Whenever A is related to B and B is related to C, then A is also related to C.
The transitive property is a simple and useful property in mathematics whose most common form is the first sentence to this story. That’s according to the math whizzes. To us sports nerds, it takes on a slightly altered version.
Whenever Team A beats to B and Team B beats Team C, then Team A is better than Team C.
It’s math, bro! We know of course that the sports world is not the math world. We can’t take things so literally. For instance, during the 2018 college football season, Ohio State finished third nationally with a record of 13–1. Just because Eastern Michigan beat Purdue and Purdue beat Ohio State doesn’t mean that Eastern Michigan is better than Ohio State.
Oh, but what if that were the case. For purposes of this post, let us merge the math and sports worlds for a brief alternate reality. We used the transitive property on teams still in legitimate contention to reach the College Football Playoff, tracing their losses back to some of the worst teams in the sport this season. The worst transitive losses belong to No. 4 Georgia, No. 7 Utah, No. 9 Oklahoma and No. 10 Minnesota. Math tells us that these teams have losses to bottom-feeders Texas State, UNLV, Arkansas and Tulsa, a group that combines for 10 wins this year.
An illustrious transitive national championship is still available for these guys. Oh, you haven’t heard about transitive national titles? They are a thing. In fact, a now-defunct website used to dedicate itself to documenting the transitive champions in each of the major sports. In college football, the most recent noteworthy transitive champion came in 2017, when 2–10 Georgia Southern took home the prize. Alabama won the national championship that season, the same Alabama that lost to Auburn, which lost to LSU, which lost to Troy, which lost to South Alabama, which lost to, yes, Georgia Southern. The Eagles are one of the more incredible transitive title holders in recent memory. They opened that 2017 season on a nine-game losing streak, which included defeats to New Hampshire and UMass.
The 2016 season brought us a transitive champion from the FCS division. That’s right–CFP victor Clemson has a loss that can be traced back to little ole Indiana State from a completely other level of college football. The Tigers’ only loss that year came to Pitt, which lost to Northwestern, which lost to Illinois State, and if that’s not bad enough, Illinois State, a 6–6 FCS program that year, dropped a game to Indiana State. The Sycamores finished 4–7 that season.
This year, Texas State and UNLV are best positioned to claim the transitive title. Georgia and Utah are in more control of their playoff destiny than most. Win their conference championship games and they’re likely in, though a UGA SEC title game upset over LSU could potentially prevent the Pac-12 champion entering the field as a 12–1 LSU might get in instead. But enough about the real playoff, let’s talk about the transitive postseason.
1 Tulsa vs. 4 UNLV
2 Texas State vs. 3 Arkansas
Let’s look at how we got here…
Texas State > Georgia
Transitive steps (3): Georgia lost to South Carolina (20-17), South Carolina lost to Tennessee (41-21), Tennessee lost to Georgia State (38-30), Georgia State lost to Texas State (37-34)
The Bulldogs should be ashamed because… they lost at home to South Carolina. Forget about transitive, Georgia has the worst loss among all the teams still chasing a playoff bid. The 4-7 Gamecocks team beat you on your home field. Making matters worse are the transitive steps that lead to a bad Sun Belt squad.
The Bobcats are… 3-7 on the season. One of those wins is over FCS Nicholls. They also beat South Alabama, the only thing keeping them from the bottom rung of the Sun Belt. You probably recognize the name of TSU’s head coach, Jake Spavital, an Air Raid disciple who’s spent time with Dana Holgorsen at West Virginia and Kevin Sumlin at Texas A&M.
UNLV > Utah
Transitive steps (5): Utah lost to USC (30-23), USC lost to BYU (30-27), BYU lost to Toledo (28-21), Toledo lost Northern Illinois (31-28), Northern Illinois lost to Vanderbilt (24-18), Vanderbilt lost to UNLV (34-10)
The Utes should be ashamed because… you committed 16 penalties in the loss to the Trojans. Look, Utah’s loss isn’t as bad as several other playoff contenders. USC is 7-4 and 6-2 in the Pac-12. The Utes played on the road and on a Friday night. If they wouldn’t have had 16 fouls, maybe they’d not be on this list at all.
The Rebels are… arguably the worst team in the country. It took several steps to get here—for UNLV to claim a victory over Utah—but here we are, a potential playoff team having a transitive loss to a 2-8 Mountain West club. Of UNLV’s two wins, one is over an SEC team and the other is over an FCS foe. Confused? Don’t be. The SEC team is Arkansas.
Arkansas > Oklahoma
Transitive steps (7): Oklahoma lost to Kansas State (48-41), Kansas State lost to West Virginia (24-20), West Virginia lost to Texas Tech (38-17), Texas Tech lost to Arizona (28-14), Arizona lost to Hawaii (45-38), Hawaii lost to Fresno State (41-38), Fresno State lost to Colorado State (41-31), Colorado State lost to Arkansas (55-34)
The Sooners should be ashamed because… their border-state rival has a transitive win over ’em. That should be more than enough, but the Sooners’ actual loss isn’t great either. Though the Wildcats are 6-4, they’ve got losses to West Virginia and Oklahoma State.
The Razorbacks are… baaaad. In all likelihood, the Hogs are the worst Power 5 conference team in 2019. They’re so bad that the school fired its coach in the middle of his second season. Poor Chad Morris—well, he’s not really poor given that $10 buyout, but the guy didn’t even get a full second year on the job.
Tulsa > Minnesota
Transitive steps (7): Minnesota lost to Iowa (23-19), Iowa lost to Wisconsin (24-22), Wisconsin lost to Illinois (24-23), Illinois lost to Nebraska (42-38), Nebraska lost to Purdue (31-27), Purdue lost to Nevada (34-31), Nevada lost to Wyoming (31-3), Wyoming lost to Tulsa (24-21)
The Gophers should be ashamed because… they lost a road game at Iowa? They really shouldn’t be ashamed of that. In fact, Minnesota’s loss is one of the more understood of those on this list, but it does still mean that the Gophers have a transitive loss to Tulsa, and that’s tough to swallow.
The Golden Hurricane has… won a single game in the American Athletic Conference and three overall on the season, and while they’ve been competitive with some strong teams, Tulsa has suffered through a five-game losing streak and is ranked 105 nationally in total defense.