# Hex Population Density

I was trying to come up with a good post for ‘H’, I’d originally had an idea for one but managed to misplace it, when I stumbled on a post from The Nine and Thirty Kingdoms (incidentally one of the first RPG blogs I started reading, a couple years ago) from Talysman on The Density of Hex Keys that fits in nicely.

Many hex crawl resources use a five- or six-mile hex (five or six miles from edge to edge, the ‘inner circumference’ of the hex). This amounts to a approximately 21.5 or 31.2 square miles per hex, respectively.

Typically no more than one feature, event, or encounter is identified for each hex — plus the terrain itself, of course. some resources (such as Carcosa) include two such elements for a hex.

It seems likely to me that in twenty to thirty square miles there should be somewhat more of interest. At these densities you are often unlikely to even find the element of potential interest because you simply won’t be in a position to see it!

Now, I can easily understand some abstractions being applied in play. The characters see more, but much of it actually isn’t of interest or is not worth mentioning, at least until you get to the most interesting bit. From a play perspective this makes sense, if you had to look carefully at every single thing potentially of interest it would make the overcautious dungeon delve where you make a Find Traps check every ten feet look exciting… but there should be some kind of middle ground, where a hex contains a credible amount of ‘stuff’ without bogging down play.

## Demographics

Let’s examine demographics, to see what might be credible.

Common knowledge and belief (which is to say, lots of people use these numbers, but I can’t guarantee their legitimacy) is that arable land in the middle ages could support about a hundred people per square mile. In relatively safe territory this might mean small villages of 80-120 people (14-20 families of about six?) roughly a mile or two apart, depending on arability and terrain. On a six-mile hex this could mean 8-32 villages (two-mile and one-mile separation respectively).

To an adventurer, this probably looks like a heavily-settled area. You’ll likely be following a dirt track from village to village, periodically passing a manor house or the like. There is likely to be a ‘market village’ three or four times bigger than most where you might find farmers gather on market days to trade what goods they can, but without outside help there probably isn’t the infrastructure needed to support a larger settlement.

In less arable or more dangerous lands, which is to say ‘less settled’, you might find the populations reduced to a quarter or even less. You might find villages three or four miles apart, where they can find more or less arable land and defensive locations. You might expect no more than 2-4 villages. In less arable but safe lands they might have just cropped up where they could (along a waterway, in clearings in the forest, and so on), in a less-safe area they might be somewhat fortified (earth berm or wooden palisade at most, probably) villages.

Probably no market villages here, but there may be a traveling merchant willing to make the rounds, possibly with a few guards or something, from village to village. While it’s not all settled by commoners, there is likely still something living around here. There may or may not be more notable sites, depending on the circumstances. In a forested (less arable) but safe area there could well be hunting lodges, manor houses, or even mill towns; in a dangerous location there may be forts or the like, if someone in power thinks there’s something worth protecting.

## Practicality

Specifying up to 30 or so villages, plus manor houses for gentry, per hex would be a crazy amount of work for the utility gained. Even the less-populated regions with a handful of villages, prominent locations, and potential encounters, would be an unreasonable amount of work. If you add in other elements of interest — even where humans can’t or don’t settle much, there will still generally be something to interact with — then you’re looking at a huge amount of work.

I don’t want to do that work, especially since most if it is likely to go unused.

## Approach

I think what I will do instead is:

• Place major known elements, such as cities, possibly towns, important ruins, and so on. An Echo, Resounding: A Sourcebook for Lordship and War from Sine Nomine Publishing has some better than average guidelines for this. They don’t even involve much math, particularly around demographics, but are quite playable.
• Identify significant regions and geographical features (nations, forests, rivers, mountain ranges, and so on). Where regions intersect (such as a forest that spans the border between two nations), consider treating them as separate regions.
• Each region should be more or less homogeneous, at least for the resolution I’m working at. Determine the element density (that is, how many interesting things there are per unit area — hexes, for the sake of conversation).
• To develop further, identify where some elements (such as villages and minor lairs) are, but do not detail them here, and build an event table (something like a wandering monster table, but it can have just about anything).
• If you like drawing them, prepare several hexes for each region when it looks like they will be needed.

Kevin Crawford suggests building a ‘campaign folder’ over time, containing things not yet used. As you get ideas (possibly based at least in part on random generation) for things, note them and store them for later use. I think this is a great idea, because here is the later use. I suggest also building a fairly large collection of village and people names — you’ll want to have that handy when the players ask.

Sometimes a hex is largely uninteresting. You’re just traveling through, the event table suggests nothing of particular interest happens. Passing through a village is probably uneventful (event table came up ‘no event’, as it were). If you need to, pull a likely event from your folder to handle the event, then carry on.

If a location is of specific interest (they’re going to a particular hex because they want to explore certain ruins, or visit a specific town or city, or so on) then prepare more concrete and specific information.

In populated areas you should be passing through quite a few villages (many of which are uninteresting to you because nothing happens there while you do so), so it’s pretty safe to describe passage through the hex as “you follow the rough track through about half a dozen villages, where the peasants cautiously watch your obviously dangerous group as you move through, before returning to their work”. This may seem kind of boring, but honestly, travel probably should be — if it was too eventful in areas like this, normal people probably wouldn’t survive it. Encounters will likely be relatively uncommon here, there may be quite a few events to find but most will probably be relatively innocuous. Of course, the party might stop to explore a bit, which you could consider as ‘inducing an event’ and draw from your folder.

In wilder places, though, things change. There may be more or fewer events, but they will likely be more dangerous — monster encounters, dangerous areas, weird things. As you move away from civilization, things become more hazardous.

A six-mile hex is actually a frightfully large area to explore on foot, and if you’re simply passing through you’re likely to see almost none of the content.

This is a wonderful opportunity for random event tables. They do a good job of managing the amount of effort spent preparing specific encounters and events that might never get used.

And when you learn to reskin and file the numbers off previous encounters (as Jack Shear says, approximately, in one of his books, “Just use bears. Give them tentacles and a horrible stench, but the players will likely never realize they’re still bears.”) you’ll be able to easily reuse them. Kevin Crawford, this time in Red Tide: Campaign Sourcebook and Sandbox Toolkit, does a good job presenting how that can be done. In one section he presents, on one page each, the pieces needed to assemble three or four different encounters of similar nature (mixes of particular creatures; the number of each might be random). Granted, this is made somewhat easier by using Labyrinth Lord rather than Pathfinder….

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1. tussock

Population density 101: modern wheat crops produce about 6.4 million calories per acre, medieval about a quarter of that on active land and quarter again by fallow land and seed requirements, or 0.4 million calories per acre. Slow-starving medieval peasants supplementing with forest nuts in winter and small pea and bean gardens for vital proteins need around 1000 calories per day, or 0.37 million calories per year.
So one adult-equivalent can live on 1 acre of farmland, Oh, plus each acre of worked land needs at least another in fields for the oxen and hay making, land in copse reserves for wood, nuts, and boar, plus rivers, roads, housing, gardens, etc.

640 acres per square mile, = 320 people per square mile. 50% of land arable in England finds them at their starvation population cap of (53k *.5 *320) around 8 million people as the plague hits. Awesome, only took a couple goes to make that match.

Now, you get potatoes, corn, rice, you get 3-4 times as many people, but less spare population to be army and government. Also, potato famine when the blight arrives. Hunters have only 5% as many at best, but are well fit by comparison.

Adventurers, nobles, clerics, and the like all need at least 4000 per day, and non-starving peasants at least 2000. That cuts you to 120 people (where children and the elderly are maybe only 1/4 people each) or so per square mile in wheat lands.

Each 30 sq-mile Hex then has ~3000 peasant-equivalents and 600 others. Enough for one town of a few thousand people in every 7-hex cluster, or one town every 12 miles along arable tracts, maybe every 18 miles if some of them are bigger (1 in 19 hexes, 5%).

Now we’re somewhere. One in twenty populated hexes has a market/service town, size related to arable/fishing hexes in reach (increased greatly upstream). Villages and hamlets serve other populated hexes. What of interest is in those others? Nothing! They’re tiny and insignificant and nothing ever happens there. If you’re not using 20-mile (340 sq-mile) hexes, you shouldn’t be using hex keys. There’s over 150 20-mile hexes in a tiny country like England, and only one of them is Stonehenge, or London, or Bath.

How far do you walk/ride in a day? 20 miles! One hex. One town. One adventure-worthy note of interest.

• Harder numbers than I’ve seen before, thanks tussock.

I didn’t realize there was quite that high a nominal maximum population, at a starvation level. It appears you’re assuming half the land is unusable for crops at any given time, and that gives me some room to play — I can probably safely ignore a moderate amount of non-tilled land.

I was thinking on the order of 3200 people per arable hex, more or less. 3000 starvation-level peasants and 600 others is a little higher, but if we pretend things are a little more equitable it’s close enough for me.

In fact, it looks like it might have been a decent enough estimate overall. The next hex size up I plan to use, and I think I’ll write about it today, is 24 miles. This would be big enough to support a small town, or perhaps two (16 times bigger than the 320 I estimated for the ‘market village’ would be 5120 — two smallish towns or one kind of big one).

• tussock

Addendum: 6-mile hexes aren’t that bad. There’s not many people, but it’d take a very long time indeed to search it for traps. A 24-mile hex certainly has more going on politically: centers of power, room for cultists and monsters, trade, but 30 square miles is already a whole bunch of land area for a cave and some bandits on the north road. Low level vs high level I guess. Or bigger hexes still for high levels, 96-mile (Wessex, Sussex, Mercia), or 384-mile (Britain).

Anyhoo, I’d go for anything up to 10 thousand people in 30 sq-miles of good land at starvation. 20k for 4′ tall Goblins, 3k for skinny Hill Giants, as food requirements scale by surface area. Wow, that’s a lot of Hill Giants, though they’re likely much higher active energy requirements in 3e D&D at least, and the mountains would be only 5% usable, so maybe 100 of them is better. Can use numbers like that for all sorts. Dragon? Doesn’t actually need all that much unoccupied land, especially with a superior slow metabolism, might only eat as much as 100 people for a 200′ dragon.

As for 50% arable, that’s as high as it gets over any large area. 20-30% is more usual, and big chunks of the world are only 1-2% arable among deserts and high mountains. Technically I should say “agricultural land”, including permanent pastures and fruit, date, and nut trees.

Oh, and English towns are all medieval or older in origin, so you can check distances between towns in relatively fertile land there on google maps. 20 miles is close.

• Given similar activity levels, energy requirements should go roughly cubically with respect to scale. So if a goblin is 2/3 the height of a human they should be able to support a population ~340% larger. But they may be more physically active, and hence have a smaller population.

The idea of applying a scale all the way up to nation-sized hexes is interesting and in fact I have some code sitting around for generating global grids that could be used here. Of course 12 of the cells need to be pentagons rather than hexagons in order to wrap the grid around a sphere; my approach for handling this was just to subdivide each pentagon into a flat grid of hexes. I only treated the subdivisions individually in that program, so there was no question of how the regions would match up at the edges. If you want to be able to zoom down continuously to a consistent grid of 1-mile hexes covering the globe then you would still need 12 pentagonal cells even at the lowest scale.

• Hold on to the code you’re talking about. I don’t expect in practice that I would need to apply the hexes at a global scale (the error involved in flattening the play area is probably less than the error involved in my estimations, to t’hell with it).

Tomorrow’s post (‘K’) is likely to be on ‘Kingdom Evolution, from Manor to Kingdom’ (or some such), showing how a demesne-game might lead to a kingdom. I anticipate (with some pleasure, honestly) the words “what is the population? Don’t actually know, don’t actually care”. The abstractions I’m pulling into this absolve me of a lot of detailed accounting — if I can get the abstractions right, and doing some arithmetic now can verify that before I charge ahead too hard.

• I’m either being more conservative in population figures, or kinder to the peasants, than you are :)

I think the six-mile hex is a lovely size for sandbox purposes. Big enough to have some population, but not a huge amount, room enough for a few things going on, including a bunch of stuff you won’t find without some effort or luck (good or bad), and a decent size for managing terrain-modified movement rates. The larger-size hexes are kind of an affectation for other purposes, primarily demesne-level play.

I do not want to play Rome vs. the Gauls at a six-mile hex scale, at least not until we get to Le Yaudet (incidentally, whoa, weird — I was trying to find the name of Asterix’ village, but it seems to never be named in the books), and I certainly don’t want to manage the demesnes at that level.

Thus, the simple model uses hexes at different scales, and assumes the governmental infrastructure picks up the slack, at least in part, so the ruler of each demesne can deal with things at an appropriate resolution. The emperor focuses primarily on ruling over kingdoms, a king focuses on ruling over duchies, and so on.

In any case, it sounds like the numbers I’m using, while not precise, are passingly accurate. This pleases me.

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