From: max@crash.cts.com (Max Callahan)
Subject: Re: Killing Attacks
Organization: CTS Network Services (crash, ctsnet), El Cajon, CA
Date: 12 Jan 93 12:38:22 GMT

t has been my experience that most people just don't understand how
killing attacks work, so here is the math behind them. Capture this file
it's long, and you'll want to have it on hand for later reference as this
flame war goes on
            Champions math 101
            an introduction to damage
For the purposes of this dissertation we are using a 6 DC superheroic game,
and thus 2d6 killing, 6d6 normal and 15 def (def calculated as per page S22
of the champions hard cover). 
Most people believe that to calculate the average of a normal attack you
take 3.5 (the average of 1 die) and multiply by the number of dice (thus
giving 21 for 6d6 normal) this is correct. 
Most people also believe to calculate the average stun of a killing attack 
you take the number of dice times 3.5 (1d6 average) times 2.5 (the average
of one die minus 1, thus the stun mult) this gives 17.5 on 2d6 killing.
This is wrong, as the average for a stun mult is 2.6666 ( (1+1+2+3+4+5)/6 )
This is also irrelevant the probability for damage in killing attacks is
not an additive bell curve as it is for normal attacks, but a
multiplicative waveform instead. When the wave form is computed the mean
average is 14.5 (50% of the time you roll lower, 50% higher).
So what does this mean, this means that 50.463% of the time a 2d6 killing
attack will fail to put any stun past 15 def, while a 6d6 normal will fail
to do stun only 9.401% of the time. This means while you have a 9.722%
chance of doing more stun with a killing attack that you can with a normal
attack, you also 9.722% chance of doing less stun with the killing attack
than is possible with the normal attack. Your chance of doing 12 stun or less
on a 2d6K is 40.272% on 6d6N it is 1.818%
In a 6DC game where a 2d6k attack becomes more likely to do stun than a
6d6N attack is 24 DEF or 4 def per DC (in a 12dc game this would be a 48
def) thus a normal attack will do more stun than a killing attack to the
huge majority of characters.
Now on to body. The average body on  6d6K is 6, the average on 2d6K is 7
however the normal body bellcurve is much more extreme with the chance of
getting a 5,6 or 7 on 6d6N being 72.197%, with the chance of 6,7 or 8 body
on 2d6k being 44.444%, and finally there is a .053% chance of rolling less
body on 6d6 normal than is possible to roll on 2d6K (sort of insignificant,
but I'd be remiss if I didn't mention it.)
So this means that killing attacks do more body than normal attacks (but neither do enough to do body)
The average knockback for 6d6N is -1 inch, for 2d6K -3.5 inches, neither
does knockback on average, but it is less probable for the killing to do
any than it is for the normal.
By now you have either a) hit n, b) had your eyes glaze over, c) or started
saying to yourself "I get it". Well, from here out are the chances to do X
amount of stun on Y dice if you really want to understand the math graph
the following 2 probability waveforms on to the same graph (I didn't fully
grasp the math until I did) 
Stun on 6d6
6   0.00214%
7   0.0128%
8   0.0343%
9   0.0986%
10  0.238%
11  0.497%
12  0.924%
13  1.576%
14  2.456%
15  3.549%
16  4.803%
17  6.121%
18  7.354%
19  8.372%
20  9.047%
21  9.285%
22  9.047%
23  8.372%
24  7.354%
25  6.121%
26  4.803%
27  3.549%
28  2.456%
29  1.576%
30  0.924%
31  0.497%
32  0.238%
33  0.0986%
34  0.0343%
35  0.0128%
36  0.00214%
Stun on 2D6k
(when numbers are skipped it means that they can not occur on 2d6k)
2   0.926%
3   1.852%
4   3.241%
5   3.704%
6   6.019%
7   5.556%
8   6.481%
9   4.630%
10  5.093%
11  1.852%
12  5.556%
14  2.778%
15  2.778%
16  3.704%
18  4.167%
20  4.630%
21  2.778%
22  0 926%
24  5.093%
25  1.852%
27  1.852%
28  2.778%
30  3.704%
32  2.315%
33  0.926%
35  2.778%
36  3.315%
40  3.704%
44  0.926%
45  1.852%
48  0.463%
50  1.389%
55  0.926%
60  0.463%
Max "mathamainac" Callahan