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# Fantasy Armor Errata

In an earlier post I jokingly included the following relationship to describe the apparent formula for determining the quality of female armor in fantasy art.

Unfortunately as I examined it, I realized how flawed the mathematics were.  The units were not meaningfully defined or definable; cup size is related to the character, not her clothing; and nudity would be the ideal armor.

By the relationship above, female armor can be optimized by having a woman try to wear nothing but a pair of earrings that are on fire and fall off under their own weight.

I intend to make up for some of my mathematical laziness below.

Upon careful inspection of the literature I resolved two main factors that seemed to influence the apparent likelihood of a woman being injured while wearing her armor in a fantasy setting: The amount of skin exposed (x) and the likelihood of having a wardrobe malfunction (m)

It also became clear that these were not simple linear relationships. Women in full armor seemed to do better than those in generic uniform half-plate and there were very few examples of anyone going out completely nude with any success.  Likewise, quality seems to increase as chances of nipple-slips and self inflicted wounds goes up, but it peaks around the modern lingerie area. In the physics defying area beyond, there are fewer successful combatants.

I was able to fit a fourth order polynomial to each of these observed trends and the final quality rating is the product of the two. The formula is as follows.

Where Q represents the apparent quality of the armor, x is the proportion of skin exposed and m is the probability of a wardrobe malfunction. This equation can be plotted as a three dimensional surface:

Let’s break down some points of interest here:

Actual Full Plate: At the 0,0 mark we have what would be fully functional full plate armor. It is rare to see any woman wearing this in fantasy art, and rarer still to find them winning any fights in it. It’s not the worst thing in the world though.

Soldier Valley: The lowest of the low are uniformed soldiers. Functional armor without decoration or flare, covering the vitals but leaving the face, hands and parts of the arms exposed. These tragic women are better off with a red shirt and a phaser.

The Sauron Effect: There is a certain point where armor is so bad-ass looking that it doesn’t matter who’s inside of it. There are so many spikes and horns and capes and chains that the wearer is clearly death incarnate. Unfortunately death incarnate tends to bite it in the end if they’re up against a pretty girl with a push up bra.

The Nudity Rift: Naked is still naked. Not wearing armor means that the survival rate of the combatant relies on their skill alone. However, the hastily grabbed bed sheet held such that the viewer sees nothing that would warrant an R rating is a near impregnable defense and thus this inexplicable outlier yields some defensive value in the naked warrior.

Steelkini Zone: This area is particularly popular with live-action fantasy. They’re still showing a lot of skin, but because the design is effectively a shiny sports bikini, it keeps everything contained and therefore safe for general consumption.

Push-up Peak: If you go by comic books and video games, this is the best thing for any woman to wear. It’s sexy lingerie made of metal. The only useful effect that this armor could actually have is that their opponent wouldn’t take them seriously. Honestly, who would even think of fighting in something that they’re going to fall out of or cut themselves on the moment they did anything the least bit acrobatic.

Epoxy Required: Abandon physics all ye who enter here. This is where the silliest armor is found. It’s the stuff that couldn’t possibly stay on without glue and tends to expose all of the most fatal bits of the body while barely covering the minimum standards for decency. This,  though, rarely seems to have a negative impact on the performance of the wearer.

Thank you for your patience and forgiveness in my lack of initial mathematical rigor.

1. {Looks down at his strongly worded letter to the Mad Art Lab peer review board.}
{Looks back up at the computer screen.}
{Briefly considers using the paper to start learning origami.}
“Damn.”
{Drops paper in the recycling and goes back to work, once again dazed and amused by the talent to be found in wilds of the interwebs.}

2. @coelecanth COTW

3. You have reminded me how much I love the universe.

4. Thank you for going the extra mile and replacing a slapdash mathematical gesture with the real thing.

5. @breadbox, I had to do it. The potential for a “divide by zero” error kept me awake at night.

6. It seems like there are 3 factors at work along each axis. Common sense, fantasy, and the point at which disbelief can no longer be suspended. First two are monotonic, and the disbelief can be modeled as a sigmoid. So I fit the above equations to such a model, and got the following.

Q = [0.38(1-x)^3 + 11.29x^3 * tanh(0.89(1-x))]*[0.36(1-m)^3+0.63m * (2.42 + tanh(3.78(0.70-m)))]

Sigmoid for nudity passing through 0 at x=1 seemed reasonable enough, but one for malfunctions clearly needed upper and lower values. The powers for common sense and fantasy were selected to make the fits work.

If there is anything to this line of thinking, I would expect the sigmoids to remain largely constant regardless of how serious particular work happens to be, while the coefficients for increasing and decreasing terms vary, shifting the peaks and valleys.

7. @ksquared, Your function is rather pretty. I like the line of thinking but I have two minor reservations about it:
1: The output of the function does not appear to have been normalized. The maximum quality would be around 1.13 assuming I’ve done my math correctly. Fair enough, the units are arbitrary anyway, but for presentation purposes, having a nice max and min would be ideal.

2: Full, proper armor is a low point on the chart and quality only increases from there. This goes against my observations that full armor is better than moderately full, functional armor. That, though, is only from personal observation and I can’t really claim that it is mathematical truth.

8. Thats.. being a math nerd in the coolest sense of the word. I take the proverbial hat off for you sir.

9. There are a few fantasy artists who illustrate women wearing full armor — Ned Dameron is one (he did a lot of work for TSR in the late 80’s). Also, the ancient Celts went into battle completely naked yet seemed to do alright.