Manifest Of the Cult of Stat-Normalization?

[JoelSammallahti]

But where did the 3d roll idea come from? Nobody rolls 3d to get a GURPS attribute.

I decided once that in my campaigns, the attributes are distributed lognormally, with 1 SD corresponding to a factor of 1.15 in DX and IQ and a factor of 1.2 in ST and HT.

[dscheidt]

Originally Posted by martinl

Corollary:
It is often quicker and almost always more efficient to represent talent with high stats rather than acual Talents and other fiddly advantages, especially for adventurers, who need broad areas of expertise.

The other corollary is that for a point or two, your stat 16 person is world class at whatever they choose to be. That's what annoys me. I don't have a problem with that, if you're playing four-color comic book games. In anything that's supposed to be at all realistic -- even if the players are high-powered -- it doesn't make sense. I generally like to play 250 pt characters or so, so they're really good, maybe best in the world, at a number of things. But they're not world-class in things outside their focus.

[Kromm]

Originally Posted by JoelSammallahti

But where did the 3d roll idea come from? Nobody rolls 3d to get a GURPS attribute.

People often assume that since you roll 3d against attribute scores, generating a value between 3-18 for comparison to scores that are generally kept in the 1-20 range, there's necessarily some correlation between the 3-18 distribution and the 1-20 distribution. In fact, there isn't . . . and the game doesn't claim otherwise. The game implicitly assumes a peak near 10 but more scores above 10 than below, a more gradual tail above 10 than below, and a cutoff for adult humans somewhere around 7 below but 20 above. And it assumes all of this for adventuring PCs, making no claims for ordinary Joes, who operate in a different success-roll regime with regular large bonuses for routine tasks.

[whswhs]

Originally Posted by JoelSammallahti

But where did the 3d roll idea come from? Nobody rolls 3d to get a GURPS attribute.

Gavynn asked

Originally Posted by Gavynn

What are the stat ranges of the normal human population if you assume a Gaussian distribution?

Now, "stat" can't refer to an actual human attribute in the real world, whether a straightforward physical variable like height or lifespan, or a psychometric construct like IQ. It must refer to something that exists in the game mechanics. GURPS stats, in particular, are ST, DX, IQ, and HT.

And "assume a Gaussian distribution" calls for something with certain mathematical properties: a bell curve symmetrical about a mean.

GURPS does not provide a statistical distribution for stats; but the implicit one to which Kromm alludes is not symmetrical, and thus cannot be considered Gaussian. But you can approximate a Gaussian distribution by rolling Nd6, where N > 2. (It sort of works for N = 2, but only sort of; a triangle's a lousy bell shape.) Given the range of GURPS scores, has about the right size, though you could do 4d6-4 instead (and get mean 10 and standard deviation 3.4, which would make IQ 0 => IQ 55 and IQ 20 => IQ 145).

Or you could just assign a mean and standard deviation, and forget about dice. But that still doesn't fit the GURPS distribution, in that one standard deviation appears to be more like 1 if you're going down from 10, but more like 2 if you're going up, at least for mental traits.

I usually prefer to treat the matter descriptively, in the form I offered previously.

Bill Stoddard

[LemmingLord]

Originally Posted by whswhs

...Though that literal a translation does not really work for GURPS, and indeed cannot. For one thing, consider IQ. You would have to say that 10/216, or just about 5%, had IQ 5 or less—which is defined as nonsapient: equivalent to mammals (other than great apes) or birds, and incapable of language use. That's a hopelessly implausible model of the human population...

Let's not forget that in the general population there are quite a number of children and lottery participants. ;)

Seriously, though, we really need to consider the population we are looking at for each stat. Older people have a different distribution than younger people. Females have a different distribution than males. Different backgrounds in wealth or poverty; care or abuse, etc...

The distribution on a first world college campus for St, Iq, Dx, and Ht is going to be different than in a third world freedom fighter camp. Expect 10 for 90% 9-11 for 5% and others at 5% in general. Strength may be different since it is quite easy to manipulate. A person in the right circumstances can easily increase their strength (or in other circumstances be quite weak for their own individual range). I'm not so sure it so easy with IQ and Dx.

[Gavynn]

Originally Posted by whswhs

Gavynn asked

I did not think that I implied stats should be generated with 3d6. Infact, the kind of information I was looking for was saying, well, human IQ tends to have a distribution of 7 to 13 and so forth, which was provided.

[the_seeker]

Originally Posted by dscheidt

The other corollary is that for a point or two, your stat 16 person is world class at whatever they choose to be. That's what annoys me.

This has annoyed me enough to ponder a house rule fix, but I've never been satisfied with enough of my alternative to actually use it beyond a simple redefinition of how Default Skill Levels are calculated.

In RAW, Default Skill Levels for [Attribute] 10 are...
Easy (-4) = 6
Average (-5) = 5
Hard (-6) = 4
Very Hard (-7 or worse) = 3 or worse [1]

In RAW, Default Skill Levels for [Attribute] 20 are...
Easy (-4) = 16
Average (-5) = 15
Hard (-6) = 14
Very Hard (-7 or worse) = 13 (or worse) [1]

With a high enough [Attribute], you don't need to spend points in any Skill to be "world class" in that Skill at least as far as routine (TDM +4) tasks are concerned, and you don't need to spend points in Easy/Average Skills to be "world class" even in "used under stress" normal adventuring circumstances. This part can be fixed very easily by calculating Default Skill Levels from half [Attribute] adjusted for difficulty (+1 for Easy, 0 for Average, -1 for Hard and -2 or worse for Very Hard). [2]

HR Default Skill Levels for [Attribute] 10 would be the same.
However, HR Default Skill Levels for [Attribute] 20 would be...
Easy ((/2)+1) = 11
Average (/2) = 10
Hard ((/2)-1) = 9
Very Hard ((/2)-2 or worse) = 8 or worse

That takes care of unrealistic (or at least discomfortingly high) Default Skill Levels. The only question remaining is whether Talents should add to the base [Attribute] before calculating the Default Skill Level or add directly to the Default Skill Level (and I haven't decided for myself because I haven't given the issue enough thought).

Unfortunately, this still leaves the issue of high [Attribute] characters being capable of becoming "world class" in almost any Skill with only a point or two of study/practice (and in several totally unrelated Skills with only a handful of points). For some, this is not a problem. For others (including me), this is a problem.

I grant that I have almost certainly never met a real person with a GURPS IQ of 20, I grant that such a person might not even exist at the moment, and I grant that I probably can't accurately imagine what such an awesome intellect could do, but I'm fairly confident that one point of study would not make him/her equal to the world's current leaders in [Skill].

The "fix" I have wrestled with so far has been buying Skill Levels up from Default, but I'm not sure how far above Default that first point spent should buy your Skill Level. Too far and the result isn't significantly different from RAW. Not far enough and some players will balk at the resulting high price of being "world class" in any Skill.

However, I haven't "run the numbers" so my intuitive concern might actually be completely inaccurate. Judging from many posts I've read in this forum, many people do not perceive Talents as realistic, practical and/or useful. Perhaps buying Skills up from Default would change that if "world class" Skill Levels were expensive even for high [Attribute] characters.

FOOTNOTES

[1] I don't have my books with me at the moment so I might be (and probably am) wrong about Default Skill Levels for Very Hard Skills. There are so few of them, it is probably best to handle them individually than as a class anyway (hence the "or worse" caveat).

[2] I came up with this HR years ago while fiddling with G3E, but I have seen it suggested on this forum more than once. That so many people independently suggested the same "fix" leads me to believe it should become RAW. If nothing else, it seems an intuitive fix.

[Gudiomen]

Originally Posted by whswhs

If you actually take the time to read my various posts carefully, you will find that they reflect a consistent overall view of the matter, which does not actually disagree with your assertions.

Bill Stoddard

Er... I was just adding to your point of how it's not relatable, and pointing out to everybody what some specific points were that prevented relation. And how, in fact, as you say, you're scale doesn't correspond to GURPS IQ, just like real life "general intelligence" doesn't relate to IQ scores. No need to get defensive.
Sorry if it sounded like an attack, I just wanted nail it a bit more. Nothing personal.

[Gudiomen]

HR Default Skill Levels for [Attribute] 10 would be the same.
However, HR Default Skill Levels for [Attribute] 20 would be...
Easy ((/2)+1) = 11
Average (/2) = 10
Hard ((/2)-1) = 9
Very Hard ((/2)-2 or worse) = 8 or worse

Hey! That's pretty good! I might start using this. No matter how agile, nimble, flexible and fast a person is, I'd still expect them to have a hard time at a skill that they have absolutely no knowledge or technique for. Just like a very vigorous person can only keep himself from drowning for so long in a heavy current.
I'll seriously consider using this.

The point about 1cp = enormous skill, well I kind of agree, but that would mess with the values of atributes too much. And a solution is bound to be less elegant than that one for defaults. Does the Cult of Stat Normalization have a webpage yet? :P

[LemmingLord]

I struggle with the problems of being world class in everything similiarly. I went so far as to have all skills built around an attribute of 10. That can have quite a normalizing affect.

If you want a character to have a 15 in karate it costs x. Period. 24 points if you have a dx 10. 24 points if you have a dx 15.

None of this, "well my character is agile so he's better at karate." That's immaterial and antithetical to the genericness factor of GURPS namesake. If you want to be agile, pay the points. If you want to be good at karate pay the points. I don't see why you should get some kind of point break for having attribute/skill synergies.

I don't know what to do about defaults. I suppose if you are willing to have a character with an attribute of 15, you are going to have quite a few skills at 10 or 11 for free.... I tend to limit defaults appropriately. People get a default to many skills - but unless you put points into it, you are "fiddling your way through;" and the quality of your work is going to be lacking in comparison of someone with equal skill with points invested.

In a contest of skills between any two characters, the one with the most points in their skill should win.

In a contest of attributes, the one with the most points in their attribute should win...

If there are factors that require multiple skills; find the primary skill and give someone a bonus for having more points in the other skills.

i.e. st 15 dx 10 karate 15 strongguy is fighting st10 dx15 karate 15 dxguy in a dojo - same points, equal chance to win.

same folks in a bar fight; less opportunties to use speed, the strongguy should have a better shot at "winning" the contest.

same folks in open terrain; more opportunities to use speed, the dxguy should have a better shot at "winning" the contest.