## UFC Referees and the Power Law

Without using Google or Wikipedia, name five American MMA referees.

If you're like 98% of the global population (ed. note: figure cannot be verified), you probably listed some combination of John McCarthy, Herb Dean, Steve Mazzagatti, Mario Yamasaki, Yves Lavigne, and Dan MIragliotta.  Why is that?

Well, it can all be explained by the Power Law.  Here's a layman's explanation from Advanced NFL Statistics:

Have you ever noticed how most of the productivity around your office seems to be accomplished by a minority of your co-workers? It’s no different in the NFL, or most anywhere else.

The power law is all around us, and is a fundamental property of natural organizations of all types. City sizes, for example, are distributed according to the power law. There are a few extremely large cities, more average sized cities, and very many smaller towns. Earthquake sizes, the structure of the Internet, stock market gains and losses, body mass indexes, gravity, social network connections, wealth distributions, and even Kevin Bacon movies all follow power law distributions. If you've ever heard people refer to the "fat tail" or the "long tail," this is what they're referring to.

The distribution of MMA referees in the UFC is no different.  Our first example highlights this concept based on the amount of fights reffed by each official since the introduction of the Unifed Rules.  (As always, click the picture to view the full-sized image.)

On the left hand side of the graph, we have the usual suspects - McCarthy, Dean, Mazzagatti, Yamasaki, Lavigne, and Miragliotta.  The trend line represents the "power law" tendency of the data.

The next graph shows main event referees over the past 5 years.

That's right, only 8 referees have guided main event action (and to be fair, the fights Waugh and Rosenthal officiated were Fight Night or TUF Finales).  Again, our core team dominates the list.

So, what does this all mean?  We turn to Advanced NFL Stats again for a summary:

Power law distributions are noteworthy because they are the signatures of mature self-organizing complex systems. It’s also a feature of ‘rich-get-richer’ systems. So when we see power law distributions, we can make some qualitative inferences about the system we’re observing. For example, the BCS system is certainly a rich-get-richer organization. We can even quantify just how hierarchical it is and how difficult it is for second-tier teams to break into the elite.

Whether it be a sign of a strict meritocracy, advantageous networking, a lack of trust from athletic commissions, a combination of those three, or an entirely separate explanation, the data clearly shows that something is at play that keeps a refereeing elite working big fights.

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