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Wrestler > boxer, also, if you scroll down far enough, a couple of paragraphs reiterating my point that Bayesian != subjectivist

Regarding my article on the boxer, the wrestler, and the coin flip, Steve Hsu writes:

A world class wrestler would easily demolish a top boxer in a no holds barred fight. This has been verified by in many experiments (Inoki-Ali doesn’t count)!

Steve has more details in this blog entry from 2007:

Ultimate fighting has grown from obscurity to unbelievable levels of popularity. It will soon surpass boxing as the premier combative sport. And it will soon be widely recognized that the baddest man on the planet is not a boxer, but an ultimate fighter. . . .

Unarmed single combat — mano a mano, as they say — has a long history, and is a subject which fascinates most men, both young and old. As a boy, I can remember serious discussions with my friends concerning which style was most effective — karate or kung fu, boxing or wrestling, etc. How would Muhammed Ali fare against an Olympic wrestler or Judo player? What about Bruce Lee versus a Navy Seal? Of course, these discussions were completely theoretical, akin to asking whether Superman could beat Galactus in arm wrestling. There was scarcely any data available on which to base a conclusion.

However, thanks to the recent proliferation of “No Rules” or “No Holds Barred” (NHB) fighting tournaments, both in the U.S. and abroad, we finally have some interesting answers to this ancient question.

As with many things, the truth of the matter was known long ago, and then forgotten and relearned many times. Part of the reason for this is that unarmed combat is a peculiar thing — it is unlikely to occur in its pure form once weapons such as knives, bottles or guns are available, and when it does occur it is usually under special circumstances involving surprise or intoxication or multiple combatants. The clean schoolyard confrontation between two individuals is something which rarely occurs again in later life. Hence, single combat can only be studied in a controlled way as a form of sport. To my knowledge, the last time this was possible was during ancient times in Greece and more recently in Asia. The ancient Greek sport of Pankration (or “All Powers”) was the most popular of all of the original Olympic competitions. It combined boxing and wrestling as well as submission holds such as chokes and arm- and leg-locks. In China and Japan, unarmed fighting was also developed systematically in environments where tests through actual combat were frequent, although the modern descendants of those arts are often far from realistic.

In its modern incarnation, NHB fighting is one of the most exciting new sports to hit the market. It has a small but rapidly growing pool of fans and practicioners, despite its undeserved reputation for being bloody and dangerous. In fact, any student of the history of boxing knows that the introduction of padded gloves, along with rules against grappling, have made that sport much more dangerous than real fighting. Padded gloves protect the hands of a boxer and allow repeated blows to the head of an opponent, increasing the likelihood of brain damage. The prohibition against grappling creates an unrealistic environment, where fighters are forced to stand toe to toe and pummel each other, rather than use more efficient takedown and submission techniques to bring the fight to the ground and end it. That wrestling and submission techniques would often prevail against striking was well known to both the ancient Pankrationists and at least some of the martial artists in Asia. This lesson has been re-learned in the NHB context, as fight after fight ends with a grappler applying a submission hold to his opponent, often with neither suffering more than superficial damage. This is in contrast to the flashy styles of fighting popularized in movies and television, as well as to the expectations of fans of boxing. . . .

What can I say? This is great stuff.

P.S. On an unrelated note, I read this entry on Bayesian statistics by Hsu where his commenters discuss probability and quantum mechanics, to which I replied (after a brief email exchange):

My take on all of this is that probability is a mathematical model. In some settings, such as quantum mechanics, the model is extremely accurate; in other settings, such as medical imaging with radioactive tracers, the model is pretty damn good; in other settings, such as genetics, it’s not bad at all; in other settings, such as political science and sociology, a probability model might be ok or it might suck. Practicing statisticians are almost always working in the realm in which models are only approximate and must be assessed using prior information and data (as we discuss in chapter 6 of Bayesian Data Analysis).

A statement such as “a Bayesian’s opinion may be of great interest to himself, and he is surely free to develop it in any way that pleases him; but why should the results carry any weight for others…” is, in my opinion, contentless snark and is easily answered in a similar vein. For example, in most statistical models, much much more information is carried by the likelihood than the prior, and yet non-Bayesian statisticians have no problem using Poisson regressions, logistic regressions, normal distributions, etc., without any worry about subjectivity. There are serious objections to any statistical method–including Bayesian data analysis–but comments about “subjectivists” don’t make the seriousness cut, as far as I’m concerned.

I think to an outsider such as yourself this must all seem silly. From a practical standpoint, Bayes methods are a way to get more stable estimates–it’s sometimes called “regularization.” Subjectivity has nothing to do with it. But if you are interested in the distinction between different sources of probability, I recommend my article, The boxer, the wrestler, and the coin flip: a paradox of robust Bayesian inference and belief functions.

Which is what got us to wrestling in the first place.

8 Comments

  1. Daniel Lakeland says:

    This epistemic vs aleatory issue comes up a lot in Engineering. Engineers like systems that have well defined mechanistic descriptions, and generally have little use for philosophical discussions. So, when they start putting probability distributions on things like the effective coefficient of friction of a tire sliding on a wet road, they will often go forward with this analysis not thinking much about the implications. I take this to mean that Engineers in the ground state are basically Bayesian.

    However, when they present the work to other engineers, especially those not familiar with the body of Bayesian statistical knowledge, someone will always eventually notice and bring up the epistemic and aleatory issue… It's especially prevalent in risk analysis where Engineering (as a field) is more familiar with frequentist confidence interval / hypothesis testing procedures.

    Testing tires out on a track under various conditions represents different random realizations of a tire-sliding system. But surely the (effective) coefficient of friction during this particular accident had some particular value for the particular tire and road combination… In what sense is the coefficient subject to a probability distribution etc… is a common type of conversation.

    In Engineering this kind of question is maybe even more important than in social sciences because there is a definite sense in which the models we build are relatively close to the "true" (causal) model at least compared with say models of voting behavior.

    For an Engineer to hear that we have a good model for how tires slide on the road, it's that the coefficient of friction is normally distributed N(.8,.15) can be a little unnerving.

    When engineers build a model involving some highly uncertain phenomena, such as what is going on deep under the ground, it is possible for the model to be mechanically wrong, but yet believable, because the large amount of uncertainty in the systems masks the failure of the model to account correctly for the "deterministic component".

    I think in this sense Bayesian methods can be a useful way to show that one model is better than another. For example:

    Model 1: f(a,b) + e = Observed data
    Model 2: g(c,d) + e = Observed data.

    If Model 1 has bad physics describing the problem, it may have uncertainties spread evenly between a, b and e… This is because the model assumes a, b are constants, but the physics is wrong so they actually vary causing the apparent uncertainty.

    Model 2, with a better physical basis, has small uncertainties on c,d and large uncertainty on e. The total prediction error is the same in some sense, but we prefer models whose deterministic component is well described.

    This kind of issue is very prevalent in earthquake attenuation relations (prediction methods for estimating how strong the ground will shake based on various observable variables like distance to fault, type of soil etc). Many people estimate these regressions and engineers often compare based on who has the smallest residual sigma… adding lots of variables can reduce your sigma, but in a bayesian analysis does it really reduce your overall uncertainty in prediction? Uncertainties in model coefficients matter and can tell us about how well our models fit.

  2. Ahmad says:

    Naturally, no boxer would be caught without any gloves. But gloves as Boxing Equipment don’t all fall into one generic category. There are speed bag gloves, heavy bag gloves, and sparring gloves that all boxers have to use at some point.

  3. Kieran says:

    However, thanks to the recent proliferation of "No Rules" or "No Holds Barred" (NHB) fighting tournaments, both in the U.S. and abroad, we finally have some interesting answers to this ancient question. … In its modern incarnation, NHB fighting is one of the most exciting new sports to hit the market. It has a small but rapidly growing pool of fans and practicioners, despite its undeserved reputation for being bloody and dangerous. [Boxing's] prohibition against grappling creates an unrealistic environment …This lesson has been re-learned in the NHB context, as fight after fight ends with a grappler applying a submission hold to his opponent, often with neither suffering more than superficial damage. This is in contrast to the flashy styles of fighting popularized in movies and television, as well as to the expectations of fans of boxing.

    But of course "NHB" is not rule-free at all. You can't gouge the eyes of your opponent, for example, or try to pull their ears off, or bite them.

    On the highly ritualized nature of fighting in general, and the difficulty of killing people close-up, Randy Collins's recent book Violence contains some very interesting material.

  4. steve hsu says:

    In the early days of NHB (particularly in Brazil) eye gouging and biting were more common. Those tactics shifted the dominant strategies a bit, but mainly only affected grappling. (It is very hard to gouge eyes in real striking.) In a famous fight, one of the Gracies (Ryan?) was gouged by his opponent. Being the superior grappler, the Gracie obtained a superior position and bit off most of the ear of his opponent. I have this on tape so it is probably also somewhere on YouTube…

    The Collins book is discussed here:
    http://infoproc.blogspot.com/2008/02/humans-bad-a

    He is correct that most people are not efficient at fighting or killing.

    However, anyone with modest skill at judo or jiujitsu can kill their opponent easily. I've choked training partners into unconsciousness on many occasions when they kept resisting and didn't tap out. Keep in mind it's a blood choke (carotid artery) not an air choke — it only takes 5-10s to put someone out.

    One big lesson of NHB is that theory sucks and experiment rules. People had all kinds of theories about what would be effective in a fight, and many of them (kung fu masters, karate world champions, boxers, etc.) had egg on their faces once real fights happened.

  5. Andrew Gelman says:

    Steve: Thanks for the info. This is fascinating!

  6. Kieran says:

    However, anyone with modest skill at judo or jiujitsu can kill their opponent easily. I've choked training partners into unconsciousness on many occasions when they kept resisting and didn't tap out.

    Collins's point is not that it's mechanically difficult or complicated to do things like that, but that in everyday face-to-face violence people are much more inclined to make a bunch of noise and find a way to back down after some initial encounter, unless there is a big advantage in strength or numbers on one side. This includes the case you mention, when of a person with a relatively more skill habituated by repetitive training can overcome an less well-trained opponent.

  7. Keith O'Rourke says:

    Glad this info was posted – I have used the picture from your paper often but suggested there would be strong prior info – somewhere.

    In lingusitics there is a claim that you can't make a meaningless grammatically correct sentence – someone will always be able to make sense of.

    Perhaps for any "meaningful" question someone will have some prior info about it.

    Really liked Steve's point about experiment ruling over theory (yes we are always wrong).

    Keith

  8. @Daniel Lakeland:

    Some engineers are very sophisticated about probability and statistics, no matter how little they initially know about the system they're given to study, model, and change.

    Others, alas, aren't.

    One thing I'd encountered among some is little sensitivity to or use of meaures of variability in estimates and results. Sensitivity or perturbation analyses are not well known or practiced, and they should be. Statistical variability is viewed as a nuisance. People want to get rid of it by DOING SOMETHING as quickly as possible. They may understand sampling variability and notions of variability in measurements, but, then, seeing how the result of a calculation varies as a result of variation in inputs is a foreign, inconvenient, and difficult notion.

    I think in these latter cases there's a lot that can be done to teach methods and techniques well shy of worrying about philosophy. Data is data. Now how to MOTIVATE such a class or why it should be taught may be tough. I'm often stuck trying to do so, when people ask, "Okay, WHAT will I gain if I learn this stuff on the problem I'm working on *right* *now*?"

    I'm often stumped with that.