The Transitive Property Fallacy

Yesterday, commenter Vrax brought up an interesting point in his response to my Fedor article.  He wrote that we have reason to believe that Randy Couture is better than Fedor Emelianenko based on Couture’s victory over Gonzaga, who defeated “Cro Cop”, who had gone to a fairly close decision against Fedor.

This, my friends, is what we’ll call the Transitive Property Fallacy of MMA.  We’ve all used it at one point or another to try and justify some unprovable statement, just like we’ve all built up straw men or confused correlation for causation (for example, my friend Dan Brooks wears glasses and and is a closeted homosexual, though this does not mean that wearing glasses has caused him to be a closeted homosexual. The real cause is most likely singing in his church choir all the way into his teens.  See how that works?).

I’m not trying to call out Vrax in particular here, because we’re all guilty of this at times.  He seems like a smart guy and so I’m guessing he won’t mind me using his comment to make a point that is long overdue. Though there are some good reasons for why we continue to employ this fallacy, we should stop it.  Failing that, we should at least realize that we’re doing it so we don’t take our own arguments too seriously.

Simply stated, the Transitive Property Fallacy of MMA is this: if Fighter A beats Fighter B, and Fighter B beats Fighter C, then Fighter A would beat Fighter C.  This works in math, or so people who went to school past the ninth grade tell me (personally, I never had a use that much schoolin’), but it doesn’t work in MMA for several different reasons.

For one, fighting ability is not quantifiable.  We can’t look at a guy and say how he will perform against any opponent on any given night.  Some fighters might look like world beaters one night, then completely choke on another.  Georges St. Pierre’s performance against Matt Serra comes to mind.

Plus, as we love to say in this business, styles make fights.  A powerhouse wrestler might dismantle a good striker, but get submitted by an average jiu-jitsu fighter.  You never can tell how the strange alchemy of MMA will turn out, which is really what makes it so damned interesting.  If we could determine everything by looking at someone’s record, we wouldn’t need to fight the fights.  It ignores the possibility that some guys have gotten better since the last time we saw them, or that others have gotten worse, or even that they’ve just changed, matured, given up booze, found Jesus, or finalized their divorce, all of which could affect their performance.

If the Transitive Property worked in MMA, we’d be living in a much different world.  For instance, Evan Tanner beat Phil Baroni (twice).  Baroni knocked out Ryo Chonan.  Chonan submitted Anderson Silva with a crazy flying heel hook.  By the Transitive Property, this means that Evan Tanner is superior to Anderson Silva, which is so untrue that I’m surprised my computer even allowed me to type it.

This could go on and on.  Josh Barnett once beat Randy Couture, and later lost to “Cro Cop”, who was defeated by Fedor.  In that equation, Fedor > Couture.  Couture also lost to Ricco Rodriguez, who lost to Ben Rothwell, who lost to Tim Sylvia.  By the Transitive Property, Sylvia should beat Couture.  And yet…he didn’t.  Need I go on?

There are many reasons why we can’t figure out who the better fighter is by comparing common opponents.  This won’t stop us from doing it, I suspect, because we’re all jerks who can’t stand the fact that we don’t know everything.  That’s why we fill in the gaps in our knowledge with twisted reasoning when necessary.   It’s stupid but, much like Dan Brooks’ sad charade of faux-heterosexuality, it goes on.

But the next time you’re having an MMA discussion with someone and they trot out this fallacy, you should make damn sure you call them on it.  Because that’s the only way we’re ever going to learn, and learn we must.  If the Transitive Property worked for MMA, it wouldn’t be very fun at all.  It would be math.  And I don’t care what those jerks at NASA say, MMA is > than math.  If Euclid were alive today, he’d be the first to admit it.

1 Comment

Filed under Math, MMA, Sports

One response to “The Transitive Property Fallacy

  1. neijia

    That is pretty funny. There are sites with purely math-based rankings that put Fedor in the middle. Of course that’s totally wrong. Fedor is the best, by far, in his own league really. I thought your previous post on the psychology of “Fedor hatin” was right on. People want to root against him or for Randy, or who knows why. Maybe because of a dearth of matchups in hw and lack of any real drama or good hype. Fedor manhandled Big Nog in Pride twice. As much as I like Randy, he is 16-8 (basically equals 67% wins in that ninth grade math) and even at a super-fit 44, not getting younger. Fedor is essentially 28-0 and still in his prime. Randy v Nog might be a good matchup. Both are decent boxers. Randy an elite wrestler and Nog an elite bjj grappler. Usually that favors bjj as far as I can tell, but you never know.

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