You know the argument: Team X beat Team Y, and Team Y beat Team Z, so Team X is way better than Team Z. The transitive win -- an application of mathematics' transitive property to college football -- is as old as the sport, a severely skewed measuring stick for a sport that has 128 teams, 12 games and three months of debate.

But what if we took the transitive property to its most extreme levels? What would happen if college football's most successful teams were measured by transitive wins? Let's set the world on fire.

Toledo won almost every Power 5 conference

The Toledo Rockets didn't win their conference. The Rockets didn't even win their own division, after falling to beat Western Michigan in the final game of the regular season. And yet, the Rockets were the transitive champions of four of the Power 5 conferences, and were just a bad call away from potentially winning the fifth.

Big 12: Oklahoma lost to Texas, which lost to Iowa State, which lost to Toledo

Big Ten: Michigan State lost to Nebraska, which lost to Purdue, which lost to Bowling Green, which lost to Toledo

SEC: Alabama lost to Ole Miss, which lost to Arkansas, which lost to Toledo

Pac-12: Stanford lost to Oregon, which lost to Washington State, which lost to Portland State, which lost to Northern Iowa, which lost to Iowa State, which lost to Toledo

ACC: Clemson almost lost [were it not for an onside kick call] to North Carolina, which lost to South Carolina, which lost to LSU, which lost to Arkansas, which lost to Toledo

The state of Utah won the Pac-12

Stanford is the only two-loss conference champion in the Power 5 this season, and 52 teams have a transitive claim to the Cardinal's throne within five moves. Among those 52: All five Division I football programs from the state of Utah.

Stanford lost to Oregon, which lost to Utah

Stanford lost to Northwestern, which lost to Michigan State, which lost to Nebraska, which lost to BYU

Stanford lost to Oregon, which lost to Washington State, which lost to Washington, which lost to Boise State, which lost to Utah State

Stanford lost to Oregon, which lost to Washington State, which lost to Portland State, which lost to Northern Colorado, which lost to Southern Utah

Stanford lost to Oregon, which lost to Washington State, which lost to Portland State, which lost to Northern Colorado, which lost to Weber State

The FCS owns the Pac-12 and ACC Coastal

In all, 13 FCS programs -- Portland State, North Dakota, North Dakota State, Northern Iowa, North Colorado, Southern Utah, Weber State, Eastern Washington, Northern Arizona, Western Illinois, Illinois State, Idaho State and Montana -- could claim the Pac-12 title within five transitive wins, the most of any conference by far.

Nine FCS teams -- The Citadel, Charleston Southern, UT-Chattanooga, Jacksonville State, Mercer, Wofford, Western Carolina, VMI and Samford -- could claim the ACC Coastal title through The Citadel's win over South Carolina and the Gamecocks' previous win over North Carolina.

The ex-Big 12 teams won the Big 12

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Texas A&M left the Big 12 for the SEC in 2012, walking away from its rivalry with Texas in the process. But the Aggies are your Big 12 champions in 2015 anyway!

Oklahoma lost to Texas, which lost to California, which lost to UCLA, which lost to Arizona State, which lost to Texas A&M

A&M isn't the only estranged Big 12 member with a claim to the crown:

Oklahoma lost to Texas, which lost to California, which lost to Oregon, which lost to Michigan State, which lost to Nebraska

Oklahoma lost to Texas, which lost to California, which lost to USC, which lost to Washington, which lost to Boise State, which lost to Air Force, which lost to Colorado State, which lost to Colorado

Oklahoma lost to Texas, which lost to California, which lost to Stanford, which lost to Northwestern, which lost to Nebraska, which lost to BYU, which lost to Missouri

The Playoff

Let's just give the title to Clemson, because it's too difficult otherwise.

Alabama lost to Ole Miss, which lost to Arkansas, which lost to Toledo, which lost to Western Michigan, which lost to Michigan State

Michigan State lost to Nebraska, which lost to Wisconsin, which lost to Alabama

Oklahoma lost to Texas, which lost to Notre Dame, which lost to Clemson

Better yet, let one of the one-loss teams win and put Toledo at the top of the mountain, where it belongs.