Tuesday 11 February 2014

Mediaeval Demographics: The View From Space

Broad Brushstrokes
Here's some really rough numbers you can use to quickly create demographics with the feel of mediaeval England (~1300ish). The objections that could be raised are almost infinite but they should be close enough for horseshoes or hand-grenades. Obviously, the idea is to start with "model" numbers and then adjust specifics to suit a campaign, or an area within a campaign.

Acres of farmland = population x 1⅔
Urban population = population / 10
Non-farming population = population / 4
Clerical population = population / 100

Number of adults (16+) = population / 3

Number of single adult homes = number of adults / 10.

Number of couple homes = number of adults x 0.45.

Forest for fuel = number of couple homes x 6 acres. (If you start with an area of land, this means that the number of people supported will be acres/2.567)

Largest city = population / 100 (or urban  population / 10)
nth largest city = largest city / n

Each acre of farmland produces 12 bushels of "grain", of which 3 (25%) support non-farming population somewhere.

20bu of grain support one person for a year.

Working backwards, each acre of land requires 0.6 head of population (man, woman, and child) or 0.45 head of rural population if you prefer, meaning that each head of rural population is producing ~26⅔ bushels per year. Obviously, in the specific case of adult males, much more than this can be worked and none of these values will hold when dealing with small numbers of population.

Large Self-Contained Model Village
Population 300, 225 in farmer families, 75 non-farmers.

75 farming adults: 8 single dwellings,  34 couples with 150 children (4.4 each).
25 non-farming adults: 3 single, 11 couples with 50 children (4.5 each).

500ac of farmland, 270ac of woodland available for fuel. So just over 1.2 sq-mile, plus space for water, waste areas, and meadow. This easily fits into a classic Judges' Guild 5-mile hex which is 20 sq-miles or 13856 acres.

Village produces 6000bu of grain per year. If non-farmers were removed, 1,500bu could be sold per year, granting a per adult income of 20 times the value of a bushel of grain (so, if 1bu=1sp, that's 1gp per year, for example).

In reality, unless there were special reasons otherwise, the majority of the non-farmers would not be in the village, they would be in towns, or serving the local lord, living in monasteries, in the army, etc.

There would be some non-farmers in a village this size, however. Widows and widowers and the "village idiot", millars, bakers, coopers, carpenters, teamsters and maybe even a full-time aletender, as well as a scattering of odd-ball tinkers and similar passers-through. Brewing would be done privately and about half the homes would be doing some and the brewing itself was traditionally the responsibility of the wife (very few single people brewed) who would be called by the female form of "brewer" - "brewster".

There are possible scenarios where the bulk of the listed non-farmers could actually be "on-site" as it were. For example, a village near a salt mine could have a substantial industry of families who extract, pack, transport and sell the salt and who pay the farming families for their food out of their income.

Alternative food sources, such as fishing, are something I'll look at in another post.

Large Model Country
Population: 4,000,000
Adults: 1m
Couple homes: 450,000
Acres of farmland: 6⅔ million acres (10417 sq miles).
Acres of forest: 2.7m (4219sq mi).
Farming population: 3m
Non farming: 1m
Clergy: 40,000
Urban population: 400,000

Largest City population: 40,000, consuming 2192bu (54t) of grain per day.
Next largest cities: 20,000; 13,300 ; 10,000 ; 8000 etc.

This represents about 465 6-mile hexes, or 19 30-mile hexes assuming 100% human land usage. Waste and marginal land will probably double or triple that.

Of the adult population, 13,333 are capable of level advancement. The "natural" level for the clergy would be 400, but if people were able to spell cast, then I imagine that they would be accepted in preference to anyone else. Given the ease of becoming a cleric then roughly 8170 would be eligible (assuming NPCs are 3d6 in order) and perhaps we can knock that down to 5,000 due to alignment requirements so that ⅛th of the clerical population would be spellcasters.

That would leave 8,333 adults capable of class advancement, some of whom may be clerics of other deities than the mainstream Church's.

Of the original 13,333 adults 7774 would qualify as fighters;  8,170 as magic users, clerics, or  thieves; 853 as assassins; 383 as druids; 50 as illusionists; 50 as monks; 27 as bards; 21 as rangers; and just 13 as paladins. Obviously, many would qualify for more than one class.

Population Density
If you plod around the web looking for information on mediaeval demographics and economics to use in your fantasy roleplaying game (and, honestly, who doesn't?) you'll see figures for the population density of mediaeval England of around 120/mi² whereas the figures here give a much higher density of about 380/mi².

If ye be a foreigner you might not be aware that there has always been a large difference in population density across England (and still moreso over the British Isles generally), with the north and southwest being much less heavily populated than the south and east. This difference was enhanced by the events of the Norman Conquest (the "harrying of the North"), boosted by Scottish raiders, and remain with us today.

So, at the height of the middle ages, England did indeed have a population density overall of 120/m², but in places like Northumberland and Cumbria it was much lower and in places like Suffolk and Cambridgeshire it was a lot higher, much higher than the figures given here which are likewise based on "average" farmland; better and worse land will exist and rural densities of 500/mi² are perfectly plausible if you're just looking at 6-mile hexes rather than whole countries.

So, don't worry too much about high population densities even before adding in fantasy elements that might allow it to go even higher.

Lot of children in those villages, aren't there? It's hard to get good estimates on what is a realistic number but my feeling is that there would be more than is usually expected. The families generated by the numbers above are a "snapshot" and the kids will be all sorts of ages and many of them - maybe 1 in 4, certainly 1 in 5 - will not live long enough to even start helping around the farm. Consequently, the average age of all people in the village will be skewed heavily towards the low end.

However, you might want to divide population by 2½ to find the number of adults.

I've abstracted grain crops into bushels of 34.83% wheat, 42.7% barley, and 22.47% oats giving ~60500 kcal per bushel.

The question of barley is a vexed one as the calorific value of this crop is largely tied up with the details of ale/beer making, with Bruce Campbell claiming that 70% of the value was wasted in the 1300's. This value seems to me to be very unlikely indeed and certainly by the 1600's it was down to ~25%. Given the size of the barley crop, the difference is very significant in terms of the land's ability to support population.

In particular, Campbell assumes that only one wort was produced in the brewing. I suspect that no brewer ever only used one wort, at least this side of the bronze age. Very early brewing was done in large troughs and it would be the most natural thing in the world to try to get more value out of the trough before having to go to the bother of clearing it out. But solid evidence from before 1400 is very thin.

Animals are abstracted away at this level. Their calorific input into the population is ultimately derived from either feed, which is included in the grain figures, or pasture, which is not.

Productivity and The Plague
Productivity per person seems to have increased after the Black Death. There's a few reasons for this. For one, the survivors could pick and choose the best land to farm, abandoning the poorer land and thus increasing the actual yield per acre. For another, survivors were often able to drive much harder bargains with their employers/landlords and so able to gain more from their efforts, thus encouraging them to work harder. Probably another aspect was the opportunity to re-jig the way any given farm was run, with fewer people to object and complain about changes. Technology did not change but, at least for a while, the survivors had more cash to invest in replacements for old tools and so on.

However, the jump does also speak of a degree of under-employment in the pre-plague period and so these figures could well be altered in favour of lower numbers of workers and higher numbers of "off-farm" people without invoking any fantasy elements.

Wednesday 5 February 2014

Magic Item: The Sword of Stone

Maybe not quite this heavy
This broadsword appears to the casual glance to be the sort of weapon a decorative statue might hold in its hand. It is extremely heavy and unbalanced but is imbued with a powerful and dangerous magic. The grip is only big enough for one human-sized hand.

When used against creatures from the material planes, the slowness of the weapon's "blade" is such that the damage done is only 25% real, and 75% temporary (recovering at the rate of 1hp per turn). However, if the target is reduced to 0 or less hit points in this manner, regardless of retaining "real" hit points, then it is turned to stone with no saving throw. Magic resistance might save the victim, rolled "as is" on each applicable strike.

When used against creatures native to the elemental plane of earth, the sword is simply treated as a +3 weapon with no special abilities.

Against creatures from any other plane, the weapon is treated as a club for weapon Vs armour and does 1d6 of normal damage with no petrification.

General properties are as follows:

Form: broadsword made of stone
Damage: 1d8
Weapon Vs Armour: as footman's mace against material beings; as broadsword against elemental Earth beings; as club against all others
Reach: 3½'
Space required: 4'
Encumbrance: 300gp
Speed factor: 12

If you don't use speed factors, limit use to STR 12 and above and bear in mind that characters under 100lbs weight can not use weapons with encumbrance of 200 or more.

Gp value: 8000
Xp value: 1200

Sunday 2 February 2014

Weights and Measures

Are your sins metric, troy or avoirdupois?
Many younger players know little of the imperial system of weights and measures even in Britain. Foreigners tend to know nothing useful while Americans have the additional confusion of a similar system with the same names but different details. On top of that, Gygax did not specifically say whether he was using British or American versions.

Here's a guide for the bewildered based on the use of British (more specifically, English, since Britain was not yet a united kingdom in mediaeval times).

Firstly, some names and abbreviations:

gr = grain (of wheat), a weight
oz = ounce
lb = pound (from libra, the Latin equivalent)
bu = bushel, a volume
ac = acre, an area
yd = yard, a length
ft = foot or feet, ⅓yd
in = inch, 1/12in
tr = troy, a system
av = avoirdupois, another system

Troy and Avoirdupois

Once upon a time there was a very clever person who decided to design a system of weights and measures. He (the chances that a woman would have been allowed to even assist at the time is remote) decided that a cubic foot of water should be defined as 1000oz. That would weigh 62½ lbs.

But, he thought, merchants clearly use two different systems of measurements - dry and liquid. He didn't really want to have to have two systems of barrels and boxes so he struck on an ingenious idea: have two types of pound instead which weigh different amounts but take up the same space. The denser would be for liquids like water, beer, and wine and called "Avoirdupois" and the less dense pound, for wheat and bread, would be the "Troy" pound possibly from Troyes, a town in France. The concept of the troy pound seems to have come over with the Normans and slowly replaced the old Saxon pound which was called the "Tower pound".

Both pounds would be based on the nominal weight of a grain of wheat. A troy pound would be made of 12 ounces of 480gr each, for a total of 5670, but the avoirdupois pound would be divided into 16 ounces of 437½gr each for a round 7000gr total. This set the ratio of troy to avoirdupois pound to 144:175, the same as the ratio of the density of wheat to water.

This meant that a barrel which was stamped "320 lbs" would hold 320 lbs avoirdupois of water or 320lbs troy of wheat.

Unfortunately, because the troy pound was already in wide-spread use, our inventor could not make a cubic foot of wheat weigh 1000 tr.oz, so although the cubic foot of wheat weighs 62½lbs in either system, in the avoirdupois system it is a nice neat 1000oz, in the troy system it is 750oz which is nice, but not as nice and the ratio of troy ounce to avoirdupois ounce is 192:175, different from the pounds' ratio and notice also that although the troy pound is lighter than the avoirdupois pound, the troy ounce is heavier than its counterpoint.

While avoirdupois has survived to the modern day and is what we normally talk about in terms of weight, the troy system was abolished some time ago and survives only in the area of precious metal. So, if you look up the price of gold and find that it is "$1251/oz" that "oz" is a troy ounce, not a normal kitchen-scale ounce.

Sticking to liquid for now, the definition of a cubic foot of water is 1000oz gives us the next fixed point, as an English pint has 20 fluid ounces (fl.oz.) which means:

1cu.ft. water = 50 pints exactly (users of purify food and water, note!)

and since 8 pints make a gallon,

1cu.ft water = 6 gallons and 2 pints.

and since a pint is 20 ounces (1¼lb),

1 gallon water = 10lbs avoirdupois = 160av.oz.


1cu.ft water = 62½lbs of water.

and so,

1 gallon wheat = 10lbs troy = 120tr.oz = 8lb 3oz 287½gr avoirdupois

Working backwards,

4½lbs of water (enough to fill a wineskin in the DMG) 0.072cu.ft and so a cubic foot of water represents just under 14 DMG wineskins (13 and 8/9ths)

1.3lbs of water (enough to fill a flask in the DMG) is 0.0208cu.ft and so a cubic foot of water represents just over 48 flasks (48 and 1/13th).

100lbs of water is 10 gallons, which is 1.6cu.ft.

Art: David Wyatt
A 320lb-capacity barrel contains 5.12 cu.ft of water. If it were a cylinder 18" across, it would be 2' 10¾" tall. Too small for a human, but a hobbit or a dwarf might just squeeze in.

Standard rations for a week for one person weigh 20lbs. Technically, that should be troy and if it was, then that represents one peck-sized container and a standard barrel would hold a week's supplies for 16 people (see table below). Iron rations would be much more space-efficient at 42⅔ man-weeks per barrel, although more water would be needed if there is no supply en-route.

Personally, I wouldn't dream of enforcing the difference between avoirdupois and troy in a game, even if the 21% difference is quite substantial. But, it could be done.

The old system generally worked on a binary pattern, so that each named unit is equal to two of the unit below. This obviously made calculations easier but over time some units - e.g., the gallon - proved to be so much more useful than the others that the underlying pattern was forgotten along with many of the under-used units like pottles and chopins.

So the theory is:

2 gills=1 chopin (chiefly in Scotland & France) = 5/8 lb
2 chopin=1 pint (20oz of water) = 1¼lb
2 pints=1 quart = 2½lb
2 quarts=1 pottle = 5lb
2 pottles=1 gallon = 10lbs
2 gallons=1 peck = 20lbs
2 pecks=1 demi-bushel = 40lbs
2 demi-bushels=1 bushel (or firkin of liquid) = 80lbs
2 bushels=1 strike (or kilderkin of liquid) =160lbs
2 strikes=1 barrel or coomb (coomb is technically dry but very rarely used) = 320lbs
2 barrels=1 quarter (or hogshead of liquid) =640lbs
2 quarters=1 pipe (again rarely encountered in dry measure) or butt =1280lbs
2 pipes/butt=1 ton (tun is mostly used for liquid) = 2560lbs

A problem arises here, which is that our unknown systematizer was largely just that - unknown. The simple system he devised was more or less forgotten and certainly not transmitted across the country. As a result, in real life, these units were rarely used so systematically and the derivation of the ton that we have today (in Britain and, by what the French call coincidence, in the metric system) is:

1 ton=20 cwt ("hundred weight")
1cwt=8 stone or 112lbs
1 stone=14lbs
1 ton = 2240lbs

In addition, all of the big above list were based off the gallon and that also varied across the country, each variation taking the other units with it. This version of the system made allowances for crating and packing. So a hundred-weight (cwt) supposedly included 12lbs of packing allowance and a ton 240lbs, leaving 2000lbs for the actual goods. In America this allowance was discarded and weights simply given in terms of delivered goods, and so their ton is this "short" ton of 2000lbs.

Anyway, the practical upshot of all this is that the weight of any of these units depends greatly on the contents. Clearly, if one piles grain into a bushel measure and levels it off there is a great deal less air in the resulting container than if one did the same thing with apples, let alone the issue of the different densities of an individual grain or apple. Meanwhile, the local definition of the bushel varied frequently.

Thus bushels vary in weight:
Wheat or rye: 56lbs is the most common size encountered, followed by 64lbs
Barley: 48lbs
Oats: 38lbs

Modern bushels are mostly encountered in the US where the wheat bushel has been rounded to 60lbs.

Notice that none of these bushel weights is very close to the theoretical weight of 65 and 29/35 lbs that the avoirdupois:troy ratio would suggest. Which tells you all you need to know about how successful the would-be systematizer was.

Since bread was made from wheat, old sources tend to talk about a 1lb loaf meaning one troy pound. This means that a pound of bread provided somewhere in the region of 920 kcals, not the 1120 that one might expect if using avoirdupois weights.

Small Weights
The pound avoirdupois was sub-divided:

1lb= 16oz = 256 drams
1oz=16drams = 32 quarters
1dram=4 quarters
1 quarter = 1/1024 lb

The pound troy was sub-divided:

1lb = 12oz
1oz = 8 drams
1 dram = 3 scruples
1 scruple = 20 grains
1 grain = 1/5760 lb

However, since the troy pound came to be the pound of silver and silver was the coinage of the realm, it could also be divided so:

1oz = 1 shilling
1 shilling/oz = 12 pennyweight
1 pennyweight = 24 grains
£1 = 20 shillings = 240 pennyweights

and this is the origin of the slogan on all English banknotes "I promise to pay the bearer on demand the sum of ..." followed by the face value of the note. It used to be that a £50 note was literally worth fifty troy pounds of silver and one could exchange it at the Bank of England. This ended in the late 1700's but the text remains essentially as a hollow endorsement of the government's non-existent commitment to financial prudence.

A foot is 12" and an inch is now defined as being exactly 127/5000th of a metre, for what that's worth.

3 feet are a yard, so a tank with a capacity of one cubic yard holds 1350 pints weighing 1687½lbs.

2yds is a fathom.

5½yds is a pole or perch.

22yds is a chain.

220 yards (40 poles) is a furlong. Dividing the furlong into 200 units gives you a metre.

8 furlongs is a mile.

3 miles is a league.

1 furlong by a chain is an acre of 4840sq.yds. or 43560 sq.ft

One inch of rain on an acre thus represents 3630cu.ft of water, which is 226,875lbs of water, or 2,2687½ gallons, or 709 barrels (minus half a gallon).

1 furlong by a furlong is 10 acres

640 acres is a square mile.

30 acres is a virgate.

4 virgates (120ac) is a hide.

100 hides is a "hundred". However, the word "hundred" actually originally mean 120 and in some places this held in the definition of the hundred of land while in other places the hundred was chopped up without changing the name. Consequently, references to "hundreds" of land in old sources can refer to quite widely differing amounts of actual land. In any case, the original concept seems to have been that each hide would be responsible for providing a warrior to the king's warband.

I think this has been abolished except in parts of Lincolnshire.