Attributes Distribution over Populations

[KarlKost]

Originally Posted by Daigoro

Looking through the list on BS p301, pretty much every IQ/Hard skill has an IQ-6 default, from Astronomy to Forensics to Pharmacy to Shiphandling.



Electronics Repair, Explosives, Falconry, Interrogation, Propaganda... all Average with an IQ-5 default. In fact, it's only bioengineer and a handful of other science skills, veterinarian, paleontology, brain hacking, etc, that don't get IQ defaults.

That's screwed up

[whswhs]

There is no indication that GURPS stats follow any kind of statistical distribution, and certainly not a Gaussian one.

[WingedKagouti]

It would seem more reasonable to have the curve range from 5 to 15 instead of going all the way to 20. Anyone with above 15 in a stat has likely spent effort in getting it there instead of it being their inborn/natural state.

[Gollum]

Originally Posted by WingedKagouti

It would seem more reasonable to have the curve range from 5 to 15 instead of going all the way to 20. Anyone with above 15 in a stat has likely spent effort in getting it there instead of it being their inborn/natural state.

Exactly.

Something that has to be understood with GURPS rules is that the system is intended to allow to play harshly realistic characters as well as cinematic ones or even super heroic ones … with the same rules!

Thus, the scale from 1 to 20 is not just designed for realistic humans, but for all humans, no matter the genre: historical ones as well as crazily above average ones. Einstein, Dr Octopus, Walter O’Brian in the Scorpion TV series (who knows everything about everything much better than most experts), and so on.

So, if he or she wants to remain in the realistic limits of our world, the GM has to be very careful about the upper limits of basic attributes. A 16 in IQ allows to know everything at level 10 or better (an amateur level). An 18 allows to know everything at level 12 or better (a professional level). And a 20 allows to know everything at level 14 or better (an expert level). Ditto for DX. A 16 or better is the score of Lara Croft and all these cinematic heroes who can pilot every kind of vehicles, use any kind of weapons, do any physical feat (swimming, climbing, riding, acrobatics, parachuting …) without having to train. And Ditto for HT (John MacClane) or ST (Conan the Barbarian) …

GURPS authors always refused to say the maximum human realistic limit in all threads which discussed about that topic. And they were right to do so, because it all depends on what we mean when we say “realistic”. Realistic movies? Realistic Novels? Scientific realism? Athletes showed time and time again that the human body (or brain) was able to go beyond what scientist said about human limits. So the realistic attribute cap is left up to the GM and his or her players, depending on the game world and their own conception of what is realistic and what is not.

And playing or meeting a human exception in a realistic world can be fun too. But one, not a dozen. Otherwise, the game is no longer realistic.

Anyway, since GURPS is a system, to be realistic, the GM has to take the default skills into account. It doesn’t mean that the default rules are broken. To the contrary, they are what allows to best understand the attribute scores, and why most of us fall in the 8 to 12 range, 14 or more being really outstanding (the kind of outstanding that everyone notice at first glance).

Then, if you really want to make a realistic attributes distribution over population, you have to choose two caps. A minimum and a maximum. 5 and 15 are good ones, in my humble opinion.

[ericthered]

Originally Posted by WingedKagouti

It would seem more reasonable to have the curve range from 5 to 15 instead of going all the way to 20. Anyone with above 15 in a stat has likely spent effort in getting it there instead of it being their inborn/natural state.

Yeah, one thing that made gurps click for me was realizing that ability scores in D&D are about twice as far from the "average" of 10 as gurps scores are. So a 14 in gurps is an 18 in D&D. That helped me get my scaling right.



Oddly, it also provides the same bonus: +4.

[Varyon]

I know a lot of people like to use the general idea that each point of variance in GURPS stats represents 1 standard deviation. That is, 11 is 1 standard deviation from the mean, 14 is +4 standard deviations from the mean, etc. This doesn't quite work on account of the stuff GURPS looks at not having quite Normal distributions - notably, extremely low stats are generally correlated with severe health issues, as well as simply having such stats being detrimental to survival, so you end up with high mortality (including simply being stillborn/miscarried) at the lower end of stats, skewing things higher. But, it's not a horrible idea, at least if you side with the Stat Normalizers. That instead gives us these numbers:

Score	Probability	Current Population
1	1.02798E-18	0
2	5.05227E-15	0
3	9.13472E-12	0
4	6.07588E-09	47
5	1.48672E-06	11,527
6	0.00013383	1,037,586
7	0.004431848	34,360,121
8	0.053990967	418,591,963
9	0.241970725	1,875,999,027
10	0.39894228	3,092,999,500
11	0.241970725	1,875,999,027
12	0.053990967	418,591,963
13	0.004431848	34,360,121
14	0.00013383	1,037,586
15	1.48672E-06	11,527
16	6.07588E-09	47
17	9.13472E-12	0
18	5.05227E-15	0
19	1.02798E-18	0
20	7.6946E-23	0

Note "En" should be read as "x10^(n)"
Also, the Current Population column represents how many out of 7.753B people (what Google gave as current would population) would have said scores, if the distribution is correct (rounded to the nearest whole person).

That puts "1 in a billion" somewhere between 16 and 17 (closer to 16). If you instead want an attribute of 20 to be "1 in a billion," you need a standard deviation of around 1.61, giving the following values:

Score	Probability	Current Population
1	4.05971E-08	315
2	1.07803E-06	8,358
3	1.94635E-05	150,901
4	0.000238928	1,852,407
5	0.00199419	15,460,952
6	0.011316727	87,738,583
7	0.043664632	338,531,890
8	0.11454954	888,102,586
9	0.204320282	1,584,095,149
10	0.247790236	1,921,117,702
11	0.204320282	1,584,095,149
12	0.11454954	888,102,586
13	0.043664632	338,531,890
14	0.011316727	87,738,583
15	0.00199419	15,460,952
16	0.000238928	1,852,407
17	1.94635E-05	150,901
18	1.07803E-06	8,358
19	4.05971E-08	315
20	1.03947E-09	8

[Stormcrow]

Originally Posted by KarlKost

To be fair thou, I did look up IQ distributions, and that may actually not be that far fetched thou.

The GURPS basic attribute "Intelligence," which is customarily abbreviated IQ, does not particularly resemble an "intelligence quotient," abbreviated IQ outside of GURPS. There is no reason to think that GURPS Intelligence has a population distribution anything like that of intelligence quotients.

Intelligence quotient measures an individual's reasoning and problem-solving abilites. GURPS Intelligence measures "creativity, intuition, memory, perception, reason, sanity, and willpower" and also governs your perception and willpower. These are not the same things.

GURPS is not designed as a tool to statistically model anything. A trait like Intelligence is meant to be chosen to represent specific characters, not followed to make predictions about populations.

[KarlKost]

Originally Posted by whswhs

There is no indication that GURPS stats follow any kind of statistical distribution, and certainly not a Gaussian one.

I know. I wasnt basing any of this on any Gurps source, I just thought it might help give an idea on how this could be distributed, so that GMs can make (somewhat) more realistic games.

Regarding IQ, apparently it DOES follow a Gaussian distribution, with a mean of 100 and deviation of 15, so it wouldnt be far fetched to apply that to attributes in general - maybe just modifying it to mean 10 and deviation 1.5 (to adjust to the values between 1 to 20).

I did slighthly adjust my own table a little to get a more smooth scale above 10 and to reduce the really low values (my second table may be a little more realistic for HT, since HT bellow 4 would be very hard to justify reaching adulthood - but the first table might still be worthed for other attributes).

What prompted me to try to do this was the several recent discussions about the practiness of the rules for inventing spells from Gurps Magic, and some exaggerated assumptions (like requiring IQ 20 and Magery 3), so perhaps understanding how insanely rare that would be might help trying to get a better picture of the problem.

I can also take the real world data on IQ distribution, but since that's a table with 200 entries (from 1 to 200) and the only source I found to it placed only the chance of IQ number/above, it means I would have to work the numbers one by one - a task I wasnt all too eager to do, so I went with a Calculator that, sadly, wouldnt give me a precision above 0.00001 (0.001%), but I could try to find another.

Anyway, I know Gurps makes no claims on such distribution, I just thought it's a good tool for GMs to form a picture on how to distribute capabilities amoung a population of NPCs

[Varyon]

Originally Posted by KarlKost

Regarding IQ, apparently it DOES follow a Gaussian distribution, with a mean of 100 and deviation of 15, so it wouldnt be far fetched to apply that to attributes in general - maybe just modifying it to mean 10 and deviation 1.5 (to adjust to the values between 1 to 20).

As others have noted, real-world IQ (Intelligence Quotient) and GURPS IQ (Intelligence) are quite different - the former is something more akin to a "Born Academic" Talent, while the latter includes that, memory, social skills, artistic ability, knowledge skills that aren't part of that Talent, etc, and is also the base for Perception and Will.

But, if you want a distribution with mean 10 and standard deviation 1.5, I've got you covered:

Score	Probability	Current Population
1	4.05059E-09	31
2	1.77087E-07	1,373
3	4.96403E-06	38,486
4	8.92202E-05	691,724
5	0.001028186	7,971,526
6	0.007597324	58,902,053
7	0.035993978	279,061,309
8	0.10934005	847,713,406
9	0.212965337	1,651,120,258
10	0.26596152	2,061,999,667
11	0.212965337	1,651,120,258
12	0.10934005	847,713,406
13	0.035993978	279,061,309
14	0.007597324	58,902,053
15	0.001028186	7,971,526
16	8.92202E-05	691,724
17	4.96403E-06	38,486
18	1.77087E-07	1,373
19	4.05059E-09	31
20	5.9406E-11	0

[KarlKost]

Originally Posted by Gollum

Exactly.

Something that has to be understood with GURPS rules is that the system is intended to allow to play harshly realistic characters as well as cinematic ones or even super heroic ones … with the same rules!

Thus, the scale from 1 to 20 is not just designed for realistic humans, but for all humans, no matter the genre: historical ones as well as crazily above average ones. Einstein, Dr Octopus, Walter O’Brian in the Scorpion TV series (who knows everything about everything much better than most experts), and so on.

So, if he or she wants to remain in the realistic limits of our world, the GM has to be very careful about the upper limits of basic attributes. A 16 in IQ allows to know everything at level 10 or better (an amateur level). An 18 allows to know everything at level 12 or better (a professional level). And a 20 allows to know everything at level 14 or better (an expert level). Ditto for DX. A 16 or better is the score of Lara Croft and all these cinematic heroes who can pilot every kind of vehicles, use any kind of weapons, do any physical feat (swimming, climbing, riding, acrobatics, parachuting …) without having to train. And Ditto for HT (John MacClane) or ST (Conan the Barbarian) …

GURPS authors always refused to say the maximum human realistic limit in all threads which discussed about that topic. And they were right to do so, because it all depends on what we mean when we say “realistic”. Realistic movies? Realistic Novels? Scientific realism? Athletes showed time and time again that the human body (or brain) was able to go beyond what scientist said about human limits. So the realistic attribute cap is left up to the GM and his or her players, depending on the game world and their own conception of what is realistic and what is not.

And playing or meeting a human exception in a realistic world can be fun too. But one, not a dozen. Otherwise, the game is no longer realistic.

Anyway, since GURPS is a system, to be realistic, the GM has to take the default skills into account. It doesn’t mean that the default rules are broken. To the contrary, they are what allows to best understand the attribute scores, and why most of us fall in the 8 to 12 range, 14 or more being really outstanding (the kind of outstanding that everyone notice at first glance).

Then, if you really want to make a realistic attributes distribution over population, you have to choose two caps. A minimum and a maximum. 5 and 15 are good ones, in my humble opinion.

Well, the real world IQ statistic have a probability of 1 to 4 billions and something for someone with IQ 201, there is of course if reality do follow the statisc. This could mean 1, 2, 3 or none people alive with that much cognition. That is more than Einstein or probably any know figure; since the amount of humans that ever lived is counted on 200 billions according to some sources, this could mean some 50 people throughtout history with that amount, and some 20 with IQ 202 (why didnt those became Einsteins? Well, natural selection is not only a matter of fittness, but also of luck. What's the chance that those 70 individuals were born at the right place and at the right time, rather than being one of the many faceless victims of wars, plagues, disasters, or simply born at the stone age etc).

Would you count the single (?) human being alive with IQ 201 to be realistic or cinematic? That insane level of cognition is cinematic to us - but granted, not impossible, even in the real world.

Was Bruce Lee the greatest martial artist to ever live, so maybe the highest DX ever? Well, maybe he were the greatest one that we know of. There could be a handful ones of anonimous people which we will never know about, just like those 70 unkown IQ 201-202 over the entire history.

Anyway, the idea here was just to have a working model - could you EVER find a real IQ17 in a game? Highly unlikely. Doesnt mean that it cant exist, just that if you're looking to hire one, you're probably not going to find one. Also, those IQ 17+ could have a serious disease, be too young or too old, be a monk living under a vow of silence that never leaves his cave, suffer from chronic depression and thus never do anything with their lives, could be simple people content in live, thus enjoy just to milk his cows and is not willing to become CEO of anything nor learn Magic or Psionics - anyway, there's a ton of reasons to why real world DaVincis or Lara Crofts simply decide not to use their gifts in full, and thus are not felt as present as the few exceptions that do.

Originally Posted by Stormcrow

The GURPS basic attribute "Intelligence," which is customarily abbreviated IQ, does not particularly resemble an "intelligence quotient," abbreviated IQ outside of GURPS. There is no reason to think that GURPS Intelligence has a population distribution anything like that of intelligence quotients.

Intelligence quotient measures an individual's reasoning and problem-solving abilites. GURPS Intelligence measures "creativity, intuition, memory, perception, reason, sanity, and willpower" and also governs your perception and willpower. These are not the same things.

GURPS is not designed as a tool to statistically model anything. A trait like Intelligence is meant to be chosen to represent specific characters, not followed to make predictions about populations.

I KNOW that. I know all that everybody is saying. This thought exercize is not meant to reflect real life IQ tests results. I just used those as a basis for creating a math model that could serve as a blueprint. This is designed to give an idea of what could be, not to set it on stone and neither to claim "oh look, so you have X millions of 16 IQ people in the world!".

It's just so people get a brief notion of how ridiculously hard would be for example to find not one but 4 assistants with a rate of 20 in any single specific skill (even if players just "casually" go over 30 or more) for an Invention roll, for instance. And also to help get perhaps a more realistic "distribution landscape".

Values bellow 6-4 or above 16 are still rare enough to be felt as "cinematic" - particularly when you take in consideration that most of those extremes wont always use their gifts (in fact, I suspect most wouldnt). So, an IQ 20 lumberjack could care nothing about building Tony Stark's gadgets, and instead be super happy with his confortable wood shackle and his dog.

Therefore, you find highly competent IQ 16 CEOs, but NOT cinematic IQ 20 ones or cinematic DX 20 athlets - even thou there is a few people with those scores