Monday, June 1, 2009

Pricing A Ghoul's Heart

A problem has come up, one of my own making. In my on-line campaign, I put a comment in an NPC’s mouth about the obtaining of ‘ghoul’s hearts’ and that it was a practice that paid well. That’s fine and all, but just how exactly does one determine the price paid for a ghoul’s heart?

Most DMs would, naturally, pull a number out of the air or out of their ass and that would be that. Clean, simple, straightforward ... no problem. Fifty g.p. No, wait, five hundred g.p. No, that’s a little high. 100? 150? Okay, let’s say 150, but if it turns out to be way too easy, I’ll knock it down to 100. Or 50 if the party gets too many. Yeah, that works.

Actually, no it doesn’t. You make a deal with the party to pay them such-and-such per ghoul’s heart, and the party gets really really clever and comes up with 75 hearts (by luring the nasties into some trap by means of magic, obviously) and you’re stuck having to either be an asshole or accepting that you’ve just enabled your party to buy a quaint little six story tower.

Wouldn’t it be nice to at least have a justification beyond some number you’re able to poop out? That’s how I see it. That’s what I try to do.

My friend Delfig has been doing some figuring on the price of beef vs. land, so I’m hoping this will be of some help to him and to others who have expressed interest.

How does one figure the price of anything? To understand a basic tenet of my method, start here, or just accept some of what I’m about to tell you. I have a tendency to rush through some of my thinking processes, so I’ll try to slow them down a bit.

To begin with, everything has a “reference.” This is my term for the point value assigned to a place or region’s production of a given thing. For all practical purposes, let us take cows, which have come up in past posts of mine and which Delfig recently addressed. Let us start with a region, say “Upper Bavaria,” which conveniently has 2 points for cows, or 2 ‘references’.

When computing the total references for a specific trading city in Upper Bavaria (Dachau, for example), one begins with the 2 references already mentioned, and then one begins to add references from other places. According to a long established economic formula, a market which is twice as far away has one half the influence on a given market. For example, if you are one day away from Cincinnati, and two days away from Columbus, then Cincinnati has twice as much influence on your local prices than Columbus.

This is true even in the modern age, when virtually everything is one day away from everything else ... where distances are measured in hours and minutes rather than days. The principal remains in place, no less so for the late medieval period, when everything travelled much more slowly.

If we set Upper Bavaria at a distance of ‘1’, so that the references from Upper Bavaria are divided by 1 (2/1 = 2), then we can create a similar modifier for every other place on earth, provided we know the distance. Cows from the lower Danube valley are divided by 20 (the river makes transport quickly), cows from Russia by 40 or 50, cows from the middle east by 70 or 80, cows from India by 120 and so on. Let’s keep in mind that I have more than 500 trade locations to calculate in order to determine exactly what the ‘cow count’ is for Dachau, which I don’t want to list one by one ... and for other reasons which will become clear, I want to resist using the actual figures for Dachau. Let’s say instead that the total number of references for cows in Dachau comes to a very convenient 2.5% of the world’s total. And just for further convenience, let’s say that everything else in Dachau also equals 2.5% of the world’s total ... so that we can move forward on the premise that nothing is extraordinarily rare or expensive, which would muck up the numbers.

After all, cows in northern Siberia would be somewhat rarer than in Dachau. Cows might be more common in Dachau than what I’m about to suggest. But the model is the important thing, not the exact numbers.

All right. 2.5% of the world’s cow references measures 8.825. This number is measured against the price of gold (used as the standard for all other commodities) and we discover that the price of a cow is 207.32 c.p.

But is it? This price only reflects the comparative availability of cattle according to the total number of cattle that exists in the world. That alone is NOT sufficient to determine its actual value. Hold onto your seats, friends, we’re about to take a bumpy ride. Just to warn you, I tend to use c.p. for everything, and oz. as well (since I find the old English system of measurement more in keeping with D&D).

To produce an adult cow takes 2 years of caring and feeding, during which time the cow will eat an average of 560 oz. a day of forage – hay, clover, vetch, whatever you have available. The value of that forage is also set by the total number of references for forage in Dachau (which calculates at 5.525). That produces a price of 0.16 c.p./oz., which must be harvested and cleaned (I call this ‘foodstuff processing’ and for this example equals 4.225 references). The price of unprepared vetch is divided by the total number of references for preparation and then added to the base price. Thus, 0.16/4.225 +0.16 = .20 c.p./oz (rounded to 2 significant digits). This is not as complicated as it seems. The overall effect is that if the number of foodstuff processing references is reduced, the price goes up. Increase the references, and the price goes down. Think of it as a representation of the available labor.

All right, let’s return to cows. Before the cow can reach maturity, it must eat quite a lot. Most of this will be from the various fields, what it can forage on its own. For argument’s sake, I’ve established that only 10% of the animal’s food needs must be provided by the herder, and thus the economic system. This is a total of 56 oz. of vetch per day, for two years ... a total of 40,880 oz., or about 1.25 tons. This is multiplied against the cost of the forage (0.20 c.p./oz.), a total of 8,504.96 c.p. for the cow, to which is added the original cost of 207.32 c.p., for a grand total of 8,712.28 c.p. In my world, at 12 c.p. per silver and 16 s.p. per gold, that’s a round total of 45 g.p. Which is the only number my players see on the equipment list.

Good, let’s continue. Obviously, we’re going to want to slaughter our cow. At an average yield of 8,000 oz. (500 lb.) of meat per cow (this being pre-industrial Europe), the value of each ounce of meat ‘on the hoof’ is 1.09 c.p./oz. That’s the above price per cow divided by 8,000. This represents the price of the cow when it is sold to the stockyard. The stockyard also has a reference number: 8.850. So again we compute: 1.09/8.85 +1.09 = 1.21 c.p./oz. This is the price for which the stockyard sells the cow to the abattoir – or if you prefer, it is the increase in price the stockyard assigns for having to house the cows before it itself slaughters them. Once again, you will please note, if the number of references is less, the stockyard will increase the price per pound; if more, the stockyard will decrease the price.

In case this isn’t quite clear yet, consider an area where there are dozens of places close by which have references to food making or livestock wrangling. Obviously the price would be lower. Compare that to a place where there are few, if any, nearby stockyards. Some number will always be indicated – as 1 recorded reference 50 days away will yield 0.025 local references. Add hundreds of references, even those far away, and you will collect a number approaching at least 1.00. Where it gets dicey is when in the whole world there are only a few references to a particular item – rubies, for example, or caviar. No matter where in the world you go, unless you are right on top of that supply the cost will be considerable. But go to the source, and it can be had for cheap. This is the basis for many English stories in the 19th century about young whelps who go to India and find gemstones by the handful. But I digress.

Once the stockyard sells it to the abattoir, we must again consider the cost of slaughtering the meat. In this case, we return again to the foodstuff processing reference number, 4.225. Thus, 1.21/4.225 +1.21 = 1.50 c.p./oz.: the price at which the abattoir sells the side of beef to the butcher after removing the offal. Slowly, the price goes up.

In case you haven’t understood this yet, all this detail gives me considerable flexibility when suggesting a price for anything not previously considered by ANY system. A character wants a bucket of cow’s blood? No problem, that’s 1.5 c.p. per oz. The character wants to buy an entire side of beef? No problem, it’s more than half the price of the cow, it’s 250 x 1.5 c.p. The genius of this system is that every single item in my world works on the same principle: build the item from scratch, identify the price.

The butcher, too, has his particular reference: in this case, the number is quite low: 0.150 represents 2.5% of the world’s references. That is because most people would butcher their own cows, rather than relying on a private individual – who will in turn charge an arm and a leg. Still, the system works just as before: 1.5/0.15 +1.5 = 11.49 c.p./oz. This is the considerable difference between having space to raise and store meat, and being a player character who must buy his meat pre-cut.

Worse, the number of references for drying or smoking the beef is only 0.250. Applying the above formula, we find that beef jerky will cost the player 57.46 c.p./oz. Ouch.

If, however, our player happens to buy his jerky in a city where it is made (and not in our imaginary city where everything is 2.5% of the world’s total), then the number of references in that place will be at least 1. If we substitute the higher number, we find that smoked beef in that city only costs 22.98 c.p./oz. Big difference. It pays to purchase wisely when one travels. What system in what game allows for that?

This is getting a little long, so let me forego explaining how one arrives at the cost of a leather boot. It is just as fascinating, I promise you.

Let us return to ghouls.

The problem, as I see it, would be establishing a reference number for ghouls, based upon A) their central location of existence; and B) their total supply. I’ve already drawn attention to the simple fact that there are more references to cattle than to butchers. Obviously there should be very few references to ghouls overall – and the farther from the source of said ghouls, the more expensive their hearts should be.

(Once we identify the base reference value, we already know how much the immediate buyer for the heart might expect to expect to get once he turns it over to the local necromancer).

There are a number of methods we might employ. In reference to this post I wrote earlier, the location of ghouls should adhere to the location of graveyards – graveyards in turn adhering to the density of population. However, it doesn’t do to suggest that more people automatically equals more ghouls, since an extensively civilized area would carefully maintain the consecration of ground, thus eliminating the possibility of ghouls.

No, what we must do is consider areas where once there were people, and now there are no longer. A logical conclusion might be to consider every ruin a point of reference for ghouls (and for the whole collection of undead, demons and nasty beasts of all forms). But there are hundreds and hundreds of ruins and lost cities in my world – too many to work with my system. Hell, there are only 23 references to diamonds (also found world-wide).

Ghouls should be rare, as rare as diamonds. Plus, it does no good to assign ad hoc numbers of references to ghouls, or any other monster, as this is exactly the sort of pulling a number out of one’s ass that started this post. No, no, we want to find something we can associate with ghouls ... and where that thing is, there ghouls are.

It turns out that I do have a reference number, specifically for things which are moderately unworldly: that number is for ALCHEMY. The total world references for alchemy are 265, of which a considerable number are in Germany. So that solves the first half of our equation: where the ghouls are. It does not remotely solve how many exist.

You remember early on that I glossed over the initial cost of cows, saying that I compared them with the total gold? That is because I have a base number for the total cows in the world, and a base number for the total gold. What I don’t have is a base number for the total ghouls in the world. If I did, I could use alchemy to identify where they were; then compare the total ghouls against the total gold. Finally, the distance the party was from ‘ghoul central’ (as determined by the alchemy) would determine the price of a ghoul’s heart.

So, how many ghouls exist in the world?

Got me.

This is the point when I usually start to fall back on the Dungeons and Dragons books. My Monster Manual tells me that ghouls are ‘uncommon.’ It further tells me (p.5) that ‘uncommon’ creatures have a 20% chance of being encountered in a region or area where there might be an inhabitant. I conjecture this to mean that there is a 20% chance that ghouls might be encountered in a 20-mile hex first established by a player character upon becoming a 9th level lord.

A 20-mile diameter hex has an area of approximately 346.41 sq.m. If we take the phrase ‘where there might be an inhabitant’ to mean arable land, then we can compute the number of hexes on earth where ghouls might inhabit: 13.31% of the earth’s land surface, or about 6,788,100 sq.m. We need not worry about the oceans, as we need not consider lacedon hearts (whole other price structure entirely). That’s a total of 19,595.57 ‘hexes’ of inhabitable land, of which 3,919 would contain ghouls.

My Monster Manual tells me that the number appearing is 2-24; an average of 13. And so our world population of ghouls is 50,948.

I must confess. At the start of this post, about two hours ago, I did not have a solution for this problem. Now it is just a question of crunching numbers. Which I’m not going to do right now, as I am tired. I’ll do it tomorrow and give the price to my players.

UPDATE:

I’ve done some additional thinking on the problem and have made the following changes to last night’s logic: 1) I have decided to base the cost on the population density, not due to the origin of ghouls, but according to the demand for ghoul hearts. Less people, less demand. 2) Rather than comparing ghouls to alchemy, I’ve decided to compare them to another product: bear’s paws (a Chinese medicinal/foodstuffs product); one body part compared to the demand for another body part. 3) Although the total population of ghouls is 50,948, not all of this number can be said to be part of the economy of the planet; many ghouls are not actually hunted for their body parts. If we apply the standard I wrote about last month of 1% maintenance per month, we can argue that 1% of all ghouls are killed per month (not necessarily by the civilized population). This is loosely 12% per year (assuming the number of created ghouls equals the number of destroyed ghouls – convenient for me). That makes the total economically important ghouls equal to 6,114.

That makes the price of a ghoul’s heart equal to 73 g.p.

7 comments:

Ragnorakk said...

I'll call up my rfiend Pickman and see what he has to say...

Delfig Kôlhupfer said...

You're right, this is one hell of a bumpy ride - but I grasp the logic of it.

I'm going to have to chew on this for awhile (pardon the cud pun...) and come back with more questions.

Wait, I know one already - assuming you were going to simplify this a bit, would you simply establish bulk references? I think I've innately done that with Enonia - deciding what was available there (farm produce and cattle, wood products) and what is not widely available (finished goods, metal goods like silver/tin, ores)

Alexis said...

That was one of my earlier incarnations. But how much 'not widely available'? Should silver and tin be equally rare? Should wood and cattle be equally common? Aren't you having to create an ad hoc scale based on your instincts or biases?

And what about other cultures ... high plateaus, jungles, oases, islands in the deep ocean ... what is widely available at each?

mordicai said...

Do the players cast "preserve corpse" on them to keep them fresh? & I think the trick here is total demand compared to upkeep; how many ghoul hearts do the alchemists of Barvaria need on hand? 75 seems...awfully flush, to me. They've outpaced their demand with supply; if I were them I'd chuck most of the hearts & start a bidding war.

Alexis said...

Mordicai,

You vastly underrepresent the population of Germany, which is about 8 million; not to mention the other 40 million living in parts surrounded by Germany, which after the previous war would certainly be ghoul heart central. At one mage per 1,000 population, and one fifth level mage per 33,000 population, that's potentially 1,440 customers yearly (depending on what a ghoul's heart might be used for) - not to mention that some of those customers might need a dozen or more such hearts per use.

Eh, I'm just mucking around here. Any number would have done.

Daniel said...

Hi. I'm working on a C++ program to generate such pricing tables. I think I follow the logic you're going by, but I'm not sure how you're coming up with the prices.

How exactly did you get from 8.825 cow references to 207.32 cp/cow?

Alexis said...

Hi Daniel,

There are a given number of references for gold, also, and a set amount of gold in the world. By dividing the number of references into the total production of gold, this tells you how much gold per reference.

There is also a set number of cattle in the world. Thus, you take the value of gold/reference, multiply this against the number of references for cattle, and divide that product by the number of actual cattle.