 | 0 | 0.800 | 2 | 2.823 |
Oregon | 9 | 11 | 9 | 9.141 | 0.832 | 5 | 8 | 2 | 0 | 0.800 | 3 | 2.688 |
Pittsburgh | 8 | 9 | 10 | 8.655 | 0.826 | 3 | 8 | 1 | 0 | 0.889 | 37 | 1.527 |
Ohio State | 10 | 10 | 11 | 7.289 | 0.807 | 4 | 9 | 2 | 0 | 0.818 | 22 | 1.918 |
Iowa | 14 | 13 | 12 | 6.292 | 0.789 | 5 | 8 | 2 | 0 | 0.800 | 24 | 1.851 |
Virginia Tech | 16 | 15 | 13 | 6.103 | 0.785 | 8 | 7 | 3 | 0 | 0.700 | 1 | 2.848 |
Oklahoma State | 12 | 12 | 14 | 5.436 | 0.770 | 6 | 7 | 2 | 0 | 0.778 | 26 | 1.812 |
Penn State | 15 | 14 | 15 | 5.061 | 0.761 | 5 | 8 | 2 | 0 | 0.800 | 40 | 1.489 |
Oregon State | 19 | 19 | 16 | 4.967 | 0.758 | 9 | 6 | 3 | 0 | 0.667 | 4 | 2.675 |
USC | 21 | 18 | 17 | 4.954 | 0.758 | 8 | 7 | 3 | 0 | 0.700 | 14 | 2.312 |
Wisconsin | 17 | 16 | 18 | 4.574 | 0.747 | 6 | 7 | 2 | 0 | 0.778 | 38 | 1.525 |
Miami (FL) | 20 | 20 | 19 | 4.544 | 0.746 | 9 | 6 | 3 | 0 | 0.667 | 8 | 2.447 |
Clemson | 18 | 23 | 20 | 4.393 | 0.741 | 9 | 6 | 3 | 0 | 0.667 | 12 | 2.365 |
Rutgers | 21 | 4.372 | 0.741 | 7 | 5 | 2 | 0 | 0.714 | 20 | 1.987 | ||
Utah | 23 | 21 | 22 | 3.965 | 0.727 | 5 | 8 | 2 | 0 | 0.800 | 56 | 1.166 |
Stanford | 13 | 17 | 23 | 3.825 | 0.721 | 8 | 7 | 3 | 0 | 0.700 | 27 | 1.785 |
California | 25 | 24 | 3.679 | 0.716 | 9 | 6 | 3 | 0 | 0.667 | 21 | 1.981 | |
Temple | 25 | 3.607 | 0.713 | 3 | 8 | 1 | 0 | 0.889 | 88 | 0.636 | ||
North Carolina | 25 | 26 | 3.504 | 0.708 | 11 | 5 | 3 | 0 | 0.625 | 16 | 2.230 | |
Arizona | 27 | 3.496 | 0.708 | 11 | 5 | 3 | 0 | 0.625 | 17 | 2.224 | ||
Georgia | 28 | 3.049 | 0.687 | 14 | 5 | 4 | 0 | 0.556 | 7 | 2.494 | ||
South Florida | 29 | 3.048 | 0.687 | 13 | 4 | 3 | 0 | 0.571 | 11 | 2.370 | ||
Navy | 30 | 3.001 | 0.685 | 8 | 7 | 3 | 0 | 0.700 | 46 | 1.400 | ||
Brigham Young | 22 | 22 | 31 | 2.900 | 0.680 | 5 | 8 | 2 | 0 | 0.800 | 71 | 0.853 |
Boston College | 32 | 2.855 | 0.677 | 9 | 6 | 3 | 0 | 0.667 | 36 | 1.537 | ||
Arkansas | 33 | 2.826 | 0.675 | 14 | 5 | 4 | 0 | 0.556 | 13 | 2.312 | ||
Houston | 24 | 24 | 34 | 2.817 | 0.675 | 6 | 7 | 2 | 0 | 0.778 | 63 | 0.939 |
West Virginia | 35 | 2.665 | 0.666 | 9 | 6 | 3 | 0 | 0.667 | 41 | 1.435 | ||
Auburn | 36 | 2.379 | 0.648 | 12 | 6 | 4 | 0 | 0.600 | 31 | 1.647 | ||
Notre Dame | 37 | 2.252 | 0.639 | 12 | 6 | 4 | 0 | 0.600 | 33 | 1.559 | ||
Mississippi | 38 | 2.228 | 0.637 | 11 | 5 | 3 | 0 | 0.625 | 43 | 1.418 | ||
Central Michigan | 39 | 2.091 | 0.627 | 6 | 7 | 2 | 0 | 0.778 | 84 | 0.697 | ||
Nebraska | 40 | 1.994 | 0.619 | 8 | 7 | 3 | 0 | 0.700 | 64 | 0.931 | ||
Florida State | 41 | 1.985 | 0.618 | 16 | 4 | 5 | 0 | 0.444 | 9 | 2.426 | ||
South Carolina | 42 | 1.748 | 0.597 | 15 | 5 | 5 | 0 | 0.500 | 28 | 1.748 | ||
Kentucky | 43 | 1.717 | 0.594 | 14 | 5 | 4 | 0 | 0.556 | 44 | 1.405 | ||
Oklahoma | 44 | 1.709 | 0.593 | 14 | 5 | 4 | 0 | 0.556 | 47 | 1.398 | ||
UCLA | 45 | 1.680 | 0.590 | 15 | 5 | 5 | 0 | 0.500 | 29 | 1.680 | ||
Tennessee | 46 | 1.648 | 0.587 | 15 | 5 | 5 | 0 | 0.500 | 30 | 1.648 | ||
Minnesota | 47 | 1.549 | 0.576 | 15 | 5 | 5 | 0 | 0.500 | 34 | 1.549 | ||
Missouri | 48 | 1.498 | 0.570 | 14 | 5 | 4 | 0 | 0.556 | 54 | 1.225 | ||
Troy | 49 | 1.447 | 0.564 | 8 | 7 | 3 | 0 | 0.700 | 86 | 0.675 | ||
Texas Tech | 50 | 1.400 | 0.559 | 14 | 5 | 4 | 0 | 0.556 | 57 | 1.145 | ||
Mississippi State | 51 | 1.372 | 0.555 | 20 | 3 | 6 | 0 | 0.333 | 5 | 2.548 | ||
Connecticut | 52 | 1.289 | 0.544 | 18 | 3 | 5 | 0 | 0.375 | 19 | 2.026 | ||
Air Force | 53 | 1.239 | 0.537 | 12 | 6 | 4 | 0 | 0.600 | 70 | 0.858 | ||
Michigan State | 54 | 1.223 | 0.535 | 15 | 5 | 5 | 0 | 0.500 | 55 | 1.223 | ||
Washington | 55 | 1.187 | 0.530 | 21 | 3 | 7 | 0 | 0.300 | 6 | 2.543 | ||
Nevada | 56 | 1.179 | 0.529 | 8 | 7 | 3 | 0 | 0.700 | 95 | 0.550 | ||
Fresno State | 57 | 1.152 | 0.525 | 14 | 5 | 4 | 0 | 0.556 | 62 | 0.942 | ||
Northwestern | 58 | 1.151 | 0.525 | 12 | 6 | 4 | 0 | 0.600 | 76 | 0.797 | ||
UCF | 59 | 1.125 | 0.521 | 14 | 5 | 4 | 0 | 0.556 | 65 | 0.921 | ||
East Carolina | 60 | 1.061 | 0.510 | 14 | 5 | 4 | 0 | 0.556 | 69 | 0.868 | ||
Duke | 61 | 1.056 | 0.509 | 15 | 4 | 4 | 0 | 0.500 | 60 | 1.056 | ||
Arizona State | 62 | 0.993 | 0.499 | 20 | 3 | 6 | 0 | 0.333 | 25 | 1.845 | ||
Idaho | 63 | 0.961 | 0.493 | 10 | 7 | 4 | 0 | 0.636 | 92 | 0.577 | ||
Middle Tennessee State | 64 | 0.943 | 0.490 | 8 | 7 | 3 | 0 | 0.700 | 102 | 0.440 | ||
Southern Methodist | 65 | 0.924 | 0.486 | 14 | 5 | 4 | 0 | 0.556 | 80 | 0.756 | ||
Iowa State | 66 | 0.874 | 0.477 | 15 | 5 | 5 | 0 | 0.500 | 67 | 0.874 | ||
Virginia | 67 | 0.820 | 0.466 | 20 | 3 | 6 | 0 | 0.333 | 39 | 1.523 | ||
Southern Miss | 68 | 0.787 | 0.459 | 14 | 5 | 4 | 0 | 0.556 | 87 | 0.644 | ||
Texas A&M | 69 | 0.757 | 0.452 | 15 | 5 | 5 | 0 | 0.500 | 79 | 0.757 | ||
Wake Forest | 70 | 0.757 | 0.452 | 21 | 3 | 7 | 0 | 0.300 | 32 | 1.622 | ||
Baylor | 71 | 0.738 | 0.447 | 20 | 3 | 6 | 0 | 0.333 | 48 | 1.370 | ||
Purdue | 72 | 0.736 | 0.447 | 19 | 4 | 7 | 0 | 0.364 | 53 | 1.227 | ||
Louisville | 73 | 0.726 | 0.445 | 20 | 3 | 6 | 0 | 0.333 | 49 | 1.348 | ||
Kansas State | 74 | 0.718 | 0.443 | 16 | 4 | 5 | 0 | 0.444 | 66 | 0.878 | ||
Kansas | 75 | 0.683 | 0.434 | 16 | 4 | 5 | 0 | 0.444 | 73 | 0.835 | ||
Northern Illinois | 76 | 0.675 | 0.432 | 9 | 6 | 3 | 0 | 0.667 | 108 | 0.364 | ||
Bowling Green | 77 | 0.624 | 0.419 | 15 | 5 | 5 | 0 | 0.500 | 89 | 0.624 | ||
Ohio | 78 | 0.624 | 0.419 | 9 | 6 | 3 | 0 | 0.667 | 113 | 0.336 | ||
Marshall | 79 | 0.612 | 0.415 | 16 | 4 | 5 | 0 | 0.444 | 81 | 0.748 | ||
Louisiana-Monroe | 80 | 0.578 | 0.406 | 14 | 5 | 4 | 0 | 0.556 | 99 | 0.473 | ||
Michigan | 81 | 0.577 | 0.406 | 17 | 4 | 6 | 0 | 0.400 | 74 | 0.833 | ||
Wyoming | 82 | 0.564 | 0.402 | 16 | 4 | 5 | 0 | 0.444 | 85 | 0.689 | ||
UAB | 83 | 0.511 | 0.385 | 15 | 5 | 5 | 0 | 0.500 | 97 | 0.511 | ||
North Carolina State | 84 | 0.510 | 0.385 | 22 | 2 | 6 | 0 | 0.250 | 50 | 1.326 | ||
Syracuse | 85 | 0.476 | 0.374 | 23 | 2 | 7 | 0 | 0.222 | 42 | 1.428 | ||
Indiana | 86 | 0.407 | 0.349 | 21 | 3 | 7 | 0 | 0.300 | 68 | 0.872 | ||
Colorado | 87 | 0.390 | 0.342 | 21 | 3 | 7 | 0 | 0.300 | 72 | 0.835 | ||
Illinois | 88 | 0.380 | 0.338 | 23 | 2 | 7 | 0 | 0.222 | 58 | 1.140 | ||
UNLV | 89 | 0.363 | 0.331 | 21 | 3 | 7 | 0 | 0.300 | 78 | 0.777 | ||
Toledo | 90 | 0.324 | 0.313 | 17 | 4 | 6 | 0 | 0.400 | 100 | 0.468 | ||
Colorado State | 91 | 0.314 | 0.309 | 23 | 2 | 7 | 0 | 0.222 | 61 | 0.943 | ||
San Diego State | 92 | 0.303 | 0.303 | 20 | 3 | 6 | 0 | 0.333 | 93 | 0.562 | ||
Kent State | 93 | 0.298 | 0.301 | 16 | 4 | 5 | 0 | 0.444 | 107 | 0.364 | ||
Louisiana-Lafayette | 94 | 0.273 | 0.289 | 16 | 4 | 5 | 0 | 0.444 | 114 | 0.334 | ||
Western Michigan | 95 | 0.243 | 0.272 | 17 | 4 | 6 | 0 | 0.400 | 111 | 0.351 | ||
Florida Atlantic | 96 | 0.242 | 0.271 | 20 | 3 | 6 | 0 | 0.333 | 101 | 0.449 | ||
Maryland | 97 | 0.226 | 0.262 | 26 | 1 | 8 | 0 | 0.111 | 51 | 1.282 | ||
Hawaii | 98 | 0.223 | 0.260 | 20 | 3 | 6 | 0 | 0.333 | 103 | 0.413 | ||
Washington State | 99 | 0.222 | 0.259 | 27 | 1 | 9 | 0 | 0.100 | 45 | 1.403 | ||
Tulsa | 100 | 0.205 | 0.248 | 20 | 3 | 6 | 0 | 0.333 | 106 | 0.380 | ||
Louisiana Tech | 101 | 0.204 | 0.248 | 23 | 2 | 7 | 0 | 0.222 | 90 | 0.611 | ||
Buffalo | 102 | 0.185 | 0.235 | 23 | 2 | 7 | 0 | 0.222 | 94 | 0.555 | ||
UTEP | 103 | 0.165 | 0.220 | 21 | 3 | 7 | 0 | 0.300 | 110 | 0.353 | ||
Army | 104 | 0.162 | 0.218 | 20 | 3 | 6 | 0 | 0.333 | 116 | 0.300 | ||
Florida International | 105 | 0.155 | 0.213 | 21 | 3 | 7 | 0 | 0.300 | 115 | 0.332 | ||
Tulane | 106 | 0.136 | 0.197 | 23 | 2 | 7 | 0 | 0.222 | 104 | 0.407 | ||
Memphis | 107 | 0.126 | 0.189 | 26 | 1 | 8 | 0 | 0.111 | 83 | 0.713 | ||
Vanderbilt | 108 | 0.124 | 0.187 | 27 | 1 | 9 | 0 | 0.100 | 77 | 0.787 | ||
Utah State | 109 | 0.117 | 0.180 | 23 | 2 | 7 | 0 | 0.222 | 112 | 0.350 | ||
Akron | 110 | 0.107 | 0.171 | 26 | 1 | 8 | 0 | 0.111 | 91 | 0.606 | ||
Arkansas State | 111 | 0.106 | 0.170 | 25 | 1 | 7 | 0 | 0.125 | 96 | 0.528 | ||
Miami (OH) | 112 | 0.105 | 0.169 | 28 | 1 | 10 | 0 | 0.091 | 82 | 0.734 | ||
New Mexico State | 113 | 0.079 | 0.141 | 23 | 2 | 7 | 0 | 0.222 | 118 | 0.236 | ||
Rice | 114 | 0.076 | 0.138 | 27 | 1 | 9 | 0 | 0.100 | 98 | 0.479 | ||
North Texas | 115 | 0.064 | 0.123 | 24 | 2 | 8 | 0 | 0.200 | 119 | 0.218 | ||
San Jose State | 116 | 0.048 | 0.101 | 29 | 0 | 8 | 0 | 0.000 | 75 | 0.815 | ||
Ball State | 117 | 0.032 | 0.074 | 26 | 1 | 8 | 0 | 0.111 | 120 | 0.179 | ||
New Mexico | 118 | 0.019 | 0.049 | 29 | 0 | 10 | 0 | 0.000 | 105 | 0.395 | ||
Western Kentucky | 119 | 0.019 | 0.049 | 29 | 0 | 9 | 0 | 0.000 | 109 | 0.353 | ||
Eastern Michigan | 120 | 0.012 | 0.033 | 29 | 0 | 10 | 0 | 0.000 | 117 | 0.250 |
November 18th, 2009 at 4:30 PM ^
a pretty ridiculous expected win percentage for OSU in The Game. I don't know if that's true for the rest of the games against the spread, but that would be worth finding out.
FWIW, OSU is something like 80% to win on Saturday based on the line. Ugh.
November 18th, 2009 at 9:46 PM ^
KRACH doesn't know it's a rivalry game, for instance, nor does it know about Tressel's tendency to turtle as soon as he gets a two-score lead (all it sees is wins and losses, no matter how nail-biting or otherwise). Vegas does. Both of those increase the probabilities of a close game (the latter may not actually increase Michigan's chances of winning, though; just the chance of keeping it close), reducing the line. I'm also fairly certain it doesn't consider home field (again, Vegas certainly does).
Not knowing that this was a huge rivalry game and putting it at a neutral site, I'd probably agree with the 93% chance of an OSU win predicted by KRACH. With the rivalry and home field factored in, I'd bring that down a bit (probably not as far down as 80%, though - Tresselball is designed to minimize variance, which makes them far less vulnerable to upsets but also far less likely to pull one off themselves should they face a better team).
Out of curiosity, where do you get the line-to-%W conversion from? Or are you looking at the money line rather than the spread?
November 18th, 2009 at 7:36 PM ^
Great work again!
Whom do I talk to about having to scroll so long before reaching Michigan?
November 18th, 2009 at 10:06 PM ^
I'll see what I can do about that for next week. Maybe a few fictitious wins here and there will do the trick.
November 18th, 2009 at 9:01 PM ^
What is Michigan's CROTCH rating?
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