Sunday, February 18, 2018

Class distributions, part 3 (modeling a society)

Part 1
Part 2

From the 2e DMG, p. 17:

Only a few people actually attain any character level. Not every soldier who fights in a war becomes a fighter. Not every urchin who steals an apple from the marketplace becomes a thief. The characters with classes and levels have them because they are in some way special. 
It's common sense, and there are numerous passages to support, that only a fraction of people in an AD&D society are classified as adventurers. Most are normal folk, perhaps trained in some vocation, with some of them being stronger, hardier, or more intelligent than even many PCs. What if we wanted to find out, given a population, how many of each class should really be present?

Let's go back to the original "fall through" algorithm that classifies everyone either as having a single class or being non-classed. When we ran the numbers previously, we said that any qualifying person was assigned to a class; the only individuals not assigned a class were those who didn't qualify.

Ultimately, that's not realistic. There should be factors other than ability scores at play in an actual society: age, alignment and training considerations, desire, upbringing, and so forth.

We determined, rolling 3d6 in order, that slightly more than one in every thousand individuals would qualify to be a paladin, based on ability scores alone. But consider what else is required: the person would need to be of sufficient age, of proper alignment and disposition, willing to adhere to the strictness of the paladin's code, and raised under conditions that would allow for the training needed to ascend the ranks of the class. What percent of those meeting the paladin's ability score requirements would also conform to the above? Ten percent? Five percent? Less?

Let's suppose, very generously, that for any individual meeting the ability requirements for a particular class, there's only a 50% chance of the class actually being attained. I can adjust the algorithm to work as it did previously, but to reject half the sets of scores that qualify for each class. In other words, half of those who would otherwise meet the paladin requirements fall through and check for the "easier" classes instead. Some will end up being bards, druids, or fighters. Others will end up having no class at all.
*** Rolling method: 3d6 (in order) ***
*** Population: 100
   Pal: 0 (0%)
   Rgr: 0 (0%)
   Brd: 0 (0%)
   Drd: 0 (0%)
   Ftr: 39 (39%)
   Thf: 26 (26%)
   Clr: 14 (14%)
   Mge: 12 (12%)
   Nil: 9 (9%)

*** Population: 20000
   Pal: 15 (0%)
   Rgr: 20 (0%)
   Brd: 107 (1%)
   Drd: 322 (2%)
   Ftr: 7254 (36%)
   Thf: 4457 (22%)
   Clr: 2845 (14%)
   Mge: 1827 (9%)
   Nil: 3153 (16%)
As we still have far more "classed" individuals than non-classed, the 50% reject rate is not nearly enough. And perhaps some classes should have lower percentages than others? The paladin's non-ability requirements are such that members of this class should be rare indeed. Rangers, bards, and druids all have alignment (and to some extent environmental) restrictions. Fighters should be more common, requiring only martial training and permitted to be any alignment. Thieves can't be lawful good, and lock-picking can't be learned on a whim. Clerics and mages require access to religion and magic.

I don't have a perfect way to arrive at these values, so to start, I'm just going to make them up:
  • Paladin - 5%
  • Ranger - 10%
  • Bard - 10%
  • Druid- 10%
  • Fighter - 20%
  • Thief - 15%
  • Cleric - 10%
  • Mage - 10%
The above should be read as "Only five percent of individuals qualifying to be a paladin will attain the class." I'm still using a fall-through procedure: those that qualify for a class but get rejected by the percentage check still have a chance to be something else.

Here are the results for populations of 100 and 20,000:
*** Rolling method: 3d6 (in order) ***
*** Population: 100
   Pal: 0 (0%)
   Rgr: 0 (0%)
   Brd: 0 (0%)
   Drd: 1 (1%)
   Ftr: 17 (17%)
   Thf: 11 (11%)
   Clr: 7 (7%)
   Mge: 4 (4%)
   Nil: 60 (60%)

*** Population: 20000
   Pal: 2 (0%)
   Rgr: 4 (0%)
   Brd: 15 (0%)
   Drd: 58 (0%)
   Ftr: 2892 (14%)
   Thf: 1945 (10%)
   Clr: 1105 (6%)
   Mge: 1087 (5%)
   Nil: 12892 (64%)
These numbers look OK at the top, but the core classes feel too highly represented. 36% of a population isn't going to have class levels. The problem may be that very few individuals can qualify for a class like paladin or ranger to begin with, so it stands to reason that a larger cut of these prodigies will end up rising to their potential, despite the narrower requirements. I'll leave the numbers for the "hard" classes unchanged but reduce the core classes to:
  • Fighter - 3%
  • Thief - 2%
  • Cleric - 1%
  • Mage - 1%
*** Rolling method: 3d6 (in order) ***
*** Population: 100
   Pal: 0 (0%)
   Rgr: 0 (0%)
   Brd: 1 (1%)
   Drd: 0 (0%)
   Ftr: 1 (1%)
   Thf: 1 (1%)
   Clr: 1 (1%)
   Mge: 1 (1%)
   Nil: 95 (95%)

*** Population: 20000
   Pal: 1 (0%)
   Rgr: 5 (0%)
   Brd: 18 (0%)
   Drd: 67 (0%)
   Ftr: 447 (2%)
   Thf: 296 (1%)
   Clr: 143 (1%)
   Mge: 137 (1%)
   Nil: 18886 (94%)
This looks a lot better. Only one in twenty receives a character class, with a single party worth of adventurers servicing a small hamlet. The prevalence of spellcasters still feels high, but these numbers are usable for modeling a population in a campaign. I don't want to worry about fractional percentages at this point.

I hope this series of posts was interesting for anyone who ends up reading. I certainly think it's something I may use in my games going forward.


  1. Interesting conjecture!

    I've always analogized adventurers to modern professional athletes, figuring the numbers might be similar. The analogy is certainly less than perfect, mage/priest types require mental, rather than physical ability, there are hard limits on jobs for pro athletes, whereas anyone can choose to call themselves an "adventurer", etc.

    It's hard to nail down numbers, but from several sources it looks like roughly 1 in 30000 people work as "pro athletes". I think this gives us a starting point for estimating the numbers of Paladins, Rangers and Bards...the "elite" physical classes.

    1 in 30000 is clearly too low, and I think that's mostly driven by the second issue mentioned above, the finite number of positions available. What if the job of "athlete" was available to anyone who had the basic chops, i.e., not just the absolute best, but the very, very good? Let's say making a college team indicates sufficient "elite" ability. Most sources indicate that about 1% of college athletes make it as pros. So, from that it follows that 1 in 30000 would drop to about 1 in 300.

    So, in a major town of 20,000, we'd be talking roughly 60-70 individuals being divvied up as Pal/Rang/Bards. This feels kinda right to me.

    Following the path, would Fighters/Thieves be roughly equivalent to high school athletes (an interest and basic ability being the requirements)? Let's play that out. My best estimate of my high school is about 10% of the student body participated in athletics. In our city of 20,000, that gives us 2000 Fighter/Thieves. If this is a reasonably civilized, lawful place, the split between Fighter/Thief should, let's say, be about 90%/10%. That gives us 1800 Fighters/200 Thieves. When one considers all the jobs as City Guard/City Watch/Security/Bodyguard, etc, along with actual mercenary, soldier, and true adventurer types, I think this number is reasonable. 200 citizens engaging in some form of "Thiefly" activity also doesn't sound too crazy to me.

    So what about the "thinking" classes? With Mages, let's say that for practical purposes any Mage with less than a 50% chance of knowing a given spell is gonna be a washout. A bit arbitrary, but let's roll with it. That means to make the grade they need a min INT of 13. As I recall, the game analogizes this to a 130 IQ. Roughly 2.5% of the population has an IQ of 130 or higher. In our town of 20000, this would give us about 500 Mage candidates. Let's say 1 in 4 of those actually have the interest/aptitude to follow the Mage path (the rest would rather apply their intelligence to being merchants, city leaders, craftsmen, what have you), leaving us 125 practicing Mages. Seems not crazy.

    I have the hardest time with Clerics/Druids. WIS as a requirement is interesting. All the other requirements are either entirely or mostly objective. If you can lift something that's that. If you can dodge something, or avoid a trap, done and done. Even INT is a basically demonstrable thing. But WIS is, for the most part, subjective. I may think my friend Bob is a font of wisdom, but you might think he's a total fool...and who's to say? In game terms we, of course, treat it as completely objective, but when trying to analogize it as I've done with the other classes, it's hard to deal with. What are the requirements to be a minister? Objectively, nothing. To be ordained you have to display a certain degree of knowledge, but that relates more to intelligence.

    So there you have it. I like where I come out with everything but the Priest classes. Thoughts? Tim

  2. Hi Tim,

    I think there are two separate-but-related pieces to this: what percentage of a population are eligible to be adventurers vs. what should be the distribution of classes among these individuals? AD&D 1e, I think, draws a hard line that 1% of a population is of adventurer caliber. You could take the perspective that only this 1% actually get 3d6-in-order worth of ability scores at all. If you do this, then you can set the population size for the class algorithm to whatever that cut is, ignoring the other 99%.

    Another option is to say that any normal person gets 3d6 for ability scores. I think this is particularly justifiable if the DM uses a method like 4d6-drop-lowest for the PCs, as you're still putting those individuals on a pedestal.

    If you're giving any random commoner 3d6, the natural follow-up is to ask how many people with strength of 9+ get to be fighters, etc.? It does seem reasonable, to me, for a population to have select, non-adventurer residents with high abilities. A local sage might be extremely well-read or very wise; a seasoned blacksmith might be stronger than many trained warriors. Being a classed adventurer is about more than raw talent: I tend to see it as a combination of ability, training, circumstance, and desire.

    One area to tread carefully is in drawing the equivalence between guards/soldiers and actual fighters. You can of course make these all fighters, if you want, but I think 1e and 2e are consistent about distinguishing fighters from fighter-like occupations held by 0-level warriors. Saying that you have 1,800 of the latter in a 20,000-person city, even accounting for age and other variance, may not be unreasonable; saying there are 1,800 actual fighters may be pushing things unless you take a more liberal definition of "fighter" than the source books would suggest. (None of this would be "wrong" if it's how you want to do it. It just may not be consistent.)

    I like the idea of raising the requirements for certain classes (Int 13 for mage, for example) for the purpose of the algorithm, as you're right that mages with an Int of 9 or 10 likely aren't making it very far. You could also qualify mages as sets of scores with Int 13+ where Int is also the highest score. I like the elite athlete analogy; it's hard for most of us to comprehend how truly skilled these people are, since we only see them compete against each other and they make what they do look easy.

    In the end, the books provide some guidance on this stuff (I think 1e provides it more concretely than 2e), but it's always going to be subjective to a certain degree. Rolling methods and class requirements aren't really intended to simulate a large-scale population, which is why I found running these experiments to be interesting.

    Thanks for the comment and appreciate the insight!

    1. Thanks, Matt..and likewise!

      I would be considering the 1800 "fighter-types" to be the equivalent of 1st level or higher. This may indeed be an over-estimate in a town of 20,000. Hard to know. I do think that the majority of able-bodied males between say, 16-50 or so should be able to pull off the equivalent of 0-level man at arms type skill, which seems roughly the same as a 9 STR requirement (and not being absurdly low in DEX or CON. I may, though, be underestimating (or misinterpreting) the idea of a 0-level fighter.

      I think the more interesting path (I have to admit I'd never given it a lot of thought till now), is the idea of WIS as a requirement. It's hard for me to picture what "failing" as a Cleric would entail. The Gods and their agents just ignore you in your lack of objective wisdom? Anyway, thanks for reading!

      Good adventures! Tim

    2. Mechanically, the low-Wis cleric's survivability will be impacted by fewer bonus spells and more failed saves and ability checks. Beyond that, I think the low-Wis cleric will struggle to effectively minister to and gain new constituents, which are critical to spreading his/her faith.

      An example would be in the session our group played the other night: the party's priest, Audric, took to spending a day in the taproom where a number of concerned villagers had congregated after the previous night's attack (and brutal slaying of two commoners) by a pair of unidentifiable creatures bearing strange marks upon their faces. Audric made a sound effort to calm the hearts of these people and maintain their poise in the wake of uncertainty.

      In game, we didn't roll for any of this, as I didn't think it was needed, but you could definitely make the case that a low-Wis cleric won't be as effective in these situations if his/her words can't resonate to a wide audience. This folds into the cleric's ability to bolster the name of his/her deity, which is the sort of non-mechanical metric by which a cleric's success or failure would be measured.