≡ Menu

Blog

Introducing The Fleming System

Since its inception in 1998, the best argument for the BCS has been that college football fans love debates.  You know it’s true.  Everyone loves a good fight.  SEC people fighting with Big 12 people fighting with Pac-12 people fighting with computers fighting with humans fighting with Condoleeza Rice and Mark May.  Nobody can agree on much of anything, which of course, makes everything somewhat interesting.

Still, the BCS is a better system than the one before it.  And in an effort to settle some pre-BCS debates, Patrick Fleming created his own computer ranking system,The Fleming System (TFS), in 1994.  Now, with our help, he’s rolling it out to a larger audience in hopes of answering some questions about the 2013 season and, hopefully, figuring out ways to make it even better.  (We’re serious about this.  Leave comments.)

But first, a little Q&A with Patrick… (or jump right to the school rankings or conference rankings)

What’s your background?

I make a living as a college chemistry professor.  It is through the study of molecular spectroscopy that I was introduced to the mathematics needed to rate college football teams (although my first attempts were applied to rating college hockey teams.)  I did my undergraduate studies at the University of Notre Dame, and graduate studies at the Ohio State University.  I also spent time at both Tulane and Arizona State as a postdoctoral researcher.  I currently teach at the Claremont Colleges in Southern California, near where I was born and raised.  

Why make your own rankings?

My intent was to “prove” that my alma mater, Notre Dame, was robbed following the 1993 season, having beaten Florida State head-to-head, but ending up ranked lower than the Seminoles. To my dismay, my computer proved me wrong and ranked the Irish behind both Florida State and Nebraska.

How do you make your own rankings?  What’s the mathematical mumbo jumbo behind this?

My system uses a least-squares fitting mechanism to find the team ratings.

It works like this: I define a function, called a game-outcome-measure (or GOM.) This is a mathematical function that indicates how much better the winning team is than a losing team in a given game. Ratings for each team are chosen such that the differences in the ratings (GOMcalculated) mimic the GOMs for the games actually played (GOMobserved).  Specifically, the least-squares method minimizes x2 played, and defined as:

formula

by choosing the optimal set of team ratings. 

The method can be applied to any definition for the GOM. For example, in one set of ratings, I use a GOM that is 10 points, meaning that the winning team is 0 points better than the losing team, irrespective of the final margin of victory (MOV.) In another, I use the MOV, a consideration for defense and the location of the game played to calculate the GOM. The choice of how to calculate the GOM is actually pretty arbitrary. However, once the definition is determined, it is applied uniformly across all of the games played.

What other rankings systems are similar, and how is this one different?

Jeff Sagarin, who has been publishing his ratings system since before the birth of the World Wide Web, also uses a least-squares fitting method. The difference between our systems (mostly based on speculation, because I have never met Jeff Sagarin or discussed computer ratings with him) are:

  1. Sagarin uses a different GOM than I do.
  2. Sagarin treats home-field-advantage differently than I do.
  3. Sagarin uses a smaller data set, including only NCAA Division I programs (both FBS and FCS.) My ratings include teams across all three NCAA divisions, plus NAIA and independent programs that belong to neither the NCAA nor the NAIA.

The results of my rating are generally very similar to those of Jeff Sagarin. Comparisons of computer ratings systems are available each week on the web at http://masseyratings.com/cf/compare.htm.

Until mid-season, everyone’s ratings are influenced by an “initial bias.” My initial bias is to assume that all teams are equal to one another, until a game is actually played. Then it is the game outcomes that determine the relative ratings for the teams. But as a result, there is no way to rate two teams that are not somehow connected through common opponents (or opponents’ opponents.) Eventually, with the exception of the NCAA DII Northern Sun Intercollegiate Conference and DIII New England Small College Sports Conference, all of the teams will be connected through the schedule. Other systems may use an initial bias system (usually based on last year’s final ratings) that does not assume teams are equal before the season. Both methods have merits, but by about mid season, there is no need to worry about the initial bias, since all of the teams will be connected. However, that can be wild movements early in the season unless, like Sagarin, a mechanism is in place to prevent it.

What are the flaws in this system?

It is important to understand that no ranking system (including the human polls) is perfect. As any football fan understands, the game of football is all about matchups. And often times, a “weak” team that matches up favorably with a “strong” team may enjoy a competitive advantage. But ratings systems have to average over these sort of considerations, and instead describe a very complex system using a single numerical index. Clearly, football teams are much more complex systems. An improvement might be to rate the offense and defense of a team separately, but even that would be too simplistic a ratings mechanism.

The problem is that to accomplish a computer rating including 752 teams and a fifteen (or so) week season, it is impractical to look at much more than just the scores of games and locations of games played. But again, all football fans know that scores can be misleading as to how completive a game may actually have been (or not have been). So the bottom line is to remember that a computer system is never perfect, but it does apply its criteria uniformly. A human poll does not apply criteria uniformly, but it does allow for adjustment based on various aspects that make one team better than another. So pick your poison!


Below, The Fleming System ranks individual schools and conferences. Please leave your thoughts in the comments section.

The Fleming System – Rankings by School

Rankings as of October 7, 2013; sort by clicking column header

SchoolWLConferenceRatingSchedule
Florida St50ACC163.752138.552
Georgia41SEC156.139144.339
Alabama50SEC156.133131.533
Stanford50PAC12155.787135.187
Clemson50ACC154.996133.296
Oklahoma50Big12151.663129.563
Missouri50SEC151.371129.171
Baylor40Big12150.581127.206
Florida41SEC150.478134.478
Ohio State60B1G149.74126.907
Oregon50PAC12149.288125.588
LSU51SEC148.846133.679
Louisville50AAC148.731122.931
Miami FL50ACC148.423126.223
Texas Tech50Big12148.085125.085
Washington41PAC12147.678132.078
Texas A&M41SEC147.518134.318
South Carolina41SEC147.277135.577
Virginia Tech51ACC146.924132.841
UCLA40PAC12146.675124.925
Northern Illinois50MAC146.149125.249
Auburn41SEC145.731134.931
Maryland41ACC144.969131.269
Michigan50B1G144.727124.927
Pittsburgh31ACC144.078134.078
Central Florida41AAC143.718128.518
Arizona31PAC12142.424129.299
Northwestern41B1G142.207129.207
Washington St42PAC12142.124132.707
Arizona St32PAC12141.754136.254
East Carolina41CUSA141.501128.401
Fresno St50MWC141.171122.471
Houston40AAC140.478119.478
Ohio U.41MAC140.429127.329
Notre Dame42Ind-FBS139.945134.279
Michigan St41B1G139.233124.533
Boston College32ACC139.109136.209
Rutgers41AAC138.983124.783
Ball St51MAC138.54123.54
Oklahoma St41Big12137.968123.068
Bowling Green51MAC137.935122.019
Georgia Tech32ACC137.162131.862
Indiana32B1G137.147132.947
Southern Cal32PAC12136.931132.231
Nebraska41B1G136.745125.745
Oregon St41PAC12136.668124.468
Tennessee33SEC136.533135.533
TCU23Big12136.394139.094
Navy31Ind-FBS135.958124.958
Penn State32B1G135.553129.553
Mississippi32SEC135.524131.824
Buffalo32MAC134.744131.544
Iowa42B1G134.392125.476
Utah32PAC12134.366129.866
Wisconsin32B1G134.284124.984
West Virginia33Big12134.259136.009
Rice32CUSA134.156131.056
North Texas23CUSA134.042136.242
Duke32ACC133.834128.434
Brigham Young32Ind-FBS133.734127.434
Arkansas33SEC133.255132.505
Marshall32CUSA132.94125.24
Toledo33MAC131.356131.106
Western Kentucky42SunBelt131.081122.664
Boise St32MWC130.706125.306
Minnesota42B1G130.346123.846
Syracuse23ACC130.306132.906
Tulane42CUSA130.129122.379
Colorado22PAC12129.387130.137
Louisiana-Lafayette32SunBelt129.228124.628
Illinois32B1G129.177125.177
Vanderbilt33SEC128.48126.314
Texas St-San Marcos32SunBelt128.439123.939
Kansas St23Big12128.014129.614
North Carolina St32ACC127.33124.83
Nevada33MWC127.327127.243
Wake Forest33ACC127.308126.308
Texas32Big12127.126123.926
UNLV32MWC127.119122.719
Mississippi St23SEC127.08130.58
Utah St33MWC127.004123.92
North Carolina14ACC126.729139.329
Wyoming32MWC125.449118.449
San Diego St23MWC125.294130.894
Virginia23ACC124.891131.191
SMU14AAC124.781138.881
South Alabama23SunBelt124.56127.36
Kansas22Big12124.467125.592
Florida Atlantic24CUSA124.291129.791
San José St23MWC124.225127.725
Middle Tennessee St33CUSA123.781125.115
California14PAC12122.974138.074
Kentucky14SEC122.821135.521
Cincinnati32AAC122.595114.395
Kent St24MAC122.025131.025
Memphis13AAC121.853130.603
Iowa St13Big12121.096129.721
Arkansas St23SunBelt121.08126.88
Texas-San Antonio24CUSA120.408128.158
Colorado St23MWC120.275124.175
Troy33SunBelt120.212120.712
Army24Ind-FBS120.152128.236
Connecticut04AAC119.423141.173
Akron15MAC119.277135.194
Louisiana-Monroe24SunBelt118.69128.94
Florida Int’l14CUSA118.63136.43
Tulsa14CUSA118.525133.025
South Florida14AAC116.174132.574
Idaho15Ind-FBS115.975133.808
Central Michigan24MAC115.645123.395
Alabama-Birmingham14CUSA114.708126.808
Eastern Michigan14MAC114.569129.269
Purdue14B1G114.379129.379
Temple05AAC113.916135.316
New Mexico23MWC113.835118.835
Louisiana Tech24CUSA111.244118.161
Hawai`i05MWC111.164133.264
Air Force15MWC109.016123.349
Western Michigan06MAC108.478130.561
Southern Miss05CUSA107.455129.555
Georgia St05SunBelt107.426130.826
Massachusetts05MAC107.35132.65
UTEP14CUSA101.305113.405
New Mexico St06Ind-FBS101.264124.097
Miami OH05MAC100.035124.635

The Fleming System – Rankings by Conference

Rankings as of October 7, 2013; sort by clicking column header

ConferenceDivisionRatingSchedule
SECDI-FBS141.942133.593
PAC12DI-FBS140.505130.901
ACCDI-FBS139.272131.952
Big12DI-FBS135.965128.888
BIG TENDI-FBS135.661126.89
AACDI-FBS129.065128.865
Ind-FBSDI-FBS124.505128.802
MACDI-FBS124.349128.27
MWCDI-FBS123.549124.863
SunBeltDI-FBS122.59125.744
CUSADI-FBS122.365127.412

 

View Patrick Fleming’s full catalog of rankings, including some for other collegiate sports, by clicking here.  Leave your comments below.

The Solid Verbal is the best podcast for college football. Because you don’t just love college football, you live it.

Next post:

Previous post: