Manifest Of the Cult of Stat-Normalization?

[DrTemp]

Originally Posted by Flyndaran

Is there a pamphlet that I can peruse?

Excellent question. Is there? Should we write one? Something like:

The stats in GURPS are meant as most people having 10 in a given attribute - most, which means, more than half. Take a group of 100 people, and at least 51 will have a score of 10, not more, not less.

Additionally, the remaining, higher attributes will be increasingly rare - while another 20% might have score 11, only 5 or 10% might have 12, etc.

Hm. Does not look complete. Additions?

[whswhs]

Originally Posted by DrTemp

Excellent question. Is there? Should we write one? Something like:

The stats in GURPS are meant as most people having 10 in a given attribute - most, which means, more than half. Take a group of 100 people, and at least 51 will have a score of 10, not more, not less.

Additionally, the remaining, higher attributes will be increasingly rare - while another 20% might have score 11, only 5 or 10% might have 12, etc.

Hm. Does not look complete. Additions?

If you're trying to imitate the actual Gaussian distribution of a lot of human traits, saying "most people will have 10" is dead wrong. Rolling 3d6 is already enough to take you close to a Gaussian distribution; you can approximate one by rolling the traits of the general population at random—in which case 27/216 will have a score of 10 on a given trait, or one in eight, or 12.5%. If you want to get in the neighborhood of "half," what you want to say is that 50% of the general population will have a score of 10 or less.

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. At the other extreme, I don't think most stat normalizers would be happy with one person in twenty having IQ 16-18.

In any case, whatever distribution you adopt for the general population need not apply to player characters. Pretty much by definition, player characters are exceptional.

I am probably a stat normalizer by basic inclination. At least, I worked with such an approach when I was contributing to GURPS Who's Who. But I didn't try to make a bunch of notable historical figures fit onto a Gaussian distribution. What I did was more in the way of making their stats exceptional to the minimal degree needed to describe them: an 11 or 12 would become visible over time to anyone who knew the person, a 13 or 14 was obvious and would be a big influence on the person's life and career choice, and a 15 or 16 was rare and extraordinary, while anything beyond that was almost unheard of.

Bill Stoddard

[Gavynn]

I'd like to hear more from the stat normalizers. I *think* I fit into the category, but am not sure. Great point about IQ. What are the stat ranges of the normal human population if you assume a Gaussian distribution?

[whswhs]

Originally Posted by Gavynn

I'd like to hear more from the stat normalizers. I *think* I fit into the category, but am not sure. Great point about IQ. What are the stat ranges of the normal human population if you assume a Gaussian distribution?

There is no established translation between the IQ that psychological tests measure and GURPS IQ. However, for the IQ that psychological tests measure, the usual convention is that mean is 100 and one standard deviation is ±15. On a roll of 3d6, mean is 10.5 and one standard deviation is 1.71 (standard deviation of 1d6) x 1.73 (square root of 3) ~ 3.0. So if GURPS IQ and psychological test IQ measured the same thing (which they do not), p.t. IQ = 5 x GURPS IQ + 47.5. The lowest sapient GURPS IQ would then translate to 77.5, whereas IQ 18 would translate to 137.5. That's a fairly narrow range.

Bill Stoddard

[martinl]

If we're talking bell curves and The Cult, I'd summarize the position as this:

GURPS stats (with the possible exception of ST) are distributed roughly in a bell curve with a sigma of one. (This applies to healthy young/middle aged individuals, not kids or old people, who have different means).

This gives the following stat distribution in the population:

7- 0.1%
8 2.1%
9 13.6%
10 68.2%
11 13.6%
12 2.1%
13+ 0.1%

Practically, this means that a stat difference of 1 is significant, a difference of 2 is obvious, and a difference of 3 or more is extraordinary.

The most co-ordinated person from a random sample of 10 will have DX 11.
The healthiest person in a medical study of 250 folks will probably have HT 12.
The smartest person in your 1000 person high school is IQ13.

Further numbers - one reason I dislike the bell curve for practical Cult apps is the far stats:
14 0.003%
15 0.00003%
16 0.0000001%
17 0.0000000001%
(etc)

I personally prefer to skip the annoying tables and oversharp tail off for:

10: 78%
11: 10%
12: 1%
13: 0.1%
14: 0.01%
.
.
.

This is easier to remember and makes estimating how rare a stat is easy.
Smartest person on Earth? Somewhere between 1 in 10^9 and 1 in 10^10, so IQ19-20. Works out nice.

That said, no one says you have to follow The Cult. Really, IMHO, it is mostly useful to make GURPS Mundane Folks work out better. If, like most gamers, you play GURPS Wild Crazy Far Out Heros, just don't worry about it.

martinl

[Qoltar]

Originally Posted by martinl

........
That said, no one says you have to follow The Cult. Really, IMHO, it is mostly useful to make GURPS Mundane Folks work out better. If, like most gamers, you play GURPS Wild Crazy Far Out Heros, just don't worry about it.

martinl

I want that supplement or pdf.

There really should be something called -

GURPS:Wild Crazy Far Out Heroes

Heck, my campaign may someday turn into that if I'm not careful.
Then again, that could be fun.

- Ed Charlton

[Gudiomen]

Originally Posted by whswhs

There is no established translation between the IQ that psychological tests measure and GURPS IQ. However, for the IQ that psychological tests measure, the usual convention is that mean is 100 and one standard deviation is ±15. On a roll of 3d6, mean is 10.5 and one standard deviation is 1.71 (standard deviation of 1d6) x 1.73 (square root of 3) ~ 3.0. So if GURPS IQ and psychological test IQ measured the same thing (which they do not), p.t. IQ = 5 x GURPS IQ + 47.5. The lowest sapient GURPS IQ would then translate to 77.5, whereas IQ 18 would translate to 137.5. That's a fairly narrow range.

Bill Stoddard

Narrow and wrong, I score around 136, and let me tell you my IQ is like 11, 12 at most. GURPS IQ measures a certain set of abilities, IQ tests measure another set, they are not directly associable. Depending on the test you're evaluating logical, mathematical, verbal, memory power and academic knowledge. GURPS IQ also measures knowledge, know-how, mental flexibility, open-mindedness, intuition, empathy, and a fair lot of other mental and mental-relational skills that aren't covered in most (if any) IQ tests. IQ tests also measure skills, a person who's used to solve logical problems is more likely to get a good score in logical problems of the IQ test. Doesn't mean that knowing wich of the 4 figures is missing is actually usefull in real-life.
IQ test problems are fairly straight-forward, standardized, normalized and built so you can find a solution. Real life is much, much more chaotic. There are tons of irrelevant data that comes with everything, part of GURPS IQ is filtering that to get to the core of the problem. Most of the time you don't have enough information and have to act on probability you instinctly calculate, not cerainty. And sometimes God just throws the dice right into the black hole.
While it is safe to say that someone with a big IQ score IRL might have a higher IQ in GURPS, it's not absolutely certain, as that sort of score is just one of the atributes of GURPS IQ. Formulas will not work, because we don't have, and probably can't have, all the factors of GURPS IQ pinned down.
I say this as both a gamer and a psychologist. Real life doesn't find much use for IQ tests too, americans seem to be fixated on it, most other countries in europe and south america have left it to very specific uses and the population couldn't care less what your IQ is, that includes companies that are looking to hire, universities looking for teachers, etc...

[whswhs]

Originally Posted by Gudiomen

Narrow and wrong, I score around 136, and let me tell you my IQ is like 11, 12 at most. GURPS IQ measures a certain set of abilities, IQ tests measure another set, they are not directly associable. Depending on the test you're evaluating logical, mathematical, verbal, memory power and academic knowledge. GURPS IQ also measures knowledge, know-how, mental flexibility, open-mindedness, intuition, empathy, and a fair lot of other mental and mental-relational skills that aren't covered in most (if any) IQ tests. IQ tests also measure skills, a person who's used to solve logical problems is more likely to get a good score in logical problems of the IQ test. Doesn't mean that knowing wich of the 4 figures is missing is actually usefull in real-life.

Please note that I pointedly said that GURPS IQ could not be equated to psychological test IQ before talking about the statistical analysis. Everything that followed was conditional on a false-to-fact supposition. So it's kid of silly for you to go to all that effort to refute something that I made a point of not saying, and to insist on points that I already granted.

The point I was making was quite narrow: If you roll 3d6, they have a certain statistical distribution that conforms fairly closely to a Gaussian normal distribution and that has a computable standard deviation of around 3.0. The resulting translation of p.t. IQ into GURPS IQ further evidences my claim in a previous post that "that literal a translation does not really work for GURPS, and indeed cannot."

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

[dscheidt]

Originally Posted by whswhs

There is no established translation between the IQ that psychological tests measure and GURPS IQ. However, for the IQ that psychological tests measure, the usual convention is that mean is 100 and one standard deviation is ±15. On a roll of 3d6, mean is 10.5 and one standard deviation is 1.71 (standard deviation of 1d6) x 1.73 (square root of 3) ~ 3.0. So if GURPS IQ and psychological test IQ measured the same thing (which they do not), p.t. IQ = 5 x GURPS IQ + 47.5. The lowest sapient GURPS IQ would then translate to 77.5, whereas IQ 18 would translate to 137.5. That's a fairly narrow range.

I take the mean to be IQ/DX 10, SD ±1. That puts 2/3 of normals with IQ/DX 9-11, 95% IQ/DX 8-12, and 99.73% 7-13. I don't actually think it's a normal distribution, though. Variance above the mean is much higher than variance below it; and there's not a real cap on values, though there is a floor.

ST and HT are different, with a much larger range of normal human values.

[Agemegos]

Originally Posted by dscheidt

I take the mean to be IQ/DX 10, SD ±1. That puts 2/3 of normals with IQ/DX 9-11, 95% IQ/DX 8-12, and 99.73% 7-13. I don't actually think it's a normal distribution, though.

Of course not. The normal distribution is continuous.

Variance above the mean is much higher than variance below it

'Variance' is technical term from statistics, and it is defined only for the whole of a distribution (ie. as the probability-weighted sum of the squares of the deviances). I think you mean that the distribution has a "long right-hand tail" or that it has "negative skewness". But I can't be sure.