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  1. - Top - End - #1
    Barbarian in the Playground
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    Default Int scores and the bell curve

    OK, so if you roll 3d6, you end up with a pretty good bell curve.

    Now, I don't like d&d Int is exactly the same as what an IQ test measures in real life, but it's the closest approximation. So, what IQ would different Int scores correspond to, and what would that mean for a character?

    I got the percentile ranks for each 3d6 roll from AnyDice, and compared it to the IQ Percentile and Rarity Chart. And I got the following:

    Int 3 - IQ 61
    Int 4 - IQ 68
    Int 5 - IQ 74
    Int 6 - IQ 80
    Int 7 - IQ 85
    Int 8 - IQ 90
    Int 9 - IQ 95
    Int 10 - IQ 100
    Int 11 - IQ 105
    Int 12 - IQ 110
    Int 13 - IQ 115
    Int 14 - IQ 120
    Int 15 - IQ 125
    Int 16 - IQ 131
    Int 17 - IQ 139
    Int 18 - IQ >139

    Now, the percentages get messed up at the extremes, because a true bell curve doesn't have a minimum or maximum score. So, looking towards the middle of the curve, one point of Int seems to equal 5 IQ points. Also, 10 is the mean here, whereas if you look at the nonelite array, the mean score for races with no racial modifier should be 10.5 instead. So, I'll smooth out the curve and move the mean a bit. I'll also fill in the tail ends.

    Int 1 - IQ 52.5
    Int 2 - IQ 57.5
    Int 3 - IQ 62.5
    Int 4 - IQ 67.5
    Int 5 - IQ 72.5
    Int 6 - IQ 77.5
    Int 7 - IQ 82.5
    Int 8 - IQ 87.5
    Int 9 - IQ 92.5
    Int 10 - IQ 97.5
    Int 11 - IQ 102.5
    Int 12 - IQ 107.5
    Int 13 - IQ 112.5
    Int 14 - IQ 117.5
    Int 15 - IQ 122.5
    Int 16 - IQ 127.5
    Int 17 - IQ 132.5
    Int 18 - IQ 137.5
    Int 19 - IQ 142.5
    Int 20 - IQ 147.5

    Now, the question is, is this actually how Int works in d&d? I don't think so, because of what the game says about Int 1 and 2 creatures.

    First, it says that animals have an Int of 1 or 2. I can't find the reference right now, but I'm pretty sure it also says that you must have at least 3 Int in order to be able to speak languages.

    This completely throws the above table off, because a person with an IQ of 52 (equivalent to Int of 1) is only mildly to moderately cognitively disabled. People with IQs from 35-49 can speak well enough to cover basic needs.

    As for the comparison to animals, well, most IQ tests simply can't be used on animals. However, Piagetian cognitive stages are strongly correlated with IQ, and people have done a lot of Piagetian cognitive tests on animals.

    Regular cats (Int 2 in d&d) typically max out at stage 4 object permanence, which human infants master at 8-12 months. Dogs (also Int 2) struggle with stage 6 object permanence tasks, suggesting that they're just barely meeting that stage - humans master that stage at 18-24 months old. Apes (also Int 2) do perform at roughly the level predicted by this scale, passing Piagetian conservation tasks (also passed by 7 year old human children), however I strongly suspect that the makers of d&d were underestimating apes. In any case, if an animal functioning cognitively like a 8-12 month old human has an Int of 2, then Int of 1 must be much lower than IQ 52.

    If I take the average of cats and dogs, that implies that a 'typical' Int 2 creature functions at the same cognitive level as a 15 month old child. According to the IQ = 100 * mental age/chronological age (with adults counted as 16 years chronological age, regardless of actual age), that's an IQ score of 7.

    So, any tips on a better approximation of how Int relates to IQ scores? Should I just assume that Int * 5 = IQ, and humans in d&d have a different IQ distribution than real-life humans?

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    Default Re: Int scores and the bell curve

    1 and 2 are outliers with special rules. I would not hold the scale to be a linear one at that stage.
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    Default Re: Int scores and the bell curve

    Quote Originally Posted by Flickerdart View Post
    1 and 2 are outliers with special rules. I would not hold the scale to be a linear one at that stage.
    Pretty much that. Consider that given how races roll for stats (INT penalties excluded), there's no way for them to get an INT below 3. Similarly, below that point on the scale, a human would be barely independent, and certainly not fit to travel the world as an adventurer.

    Also, while the 5 point step works at the middle, you can see that it becomes inaccurate at the ends.
    Last edited by Esprit15; 2016-01-21 at 12:55 PM.
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    Default Re: Int scores and the bell curve

    Keep in mind IQ is all about measured performance relative to the population - how far from average.

    One version of ability modifiers ran 9-12 as 0, 13-15 as +1, 16-17 as +2, 18 as +3, with the penalties mirrored on the other side. On the original bell curve, that corresponds to +/-1 per standard deviation from the mean. This works well if you want your hypothetical distribution of 3d6 rolls to meet the hypothetical distribution of the population.

    Most IQ tests set to a SD of 15 points, making 85-115 the center average, IQ 115 (+1) at around 13 on the 3d6 bell, etc. Now, if you scrap the actual score distribution, you can focus on the modifiers. Each +/-1 is 15 points. Using the 3.0 and later linear scaling, you could say that each stat point is about a 7 1/2 IQ points. This also shifts the SD to 12, 14, 16, etc.

    So
    Quote Originally Posted by Esprit15 View Post
    Also, where does the natural (only age and stat investment before epic levels) maximum for a human of 26 lie on the IQ test?
    is about 220, maybe. When you get past about +3 to +4, the norms simply don't exist for the tests, making scoring a crude approximation.
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    Default Re: Int scores and the bell curve

    Consider the normal range of intelligence for an independently functioning adult human is 3-18, and apply IQ scores based on that assumption. Below 3 is animal, infant or mentally disabled intelligence. Above 18 is super-human/off the scale of the test.

    In other words, a character with 3 int should be considered to have an IQ sufficient to speak and understand language, learn skills required to fight with weapons and armor, and be an adventurer, in general (can count and understands concepts like trading and paying for things with currency).

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    Default Re: Int scores and the bell curve

    As I recall, the 1e PHB said that Int was basically (IQ/10). So an INT of 10 means an IQ of 100, an INT of 6 means IQ 60 (and was the minimum INT for a character to be anything more complicated than a fighter), an INT of 15 means IQ 150.

    Seems fair to me. It does mean that the 3d6 bell curve is a bit more swingy than the distribution of the general population - but 18 INT is supposed to be something pretty special. A measly 140 IQ doesn't seem to me to meet that standard, I've known a lot of people who've tested at that level.
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    Default Re: Int scores and the bell curve

    Quote Originally Posted by veti View Post
    As I recall, the 1e PHB said that Int was basically (IQ/10). So an INT of 10 means an IQ of 100, an INT of 6 means IQ 60 (and was the minimum INT for a character to be anything more complicated than a fighter), an INT of 15 means IQ 150.

    Seems fair to me. It does mean that the 3d6 bell curve is a bit more swingy than the distribution of the general population - but 18 INT is supposed to be something pretty special. A measly 140 IQ doesn't seem to me to meet that standard, I've known a lot of people who've tested at that level.
    Except that statistically, you've likely run into far more people below that. 140 is well outside the norm, statistically.
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    Default Re: Int scores and the bell curve

    Is this for D&D? 3.x allowed you an int bonus for knowledge checks, so presumably education added to int as much as IQ. Presumably high level wizards with int scores well over 20 would be like professors and other highly educated types.

    AD&D said that strength was the amount of weight you could lift over your head in a two handed military press (which was easily my worst lift). I doubt that was ever designed to match the bell curve, especially for a medieval population. Note that AD&D strength was particularly weird. It included "exceptional strength" as a percentage between 18 and 19 (with massive bonuses for 18(00), the maximum human strength). This meant that any means to jump to 19 (or higher) gave something like a +7 to hit bonus (18 was something like +2) and fairly high damage bonus (or the other way around. If you played Baldur's Gate, it should have been in there).

    I don't think I've seen any other way of matching any D&D attribute (and few other role playing games) to real life measurements (height and weight obviously excepted).

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    Default Re: Int scores and the bell curve

    Quote Originally Posted by Esprit15 View Post
    Pretty much that. Consider that given how races roll for stats (INT penalties excluded), there's no way for them to get an INT below 3. Similarly, below that point on the scale, a human would be barely independent, and certainly not fit to travel the world as an adventurer.
    Quote Originally Posted by Thrudd View Post
    Below 3 is animal, infant or mentally disabled intelligence.
    I think anyone with less than 3 Int wouldn't even be able to take an IQ test

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    Default Re: Int scores and the bell curve

    I don't believe Intelligence is necessarily a strictly linear curve - or even necessarily related to IQ. It jumps between 2 and 3.

    Justification: Neither is 3.5e Strength, which is the only attribute score with a clear connection to real-world numbers, and starts out linear (from 1-10) and then becomes geometric from 11 onward.
    Last edited by bulbaquil; 2016-01-21 at 09:59 PM.
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    Default Re: Int scores and the bell curve

    Quote Originally Posted by Esprit15 View Post
    Except that statistically, you've likely run into far more people below that. 140 is well outside the norm, statistically.
    Yes, but not that far outside it, in my experience at least. 18 INT should be one of the smartest people on the planet. 140 IQ is just "pretty smart". 18 INT should mean "world-class smart".
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    Ettin in the Playground
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    Default Re: Int scores and the bell curve

    1e AD&D is the first version to explicitly state INT score is analogous to IQ, and Intelligence ability is quite clearly a stand in for g (=general intelligence). Mapping IQ score bell curve to 3d6 curve, like Ettina did in the first post, is the sanest way to compare the two measures. IQ = INT * 10 is the other well-known version (originating from Dungeon magazine, I believe), but it leads to a weird disparity between statistical distribution of Ability score rolls and the distribution the IQ scores would imply.

    Anyways, the idea that "INT 18", or heck, 18 in any ability should be "one of the awesomest on the planet" is stupid. The sanest way, again, is to use the actual statistics given by 3d6 roll. Especially since most versions of D&D allow for scores higher than 18!

    It ought to be remembered that g, and hence INT, is and was not intended to be sole descriptor of cognitive ability. D&D has two other abilities to rate various s (=specialized intelligences): Wisdom and Charisma. If a person or animal performs better than their IQ / INT suggests, you can chalk it up to one of those two. d20 versions of the game acknowledge this, with animals having average to good Wisdom to represent their instincts even if their INT is set at 1 or 2.

    This said, I do agree d20 undersells animal intelligence. It's worth noting that AD&D had no hard rule on how intelligent animals as a category should be, instead rating each species invidually. Most animals in, for example, 1e Monster Manual are of animal intelligence (= INT 1 or 2), but some (notably, primates) are semi-intelligent (INT 2 to 4), low-intelligence (INT 4 to 7) or even average human intelligence and above. If you wanted to make a more realistic version of d20, you might want to give higher INT scores to those animals which are known to be on par with human children (pigs, canines, corvids, parrots etc.).
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    Default Re: Int scores and the bell curve

    Quote Originally Posted by veti View Post
    18 INT should mean "world-class smart".
    Why do you say that? Any level 1 jerk can have an 18 INT. That's a very low bar for world-class.
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    I'm going to be honest, "the Welsh became a Great Power and conquered Germany" is almost exactly the opposite of the explanation I was expecting

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    Default Re: Int scores and the bell curve

    It is worth keeping in mind that IQ is not really a good measure of anything. It is to one's intelligence what your BMI is to your health. Any doctor worth their salt will tell you that BMI doesn't really mean anything. According to that every competitor in a body building competition is morbidly obese. Why? Because all that muscle adds weight to push them that far up the scale. It's an obsolete method of rating based on faulty science and reasoning. IQ is the same thing. But ignoring that, and for the sake of argument, assuming it does have value IQ only measures potential. Just because you have 18 int does not mean you will show it.
    Last edited by Dhuraal; 2016-01-22 at 10:32 AM.

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    Ettin in the Playground
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    Default Re: Int scores and the bell curve

    @Dhuraal:

    You are, quite simply, wrong.

    No-one these days pretends theory of general intelligence is flawless. But it's still widely used as a statistical tool and correlations of IQ with various other things are still a popular and important object of study. Why? Because there are no better competitors. The strongest challengers to IQ tests in psychometry are basically IQ tests with some personality test elements added on top.

    Ditto for BMI. Every good doctor knows BMI is not sufficient measure of health, but it's still useful. A complete study of body structure doesn't abandon BMI charts, it supplements them with other information, such as fat-to-muscle ratio.
    Last edited by Frozen_Feet; 2016-01-22 at 10:39 AM.
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    Default Re: Int scores and the bell curve

    Quote Originally Posted by veti View Post
    Yes, but not that far outside it, in my experience at least. 18 INT should be one of the smartest people on the planet. 140 IQ is just "pretty smart". 18 INT should mean "world-class smart".
    Yeah....no. 140 is not just "pretty smart" it's borderline genius. Pretty smart is 120-130.

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    Default Re: Int scores and the bell curve

    The issue here is that there is no real way to get the two systems to align; either 18 is genius-level IQ, and it - and 17, which is only slightly lower - are far too common, or 18 is simply "pretty darned smart", in which case geniuses cannot naturally exist.
    ~ 1 in 200 will naturally have an int of 18; without magical intervention, there's not too many ways they can exceed this maximum. Levelling up is just about the only way, and it works, but it doesn't mirror real-life.
    So, your options become:
    18 int is representative of those few who are truly exceptional; the child prodigies, the most intelligent people in the world. It just so happens that in this world there are a lot of them.
    18 int is the natural limit; child prodigies and the like don't exist, there is a ceiling of intelligence with no outliers, which doesn't mirror real life either.
    18 int is the limit of what you're born with; child prodigies still don't exist - or exist at a fairly high rate - but the truly exceptional are those who put points into Int as they level up.
    That's all I can think of, at any rate.

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    Default Re: Int scores and the bell curve

    If you want a prodigy, give them the Prodigy template from DMG2. Problem solved, moving on.
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    Quote Originally Posted by Artanis View Post
    I'm going to be honest, "the Welsh became a Great Power and conquered Germany" is almost exactly the opposite of the explanation I was expecting

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    Default Re: Int scores and the bell curve

    Quote Originally Posted by Ettina View Post
    OK, so if you roll 3d6, you end up with a pretty good bell curve.

    Int 3 - IQ 61
    Int 4 - IQ 68
    Int 5 - IQ 74
    Int 6 - IQ 80
    Int 7 - IQ 85
    Int 8 - IQ 90
    Int 9 - IQ 95
    Int 10 - IQ 100
    Int 11 - IQ 105
    Int 12 - IQ 110
    Int 13 - IQ 115
    Int 14 - IQ 120
    Int 15 - IQ 125
    Int 16 - IQ 131
    Int 17 - IQ 139
    Int 18 - IQ >139
    This seems off . . .

    Does this look right?

    INT 03 IQ 047 Percentile 00.46
    INT 04 IQ 067 Percentile 01.84
    INT 05 IQ 073 Percentile 04.61
    INT 06 IQ 079 Percentile 09.23
    INT 07 IQ 084 Percentile 16.17
    INT 08 IQ 089 Percentile 25.89
    INT 09 IQ 095 Percentile 37.46
    INT 10 IQ 100 Percentile 49.96
    INT 11 IQ 105 Percentile 62.46
    INT 12 IQ 110 Percentile 74.03
    INT 13 IQ 115 Percentile 83.75
    INT 14 IQ 120 Percentile 90.69
    INT 15 IQ 127 Percentile 95.31
    INT 16 IQ 133 Percentile 98.08
    INT 17 IQ 141 Percentile 99.46
    INT 18 IQ 150 Percentile 99.92
    Last edited by darkrose50; 2016-01-22 at 12:22 PM.

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    Default Re: Int scores and the bell curve

    There's no point trying to be more precise or accurate with a system than its creators were.

    Anybody, including the rulebook, who says that 3d6 represents a true bell curve is simply mistaken.

    The Central Limit Theorem shows that adding a large number of independent random variable together will approximate a bell curve, but 3 is not a large number, and 3d6 is not a bell curve. It's actually three quadratics - one from 3-8, one from 7-14, and one from 13-18. (Yes, they overlap.)

    If you added 30 or more d6s, you get something that approximates a bell curve.

    The rules writers may have said that INT maps onto IQ, but nobody did the necessary careful analysis of cognitive functions to make that true. INT means what the actual mechanics say it means - number of wizardly spells to cast, number of languages, ability to succeed at knowledge skills, etc. There was never a careful mathematical modeling to ensure that, for instance, the amount of IQ that improves the ability to Appraise by 10% would also allow one more language to be learned.

    [And in any event, no analysis of 3d6 can possibly apply to scores of 1 or 2.]

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    Default Re: Int scores and the bell curve

    Quote Originally Posted by Elderand View Post
    Yeah....no. 140 is not just "pretty smart" it's borderline genius. Pretty smart is 120-130.
    Yes, 140 is the starting of genius. One with an IQ of 140+ can call herself a genius. Nobel Prize winners evidently tend to have ~140 IQ.

    My babysitter has an IQ of ~167, and three masters degrees . . . she is 1/100,000 in smarts. Too bad (job-wise) her degrees are in English, and not math. All my genius friends in math (engineering and the like) get their doors busted down offering them jobs.

    One engineering guy I know (as part of his job) travels around telling other engineers how and why their ideas suck. He could find a job at a drop of a hat, and is rather sour that Google did not hire him.
    Last edited by darkrose50; 2016-01-22 at 12:56 PM.

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    Default Re: Int scores and the bell curve

    Two issues:
    On the low end, Int 3 can read (unless pure barbarian).
    On the high end: anybody want to take a stab at how smart Bede was? He knew as much than anyone in England +/- a few hundred years, and would make a great example of "top level intelligence in a fantasy society". He couldn't have grown up with too many books, no other media. On the other hand, pre-literate society had great tricks for memory (and just assume that Bede knew it, that's why I picked Bede). Even if you *were* literate, you probably couldn't afford the paper (velum, whatever) to write whatever you wanted to remember down, so you had to learn the memory tricks. I can only assume that someone who practiced strong memorization would have a higher general intelligence (all else being equal, which is strictly not true in this case) than those who don't. In any event I'd peg Bede with a 20 int (in AD&D or 5e, 3.x doesn't fit limits well).

    Don't read too much into it: int scores follow a bell curve because they are created with dice. IQ seems to follow the bell curve, but probably stops working down at the low end due to much of it due to specific genetic damage (Down's syndrome comes to mind).

    We can't even get hit points to match reality. The best explanation is that higher level characters cheat death until exhaustion, then falling does a straight 1d6 per 10' (regardless of level). Don't try to match D&D to the real world, unless you really like the jokes of the early OOTS.

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    Default Re: Int scores and the bell curve

    Quote Originally Posted by Strigon View Post
    18 int is representative of those few who are truly exceptional; the child prodigies, the most intelligent people in the world. It just so happens that in this world there are a lot of them.
    I thought PCs and NPCs get their stats rolled differently, which means the rolling of stats as we're talking about now applies only to PCs.

    As in, the extraordinary, unique, one out of a hundred PCs, as opposed to the boring old NPCs.

    If we selected from a group of extraordinary people (the PCs), there'll be many more 18 Int characters. Which is great, because we want to play extraordinary people we call the PCs.

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    Default Re: Int scores and the bell curve

    PC's normally (not always, and depending on the system) roll 4d6b3, while NPC's generally roll 3d6. PC rolling methods basically weed out the average to find the above average person that survived the dangers of their backstory.
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    Default Re: Int scores and the bell curve

    Quote Originally Posted by wumpus View Post
    I can only assume that someone who practiced strong memorization would have a higher general intelligence (all else being equal, which is strictly not true in this case) than those who don't.
    Memorization is Autohypnosis, which is WIS.
    Quote Originally Posted by Inevitability View Post
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    Quote Originally Posted by Artanis View Post
    I'm going to be honest, "the Welsh became a Great Power and conquered Germany" is almost exactly the opposite of the explanation I was expecting

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