I had tentatively chosen using a sine function as my "point difference value" function. This means I had the increasing half of a sine wave, but stretched out to domain [-14, 14] and squished into range [0, 1] instead of [-1, 1]. Recall that 14 is the maximum point difference; winning by 21 doesn't do you any better than 14 (though I would still want 3 touchdowns ahead to feel safe).
Here're the Top 25 Lists from using that sine wave in my algorithm:
Top 25 Overall:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Alabama | 1.0 | (14-0) |
| 2 | Florida | 0.8453084110356731 | (13-1) |
| 3 | Iowa | 0.7980851492713539 | (11-2) |
| 4 | Ohio St. | 0.7959272934250403 | (11-2) |
| 5 | Wis.-Whitewater | 0.7931014121688159 | (15-0) |
| 6 | Villanova | 0.7784667208618657 | (14-1) |
| 7 | Mount Union | 0.7784429732843677 | (14-1) |
| 8 | Texas | 0.7743477839757599 | (13-1) |
| 9 | Virginia Tech | 0.773191196612621 | (10-3) |
| 10 | Northwest Mo. St. | 0.7651473177760857 | (14-1) |
| 11 | TCU | 0.7561842463663239 | (12-1) |
| 12 | Boise St. | 0.7422858729365828 | (14-0) |
| 13 | Georgia Tech | 0.739435565048572 | (11-3) |
| 14 | Pittsburgh | 0.7295069053329452 | (10-3) |
| 15 | Delaware Valley | 0.7238330857064403 | (10-2) |
| 16 | Clemson | 0.7093994498215039 | (9-5) |
| 17 | Cincinnati | 0.7010812158089512 | (12-1) |
| 18 | Nebraska | 0.6966615385768201 | (10-4) |
| 19 | Penn St. | 0.6898953468548779 | (11-2) |
| 20 | William & Mary | 0.6889809994069834 | (11-3) |
| 21 | Miami (FL) | 0.6870668432299284 | (9-4) |
| 22 | Grand Valley St. | 0.685908538491301 | (13-2) |
| 23 | Montana | 0.680877393300117 | (14-1) |
| 24 | North Carolina | 0.6798263244814997 | (8-5) |
| 25 | Wesley | 0.6713242891766065 | (13-1) |
Top 25 in Division 1 (FBS):
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Alabama | 1.0 | (14-0) |
| 2 | Florida | 0.8453084110356731 | (13-1) |
| 3 | Iowa | 0.7980851492713539 | (11-2) |
| 4 | Ohio St. | 0.7959272934250403 | (11-2) |
| 5 | Texas | 0.7743477839757599 | (13-1) |
| 6 | Virginia Tech | 0.773191196612621 | (10-3) |
| 7 | TCU | 0.7561842463663239 | (12-1) |
| 8 | Boise St. | 0.7422858729365828 | (14-0) |
| 9 | Georgia Tech | 0.739435565048572 | (11-3) |
| 10 | Pittsburgh | 0.7295069053329452 | (10-3) |
| 11 | Clemson | 0.7093994498215039 | (9-5) |
| 12 | Cincinnati | 0.7010812158089512 | (12-1) |
| 13 | Nebraska | 0.6966615385768201 | (10-4) |
| 14 | Penn St. | 0.6898953468548779 | (11-2) |
| 15 | Miami (FL) | 0.6870668432299284 | (9-4) |
| 16 | North Carolina | 0.6798263244814997 | (8-5) |
| 17 | Oregon | 0.6674229741597587 | (10-3) |
| 18 | Oklahoma | 0.6456962734233938 | (8-5) |
| 19 | Texas Tech | 0.639030083187756 | (9-4) |
| 20 | Wisconsin | 0.629403113243047 | (10-3) |
| 21 | LSU | 0.624087758599014 | (9-4) |
| 22 | West Virginia | 0.6203622415831133 | (9-4) |
| 23 | Southern California | 0.6147801076029238 | (9-4) |
| 24 | Arkansas | 0.6086752158140657 | (8-5) |
| 25 | Connecticut | 0.6073067203910404 | (8-5) |
Top 25 in Division 1 (FCS):
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Villanova | 0.7784667208618657 | (14-1) |
| 2 | William & Mary | 0.6889809994069834 | (11-3) |
| 3 | Montana | 0.680877393300117 | (14-1) |
| 4 | Richmond | 0.6465949469657015 | (11-2) |
| 5 | Appalachian St. | 0.6240916117263432 | (11-3) |
| 6 | Penn | 0.5705862808700499 | (8-2) |
| 7 | Southern Ill. | 0.5693203890449489 | (11-2) |
| 8 | Lafayette | 0.5683797404977817 | (8-3) |
| 9 | South Carolina St. | 0.5545719247757372 | (10-2) |
| 10 | Prairie View | 0.5369545246114935 | (9-1) |
| 11 | Holy Cross | 0.5336628923765148 | (9-3) |
| 12 | New Hampshire | 0.5321152434443531 | (10-3) |
| 13 | Dayton | 0.5314277653219569 | (9-2) |
| 14 | Elon | 0.523911066979941 | (9-3) |
| 15 | Albany (NY) | 0.5120847879996884 | (7-4) |
| 16 | Colgate | 0.5060168197175257 | (9-2) |
| 17 | Butler | 0.4992754578291487 | (11-1) |
| 18 | Central Conn. St. | 0.49456101517492934 | (9-3) |
| 19 | UNI | 0.49175699489806335 | (7-4) |
| 20 | Delaware | 0.48472355576395554 | (6-5) |
| 21 | Jacksonville St. | 0.4793301633323951 | (8-3) |
| 22 | James Madison | 0.4705975202189122 | (6-5) |
| 23 | Grambling | 0.46987625299272295 | (7-4) |
| 24 | Harvard | 0.4694050577362635 | (7-3) |
| 25 | South Dakota St. | 0.46891425825015565 | (8-4) |
Top 25 in Division 2:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Northwest Mo. St. | 0.7651473177760857 | (14-1) |
| 2 | Grand Valley St. | 0.685908538491301 | (13-2) |
| 3 | North Ala. | 0.6561898713927847 | (11-2) |
| 4 | Central Wash. | 0.6514076575505942 | (12-1) |
| 5 | Bentley | 0.6227502205878906 | (8-2) |
| 6 | California (PA) | 0.6049365349330225 | (11-4) |
| 7 | Carson-Newman | 0.5790381838220421 | (11-3) |
| 8 | Bloomsburg | 0.5631765643839286 | (8-3) |
| 9 | Southern Conn. St. | 0.5592674450522522 | (6-4) |
| 10 | Merrimack | 0.559002250201329 | (7-3) |
| 11 | Washburn | 0.5469910644776446 | (8-3) |
| 12 | Midwestern St. | 0.5448958278187014 | (9-3) |
| 13 | Minn. Duluth | 0.5378690030295155 | (11-2) |
| 14 | Abilene Christian | 0.5377710327219685 | (9-4) |
| 15 | Shippensburg | 0.529358690152923 | (9-3) |
| 16 | Minn. St. Mankato | 0.5220260722540468 | (10-2) |
| 17 | Neb.-Kearney | 0.514085269111764 | (11-2) |
| 18 | Mo. Western St. | 0.5131292460979857 | (9-3) |
| 19 | American Int'l | 0.5105344017677981 | (5-5) |
| 20 | West Liberty St. | 0.5078047611140849 | (11-2) |
| 21 | Tuskegee | 0.5067991980412246 | (10-2) |
| 22 | Assumption | 0.49876216046245425 | (6-4) |
| 23 | Hillsdale | 0.49025596096312263 | (10-3) |
| 24 | Tex. A&M-Kingsville | 0.4832649948846188 | (9-3) |
| 25 | Saginaw Valley | 0.48264592956391617 | (9-3) |
Top 25 in Division 3:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Wis.-Whitewater | 0.7931014121688159 | (15-0) |
| 2 | Mount Union | 0.7784429732843677 | (14-1) |
| 3 | Delaware Valley | 0.7238330857064403 | (10-2) |
| 4 | Wesley | 0.6713242891766065 | (13-1) |
| 5 | St. Thomas (MN) | 0.6664158425336424 | (11-2) |
| 6 | Hampden-Sydney | 0.6265101435636997 | (10-1) |
| 7 | Albright | 0.6259725326526914 | (11-2) |
| 8 | St. John's (MN) | 0.6253033326691142 | (10-1) |
| 9 | Central (IA) | 0.6181967737796882 | (10-1) |
| 10 | North Central (IL) | 0.6004163792907738 | (8-2) |
| 11 | Johns Hopkins | 0.5863897199077175 | (10-3) |
| 12 | Ill. Wesleyan | 0.5849847531733094 | (10-2) |
| 13 | Wittenberg | 0.5644283321666279 | (12-1) |
| 14 | Ohio Northern | 0.5638373816157844 | (8-2) |
| 15 | Thomas More | 0.5633415261106778 | (11-1) |
| 16 | N.C. Wesleyan | 0.5581973916844802 | (8-3) |
| 17 | Linfield | 0.547007808560474 | (12-1) |
| 18 | Lebanon Valley | 0.546116762038962 | (9-2) |
| 19 | Wheaton (IL) | 0.541262391729009 | (7-3) |
| 20 | Bethel (MN) | 0.5386053672795033 | (7-3) |
| 21 | Coe | 0.5361263280465675 | (10-2) |
| 22 | St. John Fisher | 0.5336315659703305 | (7-3) |
| 23 | Wis.-Stevens Point | 0.5308782675653215 | (7-3) |
| 24 | Huntingdon | 0.5216159526302369 | (8-2) |
| 25 | Alfred | 0.5188360049759888 | (8-2) |
Alternatively, we could use a straight line passing through (-14, 0) and (14, 1). Here are results from 2009 using that function in my algorithm:
Top 25 Overall:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Alabama | 1.0 | (14-0) |
| 2 | Florida | 0.8375140130329837 | (13-1) |
| 3 | Virginia Tech | 0.8062562432014048 | (10-3) |
| 4 | Ohio St. | 0.7914302412242371 | (11-2) |
| 5 | Mount Union | 0.7906960724905181 | (14-1) |
| 6 | Wis.-Whitewater | 0.7833243116278779 | (15-0) |
| 7 | Iowa | 0.7780443099361634 | (11-2) |
| 8 | Texas | 0.771710868746212 | (13-1) |
| 9 | Villanova | 0.7693228747595254 | (14-1) |
| 10 | TCU | 0.7671323989983221 | (12-1) |
| 11 | Northwest Mo. St. | 0.7641126926643661 | (14-1) |
| 12 | Georgia Tech | 0.7414102812820377 | (11-3) |
| 13 | Boise St. | 0.7341101182735286 | (14-0) |
| 14 | Clemson | 0.7324192680726288 | (9-5) |
| 15 | Pittsburgh | 0.7299343880385623 | (10-3) |
| 16 | Delaware Valley | 0.720682971811248 | (10-2) |
| 17 | Miami (FL) | 0.7112748405893534 | (9-4) |
| 18 | Grand Valley St. | 0.7070348054973364 | (13-2) |
| 19 | Penn St. | 0.7051516378338119 | (11-2) |
| 20 | Nebraska | 0.7036643779241925 | (10-4) |
| 21 | William & Mary | 0.6996751927333641 | (11-3) |
| 22 | Cincinnati | 0.6950336684375533 | (12-1) |
| 23 | North Carolina | 0.6820346326334037 | (8-5) |
| 24 | Oregon | 0.6815880110703458 | (10-3) |
| 25 | St. Thomas (MN) | 0.6755087172558527 | (11-2) |
Top 25 in Division 1 (FBS):
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Alabama | 1.0 | (14-0) |
| 2 | Florida | 0.8375140130329837 | (13-1) |
| 3 | Virginia Tech | 0.8062562432014048 | (10-3) |
| 4 | Ohio St. | 0.7914302412242371 | (11-2) |
| 5 | Iowa | 0.7780443099361634 | (11-2) |
| 6 | Texas | 0.771710868746212 | (13-1) |
| 7 | TCU | 0.7671323989983221 | (12-1) |
| 8 | Georgia Tech | 0.7414102812820377 | (11-3) |
| 9 | Boise St. | 0.7341101182735286 | (14-0) |
| 10 | Clemson | 0.7324192680726288 | (9-5) |
| 11 | Pittsburgh | 0.7299343880385623 | (10-3) |
| 12 | Miami (FL) | 0.7112748405893534 | (9-4) |
| 13 | Penn St. | 0.7051516378338119 | (11-2) |
| 14 | Nebraska | 0.7036643779241925 | (10-4) |
| 15 | Cincinnati | 0.6950336684375533 | (12-1) |
| 16 | North Carolina | 0.6820346326334037 | (8-5) |
| 17 | Oregon | 0.6815880110703458 | (10-3) |
| 18 | Oklahoma | 0.6719728060096853 | (8-5) |
| 19 | Texas Tech | 0.6603394553337874 | (9-4) |
| 20 | LSU | 0.6439990579906637 | (9-4) |
| 21 | Arkansas | 0.6416866126023655 | (8-5) |
| 22 | Stanford | 0.6281654984912417 | (8-5) |
| 23 | Wisconsin | 0.6269201674880754 | (10-3) |
| 24 | Connecticut | 0.625969671660246 | (8-5) |
| 25 | West Virginia | 0.6259090774667414 | (9-4) |
Top 25 in Division 1 (FCS):
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Villanova | 0.7693228747595254 | (14-1) |
| 2 | William & Mary | 0.6996751927333641 | (11-3) |
| 3 | Montana | 0.668918978937866 | (14-1) |
| 4 | Richmond | 0.6505468941520873 | (11-2) |
| 5 | Appalachian St. | 0.6352221225251433 | (11-3) |
| 6 | Penn | 0.5853206401038488 | (8-2) |
| 7 | Lafayette | 0.5826101609367887 | (8-3) |
| 8 | Southern Ill. | 0.5758981510635751 | (11-2) |
| 9 | South Carolina St. | 0.5756766620588794 | (10-2) |
| 10 | Holy Cross | 0.5571977192558633 | (9-3) |
| 11 | Dayton | 0.5441672965977702 | (9-2) |
| 12 | Elon | 0.5438930002908253 | (9-3) |
| 13 | New Hampshire | 0.5348437763559363 | (10-3) |
| 14 | Albany (NY) | 0.5289155188666127 | (7-4) |
| 15 | UNI | 0.5244940291156869 | (7-4) |
| 16 | Prairie View | 0.5201104866585063 | (9-1) |
| 17 | Colgate | 0.509823129943224 | (9-2) |
| 18 | Harvard | 0.5036803553226694 | (7-3) |
| 19 | Central Conn. St. | 0.5015797113873409 | (9-3) |
| 20 | Jacksonville St. | 0.5015143372354974 | (8-3) |
| 21 | Delaware | 0.49778311578804924 | (6-5) |
| 22 | Grambling | 0.49130119932242156 | (7-4) |
| 23 | James Madison | 0.4881071058910479 | (6-5) |
| 24 | Butler | 0.4879963739080785 | (11-1) |
| 25 | South Dakota St. | 0.4788642961294367 | (8-4) |
Top 25 in Division 2:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Northwest Mo. St. | 0.7641126926643661 | (14-1) |
| 2 | Grand Valley St. | 0.7070348054973364 | (13-2) |
| 3 | North Ala. | 0.6589248859709883 | (11-2) |
| 4 | Central Wash. | 0.6427461121979486 | (12-1) |
| 5 | Bentley | 0.6163786167306488 | (8-2) |
| 6 | California (PA) | 0.6056960816428902 | (11-4) |
| 7 | Southern Conn. St. | 0.5949814031397045 | (6-4) |
| 8 | Washburn | 0.5747255269341602 | (8-3) |
| 9 | Carson-Newman | 0.5641517923095019 | (11-3) |
| 10 | Midwestern St. | 0.561278879677497 | (9-3) |
| 11 | Merrimack | 0.5582819018073711 | (7-3) |
| 12 | Bloomsburg | 0.5555371470467685 | (8-3) |
| 13 | Minn. Duluth | 0.5435282641120275 | (11-2) |
| 14 | American Int'l | 0.5408759795866735 | (5-5) |
| 15 | Abilene Christian | 0.5390385057283348 | (9-4) |
| 16 | Minn. St. Mankato | 0.5272422871493335 | (10-2) |
| 17 | Mo. Western St. | 0.521714002240214 | (9-3) |
| 18 | Assumption | 0.5167516769184468 | (6-4) |
| 19 | Neb.-Kearney | 0.5159111770422175 | (11-2) |
| 20 | Shippensburg | 0.5151726965350313 | (9-3) |
| 21 | West Liberty St. | 0.5026027924612839 | (11-2) |
| 22 | Tuskegee | 0.5020736136283973 | (10-2) |
| 23 | West Chester | 0.49677154950897895 | (7-4) |
| 24 | Hillsdale | 0.4946367916700576 | (10-3) |
| 25 | Arkansas Tech | 0.4876935604560573 | (9-3) |
Top 25 in Division 3:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Mount Union | 0.7906960724905181 | (14-1) |
| 2 | Wis.-Whitewater | 0.7833243116278779 | (15-0) |
| 3 | Delaware Valley | 0.720682971811248 | (10-2) |
| 4 | St. Thomas (MN) | 0.6755087172558527 | (11-2) |
| 5 | Wesley | 0.6702253903097455 | (13-1) |
| 6 | Hampden-Sydney | 0.6306122724482518 | (10-1) |
| 7 | Central (IA) | 0.6225835315978534 | (10-1) |
| 8 | Albright | 0.6218429622333305 | (11-2) |
| 9 | North Central (IL) | 0.6172499489842973 | (8-2) |
| 10 | St. John's (MN) | 0.6144304989223393 | (10-1) |
| 11 | Johns Hopkins | 0.5852825159365133 | (10-3) |
| 12 | N.C. Wesleyan | 0.5662121448561163 | (8-3) |
| 13 | Ohio Northern | 0.5649808451620524 | (8-2) |
| 14 | Wittenberg | 0.5629082650244601 | (12-1) |
| 15 | Ill. Wesleyan | 0.5622145780372327 | (10-2) |
| 16 | Bethel (MN) | 0.5537735374747976 | (7-3) |
| 17 | Thomas More | 0.5505069035752247 | (11-1) |
| 18 | Linfield | 0.5482408016061038 | (12-1) |
| 19 | St. John Fisher | 0.5412793048867931 | (7-3) |
| 20 | Lebanon Valley | 0.5407010126008093 | (9-2) |
| 21 | Wheaton (IL) | 0.5384537135255089 | (7-3) |
| 22 | Wis.-Stevens Point | 0.5286111182179198 | (7-3) |
| 23 | Coe | 0.5276532336870888 | (10-2) |
| 24 | Alfred | 0.5264389817584934 | (8-2) |
| 25 | Wabash | 0.5207325113204947 | (9-2) |
Notice, there's a big difference between the two! (Look at Virginia Tech, moving from 9th overall to third!)
Additionally, I have implemented two quarter ellipses, with the same concavity as the sine wave, and still hitting the point (0,0). Here are the 2009 results using that:
Top 25 Overall:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Alabama | 1.0 | (14-0) |
| 2 | Florida | 0.8461522831760302 | (13-1) |
| 3 | Ohio St. | 0.803790134384138 | (11-2) |
| 4 | Iowa | 0.8000892121048037 | (11-2) |
| 5 | Villanova | 0.7982815599743636 | (14-1) |
| 6 | Wis.-Whitewater | 0.7874022075280384 | (15-0) |
| 7 | Texas | 0.7845227894081565 | (13-1) |
| 8 | Mount Union | 0.7706025647593746 | (14-1) |
| 9 | Northwest Mo. St. | 0.7695655969551253 | (14-1) |
| 10 | TCU | 0.7529018530228215 | (12-1) |
| 11 | Georgia Tech | 0.7515323440365002 | (11-3) |
| 12 | Boise St. | 0.7493420870879128 | (14-0) |
| 13 | Virginia Tech | 0.7415017112855525 | (10-3) |
| 14 | Cincinnati | 0.7261247121168325 | (12-1) |
| 15 | Pittsburgh | 0.7225780691340195 | (10-3) |
| 16 | Delaware Valley | 0.7198118561716147 | (10-2) |
| 17 | Oregon | 0.6865955151109341 | (10-3) |
| 18 | Penn St. | 0.68098073031659 | (11-2) |
| 19 | Montana | 0.6785709850235997 | (14-1) |
| 20 | Miami (FL) | 0.6776511576043561 | (9-4) |
| 21 | Wesley | 0.6696404755586843 | (13-1) |
| 22 | Clemson | 0.6649307708306719 | (9-5) |
| 23 | North Carolina | 0.6646154701576453 | (8-5) |
| 24 | Grand Valley St. | 0.664204310280295 | (13-2) |
| 25 | William & Mary | 0.6629849673595576 | (11-3) |
Top 25 in Division 1 (FBS):
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Alabama | 1.0 | (14-0) |
| 2 | Florida | 0.8461522831760302 | (13-1) |
| 3 | Ohio St. | 0.803790134384138 | (11-2) |
| 4 | Iowa | 0.8000892121048037 | (11-2) |
| 5 | Texas | 0.7845227894081565 | (13-1) |
| 6 | TCU | 0.7529018530228215 | (12-1) |
| 7 | Georgia Tech | 0.7515323440365002 | (11-3) |
| 8 | Boise St. | 0.7493420870879128 | (14-0) |
| 9 | Virginia Tech | 0.7415017112855525 | (10-3) |
| 10 | Cincinnati | 0.7261247121168325 | (12-1) |
| 11 | Pittsburgh | 0.7225780691340195 | (10-3) |
| 12 | Oregon | 0.6865955151109341 | (10-3) |
| 13 | Penn St. | 0.68098073031659 | (11-2) |
| 14 | Miami (FL) | 0.6776511576043561 | (9-4) |
| 15 | Clemson | 0.6649307708306719 | (9-5) |
| 16 | North Carolina | 0.6646154701576453 | (8-5) |
| 17 | Nebraska | 0.6570709741408631 | (10-4) |
| 18 | West Virginia | 0.6346561285411506 | (9-4) |
| 19 | Wisconsin | 0.6316109082128977 | (10-3) |
| 20 | Southern California | 0.6246946847743031 | (9-4) |
| 21 | BYU | 0.6101573119103122 | (11-2) |
| 22 | LSU | 0.6088240269397646 | (9-4) |
| 23 | Texas Tech | 0.6050346790290825 | (9-4) |
| 24 | Oklahoma | 0.597718051665349 | (8-5) |
| 25 | Oklahoma St. | 0.5891883387541051 | (9-4) |
Top 25 in Division 1 (FCS):
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Villanova | 0.7982815599743636 | (14-1) |
| 2 | Montana | 0.6785709850235997 | (14-1) |
| 3 | William & Mary | 0.6629849673595576 | (11-3) |
| 4 | Richmond | 0.641486495561455 | (11-2) |
| 5 | Appalachian St. | 0.6128833917164505 | (11-3) |
| 6 | Lafayette | 0.5647588827291284 | (8-3) |
| 7 | Prairie View | 0.5588445918834902 | (9-1) |
| 8 | Penn | 0.554794232229236 | (8-2) |
| 9 | Southern Ill. | 0.5539802866985971 | (11-2) |
| 10 | South Carolina St. | 0.5445590702403283 | (10-2) |
| 11 | Butler | 0.5308817532763204 | (11-1) |
| 12 | New Hampshire | 0.5299571009280614 | (10-3) |
| 13 | Holy Cross | 0.5274911518859167 | (9-3) |
| 14 | Dayton | 0.5086518923387161 | (9-2) |
| 15 | Colgate | 0.5011849092408744 | (9-2) |
| 16 | Central Conn. St. | 0.49511226502781913 | (9-3) |
| 17 | Elon | 0.49411051626131586 | (9-3) |
| 18 | Albany (NY) | 0.482065783456753 | (7-4) |
| 19 | McNeese St. | 0.4737543394005732 | (9-3) |
| 20 | Jacksonville St. | 0.4674662431839661 | (8-3) |
| 21 | Stephen F. Austin | 0.46669341908034934 | (10-3) |
| 22 | Delaware | 0.46321669910490937 | (6-5) |
| 23 | Harvard | 0.45869674471488664 | (7-3) |
| 24 | Texas St. | 0.4534738715861214 | (7-4) |
| 25 | South Dakota St. | 0.45125824594834807 | (8-4) |
Top 25 in Division 2:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Northwest Mo. St. | 0.7695655969551253 | (14-1) |
| 2 | Grand Valley St. | 0.664204310280295 | (13-2) |
| 3 | North Ala. | 0.6504061553075171 | (11-2) |
| 4 | Central Wash. | 0.646268600494261 | (12-1) |
| 5 | Bentley | 0.6243046653547869 | (8-2) |
| 6 | California (PA) | 0.6116364842645406 | (11-4) |
| 7 | Carson-Newman | 0.6050155768966212 | (11-3) |
| 8 | Bloomsburg | 0.5562453789480943 | (8-3) |
| 9 | Merrimack | 0.5513349915057693 | (7-3) |
| 10 | Shippensburg | 0.5509938528992864 | (9-3) |
| 11 | Abilene Christian | 0.537191901361397 | (9-4) |
| 12 | Minn. Duluth | 0.5279108294568543 | (11-2) |
| 13 | Southern Conn. St. | 0.5232531043507883 | (6-4) |
| 14 | West Liberty St. | 0.5199637505018664 | (11-2) |
| 15 | Midwestern St. | 0.5190319692805384 | (9-3) |
| 16 | Minn. St. Mankato | 0.5145662259096687 | (10-2) |
| 17 | Neb.-Kearney | 0.5141940589226409 | (11-2) |
| 18 | Tuskegee | 0.511761460469959 | (10-2) |
| 19 | Mo. Western St. | 0.5082246886977225 | (9-3) |
| 20 | Washburn | 0.5061876006123867 | (8-3) |
| 21 | Hillsdale | 0.49653136894610395 | (10-3) |
| 22 | American Int'l | 0.49433402752715905 | (5-5) |
| 23 | Edinboro | 0.4915468118789883 | (9-4) |
| 24 | Tex. A&M-Kingsville | 0.4902810517577052 | (9-3) |
| 25 | Saginaw Valley | 0.4869669061773336 | (9-3) |
Top 25 in Division 3:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Wis.-Whitewater | 0.7874022075280384 | (15-0) |
| 2 | Mount Union | 0.7706025647593746 | (14-1) |
| 3 | Delaware Valley | 0.7198118561716147 | (10-2) |
| 4 | Wesley | 0.6696404755586843 | (13-1) |
| 5 | St. Thomas (MN) | 0.6449689451957051 | (11-2) |
| 6 | St. John's (MN) | 0.64387543260433 | (10-1) |
| 7 | Albright | 0.631753070936488 | (11-2) |
| 8 | Central (IA) | 0.6151994345554354 | (10-1) |
| 9 | Hampden-Sydney | 0.6092014727863571 | (10-1) |
| 10 | Ill. Wesleyan | 0.6050807504430114 | (10-2) |
| 11 | Johns Hopkins | 0.5887640289962214 | (10-3) |
| 12 | North Central (IL) | 0.5852524566462218 | (8-2) |
| 13 | Wittenberg | 0.5703325658575837 | (12-1) |
| 14 | Thomas More | 0.56046488911415 | (11-1) |
| 15 | Coe | 0.5529093379366911 | (10-2) |
| 16 | Linfield | 0.5488831746832061 | (12-1) |
| 17 | Ohio Northern | 0.547277816805124 | (8-2) |
| 18 | Lebanon Valley | 0.5426748622292078 | (9-2) |
| 19 | N.C. Wesleyan | 0.5336367989993025 | (8-3) |
| 20 | Wheaton (IL) | 0.5254412962641876 | (7-3) |
| 21 | Montclair St. | 0.5228652549270777 | (10-2) |
| 22 | St. John Fisher | 0.5196981219641389 | (7-3) |
| 23 | Wis.-Stevens Point | 0.5187885805836574 | (7-3) |
| 24 | Alfred | 0.5171784715824479 | (8-2) |
| 25 | Huntingdon | 0.5171387319022059 | (8-2) |
Again, this is different!
Finally, I implemented the "a win is a win" function which evaluates to 0 for all negative numbers and 1 for all positive numbers. Here are the 2009 results using that:
Top 25 Overall:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Alabama | 1.0 | (14-0) |
| 2 | Florida | 0.8476485258456193 | (13-1) |
| 3 | Villanova | 0.8442892786724461 | (14-1) |
| 4 | Ohio St. | 0.8025653161000093 | (11-2) |
| 5 | Texas | 0.794864106188952 | (13-1) |
| 6 | Iowa | 0.7881240537036774 | (11-2) |
| 7 | Northwest Mo. St. | 0.7869784446847706 | (14-1) |
| 8 | Wis.-Whitewater | 0.7721562178144329 | (15-0) |
| 9 | Cincinnati | 0.7720287171736322 | (12-1) |
| 10 | Mount Union | 0.7629445168638388 | (14-1) |
| 11 | Georgia Tech | 0.7569998970754799 | (11-3) |
| 12 | Boise St. | 0.754952442075711 | (14-0) |
| 13 | TCU | 0.7457294006337875 | (12-1) |
| 14 | Oregon | 0.7116595398148083 | (10-3) |
| 15 | Virginia Tech | 0.7101853636093404 | (10-3) |
| 16 | Delaware Valley | 0.7098655171560466 | (10-2) |
| 17 | Pittsburgh | 0.6917795271496436 | (10-3) |
| 18 | Miami (FL) | 0.679849807720281 | (9-4) |
| 19 | Penn St. | 0.6637701103912664 | (11-2) |
| 20 | Wesley | 0.6635346597088941 | (13-1) |
| 21 | Montana | 0.6592741700085788 | (14-1) |
| 22 | St. John's (MN) | 0.6586406870631089 | (10-1) |
| 23 | North Ala. | 0.6498206212281809 | (11-2) |
| 24 | West Virginia | 0.6455602244046351 | (9-4) |
| 25 | Grand Valley St. | 0.6427719564058352 | (13-2) |
Top 25 in Division 1 (FBS):
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Alabama | 1.0 | (14-0) |
| 2 | Florida | 0.8476485258456193 | (13-1) |
| 3 | Ohio St. | 0.8025653161000093 | (11-2) |
| 4 | Texas | 0.794864106188952 | (13-1) |
| 5 | Iowa | 0.7881240537036774 | (11-2) |
| 6 | Cincinnati | 0.7720287171736322 | (12-1) |
| 7 | Georgia Tech | 0.7569998970754799 | (11-3) |
| 8 | Boise St. | 0.754952442075711 | (14-0) |
| 9 | TCU | 0.7457294006337875 | (12-1) |
| 10 | Oregon | 0.7116595398148083 | (10-3) |
| 11 | Virginia Tech | 0.7101853636093404 | (10-3) |
| 12 | Pittsburgh | 0.6917795271496436 | (10-3) |
| 13 | Miami (FL) | 0.679849807720281 | (9-4) |
| 14 | Penn St. | 0.6637701103912664 | (11-2) |
| 15 | West Virginia | 0.6455602244046351 | (9-4) |
| 16 | North Carolina | 0.632829626276422 | (8-5) |
| 17 | Southern California | 0.6295648405662061 | (9-4) |
| 18 | BYU | 0.6244158541319746 | (11-2) |
| 19 | Wisconsin | 0.616203201283595 | (10-3) |
| 20 | Clemson | 0.6117848049167259 | (9-5) |
| 21 | Oklahoma St. | 0.5887409271868745 | (9-4) |
| 22 | Georgia | 0.5790768374223683 | (8-5) |
| 23 | LSU | 0.5788646263799647 | (9-4) |
| 24 | Florida St. | 0.5760832410035548 | (7-6) |
| 25 | Mississippi | 0.5729959308562517 | (9-4) |
Top 25 in Division 1 (FCS):
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Villanova | 0.8442892786724461 | (14-1) |
| 2 | Montana | 0.6592741700085788 | (14-1) |
| 3 | Richmond | 0.620982725257673 | (11-2) |
| 4 | William & Mary | 0.6129164145877628 | (11-3) |
| 5 | Appalachian St. | 0.5988039703506512 | (11-3) |
| 6 | Prairie View | 0.5785282067103911 | (9-1) |
| 7 | Butler | 0.5714415436238156 | (11-1) |
| 8 | Lafayette | 0.5604053944118802 | (8-3) |
| 9 | Penn | 0.5360220574676265 | (8-2) |
| 10 | South Carolina St. | 0.5349353249871499 | (10-2) |
| 11 | New Hampshire | 0.5315464457781169 | (10-3) |
| 12 | Holy Cross | 0.5290512954622827 | (9-3) |
| 13 | Southern Ill. | 0.5268033671090292 | (11-2) |
| 14 | Central Conn. St. | 0.5050883499926971 | (9-3) |
| 15 | Colgate | 0.4978612873338145 | (9-2) |
| 16 | McNeese St. | 0.4837792286000282 | (9-3) |
| 17 | Dayton | 0.4695782165989616 | (9-2) |
| 18 | Stephen F. Austin | 0.46799039639797957 | (10-3) |
| 19 | Jacksonville St. | 0.45924419241037784 | (8-3) |
| 20 | Elon | 0.45826962535282467 | (9-3) |
| 21 | Harvard | 0.4540464607840251 | (7-3) |
| 22 | Liberty | 0.439305063459948 | (8-3) |
| 23 | Florida A&M | 0.4390490824613894 | (8-3) |
| 24 | Albany (NY) | 0.43081408578374114 | (7-4) |
| 25 | Eastern Ill. | 0.4275929381619594 | (8-4) |
Top 25 in Division 2:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Northwest Mo. St. | 0.7869784446847706 | (14-1) |
| 2 | North Ala. | 0.6498206212281809 | (11-2) |
| 3 | Grand Valley St. | 0.6427719564058352 | (13-2) |
| 4 | Carson-Newman | 0.6365353745430206 | (11-3) |
| 5 | Central Wash. | 0.6207707700285833 | (12-1) |
| 6 | California (PA) | 0.6184424849636605 | (11-4) |
| 7 | Bentley | 0.6180727287168293 | (8-2) |
| 8 | Shippensburg | 0.5791801234961353 | (9-3) |
| 9 | Merrimack | 0.5424670770811285 | (7-3) |
| 10 | West Liberty St. | 0.5333383050140932 | (11-2) |
| 11 | West Ala. | 0.5289552077637287 | (8-5) |
| 12 | Abilene Christian | 0.5287807428937434 | (9-4) |
| 13 | Bloomsburg | 0.5257908765726829 | (8-3) |
| 14 | Minn. Duluth | 0.5230161734852866 | (11-2) |
| 15 | Edinboro | 0.5201871403290004 | (9-4) |
| 16 | Neb.-Kearney | 0.516407254240245 | (11-2) |
| 17 | Tuskegee | 0.5159533693786152 | (10-2) |
| 18 | Tarleton St. | 0.5096761391043202 | (10-3) |
| 19 | Minn. St. Mankato | 0.5058877167023154 | (10-2) |
| 20 | Hillsdale | 0.5004179055913341 | (10-3) |
| 21 | Mo. Western St. | 0.4991459942776022 | (9-3) |
| 22 | Saginaw Valley | 0.4925344931249338 | (9-3) |
| 23 | Midwestern St. | 0.48710305074642546 | (9-3) |
| 24 | Tex. A&M-Kingsville | 0.48657809356690607 | (9-3) |
| 25 | Arkansas Tech | 0.4811413965807063 | (9-3) |
Top 25 in Division 3:
| 2009 Final | |||
| Rank | Team | Rating | Record |
| 1 | Wis.-Whitewater | 0.7721562178144329 | (15-0) |
| 2 | Mount Union | 0.7629445168638388 | (14-1) |
| 3 | Delaware Valley | 0.7098655171560466 | (10-2) |
| 4 | Wesley | 0.6635346597088941 | (13-1) |
| 5 | St. John's (MN) | 0.6586406870631089 | (10-1) |
| 6 | Albright | 0.6422639965152028 | (11-2) |
| 7 | Central (IA) | 0.6193141797112544 | (10-1) |
| 8 | Ill. Wesleyan | 0.6156833174515683 | (10-2) |
| 9 | St. Thomas (MN) | 0.6146746382771975 | (11-2) |
| 10 | Johns Hopkins | 0.5864043182643489 | (10-3) |
| 11 | Coe | 0.5766563683144624 | (10-2) |
| 12 | Hampden-Sydney | 0.5755265535868563 | (10-1) |
| 13 | Wittenberg | 0.5754845574034458 | (12-1) |
| 14 | North Central (IL) | 0.5702138543610139 | (8-2) |
| 15 | Linfield | 0.5520500725461295 | (12-1) |
| 16 | Thomas More | 0.5512412073075309 | (11-1) |
| 17 | Montclair St. | 0.533510863489676 | (10-2) |
| 18 | Lebanon Valley | 0.5193569103339398 | (9-2) |
| 19 | Ohio Northern | 0.5193236563371716 | (8-2) |
| 20 | Alfred | 0.5120594976068551 | (8-2) |
| 21 | Huntingdon | 0.5114159767902454 | (8-2) |
| 22 | St. John Fisher | 0.5018388475460532 | (7-3) |
| 23 | Springfield | 0.5016339537038965 | (8-2) |
| 24 | Mississippi Col. | 0.49846913982344276 | (9-3) |
| 25 | Otterbein | 0.49591039197169573 | (8-2) |
My intuition leans towards the sine wave or the ellipse-chunks. This, I think, adds emphasis towards winning games, not just for getting close. Winning by that first point is more valuable than the added benefit of that second point. Sure, a bigger win is better, but the first point is the most valuable. Perhaps there is a better curve (if you think of one, I'd love to implement it!) but either of these seem to be pretty good. I'll stick with the sine curve until further notice.
Coming soon: Week 2 results for this season!
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