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Old 05-27-2022, 07:05 AM   #1
hcobb
 
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Default Population Model

Assuming that 25% (2^2) of the human population is at each of 30 or 31 attribute points (i.e. average) and each point more or less than this halves the number (due to double XPs per attribute point on the high end), then Tollenkar at 48 attribute points is from a pool that's at 2 ^ (2 +48 -31) = 2*19 or one in half a million.

Assuming that Dran has a pop of 200k (humanoids, not counting the well-fed monsters), there is a 40% chance of a Tollenkar level humanoid in Dran. (The extra memory points and mana barely nudge the total XPs required.)
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Old 05-27-2022, 07:34 AM   #2
phiwum
 
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Default Re: Population Model

Ignore this. I badly bungled the mathematics, as Henry pointed out.

And, following this model, there are only about 195 characters with 36 attribute points in all of Dran.

Since it's not hard for PCs to reach 36 character points, that would mean that challenging encounters ("realistically" speaking) will tend to a group of relative incompetents outnumbering the PCs. Which, of course, is a kind of fight that I run sometimes[1], but I don't think I'll worry too much about the fact that in some PC battles, they might kill of 1% of the available 36pt NPCs.

It's interesting to think about the distribution of experience throughout Dran, but I wouldn't let it affect my game.

[1] But I do find that this kind of fight is hard to balance. Even incompetent NPCs can be surprisingly deadly when they have the advantage of numbers.

Last edited by phiwum; 05-27-2022 at 04:10 PM.
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Old 05-27-2022, 08:07 AM   #3
David Bofinger
 
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Default Re: Population Model

We really have no idea what any of the parameters you've assumed are. I suspect population is meant to be larger than this but I don't think anyone can prove it. I suspect Tollenkar isn't supposed to be top of the page but again who knows.
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Old 05-27-2022, 08:42 AM   #4
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Default Re: Population Model

36 attribute characters are one in 128, multiplied by a presumed 200k population for the Duchy of Dran gives over one and a half thousand.

An Armsmaster would reasonably be around 38 attribute points, and there are a fourth that many (as there are 36 attributers) so a pool of around 400, with no more than a dozen of the 400 in that job.

A lesser enchanter is say ST 8, DX 12, IQ 18 for 38 attribute points so a dozen of those also. (Wizards being selected for their training on the basis of having shown above averageness at age 6 after all.)

That gives three to half a dozen greater magic item enchanters in the Duchy.
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Old 05-27-2022, 09:03 AM   #5
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Default Re: Population Model

Quite right, I used the wrong base, Henry. My mistake.
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Old 05-27-2022, 09:03 AM   #6
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Default Re: Population Model

My campaign worlds have exactly the number of high- and low-powered NPCs as is necessary for the adventures, regardless of how that number might agree with their predicted frequency as provided by statistical models.
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Old 05-27-2022, 12:58 PM   #7
Bill_in_IN
 
Join Date: Dec 2021
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Default Re: Population Model

These probabilities of certain attribute levels across a population are interesting so far as establishing the potential uniqueness of PCs. However, I'm with Shostak and Phiwum. I wouldn't let it affect the NPCs needed for an adventure. Adventures are hard enough to populate with NPCs that are balanced with the PCs for a challenging game without adding more external restrictions.
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Old 05-28-2022, 08:41 PM   #8
tomc
 
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Default Re: Population Model

Quote:
Originally Posted by hcobb View Post
Assuming that 25% (2^2) of the human population is at each of 30 or 31 attribute points (i.e. average) and each point more or less than this halves the number <snip>
I think it's reasonable to assume that the curve is a bit flatter and longer as you reach higher attribute totals. Super competent characters probably have a higher survival rate because most threats are less threatening.

In other words, I expect more than half of the 39 point characters make it to 40 points, while assuming half of the 32s make it to 33 may be generous. YMMV
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Old 05-28-2022, 09:26 PM   #9
Skarg
 
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Default Re: Population Model

I think the sort of pondering Henry suggests here is worth considering, for GMs who are interested and up to the math, but that Henry's suppositions about the math seem pretty arbitrary and are not at all like the assumptions I tend to make.


Quote:
Originally Posted by tomc View Post
I think it's reasonable to assume that the curve is a bit flatter and longer as you reach higher attribute totals. Super competent characters probably have a higher survival rate because most threats are less threatening.

In other words, I expect more than half of the 39 point characters make it to 40 points, while assuming half of the 32s make it to 33 may be generous. YMMV
This certainly seems very true for combat-involved NPCs in my experience.
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Old 05-29-2022, 03:21 AM   #10
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Default Re: Population Model

Each attribute point doubles the XP cost, and doubles the damage from each point of aging.
The existence of one 48 attribute human puts the survival of any dragons at grave risk.
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