Colley's Bias Free Matrix Rankings

*Colley's Bias Free Matrix Rankings* An Official Bowl Championship Series Ranking for 2001–2006
last updated (2007-Jan-8)

Final 2006 Football
1. FLORIDA
2. USC
3. LOUISVILLE
4. OHIO ST
5. BOISE ST
6. MICHIGAN
7. LSU
8. AUBURN
9. WVU
10. WISCONSIN
11. RUTGERS
12. CALIFORNIA
13. NOTRE DAME
14. OKLAHOMA
15. OREGON ST
16. ARKANSAS
17. TENNESSEE
18. WAKE FOREST
19. BYU
20. BOSTON COLL
21. VA TECH
22. TEXAS
23. GEORGIA
24. TCU
25. PENN ST

Football

Complete Rankings
Index to weekly 2006 rankings

FEATURES:
Detailed Conference Comparisons
Add/Remove Games at Will!
Enhanced Team Comparisons
(click your team on the rankings page)

Basketball
Final 2005–06 Rankings
2005–06, 2004–05, 2003–04, 2002–03

Method—FAQ
The Colley Matrix Method (mathematical)
Advantages in the Method (intuitive)
1998–2005 Rankings
and Comparisons with Polls

Contact Info

About Wes Colley

Contact Wes Colley

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Wesley N. Colley

Advantages in this Method

First and foremost, the rankings are based only on results from the field , with absolutely no influence from opinion, past performance, tradition or any other bias factor. This is why there is no pre-season poll here. All teams are assumed equal at the beginning of the year. If you include some kind of human input, what's the point of a computer poll in the first place? Garbage in, garbage out.

NOTE: Bear in mind that because there is no pre-season poll, the early rankings will not look much like the press polls. The rankings are based on results so far within the season of play.

Second, strength of schedule has a strong influence on the final ranking. Padding the schedule wins you very little. Furthermore, only D-IA opponents count in the ranking, so those wins against James Madison or William & Mary don't mean anything. For instance, Wisconsin with 4 losses finished the 2000 season ahead of well ahead of TCU with only 2 losses. That's because Wisconsin's Big 10 schedule was much, much more difficult that TCU's WAC schedule.

Third, as with the NFL, NHL, NBA, and Major League, score margin does not matter at all in determining ranking, so winning big, despite influencing pollsters, does not influence this scheme. The object of football is winning the game, not winning by a large margin.

Ignoring margin of victory eliminates the need for ad hoc score deflation methods and home/away adjustments. If you have to go to great lengths to deflate scores, why use scores?

What about home/away? Though reasonable arguments can be made for a home/away factor, I do not know of a simple, mathematically consistent means of rating the relative difficulty of playing at the Swamp vs. playing at Wallace-Wade Stadium. The home advantage for some teams is simply more than it is for others. There are further complicating factors, such as home weather for a northern team in November vs. home weather for a southern team in August.

Even the pollsters seem to forgive or forget big scores or surprisingly close scores, home or away, after a few weeks. Usually, after a few weeks, a W is a W and an L is an L, as it should be anyway.

Fourth, there is no ad hoc weighting of opponenents' winning percentage and opponents' oppponents' winning percentage, etc., ad nauseam (no random choices of 1/3 of this + 2/3 of that, for example). In this method, very simple statistical principals, with absolutely no fine tuning are used to construct a system of 117 equations with 117 variables, representing each team according only to its wins and losses, (see Ranking Method). The computer simply solves those equations to arrive at a rating (and ranking) for each team.
Fifth, comparison between this scheme and the final press polls (1998, 1999, 2000, 2001, 2002) proves that the scheme produces sensible results.

The fractional ranking discrepancy between my system and the polls varies between 0.200 and 0.298 in all cases, typically a quarter. In other words, a typical ranking difference between my poll and either press poll would be around 1 place at a ranking of #4, and around 5 places at #20. The press polls themselves vary between 0.037 and 0.095 over those years. So one might expect, for a given team, a ranking disagreement of about 1 in the top 15.

So the Coaches and AP pollsters agree with each other about 4 times better than they agree with me. However, one would expect that the Coaches and AP polls agree very well for a very simple artificial reason. The coaches read the AP poll, and the media voters read the Coaches' poll, so there is statistical feedback between the two polls, right or wrong. A computer scheme, like this one, does not read other polls.

The bottom line in these comparisons, is that my rankings have
1. agreed in all four years with the media and coaches on the national champion,
2. most often agreed on the top 5, and
3. agreed on the top 10 within a place or two,
which I call a remarkable success, given the radically different systems of ranking system in question. Since we don't really know the "true" rankings of the teams, we, in fact, are not able to say whether the media polls or my rankings are better, but the fact that the agreement is, in practice, quite good provides reason to believe that neither is totally out to lunch.

So, here we have a scheme to rank college football teams that is absolutely free from human influence or opinion, accounts for schedule strength, ignores runaway scores, and yet produces common sense results, which at the end of the season compare favorably with the press poll rankings. What else do you want?

The Colley Matrix Method

(Please note: This method is copyright. I present it here for anybody to peruse and evaluate, and perhaps use for personal amusement. Please contact me directly, however, before using it for any other purpose)

The Colley Matrix Method, 2002 Edition (PDF) (obtain PDF reader Acrobat Reader) ... (5/30/02).

ABSTRACT
Colley's matrix method for ranking college football teams is explained in detail, with many examples and explicit derivations. The method is based on very simple statistical principles, and uses only Div. I-A wins and losses as input—margin of victory does not matter. The scheme adjusts effectively for strength of schedule, in a way that is free of bias toward conference, tradition, or region. Comparison of rankings produced by this method to those produced by the press polls shows that despite its simplicity, the scheme produces common sense results.

About Wes Colley

Background:

Born in 1971, in Bristol, TN, smack-dab in the middle of the Hokies and the Vols. Raised in Abingdon, VA. Graduated from Abingdon High School in 1989.

Education:

Ph.D. in Astrophysical Sciences at Princeton, 1998
Thesis Title: "Statistics for New Datasets in Cosmology"
Advisor: J.R. Gott, III

Awards: Attended Princeton as Fannie & John Hertz Fellow
nominated for the Jacobus Prize

B.A. with Highest Distinction in Astronomy/Physics at the University of Virginia, 1993

Awards: Outstanding Astronomy Undergraduate, 1993
Echols Scholarship
Robert C. Byrd Scholarship
Phi Beta Kappa
Resume

Publications

Employment:
Center for Modeling, Simulation and Analysis, 2005-present
Senior Research Scientist

Virginia Modeling, Analysis and Simulation Center, 2004-2005
Senior Research Scientist

University of Virginia, 2002-2004
Lecturer, Astronomy Department

M.I.T. Lincoln Laboratory, 2001-2002
Missile defense technology development

Harvard-Smithsonian Center for Astrophysics, 1997-2000
Gravitational Lenses as Cosmological Probes
Genus Topology of Large-Scale Structure in the Universe
College Football Experience
- My brother, Will Colley, played for Georgia in the Tim Worley/Rodney Hampton hey-day. During that time, I made countless trips to Athens to see the 'Dawgs Between the Hedges, and to away venues, including the Gator Bowl. Aside from attending games, hanging around with the players was a formative experience for me. During Will's recruiting, I met such legends as Vince Dooley, and Johny Majors, and countless other big name coaches and players.
- Aside from being a life-long Virginia fan, I attended Virginia during the Shawn and Herman Moore era, when Virginia ascended to #1 in the polls. I was there when UVa beat Clemson for the first time, setting up that monster year in 1990.
- Stadiums Attended:
  1. Scott (Charlottesville, Virginia)
  2. Sanford (Athens, Georgia)
  3. Aloha (Honolulu, Hawaii)
  4. Georgia Dome (Atlanta, Georgia) (Peach Bowl, SEC Championship)
  5. Louisiana Superdome (New Orleans, Louisiana) (Sugar Bowl)
  6. Gator Bowl (Jacksonville, Florida) (Gator Bowl)
  7. Ericsson (Charlotte, NC) (Continental Tire Bowl)
  8. Alltel (Jacksonville, Florida) (Georgia-Florida)
  9. The Coliseum (Nashville, Tennessee) (Music City Bowl)
  10. Death Valley (Baton Rouge, Louisiana)
  11. Death Valley (Clemson, South Carolina)
  12. Jordan-Hare (Auburn, Alabama)
  13. Williams-Brice (Columbia, South Carolina)
  14. Neyland (Knoxville, Tennessee)
  15. Ben Hill Griffin (Gainesville, Florida)
  16. Bobby Dodd (Atlanta, Georgia)
  17. Kenan (Chapel Hill, North Carolina)
  18. Lane (Blacksburg, Virginia)
  19. Byrd (College Park, Maryland)
  20. Heinz Field (Pittsburgh, Pennsylvania)
  21. Palmer (Princeton, NJ)
  22. Harvard (Boston, MA)
  23. Jopson (Bridgewater, VA)

Previous Rankings and Comparisons with Press Polls

All 2005 Rankings

All 2004 Rankings

All 2003 Rankings

All 2002 Rankings, Comparison with AP, Coaches' Polls

All 2001 Rankings, Comparison with AP, Coaches' Polls

All 2000 Rankings, Comparison with AP, Coaches' Polls

All 1999 Rankings, Comparison with AP, Coaches' Polls

All 1998 Rankings, Comparison with AP Poll

Wesley N. Colley