Population Distribution Over Character Levels

Here’s an interesting thought exercise: what would the distribution of character levels be over an entire population? I think most people can agree that the majority would be low- or unleveled characters. My guess would be that a normal distribution could be applied. My assumptions were the following: the mean level is 0.5, with the same amount of people being level 0 and level 1 (in any class, including non-adventuring classes). Level 0 in this case is defined as a healthy, working individual that simply never excels in an area (the stuff that non-leveled henchemen are made of). “Levels” -1, -2, and -3 represent people in increasing degrees of weakness that are still alive and part of society. The rare -4 level person is a true invalid that is kept alive. Character levels are drawn on a 10-level scale, where level 10 is the top end of hero-level characters.

I further assume the deviation to be 1.3 levels, as having over 70% of the population being either level 0 or 1 seems a bit high. (There’s no fancy mathematical reason, I just chose a nice number). This gives me a table like this:

 Level Of population At most At least
-4 0.1% 0.1% 100.0%
-3 0.8% 0.9% 99.9%
-2 4.8% 5.7% 99.1%
-1 15.8% 21.5% 94.3%
0 28.5% 50.0% 78.5%
1 28.5% 78.5% 50.0%
2 15.8% 94.3% 21.5%
3 4.8% 99.1% 5.7%
4 0.8% 99.9% 0.9%
5 0.1% 100.0% 0.1%

The reason the table stops at level five is that the number of people above that was just so minuscule that the table won’t show it with only one decimal. I find this spread wholly acceptable. It looks something like this


The perccentage of level 10 characters becomes an impressive 0.00000000008% of all people, which with a reasonable 15th century world population of half a billion, becomes less than one person. Quite a bit less. Maybe the little finger of a 10th level character. Hah. But with 10th level being defined as “Mythic Hero”, it’s fine that one might come along only every hundred of years.

The total number of characters of levels 6 and above come out to about 20 000 in the entire half billion world. There’s some around, at least.

Obviously you could extend this to a larger array of levels, with some numbers changed, if you had, say 20 levels or whatever. Though you might have to add some more negative levels if you want to keep the world low level, as the curve is technically equally long on both sides of the middle.


Bonus: Random Level Table

1d20 Level
1 1d6: 1 is -3, 2-6 is -2
2-4 -1
5-10 0
11-16 1
17-19 2
20 3+, roll 1d6. Each 6 is +1 level and reroll

7 thoughts on “Population Distribution Over Character Levels

          1. Calculating experience tables for NPCs based on age and social status. The sequence serves as a constant value; I don’t recall the exact equation at the moment but if you’re interested I can send it over.


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