Attributes Distribution over Populations

[KarlKost]

Originally Posted by Varyon

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.

Yes, Gurps IQ is a catch-all trait; that's why I divide it into other attributes (mostly at least 1 social attribute, like Charisma and/or Empathy) in my games, and I also turn Will and Per independent from it.

However, even under RAW you can take "anti-Talents" to simulate incapabilities in certain areas, so if you're the "typical" socially akward genius, you can buy an anti-Talent for social skills and you can "buy down" Will and Per too.

But yes, I understand how limited it is to compare real world IQ tests to Gurps IQ, but it's still a valid workin model

Originally Posted by Varyon

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

Thanks brother! That's really helpful!

[KarlKost]

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 0.21296533 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

Never mind this post guys, I'll delete it shortly, just using this to copy it to my notes, sorry about that

[KarlKost]

Originally Posted by KarlKost

20 5.9406E-11 0

So, with this, and an estimated population for Jan 1 2022 of 7.868.872.451, that would give an amount of 0.46745823682411 "people", or more os less "half-people" with that high amount. Since there are 4 attributes on Gurps, there could be 2 people with 1 attribute lvl 20 (that's highly within the margin of error thou, so it could be 1 person, 100, or none).

I like those numbers.

[Donny Brook]

There is only one IQ 21 person in the world today and I know this because I rolled to deduce it at a -10 penalty and passed with a roll of 11.

[KarlKost]

Originally Posted by Donny Brook

There is only one IQ 21 person in the world today and I know this because I rolled to deduce it at a -10 penalty and passed with a roll of 11.

Hahahahha

Really? I was successful with a Roll of 12. Could this mean something?

On a totally unrelated topic, what would be the odd to critically fail in such roll?

Head hurts... Do the math later...

[Varyon]

Originally Posted by KarlKost

Never mind this post guys, I'll delete it shortly, just using this to copy it to my notes, sorry about that

ProTip - if you need something displayed the way it is on the forums, but don't necessarily want to actually post it, hit the Preview Post button instead of the Submit Reply one. It shows you exactly what the post will look like, and you can just use that instead.

As for getting the distribution, I personally used Excel, specifically the NORM.DIST() function. You do that in the form of "NORM.DIST([Result],[Mean],[Standard Deviation],FALSE)" if you want the type of result I got (using TRUE for the last argument instead gives you "probability to have up to this number;" the current output I believe is the probability to get a number that will round to the result (getting one specific result on a continuous distribution is basically impossible) - basically something like 9.5 to 10.4999999 for 10). Of course, I set up my spreadsheet for easy manipulation - [Result] I mapped to the Score column, Mean I set to 10, and Standard Deviation I set a cell to let me manipulate; my actual equation for the first line was "=NORM.DIST(A2,10,F$1,FALSE)" (no quotes).

[whswhs]

Originally Posted by KarlKost

Hahahahha

Really? I was successful with a Roll of 12. Could this mean something?

On a totally unrelated topic, what would be the odd to critically fail in such roll?

Head hurts... Do the math later...

One chance in 54. If your effective ability is 15 or less, which it is in this case, you critically fail on a 17 or 18, and there are four ways to roll one of those, out of 216 total possible rolls.

[KarlKost]

Originally Posted by Varyon

ProTip - if you need something displayed the way it is on the forums, but don't necessarily want to actually post it, hit the Preview Post button instead of the Submit Reply one. It shows you exactly what the post will look like, and you can just use that instead.

As for getting the distribution, I personally used Excel, specifically the NORM.DIST() function. You do that in the form of "NORM.DIST([Result],[Mean],[Standard Deviation],FALSE)" if you want the type of result I got (using TRUE for the last argument instead gives you "probability to have up to this number;" the current output I believe is the probability to get a number that will round to the result (getting one specific result on a continuous distribution is basically impossible) - basically something like 9.5 to 10.4999999 for 10). Of course, I set up my spreadsheet for easy manipulation - [Result] I mapped to the Score column, Mean I set to 10, and Standard Deviation I set a cell to let me manipulate; my actual equation for the first line was "=NORM.DIST(A2,10,F$1,FALSE)" (no quotes).

Thanks for the tips. My notebook is broken :( Im using my cellphone and I dont have Excel on it and Excel is a pain on phones.

Those numbers even gave me and idea, I could let players roll the dice not for setting their attributes, but to set the max they could reach. So, for example, Attribute 15 is +/- 0.01% - I dont remember the odds on 3d by head, but maybe that's something like 2 criticals in a roll?

(You know what, on a second thought that might not be a good idea... They would mostly be restricted to 11 or 12 at best

[Gollum]

Originally Posted by KarlKost

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.

Yes. That is another argument which explains why GURPS authors don’t want to give a precise cap for realistic human attributes. We don’t really know what is realistically possible and what is not. World records are constantly broken!

Originally Posted by KarlKost

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.

But the problem is still larger than that and your Bruce Lee example is a very good one here.

If you give a realistic version of Bruce Lee a DX score of 18, for instance, that character will be able to fight as Bruce Lee, but he will also automatically have Acrobatics 12 (professional level), Climbing 13 (professional level), Environment Suit 13 (professional level), Escape 12 (professional level), every melee weapon 12+ (professional level), some of them 14 (expert level), every missile weapon 12+ (professional level), All guns 14 (expert level), Pickpocket 12 (professional level), Riding 13 (professional level), Shield 14 (expert level), Stealth 13 (professional level), every throwing weapon 14 (expert level), all vehicle skills 12+ (professional level) and some of them 14 (expert level) …

Which would make him totally unrealistic. Bruce Lee was very good at fighting, of course, maybe one of the best martial artists (that is not sure at all, but no matter, let’s take him as a textbook case), but he surely wasn’t a professional driver, pilot, expert sharpshooter and so on.

To create a realistic Bruce Lee character, it is a much better idea to give him DX 13 or 14, some appropriate advantagess (Combat Reflexes, Enhanced Defenses, a higher Basic Speed ...), and very high skills, especially in Karate. Ditto for Einstein.

Originally Posted by KarlKost

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.

Yes. That is why GURPS authors prefer more or less clear indications like:

“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).”

How To Be A GURPS GM, page 12.

Those are good enough landmarks but still let a lot of freedom to choose the exact degree of realism the GM and players want.

The most important thing to remember here is that GURPS attributes are very broad and choosing very high attribute scores quickly make the game unrealistic. Realistic Human peaks of performances are better simulated by advantages and skills than by attributes.

But the possibility of choosing very high attributes is important too. Because it is what allows to create unrealistic fictional heroes like Indiana Jones, Lara Croft, Walter O’Brien, etc., who can use any weapon, any vehicle, and sound to know everything about any area of knowledge. And it is very important for a generic and universal system to allow to create and play them as easily as any more realistic character.

[KarlKost]

Well, maybe Bruce Lee was an expert pilot, he just simply never tried to race on a Formula 1 race.

This would enter the question of "using your gifts" that I brought above. Maybe mister Lee could've been a master climber and break records climbing high mountains, maybe he could've been a world renowned acrobat from the Cirque Du Soleil, or maybe he could've been the best sniper on human history. But instead he took interest in Martial Arts and never tried those others.

Or, indeed, he had 13-15 DX and high levels of skills. Who's to say?

The thing is that, aside from cinematic characters from movies or RPG tables, hardly anyone will be driving full speed in a car while shooting a full auto rifle and trying to hack the NSA from their phones at the same time. So, MAYBE there could be people insanely gifted that could do a ton of different things, but hardly anyone is ever pressed to do so.

And no, I dont think Bruce Lee or Einstein have just high levels of skills. Some people just simply are more gifted, and can get without any sort of effort to the same levels as someone who spend years trying.

You can try spending your life time improving your martial arts skills, you'll still not get to the level of Bruce Lee - and he died young.

There are many people who study physics their entire lives - and despite that, and despite being very knowledgeable, they still are no Stephen Hawkins or Albert Einsteins.

There IS a measure of skill that is pure gift, and that has no relation to effort.