Standard deviation on Stat distribution?

[Polydamas]

Originally Posted by aesir23

Even though it is not official doctrine, some guidelines around how common certain scores are in your world can be very helpful for players trying to determine their characters attributes.

Outside of ST (which deviates much more from person to person), I use something like:

11 = 1 person in your clique or immediate family is this smart/agile/fit. (Or 1/10)

12 = 1 person you know well is this smart/agile/fit. (or 1/100)

13 = 1 person you've met is this smart/agile/fit. (or 1/1,000)

14 = 1 person you've heard about is this smart/agile/fit. (or 1/1,000,000)

It all depends on how you feel about stat normalization. In a high point total pulp game, all of these go out the window in favor of larger than life heroes who are better at everything.

One problem with that is that it depends on your background. A teenager is less likely to know anyone with really high attributes; a grad student in a good program is likely to know lots of high IQ + Talent people; someone who does Iron Man competitions will know lots of people with high ST, HT, and Fit, ...

[roguebfl]

Originally Posted by Polydamas

One problem with that is that it depends on your background. A teenager is less likely to know anyone with really high attributes; a grad student in a good program is likely to know lots of high IQ + Talent people; someone who does Iron Man competitions will know lots of people with high ST, HT, and Fit, ...

While I agree with in general I totally disagree with your teenager. Teenage have adults in their lives. Parents, Friends of the Family, Mentors etc.

[hal]

Mind you, my perspective on this isn't neccessarily math driven, but I'd like to point out WHY some people are driven to use math and realism combined with regards to GURPS...

Can we measure the speed of individuals? Yes. Can we measure how much mass they can pick up? Yes again. Can we measure statistically how often a given population will die off of a given disease during a plague? Yup. Can we measure the size of a bullet, its velocity, and determine how much kinetic energy it has? Yup. Can we even measure real life performance in a swing of a given individual, and translate that into math?

The answer is yes on all counts, and many many more not even specified above. The problem lies in part, being able to define what means what - and as Kromm has mentioned, this has never been done with any level of intent per se, but only in what seemed to work overall.

Take another example. If you have an IQ 8 individual attempting to study a skill until they are "professional" capable of succeeding in their use of said skill, the individual has to dedicate (assuming 1 character point equals 200 hours of study) a total of 16 x 200 hours or 3200 hours. An IQ 10 person, needs only 8 points, or 1600 hours of study. An IQ 12 person, needs only 2 character points, or 400 hours of study. So what does that mean in game terms as far as human reality? Darned if I know, nor would I even TRY to say that this indicates that an IQ 12 person learns things at a rate of 4x faster than someone of Average IQ (10 in this case), nor would I even try to indicate that an IQ 12 person learns things at a rate that is 8x faster than someone with an IQ of 8. Why, because to me, it doesn't even come close to directly mapping on a one for one scale between game reality and reality itself.

GURPS, because it is a 4 stat system, can't really begin to simulate reality. Were IQ to be broken down to Reasoning, Memory, Mental Will, etc - and were ST to be broken down to upper body strength, lower body strength, fatigue, endurance, mass, etc - can we really say that it closely describes reality?

<shrug>


So, what is stat normalization? What is the purpose of stat distribution methodology? If handling flawed concepts to start with, what is the purpose of trying to use statistics to describe that, which is flawed to begin with, and will only compound the flaw the more you walk down a given path of saying how many people are described by a given flawed description?

Heck, how many of us as GMs have ever wondered at the true meaning of IQ stats in GURPS as they apply to real life? How many people do you know, who are book smart but just not very wise? How many people do you know, who have an iron will, but never really excelled at math or history, or - well, anything cerebral?

Ah well, I digress.

[Langy]

ATTRIBUTES
I like p. B14 well enough, but I might add some more categories:
6 or less Crippling (literally -- you can't live a normal life)
7 Poor (you can life a normal life, with care, but never be an adventurer)
8-9 Below Average (low side of able-bodied, probably the lowest an adventurer should ever have)
10 Average (most scores for most people)
11-12 Above Average (high side of able-bodied, probably a good average for adventurers)
13-14 Exceptional (highest you'll likely meet on the street, above average for adventurers)
15-16 Amazing (highest you'll likely see or hear about, strongly defines an adventurer)
17-18 Legendary (historical "bests" and remarkable fictional heroes)
19-20 Mythic (astounding even among great heroes in fiction and folklore)
21 or more Superhuman (off-limits to humans, barely suitable for great heroes, okay for deities)

I like this a lot. It makes the 17-18 group have only a few people in the planet (which sounds a hell of a lot more reasonable than there being 6-7 people with stat-20 around today, which is so high they're experts at almost anything they even attempt, much less actually study for), and it describes things rather well.

In an earlier, somewhat contentious thread, it is demonstrated that the values given on p. B14 establish a standard deviation of about 3 attribute points

That can't possibly be right. Look at the effects of what stat-16 or higher gives you. That's only two 'standard deviations' by your method - two standard deviations is approximately 95% of a normal population, so 2.5% of the population would have better than a 16 in any stat. That's crazy talk right there.

Besides, saying 'most people have between 7-13' just means the standard deviation is probably something less than three. Three is approximately the maximum, not the actual value. The standard deviation could be 1, leaving 9-11 as 65%-ish, 8-12 95%, 7-13 99.5%, etc., and those are still 'the majority', because 99.5% is still greater than 50%.

[MagiMaster]

A standard deviation of 2 would still give 0.5% above 16, or about 35 million people. A normal distribution probably isn't the way to go though, since it's pretty obvious that the distribution will be skewed. There's a minimum of -4 but a maximum of +10 (roughly).

Originally Posted by Gizensha

My take on 'average' was simply 'The typical protagonist in a story' and for the 8-12 stuff 'It is unremarkable for a protagonist in a story to be...' (So it's at DX13 that 'agile' would become a Big Adjective of the person)

Adjectives for a fictional protagonist is probably a good way of describing things.

[jeff_wilson]

Originally Posted by Gizensha

My take on 'average' was simply 'The typical protagonist in a story' and for the 8-12 stuff 'It is unremarkable for a protagonist in a story to be...' (So it's at DX13 that 'agile' would become a Big Adjective of the person)

The only problem with this is that protagonists are a minority of the characters appearing in most plots. Being GURPS, lots of non-protagonists characters aren't human, but lost of them *are*, and in my experience they tend to be less exceptional than protagonists, so GURPS' "average human" would seem to be relevant to them, too.

[jeff_wilson]

Originally Posted by Langy

That can't possibly be right. Look at the effects of what stat-16 or higher gives you. ...
Besides, saying 'most people have between 7-13' just means the standard deviation is probably something less than three. Three is approximately the maximum, not the actual value. The standard deviation could be 1, leaving 9-11 as 65%-ish, 8-12 95%, 7-13 99.5%, etc., and those are still 'the majority', because 99.5% is still greater than 50%.

If you care to follow the links back to the original discussion, you can see the conditionals and caveats with which I addressed the issues you bring up here, but did not include in my subsequent references for the sake of brevity, like "standard dev no more than 3" which includes your case above.

2.5% of attested GURPS humans having a given stat of 17 or more might be too many, but in my experience it isn't ludicrously too many.

[Langy]

2.5% of attested GURPS humans having a given stat of 17 or more might be too many, but in my experience it isn't ludicrously too many.

What kind of games do you play? Exclusively high-cinematic superhero campaigns where everyone has a superpower?

2.5% of humans having a stat of 17 or higher is ludicrous. Actually look at what that means, mechanically speaking. It pretty much makes you near-professionally competent at anything you try at default. That's really unbelievable for 2.5% of the population.

People that omni-competent are rare, not everywhere you look. And yes, 2.5 people out of every hundred is everywhere you look. You're expected to find at least one person with a stat over 17 in an average classroom, not just an average school. That's crazy!

[sir_pudding]

Originally Posted by Langy

What kind of games do you play? Exclusively high-cinematic superhero campaigns where everyone has a superpower?

2.5% of humans having a stat of 17 or higher is ludicrous. Actually look at what that means, mechanically speaking. It pretty much makes you near-professionally competent at anything you try at default. That's really unbelievable for 2.5% of the population.

People that omni-competent are rare, not everywhere you look. And yes, 2.5 people out of every hundred is everywhere you look.

It seems plausible if you restrict it to ST.

[Langy]

Only half-plausible at that. I'm not sure ST17+ is all that common - there was a thread recently that pegged the world recordholder for ST at 18 or thereabouts, with reasonable use of Extra Effort and Lifting skill (while the unreasonable version had the world's strongest person have a ST of 12 or so).