A beats B, B beats C, how often does A beat C?

by JCS_FM on Jan 1, 2009 5:34 PM EST Comment 31 comments

It's an interesting subject that probably comes up more in boxing than in MMA, but it's definitely more intriguing in the MMA world due to the large variance in styles. I ran the analysis with all MMA bouts that we have on record (over 68,000).

So how often does A beat C? First, let's acknowledge the potential issues in analyzing this statistic.

One problem is that sometimes these A/B, B/C, and A/C bouts take place multiple times, with varying results. Another problem lies in the timing of said bouts. So I laid out some guidelines.

A/B and B/C must both take place before A/C. This is an obvious one.
The most recent A/B and B/C results before A/C are acknowledged. In other words, if A beat B five years before A/C, but A lost to B three months ago in their most recent bout before A/C, then this chain won't be included in the analysis.
If multiple A/C results are available and all guidelines are met, then all A/Cs will be counted.

In the end, A prevailed over C at a 71% success rate (2988 of 4210).

When all three bouts occur within a 3 year window, the success rate improves to 72.3% (2144 of 2967).

Within a 2 year window, 73% (1590 of 2179).

18 months, 74.2% (1211 of 1633).

12 months, 75.2% (732 of 974).

9 months, 77.5% (488 of 630).

6 months, 80.9% (262 of 324).

3 months, 85.6% (77 of 90).

Sample Analysis: Cheick Kongo

Cheick Kongo (A) beat Andre Tete (B) on 6/10/2001
Andre Tete (B) beat Dave Dagliesh (C) on 12/1/2002
Cheick Kongo (A) beat Dave Dagliesh (C) on 12/11/2005

Cheick Kongo (A) beat Christian Wellisch (B) on 8/26/2006
Christian Wellisch (B) beat Dan Evensen (C) on 4/1/2006
Cheick Kongo (A) beat Dan Evensen (C) on 8/9/2008

Cheick Kongo (A) beat Mirko Filipovic (B) on 9/8/2007
Mirko Filipovic (B) beat Heath Herring (C) on 6/8/2003
Cheick Kongo (A) failed to beat Heath Herring (C) on 3/1/2008

Thanks to ltokuda, one of our readers, for the idea!

A FightMatrix original post

The FanPosts are solely the subjective opinions of Bloody Elbow readers and do not necessarily reflect the views of Bloody Elbow editors or staff.

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Comments

Wow..

totally interesting. If for no other reason than MMAth always seemed to be a little more reliable than people let on.

Contributing Editor - BloodyElbow.com - SBNation's mixed martial arts headquarters.

by Brent Brookhouse on Jan 1, 2009 6:34 PM EST reply actions 0 recs

Ooo…statistics…logic…

I don’t mind a bit of MMAth – it’s the only way to compare fighters – by seeing how they did against similar opponents. Obviously there are ways to make it more accurate, but it’s a handy tool.

Ever tried. Ever failed. No matter. Try Again. Fail again. Fail better. -Samuel Beckett

by themachiavellian on Jan 1, 2009 6:42 PM EST reply actions 0 recs

I could include a time window..

But wanted to put an all encompassing stat out there.

by JCS_FM on Jan 1, 2009 6:55 PM EST reply actions 0 recs

Come to think of it..

I’ll apply a 3-year window and see if it changes anything.

by JCS_FM on Jan 1, 2009 7:39 PM EST up reply actions 0 recs

Sounds cool...

looking forward to it.

Contributing Editor - BloodyElbow.com - SBNation's mixed martial arts headquarters.

by Brent Brookhouse on Jan 1, 2009 8:14 PM EST up reply actions 0 recs

When all three bouts occur within a 3 year window, the success rate improves to 72.3%.

Within a 2 year window, 73%.

18 months, 74.2%.

12 months, 75.2%.

by JCS_FM on Jan 1, 2009 11:32 PM EST up reply actions 0 recs

Not to be a pain...

but do you have the # of times for each window?

Contributing Editor - BloodyElbow.com - SBNation's mixed martial arts headquarters.

by Brent Brookhouse on Jan 1, 2009 11:38 PM EST up reply actions 0 recs

Three year window – 72.3% (2144 of 2967)
Two year window – 73% (1590 of 2179)
18 month window – 74.2% (1211 of 1633)
12 month window – 75.2% (732 of 974)

by JCS_FM on Jan 1, 2009 11:57 PM EST reply actions 0 recs

Mir-Lesnar I created some of the goofier MMAth I’ve come across (Marcio Cruz > Brock Lesnar?), and Mir-Noguiera sure as shit didn’t help. Nor do I have Matt Serra beating Jon Fitch or BJ Penn.

Still, these are the kinds of FanPosts I’m all about – fresh looks at shit. Rec’d.

by subo on Jan 2, 2009 2:50 AM EST reply actions 0 recs

This is some cool shite.

by SamCupitt on Jan 2, 2009 5:09 AM EST reply actions 0 recs

Wow. We’ve got something here.

And I thought MMAth is unreliable.

by Johann on Jan 2, 2009 1:58 PM EST reply actions 0 recs

There's a lot of MMAth

that works…. you’ve just got to know where to look.

by JCS_FM on Jan 5, 2009 3:01 PM EST up reply actions 0 recs

Is there some way to rule out matchups involving fighters where A and C are of vastly different ranking? For all we know, 40% of those matchups where A beats C are where A is way better than B, B is better than C, and A is WAY better than C.

If A, B, and C are all top 20 fighters, the numbers may drop down to something like 55%, for all we know.

by Michaelthebox on Jan 2, 2009 5:00 PM EST reply actions 0 recs

Good point..

by Johann on Jan 2, 2009 5:50 PM EST up reply actions 0 recs

I wanted to leave rankings out of it.

Would complicate things far too much.. and who’s ranking do we use? I guess I could use FightMatrix’s but I’d have to re-calculate the rankings for every single day, and our weight-related data for old bouts are poor.

The A/B, B/C, A/C + guidelines keep things consistent and simple enough to understand.

by JCS_FM on Jan 2, 2009 10:11 PM EST up reply actions 0 recs

Exactly.

While this is nice in theory, the huge disparity in skill levels in this sport keeps the numbers from having much relevance.

by George Lucas on Jan 3, 2009 10:18 PM EST up reply actions 0 recs

I think it has great relevance.

Skill levels aside.. Its got a basic premise and the statistics back it up..

Would A→B→C→D prove something to you?

by JCS_FM on Jan 4, 2009 12:48 AM EST up reply actions 0 recs

I gotta disagree with the relevance.

That 71% includes situations where A is significantly superior to both B and C. In that situation, A will beat both B and C. In fact, the skill levels of B and C related to one another are irrelevant, because one of them has to win, and thereby become B while the loser becomes C. The statistic tells us nothing we didn’t already know, that A is much better than B and C.

The number also includes situations where A and B can be of similar quality and both be much better than C. In the original fight between A and B, one of them had to win and become A. The statistic sheds no light on the fact that A and B are much better than C.

Finally, A can be much better than B, who is much better than C. We know this, and the 71% doesn’t tell us anything at all.

Where our knowledge becomes cloudy is the likelihood of A beating C when A, B, and C are all fighters of similar skill and quality. However, that 71% success rate doesn’t mean anything if it doesn’t strip out the effects of the other situations.

Its sort of like knowing league ERA for baseball. It can give you a more specific number for what we already know (teams score a lot) but doesn’t tell us much that really interests us, like what teams score more than other teams.

by Michaelthebox on Jan 4, 2009 7:21 AM EST up reply actions 0 recs

You're too busy focusing on the negative.

After all, its a summary statistic. If your negative point was the common theme, the stat would be more like 99.7% and we wouldn’t be able to bet on most fights because the answer would already be apparent through previous match-ups.

by JCS_FM on Jan 4, 2009 10:13 AM EST up reply actions 0 recs

I suppose so. I guess my issue is that I’m not convinced a single summary statistic is appropriate for this situation, without knowing the shape of the distribution of results.

As you said, if the points I made were the common theme, the stat would be more like 99.7. But there are a lot of different situations, and as a result I doubt the population follows anything like a bell curve or maybe any curve at all. If its a multimodal population, 71 doesn’t tell us much about any grouping.

by Michaelthebox on Jan 4, 2009 4:19 PM EST up reply actions 0 recs