# Colley Matrix

The Colley Matrix is a computer-generated sports rating system designed by Dr. Wesley Colley. It is one of more than 40 polls, rankings, and formulas recognized by the NCAA in its list of national champion selectors in college football.

## Methodology

In his initial paper at Princeton University, Colley states, "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." Colley claims that his method is bias free for estimating the ranking of a team given a particular schedule. The resulting values for each team are identified as a ranking, thus being a realization of Pierre-Simon Laplace’s Rule of Succession.
The formula was adjusted in 2007 to account for games against FCS teams.
Colley Matrix is a special case of the Generalized row sum method, a parametric family of ranking methods developed by P. Yu. Chebotarev (1989).$^{:4}$

## National champions

As an NCAA-designated major selector, the NCAA regards the following teams as Colley's national champion selection, however these selections are listed under the "Final National Poll Leaders" section of the NCAA's record book rather than the "National Champions" section. Unlike most of the NCAA's major selectors, the Colley Matrix does not award a trophy to its national champion.
In four years (2011, 2012, 2016, 2017) the Colley Matrix selected a national champion that did not win the BCS or CFP national championship game. In each of the years, the Colley Matrix was the only NCAA-designated "major selector" to select that champion.$^{:117–118}$
| Season | Champion | Record |
| 1998 | Tennessee | 13–0 |
| 1999 | Florida State | 12–0 |
| 2000 | Oklahoma | 13–0 |
| 2001 | Miami (FL) | 12–0 |
| 2002 | Ohio State | 14–0 |
| 2003 | LSU | 13–1 |
| 2004 | USC | 13–0 |
| 2005 | Texas | 13–0 |
| 2006 | Florida | 13–1 |
| 2007 | LSU | 12–2 |
| 2008 | Florida | 13–1 |
| 2009 | Alabama | 14–0 |
| 2010 | Auburn | 14–0 |
| 2011 † | Oklahoma State | 12–1 |
| 2012 † | Notre Dame | 12–1 |
| 2013 | Florida State | 14–0 |
| 2014 | Ohio State | 14–1 |
| 2015 | Alabama | 14–1 |
| 2016 † | Alabama | 14–1 |
| 2017 † | UCF | 13–0 |
| 2018 | Clemson | 15–0 |
| 2019 | LSU | 15–0 |
| 2020 | Alabama | 13–0 |
| 2021 | Georgia | 14–1 |
| 2022 | Georgia | 15–0 |
| 2023 | Michigan | 15–0 |
| 2024 | Ohio State | 14–2 |
† Years in which Colley Matrix selection did not win BCS or CFP national championship game.

## History

The NCAA records book indicates that the Colley Matrix has been active since 1992, however this appears to be an error and no Colley selections are listed for 1992–1997.$^{:112}$ The season rankings on Colley's own website begin in 1998. The Colley Matrix was one of the computer rankings used during Bowl Championship Series (BCS) system of determining national championship game participants starting in the 2001 season. The Peter Wolfe and Wes Colley/Atlanta Journal-Constitution computer rankings were used in place of The New York Times and Dunkel rankings. The change was made because the BCS wanted computer rankings that did not depend heavily on margin of victory.
The Colley Matrix has chosen a different national champion from the Bowl Championship Series or College Football Playoff champion four times:$^{:117–118}$
* 2011 — Colley Matrix ranked Oklahoma State as first, although the team did not play in the 2012 BCS National Championship Game and finished No. 3 in both the AP Poll and Coaches Poll.
* 2012 — Colley Matrix ranked Notre Dame as first and Alabama second despite the Crimson Tide defeating the Fighting Irish 42–14 in the 2013 BCS National Championship Game.
* 2016 — Colley Matrix ranked Alabama first and Clemson second despite Clemson beating Alabama 35–31 in the 2017 College Football Playoff National Championship.
* 2017 — Colley Matrix ranked UCF first, while UCF finished No. 6 in the AP Poll and No. 7 in the Coaches Poll. UCF was not selected for the 2018 College Football Playoff despite being the only undefeated FBS team that season, albeit with a much weaker strength of schedule than the teams picked above them (103 at the end of the regular season, while playoff semifinalists Clemson, Oklahoma, Georgia, and Alabama's strengths of schedule ranked 38, 24, 27, and 34, respectively).
In each of the above instances, the Colley Matrix was the only NCAA recognized selector to choose a champion other than the BCS or CFP winner.$^{:117–118}$

## Criticism and controversies

The methodology of the rankings have been questioned by others on the grounds of subjectivity and specifics of the statistical math. It has also been criticized for placing too much weight on a team's win-loss record and not correctly emphasizing a team's strength of schedule, margin of victory, and head-to-head results, as well as for problems with the formula used for the calculation. Dr. Ed Feng, a mathematician at Stanford University, criticized the system because it does not consider specific game results, stating that "[t]he method does not care who a team loses to in ranking them. It considers the win loss record of each team and the number of games played between each pair of teams. However, the specifics of who won each game are not an input to Colley’s method".
In the final BCS rankings for the 2010 season, LSU was incorrectly ranked ahead of Boise State, at No. 10 instead of No. 11. The error was a result of Colley failing to input an FCS playoff game (Appalachian State vs. Western Illinois) correctly, a mistake that affected an order that helped determine bowl pairings that season.
The ranking system was widely criticized after ranking Notre Dame ahead of Alabama following the 2012 BCS National Championship Game, in which Alabama defeated Notre Dame 42–14.
The Colley Matrix is most well known for ranking Central Florida ahead of Alabama in 2017 despite Alabama's victory in the 2017 College Football Playoff. Central Florida later proclaimed themselves as co-national champions because of the ranking, becoming the only school to claim a national championship based solely on the Colley Matrix.
In 2018, the Mountain West Conference moved away from using four polls, one being Colley Matrix, to determine the host site for its conference championship game in football, due to "a shift to place a priority on head-to-head competition."
Since its creation, the four instances in which the Colley Matrix has chosen a different national champion from the BCS/CFP winner are the most of any NCAA recognized selector in that timeframe.$^{:117–118}$ Colley Matrix is also the only NCAA recognized selector to ever choose a different champion than the CFP (in use since the 2014 season), which it has done twice.$^{:117–118}$