[Ar-list] Human ranges in AR

[Carter T. Butts]

Matthew Selznick wrote:
> Has anyone done any work on translating character attributes to human
> ranges, where possible?

Yes, in various ways -- some of this is implicit in the suggested 
modifiers found in the PRG, for instance.  The revised firearm damages 
were actually derived by fitting the AR damage rules to empirical 
stopping power statistics; the approach was crude (essentially an ad-hoc 
method of moments fit by heuristic optimization), but servicable.

More generally, the best way to understand attributes is via their 
impact on performance.  Consider a task (any task you like), and call it 
T.  Consider the expected chance of success at T for a person drawn at 
random from the population, on a single attempt: call this p_T0.  Then 
d_T=-IDRF(p_T0) is the difficulty of T.

We can use this to estimate a character's attribute scores, as follows. 
  Let's say that we have a character whose chance of success at T 
(again, on a single try) is p_TC.  Then, it follows that his or her 
relevant attribute (a) must satisfy the relation

    DRF(a-d_T)=p_TC

ergo

    a-d_T=IDRF(p_TC)

and thus

    a=IDRF(p_TC)+d_T.

For instance, let's say that Merlin is attempting to solve an INT based 
puzzle.  Merlin's chance of success on any given try is a fairly meagre 
8%, but this is a lot better than the 5% chance which is typical for the 
population at large!  Following the above, we can see that the 
difficulty of the task must be

    d_T=-IDRF(0.05)
       =198.35

which is pretty substantial.  This is a very hard task!  Now, to get 
Merlin's INT attribute, we simply substitute this into the relation 
given above

    a=IDRF(0.05)+198.35
     =-122.36+198.35
     = 76 (apx)

This is a very high score indeed, but that shouldn't surprise us unduly 
-- for tasks of extreme difficulty, very large attributes are needed to 
show any noticable improvement.  As a practical matter, one is often 
better off trying to find tasks whose base success rates are close to 
0.5.  Such a task has a difficulty of approximately zero, which means 
that a character's attribute will be (simply enough) the IDRF of his or 
her success rate.  (We call these "standard tasks," since they form the 
baseline against which other things are measured.)

In general, it may be helpful to make a list of tasks with increasing 
difficulty, and think about how your character stacks up against those 
tasks...this should give you an idea of where the scores will be.

> 
> If not, I might give it a shot -- it's difficult to conceptualize just
> how much a person with a STR of 1000 can lift, for example.

Well, a person with STR of 1000 has about a 99% chance of being able to 
perform a strength-related task which a typical person could perform 
half the time.  Likewise, he or she would be able to perform a task 
which the typical person could only perform one time in one hundred with 
a 50% chance of success.  This is a pretty tremendous rating, and few 
persons (if any) would be expected to attain it.  Still, it could 
surface in a fantasy setting....

-Carter