Standard Deviation and Intelligence

[Agent X]

Ever arguing against the idea that Normal Characteristic Maxima should be the standard for what is "humanly possible" in the Hero Game I present Standard Deviations. This is statistical mumbo jumbo that I barely understand but was taught in college and it is supposed to reflect "groupings" in aptitude on tests. These are the numbers routinely used to illustrate the difference between groupings and where I think Champions Intelligence Stats should correspond.

 

-3 .13% Intelligence of 1

-2 about 2% Intelligence of 3

-1 about 14% Intelligence of 5

0 about 34% Intelligence of 8

mean

0 about 34% Intelligence of 10

+1 about 14% Intelligence of 15

+2 about 2% Top 2% Intelligence of 20

+3 .13% Intelligence of 25

 

Ratio of 0 to +1 is roughly 5 to 1

Ratio of +1 to +2 is roughly 7 to 1

Ratio of +2 to +3 is roughly 15 to 1

So I would assume the ratio of +3 to (+4 or 30 Intelligence) to be roughly 150 to 1

An intelligence of 30 to 35 would be something like 7,500 to 1.

 

Normal Population of 100,000 people

Intelligence 1 approx. 130

Intelligence 3 approx. 2,000

Intelligence 5 approx. 14,000

Intelligence 8 approx. 34,000

Intelligence 10 approx. 34,000

Intelligence 15 approx. 14,000

Intelligence 20 approx. 2,000

Intelligence 25 approx. 130

Intelligence 30 approx. 1 or 0

 

In a State of 3,000,000 there would be about 2,600 people who would rate a 30 intelligence and would be unlikely to have anyone of a 35 intelligence or above.

 

In the United States, there would be something like 32 people with an intelligence of 35.

 

There should be roughly one person with a 40 intelligence for every 46 Earths!

 

This is based on my very limited understanding of mathematics and some huge assumptions.

 

So, the top ten intelligences on the planet - 35

The top 100 intelligences - between 30 and 35

 

Anyone have some information on standard deviations of strength in a human population?

[Doug Limmer]

Why are you choosing jumps of 2-3 points of Intelligence per standard deviation on the low side, yet choosing jumps of 5 points on the high side? If you're going to pick a set value per standard deviation, shouldn't it be the same on either side of the mean?

 

And how do you choose the 'right' number of points per standard deviation?

 

And wouldn't a normal curve (which you are using) mean that there would be people with negative intelligence? Maybe you should use a different distribution.

[McCoy]

No info on Standard Deviation on STR, but the modern Olympic records could be accomplished with a STR 20 with a 5-7 point push.

[Derek Hiemforth]

A simpler explanation for INT in HERO is INT=IQ/10.

 

Average IQ: About 100.

Average HERO INT: 10.

 

Maximum IQ: About 200.

Normal CHA Max HERO INT: 20.

[Snarf]

Average IQ: About 100.

Average HERO INT: 10.

But the average for normal people is now 8. 10 is supposed to be somewhat exceptional.

[OddHat]

Originally posted by Snarf

But the average for normal people is now 8. 10 is supposed to be somewhat exceptional.

 

Have you SEEN the normal people out there?!?

 

[Agent X]

Originally posted by Doug Limmer

Why are you choosing jumps of 2-3 points of Intelligence per standard deviation on the low side, yet choosing jumps of 5 points on the high side? If you're going to pick a set value per standard deviation, shouldn't it be the same on either side of the mean?

 

And how do you choose the 'right' number of points per standard deviation?

 

And wouldn't a normal curve (which you are using) mean that there would be people with negative intelligence? Maybe you should use a different distribution.

I understand your problem on the low side. My problem is that there aren't a whole lot of positive numbers on the low side and I haven't read up on how they are handling "negative" intelligence. It could just as easily be 5 to 0 to -5, etc. depending on how negative numbers are handled.

 

I am assuming that a +1 on the Standard Deviation = a +1 on a base intelligence roll - so people with a 12 or less intelligence roll (13-17 INT) would be +1 SD. The percentages assigned to different groups in the SD are based on what I have seen used as an example from the few sources I have looked at.

 

0 = INT 9-12

+1 = INT 13-17

+2 = INT 18-22

etc.

+3 = INT 23-27

[Agent X]

Originally posted by Snarf

But the average for normal people is now 8. 10 is supposed to be somewhat exceptional.

They are in the same Intelligence Roll category of 11 or less. I arbitrarily decided the 34% just above the mean had an intelligence of 10 and the 34% just below had an intelligence of 8. Practically speaking there isn't any real difference.

[Agent X]

Originally posted by Derek Hiemforth

A simpler explanation for INT in HERO is INT=IQ/10.

 

Average IQ: About 100.

Average HERO INT: 10.

 

Maximum IQ: About 200.

Normal CHA Max HERO INT: 20.

This method is perfectly fine but doesn't really reflect the difference between an 80 IQ and a 120 IQ to my satisfaction (and probably a some others). Using this method, someone with an 80 IQ has the same chance to succeed on an intelligence roll as a person with a 120 IQ.

 

And Snarf pointed out that the average person should have an intelligence of 8 and an IQ of 100 so the INT = IQ/10 doesn't really work if you use official benchmarks.

[Snarf]

Originally posted by Agent X

They are in the same Intelligence Roll category of 11 or less. I arbitrarily decided the 34% just above the mean had an intelligence of 10 and the 34% just below had an intelligence of 8. Practically speaking there isn't any real difference.

It works fine in game terms, my only complaint is the difference in statistical terms.

 

100 IQ - 20 IQ = Forrest Gump.

 

But this is just nitpicking. I certainly wouldn't make players roleplay 2 point IQ differences.

[McCoy]

Originally posted by Agent X

This method is perfectly fine but doesn't really reflect the difference between an 80 IQ and a 120 IQ to my satisfaction (and probably a some others). Using this method, someone with an 80 IQ has the same chance to succeed on an intelligence roll as a person with a 120 IQ.

 

And Snarf pointed out that the average person should have an intelligence of 8 and an IQ of 100 so the INT = IQ/10 doesn't really work if you use official benchmarks.

 

Could go on the INT roll rather than the raw score.

 

-2 SD 1-2 9-

-1 SD 3-7 10-

mean 8-12 11-

+1 SD 13-17 12-

+2 SD 18-22 13-

 

This covers IIRC 90% of the population.

 

Personally, Derek's IQ/10 is good enough for me. Or if 100 IQ must equal 8, go with IQ/12.

[Agent X]

Originally posted by McCoy

Could go on the INT roll rather than the raw score.

 

-2 SD 1-2 9-

-1 SD 3-7 10-

mean 8-12 11-

+1 SD 13-17 12-

+2 SD 18-22 13-

 

This covers IIRC 90% of the population.

 

Personally, Derek's IQ/10 is good enough for me. Or if 100 IQ must equal 8, go with IQ/12.

Once you go IQ/12 it sort of loses its "air" of simplicity though. I don't really worry about IQ so much as an adequate way to functionally represent the difference between an average, above average, genius, and supragenius intellect. A range of 10-20 just won't do that when there are only three "thresholds" concerning intelligence rolls.

 

Here is a site that discusses the issue of standard deviation and IQ: http://sweb.uky.edu/~jcscov0/ratioiq.htm

[Agent X]

After doing some reading, this is where I would place IQ ranges in with the Intelligence Characteristic:

 

Average IQ 85-115 = INT of 8-12 (68% of population)

Above Average 116-125 = INT 13-17 (16% of population)

Gifted Borderline Genius 126-135 = INT 18-22 (2% of population)

Highly Gifted and appearing to be a Genius to most others 136-145 = INT 23-27 (.13% of population or 1 in 769)

Genius 146-165 = INT 28-32 (.013% of population or 1 in 7,690)

High Genius 166-180 = INT 33-37 (1 in 8,750,000) 800 in the world

Immeasurable Human Intelligence 181+ = INT 38-50 (1 in 328 billion) This is too rare as we usually have a some individuals who have scored at this range in the real world and I have every reason to believe there are far more than 800 individuals who have scored in the 166-180 range.

Superhuman Intelligence ?IQ = 51+

 

Modifications on the Upper End without worrying about IQ correspondence:

38-50 Intelligence - anywhere around a dozen to a score at any given moment.

 

Note that Dr. Destroyer and Menton would be in the top 800 but not in the top 12-20 so you may want to modify either his intelligence or the scale. Telios fits in that top 12 to 20 though. Binder would only rate a 136-145 IQ.

[OddHat]

Originally posted by Agent X

Note that Dr. Destroyer and Menton would be in the top 800 but not in the top 12-20 so you may want to modify either his intelligence or the scale. Telios fits in that top 12 to 20 though. Binder would only rate a 136-145 IQ.

 

There are countless very qualified and successful engineers, scientists, etc. who only score somewhat above average on IQ tests. In an RPG we're talking about an approximation of an approximation of "intelligence."

 

So I'm not too worried if Dr.Destroyer is only one of the 800 smartest people in the world. The others all majored in the humanities and ended up working in comic book shops while Dr.D majored in engineering and learned something useful.

 

[Agent X]

Originally posted by OddHat

There are countless very qualified and successful engineers, scientists, etc. who only score somewhat above average on IQ tests. In an RPG we're talking about an approximation of an approximation of "intelligence."

 

So I'm not too worried if Dr.Destroyer is only one of the 800 smartest people in the world. The others all majored in the humanities and ended up working in comic book shops while Dr.D majored in engineering and learned something useful.

 

You have a good point. I like to use the example of Tarzan as being one of the smartest, if not the smartest, characters in novels. He taught himself English with a book - without anyone to demonstrate the sounds the alphabet represented!

[Fireg0lem]

First up, my understanding of the rule about the average human having an 8 intelligence was that that is the score of Joe Boring, not the average of all humans. The average was 10, but an average man has 8, because of the height which many "above average" people go to. But, I may be wrong.

 

Second, as far as strength goes, the strongest recorded human being IIRC was the Barnum & Bailey performer Angus McAskill, and his greatest feat of strength (lifting an anchor) could be done with a 33 STR score.

[megaplayboy]

I think a good rule of thumb is that "superhuman" stats start at about 35+ for physical stats, and 60+ for non-physical stats.

That is, anyone with a physical stat of 35+ or a non-physical stat of 60+ is indisputably superhuman. The rationale? In FRED, a skill roll of 21- is considered a "superhuman" level. To get that level with purely stat based rolls requires a 60 INT or PRE, for example. For physical stats, the equivalent is a +12 to OCV, which requires a 35 DEX.

So I think the guidelines in the Champions genre book and in Champions Universe are a good delineation of the difference between legendary and superhuman.

Remember, INT is a measure of perceptual speed, memory, and quick thinking and insight in real time. It is not a measure of knowledge or "IQ".

I like the original proposition stated some time ago--stats above 20 are one in a million, and possibly only 1 in a thousand for the non-physical stats. Mental stats over 30 are definitely 1 in a million for humans, though.

[Trebuchet]

Originally posted by megaplayboy

I think a good rule of thumb is that "superhuman" stats start at about 35+ for physical stats, and 60+ for non-physical stats.

That is, anyone with a physical stat of 35+ or a non-physical stat of 60+ is indisputably superhuman. The rationale? In FRED, a skill roll of 21- is considered a "superhuman" level. To get that level with purely stat based rolls requires a 60 INT or PRE, for example. For physical stats, the equivalent is a +12 to OCV, which requires a 35 DEX.

Remember, INT is a measure of perceptual speed, memory, and quick thinking and insight in real time. It is not a measure of knowledge or "IQ".

I like the original proposition stated some time ago--stats above 20 are one in a million, and possibly only 1 in a thousand for the non-physical stats. Mental stats over 30 are definitely 1 in a million for humans, though.

I don't disagree with your basic point, but why a different standard for physical and non-physical stats? Skill rolls are figured the same, so why is 35 DEX "superhuman" but it takes a 60 INT to be superhuman? Instead of looking at OCV, why not look at the Acrobatics or Breakfall skill rolls figured from DEX?

 

To me it makes more sense to have any Characteristic above 30 considered "superhuman" just as the rules state. Face it, hw many characters have Skill rolls of 21- or higher at anything? Except for characters with Power Pools who need a large Skill roll to change powers and offset active point penalties, I've only ever seen one character personally with a skill roll over 18- at anything. That character is my own gymnast/martial artist Zl'f, who has an Acrobatics roll of 22- (With a 43 DEX, her base roll for DEX-based skills is 18-). For most players the stock numbers they get from their characteristics are enough; most are quite satisfied with a 15- or 16-.

 

Your point about INT in HERO being "a measure of perceptual speed, memory, and quick thinking and insight in real time. It is not a measure of knowledge or IQ" is well taken. IQ is a totally subjective term, and an IQ of 100 is considered "average" in any case. If you really have to assign numbers, then 8 INT can be used to represent 100 IQ since both are average. But it should not be forgotten that they are not measures of the same thing. A character could still be a Nobel-Prize winning physicist in HERO with a 10 INT because he proceeds slowly and methodically.

[Agent X]

Originally posted by Trebuchet

I don't disagree with your basic point, but why a different standard for physical and non-physical stats? Skill rolls are figured the same, so why is 35 DEX "superhuman" but it takes a 60 INT to be superhuman? Instead of looking at OCV, why not look at the Acrobatics or Breakfall skill rolls figured from DEX?

 

To me it makes more sense to have any Characteristic above 30 considered "superhuman" just as the rules state. Face it, hw many characters have Skill rolls of 21- or higher at anything? Except for characters with Power Pools who need a large Skill roll to change powers and offset active point penalties, I've only ever seen one character personally with a skill roll over 18- at anything. That character is my own gymnast/martial artist Zl'f, who has an Acrobatics roll of 22- (With a 43 DEX, her base roll for DEX-based skills is 18-). For most players the stock numbers they get from their characteristics are enough; most are quite satisfied with a 15- or 16-.

 

Your point about INT in HERO being "a measure of perceptual speed, memory, and quick thinking and insight in real time. It is not a measure of knowledge or IQ" is well taken. IQ is a totally subjective term, and an IQ of 100 is considered "average" in any case. If you really have to assign numbers, then 8 INT can be used to represent 100 IQ since both are average. But it should not be forgotten that they are not measures of the same thing. A character could still be a Nobel-Prize winning physicist in HERO with a 10 INT because he proceeds slowly and methodically.

The rule I've seen sets Nonphysical Stats at 51+ for Superhuman. Just because you can mimic a Nobel-Prize winning physicist without raising his intelligence beyond 10 doesn't mean it's the way to do it.

[Trebuchet]

Originally posted by Agent X

The rule I've seen sets Nonphysical Stats at 51+ for Superhuman. Just because you can mimic a Nobel-Prize winning physicist without raising his intelligence beyond 10 doesn't mean it's the way to do it.

I guess I'm not quite grasping what exactly it is you are trying to do, Doug. Both HERO's INT score and IQ scores are totally subjective items. INT at least has an effect in the game system, but why worry about IQ and how it relates to INT? It's not a real thing even in the "real" world.

 

Read Stephen Jay Gould's excellent book The Mismeasure of Man for an excellent analysis of the pointlessness of IQ tests.

[Agent X]

Originally posted by Trebuchet

I guess I'm not quite grasping what exactly it is you are trying to do, Doug. Both HERO's INT score and IQ scores are totally subjective items. INT at least has an effect in the game system, but why worry about IQ and how it relates to INT? It's not a real thing even in the "real" world.

 

Read Stephen Jay Gould's excellent book The Mismeasure of Man for an excellent analysis of the pointlessness of IQ tests.

My motivation is from my first sentence of my first post: "Ever arguing against the idea that Normal Characteristic Maxima should be the standard for what is "humanly possible" in the Hero Game I present Standard Deviations.

[Trebuchet]

Originally posted by Agent X

My motivation is from my first sentence of my first post: "Ever arguing against the idea that Normal Characteristic Maxima should be the standard for what is "humanly possible" in the Hero Game I present Standard Deviations.

And just how does that concept relate to your statement that non-physical characteristics require 50+ to be considered superhuman? I would think that you'd be advocating against the very idea of HCM.

 

A simpler way than what you propose would be to figure out a way to reduce the granularity of Skill rolls so that an 8 INT is not as likely to succeed at an INT-based task as someone with a 12 INT. The simplest way to do that is not to buy 12 INT, but to use the system as designed and buy 13 INT. That's why the system has break points. Why waste effort trying to reinvent the wheel? I don't consider efficient design to be meta-gaming; it's merely using the system as designed. I've never built a PC with only a 10 INT in my 21+ years of playing Champions/HERO.

 

This is a purely academic exercise IMHO anyway. Most Champions campaigns don't even use HCM, and in every non-Champions HERO campaign I've ever seen HCM is defined by the GM. Whether he sets it at 20, 30, or 15 is entirely up to him.

 

BTW, have you noticed you are now a quadruple millenial master?

[Agent X]

Originally posted by Trebuchet

And just how does that concept relate to your statement that non-physical characteristics require 50+ to be considered superhuman? I would think that you'd be advocating against the very idea of HCM.

 

A simpler way than what you propose would be to figure out a way to reduce the granularity of Skill rolls so that an 8 INT is not as likely to succeed at an INT-based task as someone with a 12 INT. The simplest way to do that is not to buy 12 INT, but to use the system as designed and buy 13 INT. That's why the system has break points. Why waste effort trying to reinvent the wheel? I don't consider efficient design to be meta-gaming; it's merely using the system as designed. I've never built a PC with only a 10 INT in my 21+ years of playing Champions/HERO.

 

This is a purely academic exercise IMHO anyway. Most Champions campaigns don't even use HCM, and in every non-Champions HERO campaign I've ever seen HCM is defined by the GM. Whether he sets it at 20, 30, or 15 is entirely up to him.

 

BTW, have you noticed you are now a quadruple millenial master?

1. I was just pointing out that FRED sets physical stats that are superhuman at 31+ and nonphysical at 51+. This was in reference to your statement that there was no indicator in the rules and there is, semi-buried in the book.

 

2. I don't like Normal Characteristic Maxima. I think it's silly.

 

3. I have, on occasion, not set characteristics at their "ideal" performance value. It can be an investment in the future at the very least.

 

4. What's wrong with an academic exercise? I am a teacher after all.

 

5. Yeah, I am the Quadruple Millenial Master at the moment. I'm actually catching some flak for it from some people. They're starting to criticize my "posting style" and they seem really upset that I play the Word Association Game. I think they might be surprised at how little of my posting comes from that game or how many times I choose not to post. I am quite surprised that they are worried about how many times I post.

[Trebuchet]

Originally posted by Agent X

1. I was just pointing out that FRED sets physical stats that are superhuman at 31+ and nonphysical at 51+. This was in reference to your statement that there was no indicator in the rules and there is, semi-buried in the book.

 

2. I don't like Normal Characteristic Maxima. I think it's silly.

 

3. I have, on occasion, not set characteristics at their "ideal" performance value. It can be an investment in the future at the very least.

 

4. What's wrong with an academic exercise? I am a teacher after all.

 

5. Yeah, I am the Quadruple Millenial Master at the moment. I'm actually catching some flak for it from some people. They're starting to criticize my "posting style" and they seem really upset that I play the Word Association Game. I think they might be surprised at how little of my posting comes from that game or how many times I choose not to post. I am quite surprised that they are worried about how many times I post.

1) Could you point me at that rule?

 

2) I think NCM is silly in a supers game. In fantasy or modern games it might have some use, but generally a point cap works better. I played in a Fantasy Hero game where one of the PCs had a 28 STR. That guy was strong.

 

3) I've used non-optimal numbers too at times, but generally for the same reason you have: As a stepping stone to further increases.

 

4) Nothing wrong with teachers. I sleep with one.

 

5) Who cares? I've never found your arguments or comments to be irrelevant even when I don't agree with them. So call yourself "Aspiring Pentennial Master".

[Agent X]

Originally posted by Trebuchet

1) Could you point me at that rule?

 

2) I think NCM is silly in a supers game. In fantasy or modern games it might have some use, but generally a point cap works better. I played in a Fantasy Hero game where one of the PCs had a 28 STR. That guy was strong.

 

3) I've used non-optimal numbers too at times, but generally for the same reason you have: As a stepping stone to further increases.

 

4) Nothing wrong with teachers. I sleep with one.

 

5) Who cares? I've never found your arguments or comments to be irrelevant even when I don't agree with them. So call yourself "Aspiring Pentennial Master".

1. The Rule is more of a Guideline: Champions page 58 and Allston is pointing to Champions campaigns. I don't see any reason not to extend it to any other "High Adventure" sort of game.

 

2. I think letting people get dibs on being the best in certain categories can fix this problem.

 

3. K

 

4. What a coincidence. My wife sleeps with one too. Hey:confused:

 

5. Heh:D I might have to do that... and I never said I cared, just that I was surprised.