Intelligence scores matched to IQ scores

[Half-Wizard]

After reading through a lot of discussions about monster intelligence and wizards with high Int scores, I decided to work out how to convert between Int and IQ, and figure out what the scores actually mean. I put together the following handy table which players and DMs may find useful for roleplaying characters with both high and low Int:


Int
scoreIQ
scoreDescription

0
47Moderate mental disability, unable to live
independently

1
52Still can do very basic domestic work

2
57

3
62Still able to harvest vegetables, repair furniture

4
67Can be diagnosed with intellectual disability

5
72

6
77Borderline intellectual disability

7
82

8
87Unskilled workers, minimum for the military

9
92Elementary school graduates, semi-skilled workers

10
97High school graduates, skilled workers

11
103Managers and administrators

12
108

13
113College graduates, professional workers

14
118

15
123

16
128Average medical doctor or PhD, approximate
minimum for genius

17
133Intellectually gifted

18
138

19
143

20
148Ancient red dragon (http://www.d20pfsrd.com/bestiary/monster-listings/dragons/dragon/chromatic-red/ancient-red-dragon)

21
153

22
158

23
163IQ tests have difficulty providing meaningful
or reliable scores beyond this

24
168

25
174Baal (http://www.d20pfsrd.com/bestiary/monster-listings/outsiders/devil/devils-unique/devil-baal-duke-of-hell-tohc)

26
179Great wyrm gold dragon (http://www.d20pfsrd.com/bestiary/monster-listings/dragons/dragon/metallic-gold/gold-dragon-great-wyrm)

27
184

28
189Lucifer (http://www.d20pfsrd.com/bestiary/monster-listings/outsiders/devil/devils-unique/devil-lucifer-prince-of-darkness-tohc)

29
194Dagon (http://www.d20pfsrd.com/bestiary/monster-listings/outsiders/demon/demon-lords/demon-lord-dagon)

30
199

31
204Cthulhu (http://www.d20pfsrd.com/bestiary/monster-listings/aberrations/great-old-ones/great-old-one-cthulhu)

32
209

33
214

34
219Level 20 Wiz, venerable, max Int, +2 racial,
and headband of vast intelligence +6 (http://www.d20pfsrd.com/magic-items/wondrous-items/wondrous-items/h-l/headband-of-vast-intelligence)

35
224Hastur (http://www.d20pfsrd.com/bestiary/monster-listings/aberrations/great-old-ones/great-old-one-hastur)

36
229

37
234Baphomet (http://www.d20pfsrd.com/bestiary/monster-listings/outsiders/demon/demon-lords/demon-lord-baphomet)

38
239

39
245Wiz as above after Tome of Clear Thought +5 (http://www.d20pfsrd.com/magic-items/wondrous-items/wondrous-items/a-b/book-tome-of-clear-thought)

40
250Gibbering orb (http://www.d20pfsrd.com/bestiary/monster-listings/aberrations/gibbering-orb-fgg)

The real-world information I placed in the table is drawn from Wikipedia's articles on intelligence quotient (https://en.wikipedia.org/wiki/Intelligence_quotient#Classification), IQ classification (https://en.wikipedia.org/wiki/IQ_classification), intellectual disability (https://en.wikipedia.org/wiki/Intellectual_disability), and intellectual giftedness (https://en.wikipedia.org/wiki/Intellectual_giftedness). It should be fairly accurate, but let me know if you find more reliable sources which contradict anything.

If you want to have some comparison between two IQ scores, the table gives you a pretty good idea of how significant the difference is. For example, Int of 6 (IQ 77) falls under borderline intellectual disability; it's less than the average unskilled worker or elementary school graduate and too low for the military to put in the effort to train you. An Int of 16 (IQ 128) places you at the level of an average PhD, and it's the bare minimum to be called a genius, although that depends on what you actually do with your intelligence. So, a 10 point difference in intelligence is like the difference between these two categories.

How would that impact a fight? Well, suddenly thrown into an empty room to fight with their bare fists alone, these two would probably be about equally matched. If you add a complex environment with weapons, cover, concealment, rough terrain, and hazards, the high Int character will gain a significant upper hand because they'll do a much better job of using that environment to their advantage. The Int 16 character will bait his opponent into the hazards, attack and drop behind cover, and try to take paths that force his enemy through rough terrain. The low Int character may do some of that, but not nearly as much and not nearly as effectively. If you add resources and time to prepare, the high Int character will probably win every single time.

So, if your party has Int 10, and they're up against an ancient red dragon, this should give you some idea of how the dragon is going to fight. From the player's point of view, the dragon will be fighting dirty. Very dirty. Oh, you came to kill me in my cave? Yeah, the cave is a trapped decoy. And it just collapsed on you. Good job, mortals. You're not even looking on the correct plane.

Now consider a 20 point difference, like Int 3 (IQ 62) versus Int 23 (IQ 163). At Int 3, you're in special ed and you're receiving welfare for your intellectual disability because it impedes your ability to earn money by working. At Int 23 (IQ 163), you're intelligent enough that it's difficult for people to write IQ tests which can accurately distinguish you from others who are even more intelligent. Various websites claim Einstein was around this level (IQ 161), but they don't cite an actual IQ test, so take this with a grain of salt.

With an intelligence gap like this, you still might have even odds if you throw these two into an empty room barehanded and force them to fight. However, in any normal setting, with a complex environment and time to prepare, it would be cruel to force a fight between these two. The Int 23 character would be able to win in ways that the Int 3 character wouldn't even understand. The gap in Int is so wide here that the Int 3 character probably wouldn't understand even if the Int 23 character explained everything.

So, if your party has Int 11 and they're up against Cthulhu (Int 31), they've lost and they don't even know it. Even if Cthulhu explained to them exactly why and how they've lost, they still wouldn't understand. The technology and concepts would be entirely beyond their comprehension, like having Einstein try to teach general relativity for a special ed class.

As for the 20th level wizard? We're looking at an Int of at least 39, resulting in an IQ of 245 or higher. You would need to be a genius with an Int of 19 merely to be like a special ed student trying to understand Einstein when dealing with this wizard. Give it 10-20 years of concentrated effort and you might just barely begin to understand the most superficial aspects of his plans and methods. His approaches to magic and the world would use inconceivable methods to solve unimaginable problems. He would casually create new forms of math and logic to solve problems that you wouldn't understand if you spent decades trying. He would know just about everything there is to know and be able to do just about anything that can be done. The level 20 Wizard is not scary because he can magically alter the world to fit his needs: he's scary because he can do that even without magic.

Conversion:
To convert Int score to IQ score: 100 + (Int - 10.5)*5.0709255283711
To convert IQ score to Int score: 10.5 + (IQ - 100)/5.0709255283711

Calculating this:
For those who care how I worked this out:

Average Int score (3d6): 10.5
Standard deviation (3d6): 2.958039891549808

Average IQ score: 100
Standard deviation: 15

Since these are both bell curves, we can standardize scores on one curve to fit scores on the other curve. We can subtract the average from a score to get the score's deviation from the average, and then divide that by the standard deviation (https://en.wikipedia.org/wiki/Standard_deviation) to get the number of standard deviations from the average for that score. So, with Int 18, the deviation from the average is 18-10.5 = 7.5 points. Divide that by the standard deviation for Int, 2.958039891549808, and we find that an Int of 18 is 2.54 standard deviations from the average. The same principle works for IQ, but you'd use the mean and standard deviation for IQ in that case.

Once we know how many standard deviations we are from the average on one scale, we can multiply by the standard deviation of the other scale to get how many points we are from the average on that scale. Then we add the average of that scale and we get the score. So, with Int 18, we know it's 2.54 standard deviations from the average on both scales. Multiply that by 15 and we find out how many points it is from the average on the IQ scale. 2.54*15 = 38.1, so an Int of 18 is 38.1 points above the average on the IQ scale. The average on the IQ scale is 100, so an Int of 18 matches an IQ of 100+38.1 = 138.1

Roleplaying a 20th level wizard:
It's easy to roleplay a character with lower Int than you have, but not so easy to do that for a character with higher Int. How would this kind of wizard talk? What would this kind of wizard do, or avoid doing? As the DM, how would you show your players that this wizard is smarter than they can possibly imagine?

[Giddonihah]

I will tell you what you dont do. You dont allow a Player who has a Lvl 20 Wizard to ever say "My character is so smart I can do X" despite not having put any skill points in it, or "My wizard would have totally figured out this broken spell combination with his super genius IQ, so it should be allowed"

..In general Int to IQ and letting a player benefit is giving Wizards an unneeded buff. For enemy Wizards? Sure let them act all high and mighty and aloof with their plans, just not players.

[The Grue]

This again?

[Mellack]

Int 0 does not have an IQ score. It is unintelligent. It is a rock or a tree. Your starting point is flawed.

[Jeff the Green]

Int 0 does not have an IQ score. It is unintelligent. It is a rock or a tree. Your starting point is flawed.

That's Int –. Int 0 is unconscious.

[The Grue]

That's Int –. Int 0 is unconscious.

I would qualify Int 0 as "comatose", but Mellack's point stands.

[Shining Wrath]

I think your table breaks down at the extremes. Per SRD:
An animal has an Intelligence score of 1 or 2. A creature of humanlike intelligence has a score of at least 3.

Therefore, no person capable of speech has an INT less than 3. No person capable of knowing they have a body and feeling pain has an INT of 0.

This is why I dislike riddles and puzzles in D&D. You've got players with IQs that probably start at the "college graduate" level and go up from there trying to solve intellectual puzzles, but one is playing an INT 10 fighter (and therefore is much smarter) and one is playing an INT 24 Wizard (to say nothing of 34) and therefore cannot possibly be as smart as his player.

So I try to translate all puzzles into game mechanics - skill rolls.

Working as I do at a place full of rocket scientists, I would also say that the smartest guy in the room is not the smartest guy on every topic. To put it another way, Einstein might be capable of learning everything there is to know about cars - but he hasn't bothered, and so he takes his car to the mechanic when the Check Engine light comes on. In your combat example, an IQ 10 Marine might make much better use of terrain, improvised weapons, and so on, than an IQ 30 Nobel Laureate, because of training.

[Jeff the Green]

This is why I dislike riddles and puzzles in D&D. You've got players with IQs that probably start at the "college graduate" level and go up from there trying to solve intellectual puzzles, but one is playing an INT 10 fighter (and therefore is much smarter) and one is playing an INT 24 Wizard (to say nothing of 34) and therefore cannot possibly be as smart as his player.

So I try to translate all puzzles into game mechanics - skill rolls.

There are a couple other ways to handle it. Intelligence (or occasionally Wisdom or Knowledge) checks for clues, and, when I'm playing PbP and thus time isn't an issue, croudsourcing it on the Playground. And then once we've figured it out it comes from the most appropriate party member (usually mine, since I tend to play high-Intelligence characters) regardless of who came up with it.

[Shining Wrath]

There are a couple other ways to handle it. Intelligence (or occasionally Wisdom or Knowledge) checks for clues, and, when I'm playing PbP and thus time isn't an issue, croudsourcing it on the Playground. And then once we've figured it out it comes from the most appropriate party member (usually mine, since I tend to play high-Intelligence characters) regardless of who came up with it.

There are different ways to do it, but the point is to somehow have the characters solve the puzzle or riddle, not the players. Especially when you've got a table with some people who are smart about one thing and some about another; if I throw out a riddle dependent upon knowledge of history it favors the guy who reads histories over the not-history buffs.

[dascarletm]

Int scores don't translate well to IQ... at all.

It breaks down imo when it comes to the all mighty d20. Someone with 20 int (+5 bonus) has merely a 25% better chance at answering an IQ test question right, than someone with 10 int.

Does that make any lick of sense when compared to someone with an IQ of 150 vs 100?

[Half-Wizard]

I would qualify Int 0 as "comatose", but Mellack's point stands.

That's actually not far from what the corresponding IQ score would be. Here's a study of autistic children with IQs above 50 (http://moodle.capilanou.ca/pluginfile.php/197015/mod_resource/content/1/adult%20outcome%20for%20children%20with%20autism.p df#page=6) with a follow-up when they reached adulthood. More than half were not independent, meaning unable to feed themselves, unable to clean themselves, unable to get up and get food or do any of the basic things required to keep living. 40% of them had severe language impediments, and 9% were not verbal at all. At Int 0, we're looking at an IQ of 47, which is below the group this study looked at. Someone with Int 0 might open their eyes, might make some noises, but they're not going to be able to do much of anything for themselves.

[The Grue]

That's actually not far from what the corresponding IQ score would be. Here's a study of autistic children with IQs above 50 (http://moodle.capilanou.ca/pluginfile.php/197015/mod_resource/content/1/adult%20outcome%20for%20children%20with%20autism.p df#page=6) with a follow-up when they reached adulthood. More than half were not independent, meaning unable to feed themselves, unable to clean themselves, unable to get up and get food or do any of the basic things required to keep living. 40% of them had severe language impediments, and 9% were not verbal at all. At Int 0, we're looking at an IQ of 47, which is below the group this study looked at. Someone with Int 0 might open their eyes, might make some noises, but they're not going to be able to do much of anything for themselves.

Yeah...not the case.


Intelligence 0 means that the character cannot think and is unconscious in a comalike stupor, helpless.

[holywhippet]

I'd have to include both intelligence and wisdom as part of IQ. Intelligence is raw processing power, wisdom is seeing the larger picture. For example, intelligence might tell you that you should build a car out of the lightest material that can handle the weight and stresses you'd expect from normal use so you might build a cart body out of plastic. Wisdom will tell you the car is likely to be involved in a crash some day so you need to use something stronger.

[Zanos]

Int scores don't translate well to IQ... at all.

It breaks down imo when it comes to the all mighty d20. Someone with 20 int (+5 bonus) has merely a 25% better chance at answering an IQ test question right, than someone with 10 int.

Does that make any lick of sense when compared to someone with an IQ of 150 vs 100?
That's not correct. See the SRD on ability checks.

Ability Checks
Sometimes a character tries to do something to which no specific skill really applies. In these cases, you make an ability check. An ability check is a roll of 1d20 plus the appropriate ability modifier. Essentially, you’re making an untrained skill check.

In some cases, an action is a straight test of one’s ability with no luck involved. Just as you wouldn’t make a height check to see who is taller, you don’t make a Strength check to see who is stronger.


Answering a question on a (well-designed) IQ test should not involved a luck component.

IMO it's better to use Int scores as a percentile measure. The "common" roll is 3d6, giving a chance of 0.46% of getting an 18 in intelligence. So people with 18 int are in the top .46% or IQs, and do likewise for the other potential scores. This breaks down with other creatures, obviously, but the system was never really meant to measure intelligence in non-humans anyway.

[Jeff the Green]

There are different ways to do it, but the point is to somehow have the characters solve the puzzle or riddle, not the players. Especially when you've got a table with some people who are smart about one thing and some about another; if I throw out a riddle dependent upon knowledge of history it favors the guy who reads histories over the not-history buffs.

Well, hopefully you aren't making riddles whose answers are dependent on real-life history since there's no way the characters could solve them.

I get your point, though. I think it's still solvable with the "players solve it, and then the characters do" paradigm. I'd do basically what I'd do if I had a player who's bored by combat and one who's bored by social encounters: have a mix. If you have one person who's good with lateral thinking puzzles, one who's good with logic puzzles, and another who's good with cryptography, you have a 1:1:1 mix of the three types.

[dascarletm]

That's not correct. See the SRD on ability checks.


Answering a question on a (well-designed) IQ test should not involved a luck component.


Eh, substitute in a game of chess instead of an IQ test, or a proper int based skill with equal ranks (tainining).

The mechanics of ability scores doesn't translate well to real life. In practical application (the vast majority of actions requires a roll) the difference between the upper natural echelon and average is 25%.

[The Grue]

Eh, substitute in a game of chess instead of an IQ test, or a proper int based skill with equal ranks (tainining).

The mechanics of ability scores doesn't translate well to real life. In practical application (the vast majority of actions requires a roll) the difference between the upper natural echelon and average is 25%.

Chess is a bad example, since it is solvable.

[dascarletm]

Chess is a bad example, since it is solvable.

:smallsmile:
:smallconfused:
:smallannoyed:
:smallamused:

But seriously all the other examples are solvable.

[Baroknik]

:smallsmile:
:smallconfused:
:smallannoyed:
:smallamused:

But seriously all the other examples are solvable.

What's in my pocket?

[atemu1234]

Int 0 does not have an IQ score. It is unintelligent. It is a rock or a tree. Your starting point is flawed.

Wrong again. It means "mindless", not completely unintelligent. Some things act mindlessly but aren't rocks or trees.

[Raven777]

What's in my pocket?

"Your hand". Gollum was an idiot.

[Zweisteine]

Wrong again. It means "mindless", not completely unintelligent. Some things act mindlessly but aren't rocks or trees.
As state above, that would be Int –. Int 0 means you're in a coma.

A while ago, I tried to align IQ and Intelligence. After a few hours of research and math, I determined that it was really hard to do. I would have needed math beyond my not-inconsiderable capacity, and Wolfram Alpha couldn't do it for me.
Inverse cumulative distribution, or something like that.

I managed to discover that 9-12 intelligence was still within the IQ range of 80-120, or something like that. And that an IQ of 200 is probably over 18 Int.

I don't remover exactly what I got with my less accurate ideas, but, off the top of my head, this looks about right:

Intelligence * 10 - 5 = IQ

Never mind, that is horribly wrong.

I'll try to fish up those posts. Yay for search being back!

[Raven777]

I wonder how this translates to other stats. For example, the difference between a Commoner with Cha 10 and a 20th level Sorcerer with Cha 40.

[Zweisteine]

I wonder how this translates to other stats. For example, the difference between a Commoner with Cha 10 and a 20th level Sorcerer with Cha 40.

Exactly one stat can be easily measured and compared: Strength

Measure by seeing how much someone can hold off the ground for any length of time.

Check maximum lift tables.

Done.

[Flickerdart]

I wonder how this translates to other stats. For example, the difference between a Commoner with Cha 10 and a 20th level Sorcerer with Cha 40.
Well, there's an EQ (emotional quotient) but until someone figures out a way to quantify empathy and self-awareness, it doesn't come with a scale. In fact, our society doesn't really test for anything other than Intelligence - a bunch of people have done various non-standardized Strength evaluations, and it might be possible to measure Constitution by some mixture of how well someone can run a mile while resisting the flu, but the various physical ability scores change too quickly and unpredictably, whereas IQ pretty much stays the same. Wisdom is kind of an odd one since it can be testable, but again is very inconsistent over a lifetime.


Exactly one stat can be easily measured and compared: Strength

Measure by seeing how much someone can hold off the ground for any length of time.

Check maximum lift tables.

Done.
Except that Strength governs so many other things than just picking things up and then putting them back down - and you'll be hard-pressed to find a weightlifter who could jump as far as his STR score "evaluation" says he should.

[hamishspence]

"Your hand". Gollum was an idiot.

Bilbo had (luckily for him) taken his hand out right before Gollum made that guess, in the novel.

[Socksy]

I agree with the method in the OP, and will also add it's far better than the "divide/multiply by 10" some people seem to use.

It also gives me INT 22, so there's that.

Looking at some later posts, I have to disagree with the idea that Wisdom is part of IQ. I'm a genius, but the amount of times I've come up with the dumbest ideas ("I'll put this (metal) tin in the microwave to melt the contents!" followed by watching the pretty sparks instead of quickly removing it is one which comes to mind) would give me a horrible WIS.

Sorry about lack of quotes, I'm on mobile.

[Shinken]

IQ is more about how many ranks in have in how many Knowledge skills than anything else.

[Chronos]

IQ tests are designed to be independent of specific knowledge. I think it's fair to say that real-world IQ and D&D Int score are meant to measure the same thing.

And "Moderate mental disability, unable to live independently" from an IQ of 47 definitely does not mean "Int 0". The first clue there is the word "moderate". Someone with an IQ of 47 might not be able to go grocery shopping or cook, but they can still put food in their mouth, chew, and swallow. When you read "unable to live independently", think of about the amount of care you need to provide for a very young child. Someone with Int 0 can drool, and that's about it.

Ashtagon, 3d6 might not be exactly an ideal Gaussian distribution, but it's pretty darned close until you get way out into the tails.

[Gemini476]

I agree with the method in the OP, and will also add it's far better than the "divide/multiply by 10" some people seem to use.

It also gives me INT 22, so there's that.

Looking at some later posts, I have to disagree with the idea that Wisdom is part of IQ. I'm a genius, but the amount of times I've come up with the dumbest ideas ("I'll put this (metal) tin in the microwave to melt the contents!" followed by watching the pretty sparks instead of quickly removing it is one which comes to mind) would give me a horrible WIS.

Sorry about lack of quotes, I'm on mobile.

Did you take an actual IQ test or was it just one of those free online ones? Because a lot of them aren't very accurate.

[Shining Wrath]

"Your hand". Gollum was an idiot.

He guessed that, but fortunately for Bilbo he had just taken his out.

[Shining Wrath]

I wonder how this translates to other stats. For example, the difference between a Commoner with Cha 10 and a 20th level Sorcerer with Cha 40.

Thus the Diplomancer builds that break the game by turning everyone into the PC's friend.

[Z3ro]

I'm going to leave the whole IQ=Int thing alone (as I completely disagree, and several people have already elucidated my opinions better than I could), but I want to touch on this:


How would that impact a fight? Well, suddenly thrown into an empty room to fight with their bare fists alone, these two would probably be about equally matched. If you add a complex environment with weapons, cover, concealment, rough terrain, and hazards, the high Int character will gain a significant upper hand because they'll do a much better job of using that environment to their advantage. The Int 16 character will bait his opponent into the hazards, attack and drop behind cover, and try to take paths that force his enemy through rough terrain. The low Int character may do some of that, but not nearly as much and not nearly as effectively. If you add resources and time to prepare, the high Int character will probably win every single time.


This has been, in my experience, demonstratably false. Just being plain smarter has absolutely zero to do with combat ability. Being smart may make you quicker to learn how to do something like use terrain effectively, but it says nothing about inborn knowledge. People who haven't spent significant time studying things like combat, then suddenly dropped in those situations, tend to do exceedingly poorly.

The easiest example is the one I have the most experience with; MMA. You can take two untrained (but mismatched intelligently) people, and the smarter one won't necessarily be the better fighter. Heck, some of the best fighters I've known weren't exactly geniuses, but they put in the work and became great fighters. I've even seen people who's main problem was they were thinking too much; trying to puzzle out a solution when they should let their instincts take over.

So no, I don't agree that being smart will necessarily translate to better combat ability, even in the situation you presented.

[atemu1234]

Ashtagon, 3d6 might not be exactly an ideal Gaussian distribution, but it's pretty darned close until you get way out into the tails.

This. There may be "special cases" with more, but you have to realize that 18 intelligence would probably put you in the 2.5% category at the end of an IQ bell curve. From there the exceptions are such a small percentage that they can be effectively ignored without breaking the game.