Re: [HOE] Cheap trick to avoid telling posse AV's

[Matt Crawford <matt@severian.chi.il.us>]

I don't see why there was spoiler space, but ...

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> For heavy armor: For each AV of 1 increase the thing's size
> by 1/2 its original size for the purposes of taking wounds.

That's not to bad an approximation *if* the damage dice started as
d20.  If they were less, this cuts down the damage way too fast.

Look at the stats.  Of course, everyone knows that the average
open-ended roll of a single N-sided die is A = N(N+1)/2(N-1).
Multiple dice simply multiply the average result (which is not the
case for aptitude or trait checks).  Fewer, perhaps, know that the
variance of the single-die result is V = N(N+1)(N^2+7N-2)/12(N-1)^2.
Multiple dice also raise this in proportion.  The square root of the
variance V is the standard deviation, S, and has a more familiar
significance: roughly 2/3 of the time the result will be within plus
or minus S of the average.  95% of the time it will be within 2S.
The standard deviation of the result of multiple dice grows as the
square root of the number of dice.

Here's a table (rounded to the nearest 0.1):

 N       4       6       8      10      12      20
 A      3.3     4.2     5.3     6.1     7.1    11.1
 S      2.8     3.3     3.8     4.4     4.9     7.2

So approximating the effect of AV1 on d20-class damage by multiplying
by 2/3 (equivalent to using a target "size" 50% greater) is pretty
darned close.  But for greater AV it is not so good.  For smaller
initial dice, the approximation is quite poor.

You could derive a muliplicative correction factor from the middle
row of the table, but that would drive the damage a little "too
close" to the average compared to actually rolling the smaller dice.
Still, this isn't Squad Leader, is it?