Being a man subject to his vices, I’ve started up again on World of Warcraft. Not the new stuff, the “Classic” servers. “Is that what’s taking up your time?” I hear you all saying, “I had wondered why it was slightly less nerdy and pedantic around here.” Well, worry no more! For the joy and edification of the Ricochet audience, here I reproduce the work I did with the damage formulas. Because a simple post about Warcraft wouldn’t be nearly nerdy enough.
It all stemmed from a simple question; which is better, strength or agility? Strength adds damage, but agility adds some damage as well, and some critical hit chance too. So how do you compare them? You can’t categorically say that one is always better than the other. Well, you can, and people often do. But you can’t and still be right. In a broader sense, how do you decide between two items? Here, let’s go shoe shopping. Which pair of boots do you think goes better with my yellow damage?
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But maybe you’re lucky. Maybe you have a convenient kitchen sink and exciting backsplash tile. If your backsplash tile is laid in a hopscotch pattern, you even have the Pythagorean theorem lurking right behind your sink. To the left is a backsplash much nicer than mine, tastefully tiled in a hopscotch pattern (well, tasteful aside from the peculiar choice of blue grout). To mathematicians, the hopscotch pattern is known as 
Imagine a perfect cube. It could be a perfect cube of cheese, but at this point it’s more helpful to picture the cube as transparent – made of jello, for example. Picture lines inside the cube connecting each corner of the cube to its most opposite corner. The surfaces connecting these lines divide the cube up into six identical pyramids, primordial pyramids. The height H of each primordial pyramid is one-half the height of the cube, so the volume of the cube is (2H)^3. Because six of these pyramids together form the cube, the volume of each pyramid is (2H)^3/6. The base of each pyramid has area A = (2H)^2. Writing the volume of the primordial pyramid in terms of base and height, the volume is 2HA/6 = 1/3 HA. Now suppose we build a primordial pyramid out of that American kitchen staple, cheese singles (very thin, identical squares of cheese food product):
