Bizarre yet predictable film cliches

No doubt you have heard of the famous Inverse Ninja Law, which states that in a movie or other work of fiction, the effectiveness of a group of villains attacking the hero is approximately inversely proportional to the number of said villains.

Well, I have a strange anecdote about the discovery of another such cinematic cliche law which we have taken to calling the "Inverse Clothing Law."  I am not the first to notice it, but I may be the first to formulate it mathematically.  Note to the easily offended: this post is only as immodest as your imagination makes it.

Some friends of mine were sitting around watching a kung fu movie on tv when I came in to the sitting room.  On the screen, the characters were engaged in a martial arts tournament.  As I sat down, a man and a woman prepared to face off.  One of my friends declared, "Well, she's going to lose," as if this should be totally obvious to everyone.  When I inquired how he knew, he replied that he could tell because she was wearing too much clothing to be able to win.  I was confused, because she had on a traditional costume designed for martial arts, such as this one.  He informed me that I was thinking about it the wrong way.  Sure enough, her opponent defeated her with the greatest of ease.  Soon after came a match of a man vs. a woman, but this time the woman was wearing kung fu-suit pants and a sports bra as her top.  I was informed that she had a reasonable chance of winning.  And sure enough, she emerged victorious in a close match.  My friends explained that for women (not men) in martial arts movies, the less clothing they are wearing, the stronger of an opponent they will be.  So then I observed with some sarcasm that if a woman engaged in martial arts wearing nothing at all, then clearly she would be unbeatable.  No, my friends replied, if she was wearing nothing at all, she would be very vulnerable and completely ineffective in combat.  So, I came back, it's not really the less clothing she has, it's some other function of clothing area.  They conceded that this was the case. 

So (this is the way that physicists think about things, by the way, at least really nerdy ones) I sketched for them on a napkin the relation between Amount of Clothing A and Martial Arts Effectiveness M.  As clothing amount approaches infinity, martial arts ability approaches zero.  Judging from the ineffectiveness of the woman in the kung-fu suit, the effectiveness M does not really attain a significant level unless the clothing amount A is quite small, at which point the marginal increase in M for a given decrease in A is large, so long as A does not actually reach zero.  And, I was informed, in the vast majority of movies and video games, the women most proficient in martial arts will be very scantily clad.  The function this suggested looked rather like an inverse, f(x) = 1/x:

It then occurred to me that this theory could be further refined.  The 1/x graph seems to be a good rule of thumb, but it does not seem to predict M very well in situations where A is very small.  To wit, in real life, A cannot arbitrarily approach zero, because there will come a point when making A any smaller will at least partially uncover something that should be covered up, causing the vulnerability factor to come into play.  Also, when A is very small, removing even a thread, mathematically speaking, could cause M to increase dramatically, whereas it is more probable that each woman's fighting ability maxes out somewhere. Therefore M has some maximum value which corresponds to a particular (low) value of A.  A good candidate for this function might be the following:

As you can see, as you approach 0 from the right, M increases more and more until it reaches a maximum value at A-nought and then falls off sharply, reaching zero at A=0.  The constants a, b, and c remain to be determined by an experiment which for reasons of prudence I would be highly unlikely to conduct.  Also, although I had to assign one of them to the x axis, it has not been determined which is the independent variable, or if both things are caused by a third thing.

Now, what this has to say about how women are portrayed in the movies is another thing.  A good friend of mine has mused on this curious law over at his blog Theology of the Body in DC.

Comments

[PeterTerp]

And, of course, the same rule might apply fairly well to men as well as women. You don't often see Bruce Lee with his shirt on. Ninja Turtles do pretty well, and they are naked except for belts and masks (whereas the foot clan are completely covered, but are pretty lousy).

It's also worth considering (albeit in a far too earnest way for this topic) that a fighter who is covered up might be more self-conscious of their body, because they are not perhaps as muscular as their rivals.

If you are physically weaker, you would do better to conceal your flab under clothes. If your opponent isn't sure how strong you are, you might still have a chance to bluff your way out of a fight.
At least, that's how I usually choose what I am going to wear on a night filled with confronting ninja in dark alleys.

[John]

This is similar to a general rule in professional football. The home team' chances of winning increase in inverse proportion to the amount of clothing worn by their cheerleaders, and vice versa. This phenomenon would be graphed in an almost identical manner to the phenomenon in your post.

[Neil]

I noticed when I shaved my head I was getting the right of way a lot. Maybe the increased visible skin surface area scared other umd students right off the sidewalk. You might consider that strategy when embarking on dark nights with high probability of a ninja encounter. Or it could have had to do with the tendency of the veins in my body to show through my skin, or the ridges my skull came with. Also it was summer so I was wearing less clothes than in winter, so that could have had to do with the intimidation factor.

It's a good thing I don't get in many fights because it's too cold here to show any skin in order to intimidate the enemies I don't have.