Friday, June 3, 2011

Spoilage Drift & The Trickle Down Theory

An engineer, a chemist and an economist are stranded on a desert island with nothing to eat except coconuts and a crate of tomato soup.  Unfortunately, they have no way to open the cans.  Experiments with rocks show they don't have the strength to bash open the cans.  But the engineer believes he can construct a framework that will drop one of the island's boulders on the cans and break them open.  Unfortunately, the soup will run all over.  The chemist argues they could store the cans in the lagoon, where the salt water will weaken the metal after a number of years.  Then, suddenly, the economist brightens.  "I've got it!" he says.  "What is it, what do we do?" asks the others.  "Okay," says the economist, quite excited.  "First of all, let's assume that we have a can opener ..."

I include this joke to indicate my awareness that what is about to follow will be true silliness of the first order.  Nevertheless, I think there may be some value in it, even as a mental exercise.  It hit me as I was in the tub last night - this being the third significant mental jump I've had on a Thursday night while in the bathtub.  It's gettin' kinda creepy.  Anyway, let's assume we have a can opener and see where it takes us.

If we consider the economy of a civilized location, a set amount of wealth is created by the civilization on a yearly basis.  This is value created by raising livestock, growing crops, mining, fishing and so on.  A certain amount of this value is consumed, naturally, but certain valuables - durables, we can call them - are not destroyed as a condition of their existence.  These would be items such as gold, gems, marble statuary, constructed assets and so on.

However, these items still experience a certain degree of 'spoilage' ... even gold.  Construction crumbles, objects break or are smashed; and coins and gems are dropped or lost.  No matter what the item, a certain percentage of it will be lost to civilization, even if that means it was taken aboard ship and the ship lost at sea.

In D&D, it is presumed that a certain amount of this makes its way into the hands of the 'alternate civilization,' that which is operated and maintained by humanoids, supernatural villains or any creature able to identify a given object and horde it for its value (birds swallowing brightly colored gems included).  From an economists point of view, the question to be posed is how much, exactly, of this 'spoilage drift' slips out of the hands of the human/demi-human world and into the hands of this alternate civilization?

Of course, the alternate civilization too is wrapped up with the creation of wealth, so the measure of a civilization's capita income is not dependent upon spoilage drift alone.  Nevertheless, we can isolate this one circumstance of our fantasy economy and see how much impact it has.

I have long been a fan of the 1% maintenance cost per month rule of the DM's guide, and have mentioned it on my blog before.  I see no reason why spoilage drift shouldn't be measured in the same amount.  Call it the can opener we started the post with.  Some percentage is called for, and surely this is a simple enough one to apply.  To keep things simple, we'll call it 12% per year, and presume that a little less than an eighth of all transportable durables are being plundered, moved or lost in the alternate civilization's lands.  Some of it, obviously, would be adventurers going into those lands to plunder and dying there.

Now, suppose we imagine a series of ... oh, I don't know, let's call them 'levels' ... that describe the alternate civilization's 'distance' from the prime civilization (ours).  Think of distance as being a measure of the alternate civilization's remoteness, the difficulty with which it is reached or the general strength and power of the monsters overseeing that part of the world.  Let's presume that the prime civilization is buffered by a circle of 1st level alternate civilization - which may be of any thickness - and that in turn is buffered by a 2nd level circle, then a 3rd level circle and so on.  It can be presumed that while the 1st circle gains from the prime civilization, the 2nd Circle gains from the 1st and the 3rd from the 2nd.  Think of it as a dungeon, where the gold trickles down steadily from the upper levels to the lower.  Such as in this figure here:

Thus, as you move through the levels, durables are flowing downwards.  I have modified the amount of change from level to level to incorporate more fluidity in the process, so that as you go deeper the monsters from those levels take more from the levels above them - 24% from the 1st level to the 2nd, 30% from the 2nd level to the 3rd, 34% from the 3rd level to the 4th and so on.  I'm adding 12 divided by the Fibonacci Sequence for each level, so the reader can determine the changes at deeper levels as they like ... though the change will not be much after the 4th level.

The reader will take note that a certain amount of the wealth accumulated in the alternate civilization is restored by adventurers who enter into the wilderness and plunder, bringing back a portion of the money therefrom less and less frequently.  The number of years of accumulation before half of it is plundered is the square of the level.

We can do a little calculation, then, to see how much wealth is drifting from level to level.  If we postulate that the prime civilization is producing 10,000 g.p. of wealth every year, how much of this wealth is distributed into the various levels?  For simplicity, let's assume a period of one year passing before the gold from the prime civilization spoil drifts into the 1st circle/level, another year before a percentage of the 1st circle/level spoil drifts into the second circle/level and so on.  And of course, let's incorporate the 50% return to civilization that I've postulated.

This produces the following table:

I have thoughtfully highlighted those years for the 2nd level and below where half the wealth has been returned to the prime civilization's economy.  This happens every year on the 1st level.  While the total gold remains unchanged, more and more of it steadily drifts out of the prime and into the alternate.

However, note that the amount of gold still declines with each commensurate level.  The 4th level may seem to jump up, but in fact that is only because I have not accounted for how much of the 4th level drifts into the 5th and so on.  Overally, there is more shifted money to be found in the circle immediately adjacent to the civilized world, and NOT in the deepest darkest tomb of the deepest darkest dungeon.  There may be more overall in the levels fourth and down, but this greater accumulation is divided and subdivided again and again by what creatures occupy each deepening level.

In other words, you will do better to slaughter the whole goblin army posted on the fringes of civilization than their equivalent-power opposites on the fourth level of the dungeon.  What's more, those goblins are more likely to dwell in lands where wealth is something they create, as well.  Rock dungeons only yield minerals, and rarely in great amounts.  (If you're arguing that its a fantasy world and you can put any amount of wealth anywhere you like, you should have stopped reading this post ten paragraphs ago).

And this brings up an interesting question, the one that occurred to me as I steeped myself in hot water last night. 

Instead of assigning the amount of gold and valuables based upon the presence of monsters, perhaps a treasure table might to better to assign the number of monsters based upon the prevalence of wealth.  After all, things progress towards and congregate where wealth is abundant, and venture away from where wealth is hard to come by.

Would it be true that the deeper the party went into the dungeon, the last and bottom level of that monstrous pit would be, in fact ... empty?


Zzarchov said...

To go with your "imagine we had a can-opener" opening.

Consider that a "value" is subjective onto who wants it. The cowrie shell may not be worth much in some places, but its gold in others.

So lets look at some things that may be worthless down below but quite valuable up above. Amethyst as something that was very valuable until deep mining and world trade became common.

We also get to the level of magic involved. Is there an underworld? If you dig down deep enough do you find the spirits of the dead? Can you dig down enough to ask Aristotle his opinion on something? Lets assume no for this purpose. The "less gold, more magic items" is a cop-out.

So we get back to things rare up to top but common below. There may not be much, but if you have an underground sea of oil, and the surface world is relegated to collecting bits of black slime that wash up on Byzantine beaches you've got some real value.

Oddbit said...

An interesting though I have is the actions of the lower dungeons. While applicable trickle concept for very passive inhabitants just making their way, what about downwards theft?

Lich lords actively stealing wealth in the form of tomes and the like from above, Dragons hording and stealing from the upper levels.

And for levels with the more passive mobs such as crypts, vaults, ancient ruins and the like you have the initial burst of whatever was stowed there to be protected by the passive undead, constructs and traps. While that would be less evident after the first theft the lower ones raided less often should have a decent size head start.

You still have the downwards spiral for the passive zones, but the active ones should definitely be stealing or creating wealth.

Alexis said...

Theft was one of the reasons I expressed that accounted for spoilage; remember that gold doesn't actually spoil, so loss and theft are the primarily reasons for it changing hands. The deadliness of the lower levels was one of the reasons for me increasing the spoilage percentage as the levels increase.

Carl said...

"Instead of assigning the amount of gold and valuables based upon the presence of monsters, perhaps a treasure table might to better to assign the number of monsters based upon the prevalence of wealth."

This is why I read your blog, Alexis.

I have long enjoyed creating treasure hordes first and then assigning guardians to it. This reversal of concept makes so much more sense than assigning a treasure type to a monster.

I think I'm going to sort my treasures by monster type instead of monsters by treasure type. This is a great data pivot point.


Higgipedia said...

Wonderful food for thought. I'm taking quite a bit of it away for use on my sandbox. I'll let you know what I do with it.

Sigilic said...

Would it be true that the deeper the party went into the dungeon, the last and bottom level of that monstrous pit would be, in fact ... empty?

Well - there at least would be hellworms.

Oddbit said...

So estimated parties of adventurers can wipe out half the wealth of a level, however estimated 'big baddies' politely grab less than a percent.

I think the above idea is great as a first step, but I think further modifiers should be applied similar to adventurers in the opposite direction.

Joseph Browning said...

Cool idea. I'd think about making a system with at least 2 sources of wealth (surface and depths spring to mind immediately) and then looking at the flow between them. Hrm...

Shane S said...

Would it be true that the deeper the party went into the dungeon, the last and bottom level of that monstrous pit would be, in fact ... empty?

Only in the infinite layers of the Abyss. Most dungeons have a bottom after all, so the accumulation of wealth in the fourth column of your table is not an artifact from not continuing the calculation, but a physical fact that the table demonstrates.

One thing not accounted on the table is the per-capita wealth. There is a lot of wealth in civilization, but it takes a lot of work to squeeze it out of the peasants. That is why orcs need to plunder the whole countryside to get their share (or plunder the merchants and nobles who have already plundered the countryside). The 12,000gp on the 4th level might be in the hands of a few powerful creatures.

An ambitious person in such a world would have a choice then of going the safe, dependable route of business, or of playing the dungeon lottery.

To counter what I have just said, a "wilderness" (where the levels are spread out instead of concentrated) would have the wealth stretched over a much larger population. Like barbarian tribes plundering Rome, the wealth is lost.

I do like the idea of watching the flow of wealth though. I am working on a world where very little real wealth is being produced, so this and your early posts on pricing are rumbling in my head.

Alexis said...

Oddbit and Shane, I bow to both of you. That is sound logic all around. Rest assured, I had not felt definite in my suppositions, and I appreciate having it pointed out where I am in error.

I am wondering about a world-wide table, as Shane is, and what it would look like. No plans to get on that anytime soon, though.