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Old 07-20-2010, 09:40 PM   #1
Talonos
 
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Default Standard deviation on Stat distribution?

Recently, I was talking to a friend about GURPS stats, and mentioned that only about three in a thousand people would have an IQ over 13, making his IQ 15 character even more incredibly smart. He asked why I said that. I said "Didn't you know? Each stat point represents a standard deviation either above or below the mean." He asked what made on earth made me think that.

About a week later, after being unable to find anything to that effect, I lamely said "Well, gee... I dunno. I thought somewhere I read something about... well, never mind. Oh well."

So, this is my question. How rare are high stats? About how many people in a population have IQ at certain levels? How about int? If I wanted to create a computer program that would randomly create a person, what distributions would I give it to work with?

Also, on a less related note, how good common would skill levels above 20 be?
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Old 07-20-2010, 09:59 PM   #2
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Default Re: Standard deviation on Stat distribution?

Quote:
Originally Posted by Talonos View Post
Recently, I was talking to a friend about GURPS stats, and mentioned that only about three in a thousand people would have an IQ over 13, making his IQ 15 character even more incredibly smart. He asked why I said that. I said "Didn't you know? Each stat point represents a standard deviation either above or below the mean." He asked what made on earth made me think that.

About a week later, after being unable to find anything to that effect, I lamely said "Well, gee... I dunno. I thought somewhere I read something about... well, never mind. Oh well."

So, this is my question. How rare are high stats? About how many people in a population have IQ at certain levels? How about int? If I wanted to create a computer program that would randomly create a person, what distributions would I give it to work with?

Also, on a less related note, how good common would skill levels above 20 be?
I would say that it's fair to consider each point in a stat about a standard deviation.

Kromm's analysis is as follows (I can't find the original post but I copied it into a notepad document for reference):

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)

* Most people have ST, DX, IQ, HT, Will, and Per at 10; a Basic Speed of 5.00; and a Basic Move of 5.

* If an ordinary Joe is stronger, more agile, smarter, healthier, stronger-willed, or more perceptive than average, odds are good that he has an 11 instead of a 10. If his edge is so great that his friends talk about it, he might rate a 13. People in the middle are at 12.

* If an ordinary Joe reacts more quickly than average, he probably has Basic Speed 5.25. If he runs more quickly, he might rate Basic Move 6.

* I would seriously think about rating greater apparent competency using skills, not attributes. A really good hunter probably has all of Guns, Stealth, and Tracking at Attribute+1 or perhaps +2, and that sets him above his pals with only one or two of those skills at Attribute level. He almost certainly doesn't have DX 12 and Per 12!

* If an ordinary Joe is weaker, clumsier, duller, less healthy, weaker-willed, or less perceptive than average, he likely has a 9 instead of a 10. If his lack is so great that his friends talk about it behind his back, he might rate a 7. People in the middle are at 8. Likewise, if he reacts less quickly than average, he might have Basic Speed 4.75. If he can't keep up on the run, he probably has Basic Move 4.

* Don't mistake Incompetence at a skill for low attributes! Every workplace has some poor guy who -- let's face it -- sucks. My money is on him having Incompetence at a needed skill, not DX 7 or IQ 8.
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Old 07-20-2010, 10:43 PM   #3
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Default Re: Standard deviation on Stat distribution?

GURPS Fantasy p. 103 might help you 8)
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Old 07-21-2010, 01:29 AM   #4
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Default Re: Standard deviation on Stat distribution?

Quote:
Originally Posted by lexington View Post
I would say that it's fair to consider each point in a stat about a standard deviation.
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. Of course, you are free to alter these assumptions for your game, but it's important to know what you are doing, or you can end up with a situation where a large majority of the population is above average, for example.
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Old 07-21-2010, 11:39 AM   #5
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Default Re: Standard deviation on Stat distribution?

Canonically, the game system attaches no statistical meaning to attribute scores beyond your odds of success when you try to roll under them on 3d. Within the population of the game world, these scores are dramatic descriptors only. In some campaigns, any score under 12 makes you a putz among adventurers, who are off on their own little curve separate from the rest of the universe. In others, everybody is a horror victim with scores in the 9-11 range. Both could take place in the same world . . .

But FWIW, "Every +N to GURPS attributes represents a sigma!" is a bit of an urban myth akin to "GURPS IQ is just the standard test score divided by 10!" Lots of gamers spout this stuff, but SJ Games has never, ever agreed. In fact, we've often disagreed. Despite the system's reputation for realism and popularity with simulationists, the numbers are and always have been assessed in the service of drama.
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Old 07-21-2010, 07:44 PM   #6
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Default Re: Standard deviation on Stat distribution?

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Originally Posted by Kromm View Post
Canonically, the game system attaches no statistical meaning to attribute scores beyond your odds of success when you try to roll under them on 3d. Within the population of the game world, these scores are dramatic descriptors only. In some campaigns, any score under 12 makes you a putz among adventurers, who are off on their own little curve separate from the rest of the universe. In others, everybody is a horror victim with scores in the 9-11 range. Both could take place in the same world . . .
I'll be the first to agree that adventurers are not a representative sample of humanity, but I don't see how it is supportable to disclaim the statistical meaning of the canonical statements that a score of 10 represents the human average and that most normal humans have scores in the 8-12 range without also discarding their meanings as commonly understood by non-statisticians.

Once the authors assign abstract quantities to represent individual qualities and make statements about how common they are among a group of such individuals, how are they not practicing statistics?
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Old 07-21-2010, 08:25 PM   #7
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Originally Posted by jeff_wilson View Post
I'll be the first to agree that adventurers are not a representative sample of humanity, but I don't see how it is supportable to disclaim the statistical meaning of the canonical statements that a score of 10 represents the human average and that most normal humans have scores in the 8-12 range without also discarding their meanings as commonly understood by non-statisticians.

Once the authors assign abstract quantities to represent individual qualities and make statements about how common they are among a group of such individuals, how are they not practicing statistics?
Well the fundamental problem here is what population are we talking about? Are we talking about the rapidly aging population of Canada in 2040 with the baby boomers on their way to the grave? Or are we talking about the depression-era United States where malnutrition is endemic in the cities and they'll have trouble with so many guys being unfit for military service as a result? Or could we be talking about 12th century Norway where every male seems to be a burly farmer or oarsman? 10 is an arbitrary "average"
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Old 07-21-2010, 08:53 PM   #8
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Default Re: Standard deviation on Stat distribution?

David Johnston does bring up an important point. In a time travel game, you could easily say: Humans from the 20th century have +1 HT (or it's opposite, since we are not resistant).

But, I also agree that within a specific game setting GURPS attributes can be used to determine average. However, I don't go as far as assigning stand deviation and such (Yay, Humanities!). All I use it for is to baseline mooks and NPCs, and to satisfy my "stat-normalization bug" with statements like: "The universe is more likely to provide a scientist with IQ 11 and Talent than with IQ 15"*

But I digress. Basically, I think what's being said is that statistics, while being used in a game, ought not reflect realism but the tone, scope, and mood of the game. But Kromm said this more eloquently than I, anyway.

*I know this statement is meaningless to gaming or anything. Is usually followed my a smug "mwuck mwuck mwuck".
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Old 07-21-2010, 08:53 PM   #9
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Default Re: Standard deviation on Stat distribution?

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Originally Posted by David Johnston2 View Post
Well the fundamental problem here is what population are we talking about?
If you read the page, you can confirm that the groups are humans and normal humans, as I wrote, but that's not espcially important. Statistics can be applied to a particular population, even a specific population of actual people, but it is not required for the statistical statements and operations to be valid.

It would analogous to the difference between a word problem or story problem ("Alice has five apples and gives two to Bill. How many apples does Alice have left?") and an abstract exercise ("5-2=?") in arithmetic; both solutions involve a quantity of [three], despite there being no particular Alice or Bill, or even any apples, and the story problem sitting atop a pile of assumptions like apples being accurately modeled as discrete units, having a useful duration longer than the implied timeframe of the exchange, being able to be measured reliably in a short time relative to their further exchange for other goods and services, etc.
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Last edited by jeff_wilson; 07-21-2010 at 09:00 PM. Reason: heh, bad arithmetic is still arithmetic
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Old 07-21-2010, 09:13 PM   #10
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Default Re: Standard deviation on Stat distribution?

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Originally Posted by jeff_wilson View Post
If you read the page, you can confirm that the groups are humans and normal humans, as I wrote, but that's not espcially important. Statistics can be applied to a particular population, even a specific population of actual people, but it is not required for the statistical statements and operations to be valid. .
"Valid" not necessarily meaning "having some
thing to do with the real world"?
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