Ranking all 136 FBS football teams through the conference championships with matrix algebra and hill climbing

Following up on our post on a new approach to ranking college football teams, which we applied to the Big Ten conference, this post expands that approach to all 136 FBS teams, ranking those teams through the conference championship games. We considered only games played between FBS teams. There were 126 FBS vs. FCS games in 2025 and the FCS teams won only four. Certainly, the four FBS teams that lost those games (Army, Eastern Michigan, Massachusetts, and Middle Tennessee State) would be ranked lower if those games were included. But none of those teams are in the top 65 of any of our rankings anyway.

In expanding the approach, we found it necessary to make one change. We still weighted cells below the diagonal by the distance below the diagonal divided by the number of teams. But if we used the same approach for cells above the diagonal, it ranked teams that played weak schedules far too high. So, we needed to rethink the weighting of those cells. Certainly, the farther a cell is below the diagonal, the more evidence it provides against the current ordering. So, it seems appropriate to continue to assign increasing weight as the distance below the diagonal increases. But that result isn’t as clear above the diagonal. A win by the highest ranked team over the lowest ranked team does not really provide more evidence for the current ordering than a win by the highest ranked team over the second ranked team. So, we decided to give equal weight to all cells above the diagonal. The only remaining issue was how to distribute the weight between cells above and below the diagonal. We decided to assign 20 percent of the weight to the cells above the diagonal and 80 percent to the cells below the diagonal. But our results were not very sensitive to that weighting.

So, in a ranking of ten teams, the cell weights are as shown in the table below. Of course, most cells below the diagonal will have 0’s; the lower ranked team won only about 9 percent of games in our final ordering. So, the table for the final ordering still has a net positive value, with more weighted value above the diagonal than below.

We again ran three models. The basic model considers only wins and losses. The second model is adjusted for both margin of victory and game location, using codes designed so a win by 17 points or more is worth twice as much as a 1-point win, with an average bonus of 3 points for road victories. The third model is also adjusted for timing of the game during the season, with a 5 percent weekly inflation factor, so a win in week 2 is worth 1.05 times as much as a win in week 1, a win in week 3 is worth 1.1 times as much as a win in week 1, etc. The following table shows the final CFP ranking of the top 25 teams, the final FPI ranking of all 136 teams, and the results of our three models for all 136 teams. Teams in bold type would have been selected for the College Football Playoff.

Comparing the third and fourth columns of the table, some of the most notable differences are:

• BYU (12 higher): Our approach ranks Texas Tech, BYU, and Utah all higher. Other than Texas Tech’s loss to Arizona State, these three teams lost only to each other. And they collectively had good wins over Iowa State, Houston, Arizona State, and Arizona. These three teams should be ranked ahead of Iowa State, which our approach ranks ahead of Iowa, but it’s not clear why they rank quite so high.
• Texas (7 higher): Although Texas had one bad loss to Florida, its other two losses were to higher ranked teams and it had good wins over Texas A&M, Oklahoma, and Vanderbilt. Our approach ranks it between Georgia, which it lost to, and Texas A&M, which it defeated.
• LSU (12 higher): LSU had a good win against Florida and no bad losses. Our approach ranks it between the five SEC teams it lost to, and Florida, which it defeated, but it’s not clear why it ranks quite so high.
• Oregon (11 lower): Oregon’s loss to Indiana doesn’t hurt it, but its best win was against USC. Our approach ranks it between Indiana and USC, but it’s not clear why it ranks quite so low. When considering BYU, Utah, LSU, and Oregon, in particular, it would help if there were more games between the top teams in the Big Ten, SEC, and Big 12. With only two games between top Big Ten and SEC teams (Ohio State’s win over Texas and Oklahoma’s win over Michigan) and no games between top teams from those conferences and top Big 12 teams, it’s challenging to compare top teams in those conferences.
• Miami (9 lower) and Notre Dame (13 lower): Miami’s head-to-head win ranks it ahead of Notre Dame and Notre Dame’s head-to-head win ranks it ahead of USC. Because of Notre Dame’s loss to Texas A&M, our approach ranks both teams between Texas A&M and USC. Miami’s two bad losses to SMU and Louisville drive that ranking as low as possible within that range.
• Tulane (31 higher): Tulane had one bad loss to UTSA. Our approach ranks it just ahead of North Texas, which was its best win.
• Minnesota (37 higher) and Wisconsin (34 higher): Minnesota’s head-to-head win ranks it ahead of Wisconsin. Wisconsin’s seven losses were all to higher ranked teams, so our approach ranks it just ahead of Washington and Illinois, which it defeated.
• New Mexico (38 higher) and UCLA (37 higher): New Mexico had one bad loss to San Jose State, but New Mexico’s and UCLA’s other losses were all to higher ranked teams. Our approach ranks New Mexico ahead of UNLV and UCLA, which it defeated, and ranks UCLA ahead of Penn State, Michigan State, and Maryland, which it defeated.
• Western Michigan (32 higher): Western Michigan had one bad loss to Miami-Ohio. But its win over Ohio and Ohio’s win over West Virginia determine the ordering of those teams and Ohio’s and West Virginia’s other losses to lower ranked teams further separate those teams.
• SMU (33 lower): SMU had one good win over Miami. But that win is offset by a bad loss to California. Our approach ranks it between Baylor and Wake Forest, which it lost to, and Clemson and Louisville, which it defeated.
• Louisville (31 lower): Louisville had good wins against Miami and Pittsburgh. But those wins are offset by a bad loss to California. Our approach ranks it between Virginia, SMU, and Clemson, which it lost to, and Kentucky and James Madison, which it defeated.
• Florida State (30 lower): Florida State had a good win against Alabama. But that win is offset by a bad loss to Stanford. Our approach ranks it closely behind North Carolina, Virginia, and Clemson, which it lost to.
• James Madison (36 lower): James Madison didn’t have any bad losses or good wins. Our approach ranks it between Louisville, which it lost to, and Washington State and Old Dominion, which it defeated.
• Kansas State (31 lower): Kansas State had one good win against TCU and no bad losses. But our approach ranks it between Army, which it lost to, and Kansas and Central Florida, which it defeated. It’s not clear why its good win didn’t help it to rank higher.
• Auburn (55 lower): Auburn had one good win over Baylor and no bad losses. Our approach ranks it between Kentucky, which it lost to, and Arkansas, which it defeated, but it is not clear why it ranks quite so low or why its good win didn’t help it to rank higher.
• Toledo (31 lower): Toledo had no good wins and one bad loss to Bowling Green State. Our approach ranks it just above Miami-Ohio, which was its best win.
• Memphis (38 lower): Memphis had one good win against South Florida and one bad loss to Alabama Birmingham. Our approach ranks it just above Arkansas and Troy, which were its next best wins.
• Arkansas (46 lower): Arkansas had no good wins or bad losses. Our approach ranks it just behind Memphis, which it lost to.
• UTSA (32 lower): UTSA had good wins against Tulane and East Carolina and no bad losses. But our approach ranks it between Temple, which it lost to, and Rice, which it defeated. It’s not clear why its two good wins didn’t help it to rank higher.
• Kent State (32 higher): Kent State had no good wins and no bad losses. Our approach ranks it between Central Michigan, Buffalo, and Ball State, which it lost to, and Akron and Bowling Green State, which it defeated.
• Boston College (33 lower): Boston College had no good wins or bad losses. Our approach ranks it between Stanford, which was its worst loss, and Syracuse, which was its only win, but it’s not clear why it ranks quite so low.

Comparing the fourth and fifth columns of the table, some of the most notable differences are:

• Missouri (14 higher): Missouri had three wins against FCS teams by at least 17 points and only one loss by at least 17 points to highly ranked Texas A&M.
• Tennessee (14 lower): Tennessee’s five wins against FCS teams by at least 17 points were all against lower ranked teams. But its two losses by at least 17 points were to highly ranked Alabama and Vanderbilt, so it’s not clear why it descended in this model.
• Auburn (34 higher): In addition to Auburn’s one win against FCS teams by at least 17 points, it also had a 16-point win and a 14-point win and its largest loss was by 10 points to highly ranked Georgia. It’s 14-point road win over Baylor, in particular, helped it advance ahead of Baylor.
• Hawaii (14 higher): Hawaii had four wins against FCS teams by at least 17 points and only two losses by at least 17 points.
• Stanford (18 higher): Stanford had five losses by at least 17 points, but those losses were all to higher ranked teams. Its one win by at least 17 points against California helped it advance ahead of California.
• Western Michigan (21 lower): Western Michigan’s two losses by at least 17 points were to higher ranked teams. But its two wins against FCS teams by at least 17 points and its 16-point win were all against lower ranked teams, so it’s not clear why it advanced in this model.
• Ohio (11 lower): Ohio’s two wins against FCS teams by at least 17 points were against lower ranked teams. But its only loss by at least 17 points was against highly ranked Ohio State, so it’s not clear why it descended in this model.
• Navy (35 lower): Navy had only one win against an FCS team by at least 17 points. But its only loss by at least 17 points was to highly ranked Notre Dame, so it’s not clear why it descended in this model.

Comparing the fifth and sixth columns of the table, some of the most notable differences are:

• Penn State (17 higher): Penn State won its last three games over Michigan State, Nebraska, and Rutgers, which were its three best wins and helped it advance in this model.
• North Texas (17 lower): North Texas’s 13-point loss to Tulane in the American Conference championship game in Week 15 caused it to descend in this model, despite the fact that it had won its prior six games.
• Navy (40 higher): Navy won its last two games (not counting the Army-Navy game, which is not included in our results) over South Florida and Memphis and those were two of its three best wins, which helped it advance in this model, despite the fact that it had lost its prior two games.
• Hawaii (11 higher): Hawaii won five of its last seven games after starting the season 2-2 against FCS teams. That second half improvement helped it advance in this model.
• Maryland (33 lower): Maryland lost its last eight games after starting the season with three wins against FCS teams. That second half collapse caused it to descend in this model.
• Auburn (31 lower): Auburn lost seven of its last eight games with FCS teams after starting the season with three wins. As with Maryland, that trend caused it to descend in this model.

Overall, we believe our second model best ranks each team’s overall performance during the season and would be most appropriate for choosing playoff teams. Our third model considers which teams are playing best at the end of the season and would be more useful to predict playoff games, although it still is not intended to be a predictive model. Indeed, it would be 3-5 so far in predicting playoff games and seems to have underrated Oregon and Miami, in particular.