Ability Score Breakdown by Population?

[Glyfair]

If you assume the general NPC population has 3d6 stats, there's a 1 in 216 chance of getting an 18 for each stat, a 1 in 72 chance of getting a 17, etc.

This is the key, though. That's the method used for PCs (one method anyway). NPCs have 3d6 according to the DMG, but that seems to be focused on PCs that characters interacti with.

My personal preference is to have "commoner average" be 8. In practice, though, I prefer to flatten the bell curve in some areas with more in the middle, some in the bottom and the least at the top.

 

[Nyeshet]

Then how do you rationalize 1-in-216 people having a stat of 3? Isn't that a bit high?

Not according to the 3d6 method of rolling (which just goes to show its weaknesses in regards to emulating real life). Besides, if you look at modern statistics you will be surprised at how many people are considered mentally or physically disabled. Recall that 1/216 is just shy of half of one percent.

Recent disability statistics for Japan, for instance, gives us the following:

Motor dysfunction (limb and body) 1,657,000 (56,5%)*
Visual disability 305,000 (10,4%)*
Hearing and speech disability 350,000 (11.9%)*
Internal organ disorder 621,000 (21,2%)*
Total 2,933,000
* (of the Total number of disabled: 2,933,000)

This is about 1% of thier population - and it is only for physical disabilities. Even if you ignore the visual / hearing, you still have organ disability (Con) equal to ~0.212% and limb / body disabilities (not necessarily just low str, which may or may not be considered a disability) at ~0.565%. If you consider the fact that Str and Dex problems are more or less lumped together, then the ~0.565% is suddenly halves to ~0.2825% Str, ~0.2825% Dex, and ~0.212% Con disability / severe penalty / etc.

Statistics for mental retardation / disability suggest a somewhat different view, however:

Mentally retarded persons 390,000
Mentally disabled persons 1,570,000
Total: 1,960,000

Mental Retardation, if we view this as extremely low Int, suggests only half as many as would be expected using the 3d6 system - if not less. Mental disabilities, on the other hand, are extremely high. However, if we take the total and divide by three (assuming retardation is but one factor of unusually low Int, and assuming low Int/Wis/Cha are equally divided among the population), then we find about .22% of the population suffers from either low Int, low Wis, or low Cha. This is -as with physical disabilities - half the expected score.

~0.25% vs half a percent. That suggests that - at worse - the extremes are off by a factor of two. Not bad, considering. More than close enough for most RPG work. So, perhaps it should be:

03,18 . . . 0.00231 (01/216 * .5000)
04,17 . . . 0.00992 (03/216 * .7143)
05,16 . . . 0.02579 (06/216 * .9286)
06,15 . . . 0.05291 (10/216 * 1.143)
07,14 . . . 0.09424 (15/216 * 1.357)
08,13 . . . 0.15278 (21/216 * 1.571)
09,12 . . . 0.20668 (25/216 * 1.786)
10,11 . . . 0.25000 (27/216 * 2.000)

So, 50% of the population is average in at least one stat, and 0.002% of the population (1 out of ~500) is phenomenally low or high in one stat. That sounds about right to me.

Granted, I only used statistics from one country, but it was the first that came up when I googled for such. I will also note that most disabilities might fall under higher stats than a '3'. Mental retardation, for instance, has several grades of variance. Some might easily be considered a 6 or 7, while others would likely be considered a 3. But they are all grouped together in the statistics above, which suggests that lower scores are even less common than the ~1/500 suggested above, and mid-level scores are even more common.

Perhaps, instead of varying from 0.5 for lower scores to 2.0 for higher scores, I should have used 0.25 for lower scores and 4.0 for higher scores. There is not enough data to be certain if this would be more accurate or not, however. In the end, it is mostly guess work, and I think the scheme I wrote above is accurate enough for most suppositions and approximations for RPG worlds.

Of course, trying to use real world statistics for something as relative as RPG is likely an act of futility. But it does suggest a more moderate view than 3d6 would typically allow.

 

[Ace]

My habit is to asssume that anyone that most folks have stats from 6-12 . Anything more than this and they would be adventurer types -- any less than this they would be dead ....life is dangerous in D&D worlds

Something to consider though with the RAW-- every Village of 200 people has 6 persons either adults or children with an 18 stat -- 1 for each stats -- thats a lot of people

 

[S'mon]

Looking at this recently & basing it off Point Buy instead of 3d6 I used something like:

Base person 16 Point Buy;
1/8 14 PB, 1/16 12 PB, 1/32 10 PB 1/64 8 PB 1/128 6 PB 1/256 4 PB etc

1/8 18 PB 1/16 20 PB 1/32 22 PB 1/64 24 PB ("adventurer" level) 1/128 26 PB 1/256 28 PB etc

 

[Conaill]

I do mine by distribution according to a point buy now. I use something roughly like the following:

10% of the population: Point buy less than 13 (
80% of the population: Point buy 13-17 (ordinary folks, thugs, mooks)
9% of the population: Point buy 18-22 (important NPC's)
0.9% of the population: Point buy 23-27 (PC's allies, sub-bosses)
0.09% of the population: Point buy 28-32 (PC's fall here, PC peers and mentors)
0.009% of the population: Point buy 33-37 (BBEG)

Interesting idea. You could also link this to the deafult assumption that the population as a whole fits a s3d6 stat distribution. Here's the pointbuy distribution you would get from 3d6:

10% of the population: Point buy less than 10 (yikes!)
50% of the population: Point buy less than 18 (median is 17, average is 18)
80% of the population: Point buy 11-27 (quite a wide range... 50% between 13-22)
9% of the population: Point buy 28-37
0.9% of the population: Point buy 38-45
0.1% of the population: Point buy > 45

That's a lot more variation from the 20 point default NPC pointbuy than I had expected. So if PC's are the top 1% of the regular population, we should be rolling up PC stats closer to a 40 point buy!

Then again, personally I don't really have any problem with the idea that my budding young hero may very well start out with stats that are below those of the town's blacksmith, constable or major. After all, it's not the stats that make the hero! If we were to say that beginning heros are roughly in the top 1/3 of the general population, that would correspond to to an average pointbuy of around 26, which seems much more reasonable. (The top 1/4 of the total population averages around point buy 28, top 15% around point buy 30, top 10% point buy 32.)

 

[orsal]

Your numbers don't work out right:

03,18 . . . 0.00231 (01/216 * .5000)
04,17 . . . 0.00992 (03/216 * .7143)
05,16 . . . 0.02579 (06/216 * .9286)
06,15 . . . 0.05291 (10/216 * 1.143)
07,14 . . . 0.09424 (15/216 * 1.357)
08,13 . . . 0.15278 (21/216 * 1.571)
09,12 . . . 0.20668 (25/216 * 1.786)
10,11 . . . 0.25000 (27/216 * 2.000)

I'm not sure where you got your multipliers from, but the probabilities don't add up to one. Since each probability is the probability of two different values, each one should count twice. Add up all those probabilities, times 2, and you get around 1.6. You should get exactly 1.

So, 50% of the population is average in at least one stat, and 0.002% of the population (1 out of ~500) is phenomenally low or high in one stat.

1 out of 500 is 0.2%, not 0.002%.

Also, you don't have the probabilities for "at least one stat", you have the probabilities for any given stat. If your numbers were right (which, as I noted above, they couldn't all be), then you have 50% have either 10 or 11 on any given stat. If the probabilities for different stats are independent, that means 63/64 of the population have at least one 10 or 11. If 0.2& of the population have 3 in any given stat, and another 0.2% have 18 in any given stat, then a little over 2% have at least one stat which is either 3 or 18.

That sounds about right to me.

Any probabilities could sound "about right", depending on how narrowly you define "average" and "phenomenally high or low". I do the reverse of your process. I start with the distribution; that's dictated by the mathematics of 3d6. I then use that as my guideline for interpreting what various ability scores mean. So, how strong is a human with 18 strength? As strong as the strongest 0.5% of the population. How stupid is a human with 3 intelligence? Think of the dumbest 0.5% of the population. The top 25% have scores 13-18, so a score of 13-14, for example, is noticeably above average but not exceptional, while a score of 7-8 is likewise noticeably but not exceptionally low.

 

[Celebrim]

Interesting idea. You could also link this to the deafult assumption that the population as a whole fits a s3d6 stat distribution.

The thing is, I'm no longer convinced that the 3d6 distribution has any real meaning. It's one of those legacy assumptions that is hanging around in defiance of the fact that the rest of the game has completely changed.

A similar situation in 1st edition concerned the cost of labor. EGG knew quite abit about medieval economies, enough to know that a working wage was about 1 s.p. per day. This assumption underlies everything from his cost of hiring labor, to the ammount of money that a PC could collect in taxation once he reached name level and built a stronghold. EGG also knew that historically, the price of gold was fixed at 1 gold coin per 20 silver coins. But these historically derived numbers continued to exist in a game in which for various reasons, PC wealth was measured in terms of gold coins and in which treasure was a necessary measurement of player experience (and advancement). Hense, by the time a character reached 9th-12th level he was so fantasticly wealthy that not only was the taxes he could collect from silver peice earning farmers basically irrelevant, but he could leverage whole populations to work for him for years at wages far above the rest of society. One standard's assumptions just didn't match with the assumptions of the other standard.

The assumption that attributes are distributed to the members of society along the bell curve generated by rolling a 3d6 is one of those assumptions that just doesn't agree any more with the assumptions of the rest of the game. Back in 1st edition, it was not really necessary for the PC to have anything like extraordinary attributes to be an extraordinary character - that is to find him or herself in the roll of a hero. Back in 1st edition, the thing that made a Player Character more extraordinary than your average Non-Player character was PC's could gain experience points. It's an assumption so common to 3rd edition that I doubt anyone much notices it, but everything in 3rd edition can presumably gain experience points. In first edition, most everything could not gain experience points. The ability to gain class levels was an extraordinary and supposedly rare ability. The vast majority of the characters in the world regardless of race were stuck as fixed HD 'monsters' that were incapable of advancement. Your average human was stuck as a fixed 1/2 HD 'monster' and no ammount of experience could change that. A careful reading of the description of NPC's reveals that even most leveled NPC's - even those of say 8th level - were incapable of gaining any more levels. They simply had been 'made' that way and that was that. Only a tiny portion of the NPC's - 'henchmen' - in the world possessed the extraordinary power of bettering themselves the way the PC's did. So every PC was by definition extraordinary, and as we all know experience was far more important in AD&D than your attributes (as lampooned in Terry Pratchett's 'Interesting Times' for example).

Contrast this to the situation in 3rd edition. Everything in the game can presumably level up. Even your lowly 'commoner' has a 20 level progression table. If the PC's do not possess extraordinary attributes, then it is highly unlikely that they will stand out in way as potential heroes. If the PC's are mere 25 point buy characters or even 28 point buy characters, and some 10% of the population is - even assuming nobody else out there has any experience - more capable than them by virtue of superior attributes, why does society need the PC's to do anything? Why isn't it that group of 48 point buy NPC's that the community is depending on to save the day? Surely they are more qualified, more likely to have this skills to do the job, and more likely to be in a position to do the job should it come up? If the PC's are merely 'a bit above average' it makes coming up with good hooks all that much harder. I balk at the notion that the PC's are merely lucky (or 'unlucky'). They are heroes. They are supposed to stand out as extraordinary. They dont' have to be veritable demigods, but they have to at least stand out in a crowd.

 

[No Name]

Why not just use a real bell curve instead of one created by 3d6?

For example, the top 2% of people tested have an IQ of ~130+. Let that equal a 13 in D&D. With 10 as an average, 2% of people should have a 7 or less. Apply that curve to all six stats. So for any given stat, 96% of the population will score from 7 to 13.

Sure, it's very generalized, but only 4% of a world population outside of the norm seems reasonable. Of course, that's still a wide range of stats. You could have anything from the strongest man (14 STR) in Generic D&D Village Name to the old sage (17 INT, 18 WIS, 15 CHA) on the mountain, as well as the other end of the extreme.

 

[S'mon]

The thing is, I'm no longer convinced that the 3d6 distribution has any real meaning. It's one of those legacy assumptions that is hanging around in defiance of the fact that the rest of the game has completely changed.

It's funny how these things change over time - when D&D started, 3d6 created the typical _adventurer_, average 10.5, "normal" people didn't have stats; if they did have stats they'd be well below 3d6 average 10.5. Then adventurers got best 3 out of 4d6 and average people got 3d6, creating the bell curve analysis we're discussing now. Then came 3e and Point Buy, with heroes getting 25 PB or Default Array - and these days I see many products (Conan, Grim Tales, etc) where "average" people get the Default Array of 15 14 13 12 10 8*! It seems like stat inflation is inevitable.

IMC now PCs get 28 PB or best 3/4d6; while typical competent NPCS are typically +2 in 2 stats, which is 20 PB. Elite NPCs IMC get 24 PB (eg +2 in 3 stats), average NPCs get 14 or 16 PB (+2 in 1 stat). I then give +1 stat per 2 levels so high levellers have high stats.

*Edit: Although this is technically 25 PB it's so inefficient a distribution it's really more like 22 PB in value terms.

 

[Al]

Why not just use a real bell curve instead of one created by 3d6?

For example, the top 2% of people tested have an IQ of ~130+. Let that equal a 13 in D&D. With 10 as an average, 2% of people should have a 7 or less. Apply that curve to all six stats. So for any given stat, 96% of the population will score from 7 to 13.

Sure, it's very generalized, but only 4% of a world population outside of the norm seems reasonable. Of course, that's still a wide range of stats. You could have anything from the strongest man (14 STR) in Generic D&D Village Name to the old sage (17 INT, 18 WIS, 15 CHA) on the mountain, as well as the other end of the extreme.

The problem with this is of course the question of where one starts. One can begin by taking the bell curve, buying the old canard that IQ = Int x 10 and then shoe-horn the statistics necessary. The major deficiency with this approach is that it de facto makes any PC with an Intelligence of 7 of less unplayable. With a score of 5 or below, our friend the half-orc will be instutionalised, not saving the world. The same could apply for other low PC statistics: the odd 5 or 6 here or there is certainly a disability, but when one jury-rigs the system so that a 5 moves from being "within the scope of normality but deficient" to "utterly handicapped" it queries the playability of certain characters.

To compensate, I have long-maintained that IQ should be modelled as (Int x 5) + 50. This approximates reasonably well to a standard 3d6 bell curve, centres the 10/11 at roughly the mean of IQ distribution and has the advantage that means that the poor soul with a 5 in Intelligence didn't do very well at school but can at least count if he takes his gloves off.