I must create a system, or be enslaved by another man's. I will not reason and compare: my business is to create.

- William Blake

Saturday, August 21, 2021

Easy worldbuilding with Pareto, Price, fractals and bell curves

This ended up very random and "rambly"... hope you can find some practical use for it!

Things such as the Pareto distribution, Price's Law, the Matthew principle and bell curves seem to have a strong effect on nature; in other words, you can find it not only in sociology, economics, etc., but also in trees, mountains, and so on. I won't spend much time explaining things (google them if you must); let's start playing and building right away!

(These numbers are not exact and I'm not great at math anyway - I just enjoy playing with it, so take this with a grain of salt, and feel free to correct me when I'm wrong).

BTW, if you need a few random tables for your world-building, check Dark Fantasy Places - you can get it for free.


Take a piece of land; this map is a good example. 

Half is low altitude (green), half is high altitude (brown, white). If you take the high altitude part, you'll see that about half of it is even higher (the white part compared to the brown part). You can extend this as much as you want. Half the white part is going to be highest than the other half, etc.

The "halves" are distinguishable but not perfect. There are "pockets" of high altitude in the low altitude areas and vice-versa. When you create your map, think of the yin-yang symbol.

Now let's think of adventurers. say that 50% of 1st level adventurers perish before getting to 2nd level, same for 3rd, and so on. If you start with about one million (1048576) adventurers, you end up with...

Level 1 1048576
Level 2 524288
Level 3 262144
Level 4 131072
Level 5 65536
Level 6 32768
Level 7 16384
Level 8 8192
Level 9 4096
Level 10 2048
Level 11 1024
Level 12 512
Level 13 256
Level 14 128
Level 15 64
Level 16 32
Level 17 16
Level 18 8
Level 19 4
Level 20 2

Even if your world has one million of adventurers all over, maybe it has only a couple of 20th level characters.

However, your world might have a lethality greater or smaller than 50% for each adventurer level. Undoubtedly, some will cut their losses before level 20 - or maybe die due to disease or accidents.

What about the rest of the population? Again, it depends. being an adventurer takes some effort and skill. There are people that might be too young, too old, too frail or too coward to adventure. Others might be decent doctors, scribes, priests, etc., having no need to adventure (they might have some levels anyway). If we say one out of fifty people are leveled adventures, it might take a population of one hundred million to create a 20th level adventurer. 

If anyone considerably above average is an adventurer (maybe 15% of the population; seems like a good approximation) 15 million people might be enough. So maybe there is only one 20th-level character in medieval France.

BTW, demographics are similar. One huge city, a few big cities, a lot of small cities and lots and lots of hamlets. Maybe half the land cannot be occupied due to weather etc., so you have a few nomad tribes at most.

Power and wealth might follow a similar distribution. There is only an emperor, and a few kings, but there are many nobles, and even more knights; the majority of the population, however, are commoners, serfs, etc. Apply the yin-yang here too: there are a few knights and commoners that are disproportionately influential. Do not mess with the king of beggars!

Now think of names. Every time a new NPC appears, you want to give it an unique name. However, when world-building, consider that names might also follow a Pareto distribution or something similar. So, about 80% of folks will share the 20% most common names (example: almost 30 percent of Americans have a given name that appears in the top 100 list).

You are unlikely to have hundreds of NPCs, but a repetition or two might add some verisimilitude to the setting.

One third, golden ration

You might use thirds instead. It might be less symmetrical, more organic. Or maybe choose something closer to the golden ratio (which means, about 38%). This isn't exact science after all.

So, two thirds of the world in water. One third of the land is high altitude, and one third of that is high mountains. One third of these mountains are REALLY tall, etc.

Building from the top down

One quick way to build your setting is choosing a piece of land (maybe a duchy or even small nation; but you might start with a single city) and just naming the highest peak, the most powerful aristocrat, the best fighter, the most powerful wizard, the biggest monster, etc. The highest peak is probably surrounded by mountains, and the most powerful noble is surrounded by lesser ones.

The biggest city might have a few medium cities around; the biggest city in the world will probably be found in a densely populated area.

Ten easy steps (top down)

Someone MUST have compiled this before me, but anyway...

1. Separate earth from water.
2. Place the highest mountains in the map; create mountain ranges around them. You can add a few islands along the same line.
3. Rivers flow from the mountains to the sea. They do not cross, bifurcate, or go up in altitude.
4. Place cities near the seas and the shores. Dry rivers might have ruins.
5. Roads/trails connect the biggest cities.
6. Mountains create deserts by stopping the moist currents that come from the seas.
7. The poles are cold, tropics are hot. Think of jungles as tropical forests. Deserts can be hot or cold, etc.
8. Forest, jungles and swamps require rivers. Lakes need rivers to feed AND drain.
9. Extreme changes are rare (you don't usually go from forest to desert in a mile; add some savannah between them, same goes for altitude - but not always).
10. Spicy things up if you want to - a lonely mountain, an unexplainable forest in the middle of the  barren wasteland, a big isolated city-state somewhere.

Here is something I've made in 5 minutes using paint. Looks horrible but I hope you get the idea.

Building from the bottom up (bell curves and regression to the mean)

If you start small, what happens if the PCs go beyond the borders of your map? Well, you can use a 3d6 table.


3--3Extremely low

4-5-2A lot lower

6-8-1A bit lower

9-120Same as the one before (or average)

13-15+1A bit higher

16-17+2A lot higher

18++3Extremely high

This answers questions such as "what is the altitude of the next hex", or "how densely populated is the next hex", what is the humidity, vegetation, temperature, etc.

The "modifier" part is something you'll add to your NEXT roll. You can compare it to the average or to the previous hex.

For example, you're in an elevated plain ("a bit higher" than average on that nation), you roll with a +1 bonus to see how high is the next hex when compared to the average. Or how rainy is the next day. Etc. Mountains and rainy days will tend to clump together.

But if you want to compare it to the previous hex, that works too. There is still a regression to the mean, but it takes longer. You could be in a "extremely high" mountain and find out that in the next hex there is a mountain that is even higher!

Likewise, if the new hex is close to three or four hexes that are already know, you can give it a modifier to reflect the likelihood of things staying the same; or just roll unmodified 3d6 and, if the result is between 9 and 12, this hex is the same as the ones that surround it.

So, start big or start small?

I'd say start small, but keep a very low resolution world map if you want to

Which basically means knowing where you starting village or duchy is in relation to the North, the equator and the sea. You can also describe what lies to each cardinal direction with a single word or sentence ("the sea lies to the east, a friendly kingdom to the south, bands of dangerous raiders and mountains to the north, and a big forest to the east").

At the same time, keep a more detailed map of 10 to 50 miles around the PCs. The rule is: the closer they are, the more they know. What the PCs know should fit less than one page. If they don't live near the nation's capital, even their king should be described in a line or two at most (unless the Pcs have a history with him etc.).

And then see where it takes you. Maybe you want to run a jungle campaign next, and you can look at your low-res map to see where a jungle would fit. Maybe the PCs want to explore a big city - where would it fit? and so on.

Special stuff

We are creating a map that looks "realistic". by itself, this is a bit boring. Add random, memorable features to it - maybe at least on e memorable feature per important location. Here are some examples adapted from Dark Fantasy Places:

- A village might be: Suspended over water, Dug up in rocks, or Built amidst ancient ruins.
- A group might have No concept of privacy, Casual cannibalism or an Universal vow of silence.
- Non-traditional government types include The winners (or losers) of the annual lottery, A genetically-altered ethnic minority or Whoever can survive the local deities’ ordeal.
- Mythical Ruins might be recognizable for their Non-Euclidian angles, Impossibly tall buildings, or Levitating structures.
- The wilderness in this are is known for being Covered in prismatic fungus, Devoid of fauna, or Littered with bones.

Further reading and useful tools


  1. This is great stuff - once you have some high level principles like these for setting out your realm you can turn to all your random generation tables and roll up whatever you like knowing it will still broadly fit in and make sense.

    2 rolled up results that look incompatible? Time to deploy the halves rule and make each characteristic of their side of the split, etc, etc.

  2. Zapf's Law falls along these lines too. Your biggest (whatever) is going to be about twice the size of the second biggest, three times the size of the third biggest, four times the size of the fourth biggest, etc.