[Classicmerp] GURPS Normal Distribution Curve vs Linear Approaches

[Lev Lafayette]

The 3d6 normal distribution is great when you want results clustered
around an average (e.g., reaction rolls, weapon damage), keeping in mind 
a mean of 10.5 ((min+max/2)) and a standard deviation of 2.958
(sqrt(3)*sqrt((6^2 - 1)/12)).

The standard deviation is important to keep in mind; it's why a simple
"multiply IQ score by 10 to get a real-world rating" isn't accurate, nor
is height-weight multiples from a 3d6/3-18 range either; both are more
heavily clustered around the middle and have longer tails. But as a rule
of thumb, the normal distribution works fairly well.

However in other circumstances it is almost broken, particularly when
you're applying a modifier which ought to be linear. "Almost broken" in
this sense means that it doesn't give impossible results, merely
unrealistic and unfair results. For a game that prides itself on realism
the continued use of 3d6 for many action rolls is inappropriate. I suspect
it has *much* more to do with the game's heritage with its predecessor,
The Fantasy Trip, rather than any "reality checking".

As an example, consider a range/speed modifier of -4 against characters
with skills 18, 12, and 8. What should be the same effect for all
characters ends up being about less than 10% for the skill 18, a whopping
49% for the skill 12 character, and 24% for the skill 8 character. Varying
the effective modifier according to skill level is, in effect, changing
the actual distance that a range attack occurs based on the character's
skill level!

It should also be quickly pointed out that the "diminishing returns"
argument is invalid. The claim that improvements on skill level result in
reduced improvements in ability after an initial big jump is only true for
characters of average attribute scores. A character with a very low
attribute score actually gains a bigger bonus on their second or third
improvement (depending on their rating), and a character with a very high
attribute score does not receive the initial big jump (their default is
already high).

Statistically, a marginal diminishing returns graph on a dual axis
progression simply is not a normal distribution graph. In any case, GURPS
already incorporates diminishing returns with a learning curve in point
costs; 0.5 points for the initial gain, then 1.0, 2.0, 4.0 etc.

Different games do different things better, depending on the design
orientation. GURPS mostly does simulationism quite well, and is innately
quite heavy on the "number-crunching". It isn't that good at the
narrativist approach, although there were hints of it in 4th edition,
albeit poorly executed.

I think Michael's rules of 1 character point to change 1 degree of success
is a good method (basically what is used in HeroQuest), although it is
worth looking at using 2 points to turn a critical failure into a failure
and a success into a critical success (reason: criticals in GURPS are
*harsh*) as per GURPS 4th edition, p347.

The following articles in RPG Review may be of interest:

SLURPS for GURPS by Karl Brown
http://rpgreview.net/files/rpgreview_4.pdf‎

Narrativism for GURPS by yours truly
http://rpgreview.net/files/rpgreview_17.pdf‎



-- 
Lev Lafayette, BA (Hons), GradCertTerAdEd (Murdoch), GradCertPM, MBA (Tech
Mngmnt) (Chifley)
mobile:  0432 255 208
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