Fun with population and levels

[Alzrius]

Recently, I was reading a thread over on a thread on the Paizo forums about character populations and levels, when someone posted about how they thought that an old Greyhawk supplement had said that one-half the population was 1st level, and that segment halved each time you went up a level. That meant that one-fourth of the population was 2nd-level, one-eighth of the population was 3rd-level, etc.

He couldn't cite what Greyhawk book said this, and I suspect he's misremembering, but it struck me as a very cool way of calculating the relative ratio for character levels, especially higher-level and epic-level characters, against the background of the general population. Just for fun I decided to plug in some higher numbers.

For example, let's calculate how many 30th-level characters exist in the world under this system.

Since the denominator of this particular fraction (e.g. 1/X) needs to double each time it goes up a level, we'll need to figure out what it would be by the time we reach thirty places. Luckily, we can calculate that fairly easy as follows: X = 2^N, where N is the level we're inputting. Given that, the number we're searching for here is 1,073,741,824.

Now that we know that, we can properly compute what we're looking for: only 1 person in every 1,073,741,824 is level 30. So we divide 1 by 1,073,741,824 and get 0.000000000931322574615478515625.

Wow, that's a big, long, ugly number! It is, however, just a fraction (multiply it by 100 to turn it into a percentage) and so doesn't seem to have much practical value.

The practical value comes from multiplying this fraction into the total population. Suppose that Greyhawk had a population equal to our own world, or seven billion. If we multiply 0.000000000931322574615478515625 with 7,000,000,000 we get a result of 6.5, which we'll round down to 6.

Long story short, then, is that (using the above metric) there are six level 30 characters in a population of seven billion. That can be a fun sort of number to world-build (or just theory-craft) with, particularly if you use U_K's standard of assigning (in IH: Ascension) a link between divinity templates and equivalent levels - for example, Ascension tells us that level 30 is the minimum level needed to be a demigod. So out of a population of seven billion, only six people would ever ascend far enough to become demigods.

Plug in higher levels (e.g. a level 100 greater deity) against a greater background population (let's say 700,000,000,000,000,000 for the population of an entire galaxy), and as soon as you get a non-fraction number, you can figure out the amount of people you'd need to get someone of that level (e.g. the ruler of that entire galaxy).

Who says uber-epic levels aren't fun?

 

[Upper_Krust]

Hey Alzrius mate!

We always used that rule of thumb in our campaigns. I think I even used it in Ascension with regards determining priest numbers.

The quick rule of thumb is:

Level 10 = 1 in a thousand
Level 20 = 1 in a million
Level 30 = 1 in a billion
etc.

However, the formula breaks down when you consider that it basically exists for mortals not immortals and uses time as a variable (where old heroes will die and new ones take their place as part of the next generation).

Given that immortals do not die of old age or natural causes, we probably have to represent that on the formula. One quick suggestion might be to take the square root.

So the number of immortals goes down x1.41 per level.

If we assume Einheriar are Level 21 then there would be 32 L21 for every L31 or 1000 for every L41 (Norse Demigod) or 32,000 for every L51, 1 million for every L61.

etc.

 

[Khisanth the Ancient]

IMO that worked fine in older editions, when non-adventurers were non-leveled or "0-level". If gaining levels is inherently really dangerous, it makes sense.

In a 3.X/Pathfinder world where there are NPC classes that aren't necessarily adventurers, the formula probably only applies to PC classes. I'd imagine that whatever the level of Commoner/Expert/etc. most people can manage to get to in a lifetime is, below that level it's probably pretty even. And since those classes don't adventure, there'll probably be basically zero high-level equivalents.

E.g. there might be about equal numbers of 1st, 2nd, 3rd level Commoners, significantly fewer 4th levels, much fewer 5th, 6th+ being basically unknown.

As for adjusting for immortality/long lifespans... depends what proportion of the dropoff is because of old age. Retirement (for adventuring classes) and adventuring deaths might be bigger factors.

EDIT: It should also depend on the world, IMO. I bet there's significantly more than 1 in a billion 30th level characters in Forgotten Realms. It really shouldn't have more than a billion or so inhabitants total...

Dark Sun would have at least 10 known super-high-level characters (the seven sorcerer-kings, the Dragon, Oronis, Dregoth) and the total population of the Tablelands is probably tiny. (Was it ever stated? A million or two seems about right.)