Tuesday, March 22, 2016

Undeveloped Goods Prices

The wiki tutorial on setting prices for undeveloped goods took me four and a half hours - gawd.  This is counting the time I was interrupted to grant a brilliant interview for a job opportunity with Shaw Cable.  I must have just been on.

Here's the frontispiece:
Goods in the trade system are divided into two categories: those resources that possess a natural value at the moment they are found or uncovered and those resources that have value only after processing. This page will concern itself with pricing natural and undeveloped goods.
Undeveloped goods include materials that are dug up, caught, harvested from fields, chopped down or picked from trees. In our tutorial, we are counting 'bricks' as a raw material because our use of the term is meant to include stone; however, a more proper and detailed system would have separate references for stone and count bricks as manufactured products made from clay and other materials.
Similarly, while it would seem that animals are 'naturally' born and therefore collected as undeveloped goods, the fact is that before an animal can become valuable it must be fed for periods up to several years - the cost of this feed represents a form of 'processing' that we are not taking account for in this system at this time. Later, I will be describing how to make these sorts of distinctions - but for now, our primary goal is to create a simple system that accounts for most things the players will want to buy. We can add nuance later.
Some readers will be familiar with the post on my blog describing my trade system in 2010. It should be clear that I have made adjustments to the details described on that post in the last year - changing the overall behaviour of my trade prices. While much of what I described 6 years ago still reflects things I do today, my old method should not be confused with the method described here.
Also, the details below will be presented as calculations done in Microsoft Excel. While calculations for the system can be done with pencil and paper, the reader will discover that once ten or more markets have been added to the system that working without a computer calculating tool will quickly make the system impractical. My use of excel will be simple and I shall try to make it as easy to understand as possible for those who have never taken the plunge and used the system.

It rather goes into great depth on the matter, for those looking to actually build a trade system. That is, after all, the point.  Look to the end of the page for a copy of my excel file that I built to write the tutorial.


And then, if it interests you, please remember that I am still looking to support myself with donations either to my Jumpstarter or to Patreon.  I trust no one doubts that I'm working here . . . heh heh heh.

26 comments:

Tim said...

These rules are golden!

If 1,729 copper pieces buy one ounce of gold in Marzarbol, does that then tell us anything about coinage in Marzarbol? Presumably there's a mint somewhere which makes all coins with about the same amount of gold in them (which you mention in Quantity of Goods), but if you're paying 17 gold pieces for an ounce of gold in Marzarbol - when an ounce of gold is worth 8.715 gold pieces - you'd seem to just be wasting money. On the other hand, then, could the reverse ever occur? As in, you can buy an ounce of gold for less than 8.715 gold pieces?

Alexis Smolensk said...

I get around 9 g.p. per ounce of gold - dividing 1729/192 cp.

I wanted a bottom price for gold pieces (and for everything else) as I tried a system without that bottom price and it is . . . well, let's just say problematic.

If I wanted to fiddle with the system at a specific place and time, I could just manually insert any number into the gold cp/unit cost, right?

Alexis Smolensk said...

Incidentally, for people who have read through the tutorial thus far, this page may have a little more meaning:

Total references in my campaign

Mujadaddy said...

"we will need an adjustment for the relative rarity of gold in the market as compared to other markets. This is the adjustment for rarity... Call it an approximation based on experience."

Rarity: n., a factor which increases cost per unit of a given good in a given market, derived from the proportion of the market's share of total trade in the good and _____________.

You've said that, in this small of a total market, Rarity's impact seems negligible. You've also said that these wiki pages represent a change to the 2010 methods. My notes seem to indicate that you were utilizing a Rarity factor of 20 (.05), or as my notes read, "If a market controls 5% of the trade in a good, it will have the base price for the good."

Might I request some detailing of the math and logic behind the need for and applications of Rarity? Specifically, what it achieves, why that is important, and why a factor of 50 (.02) was settled on. It is, as you've said, "an approximation" but what is it approximating? I have some insights into what it achieves, but if you have the opportunity to detail some of the thinking which went into it, I'd love to read it, even if it can't be addressed meaningfully or at all until after all the current Trade posts are finished.

Alexis Smolensk said...

The math and logic behind the need for rarity is simple: things need to be rare. I would suggest removing that specific calculation from the system as shown and you will see that without it, the final price doesn't change at all, no matter how many local references there are.

If there is no change in price by virtue of the availability of references, what would be the point?

I've already explained my reasons for the rarity factor I've chosen. I have no further comments to make on this subject.

I think I've been extraordinarily forthcoming on the whole process, admitting when necessary that I am just making shit up.

Maliloki said...

2 things:

When changing the production of ore from tons to pounds, you mention that you multiplied the number of tons of or per reference by 16, in order to get the number of pounds. I believe this should be 2000.

For the formula to create the "world value (oz. gold)" for ore you reference cell K4, which is the "cp/unit" cell. Is that just an issue of copy and paste of cell title for the undeveloped goods section?

I may just be missing something because I'm dumb, though.

Alexis Smolensk said...

Thank you Maliloki,

I discovered the error myself as I was completing writing the page on Tuesday; it required that I go back and remake the six images that had the wrong figure to get it straightened out. You are, of course, correct.

When keeping a lot of details like that in my head, it is easy to get dopey and misread something - for some reason I thought I was changing pounds into ounces, not tons into pounds. Sigh.

Go back, refresh the page and you'll see it is all corrected.

Maliloki said...

The image relating to the "tons to pounds" is correct, but the text below it that describes the process is wrong. It's a minor thing, but its there.

Alexis Smolensk said...

I thought I caught it all. I'll go back and fix it.

Maliloki said...

Didn't mean to nit pick or anything, but from what I've read here, I figure you'd want it fixed.

Looks good now though. :)

Thank you for all the work you're putting in to explain this stuff.

Alexis Smolensk said...

That's okay, Maliloki, I like that kind of correction. It's an easy to fix, easy to agree upon error that I like to see made right. It's why I brought on some volunteers to comb through the wiki occasionally and make grammatical corrections. Huge amount of content there; now and again, something is bound to slip past me.

Been working on my book all day. Not an easy day. Sometimes I think I must be an idiot for putting magic in it.

Magic almost always spoils everything. Takes great amounts of effort to make a magic passage work decently.

Wandrille Duchemin said...

I would like to reiterate on what Malikoli commented:

"For the formula to create the "world value (oz. gold)" for ore you reference cell K4, which is the "cp/unit" cell. Is that just an issue of copy and paste of cell title for the undeveloped goods section?"

As I did not really understood the calculation I re-did same along with a dimensional analysis which resulted in some very weird results.
So I find myself in accord that this step might be erroneous in the presented excel document.

Furthermore, this particular error cause the "oz. per local availability" to be the same, despite having different number of local ref. For instance, replace the number of local ore ref (C8) from 1.2 to 2 and J8 shouldn't change (If I'm way too tired to do math).

Coincidently, this may explain what you commented:
"I would suggest removing that specific calculation from the system as shown and you will see that without it, the final price doesn't change at all, no matter how many local references there are."

Because the mentioned "discrepancy" negates the impact of local refs on "oz. per local availability" (J8), so that only the adjustment for rarity is left to account for that.

Then again, there might be something I'm not understanding correctly.

Alexis Smolensk said...

I obviously need to piece this out with you Wandrille, but I'm just stepping out for a shift. I'm pretty confused by your question; we can talk about it after.

If someone else wants to take a shot, I'll be out of touch for seven to nine hours.

Alexis Smolensk said...

It could help if you tell me which exact document and page you're referring to; I've written a lot lately and I don't know if you're talking about a page on the blog or the wiki.

Wandrille Duchemin said...

Sorry for the lack of precision.
I kind of forgot that all this was several weeks ago for you while I just stumbled upon it.
I talk about this wiki page: http://tao-of-dnd.wikispaces.com/Undeveloped+Goods+Prices

and the excel sheet is the one that is in that page.

More specifically, it is centered around these images:
http://tao-of-dnd.wikispaces.com/file/view/Ore%20C.png
http://tao-of-dnd.wikispaces.com/file/view/Ore%20E.png

I hope this helps you understand my previous comment. Otherwise I will be happy to expand on some points.

Have a nice shift; I, myself, am going to bed.

Alexis Smolensk said...

Wandrille,

Ah, I see the issue. The heading for H7 should read, "c.p./oz. gold." Heck, it means I have to make all those pictures over again. Darn.

All we're trying to do is to compare the base price for all the total references of a thing (in this case, ore) against all the total references of gold, so as I establish a base price, that is then modified by the "adjustment for rarity."

I can only think of two kinds of "very weird results" you could be getting. Either the numbers are too high or they are too low. Both of these problems stem from either a) the amount of total references you've added for the thing vs. the amount of total references you've given for gold; or b) you're assigning way too little or way too much physical material for either.

For example, I have 10 times as many references for grains in the world than I have for gold; and 800000 times as much weight of grain in the world than of gold. These are numbers I've arrived at through research; you're stuck sort of shooting blind, but you can always look up "world production" for things on the net then rig the amounts as it suits you.

I strongly suggest NOT changing the algorithm.

I hope that helps.

Wandrille Duchemin said...

(I read my comment before posting it and I fear that it may appear a bit authoritarian or mean. I want to assure you that this is only due to my bad English and overall bad writing style, I have a lot of respect for you and your system, and I would not comment if I just wanted to propose a 'variation' of the algorithm.)

Alexis,

thank you for your answer.

In terms of number, I use the one provided on the ore example in order to familiarize myself with your system.
However, when I was writing about "very weird result", I was not speaking about number but about the dimensional analysis I performed. Dimensional analysis does not look at number values, it looks at number units (meters, grams,...).

You are correct when you are stating that the heading for H7 should not just be "oz. gold", but I don't think it should read "c.p./oz. gold." either.

If I read the formulae correctly, I have H8 = D8 * $K$4
(http://tao-of-dnd.wikispaces.com/file/view/Ore%20C.png)
the unit of $K$4 is: cp / oz. gold
and the unit of D8 is : "ore reference" , that, for clarity, I will write Oref
So it follows that the unit of H8 is: Oref * cp / oz. gold

(We could debate whether or not Oref is really an unit, but that does not really change the rest of the comment)

Following the same dimensional logic, we determine the dimension of the various number you compute in I8, J8 K8 and L8.
And for L8, we have the "very weird result": this cell is not in "cp / unit", but actually in:

( Oref * cp * cp )/ (oz. gold * oz.gold)

So, Ore references times copper pieces squared divided by ounces of gold squared.

I could expand all the calculation in the comment, but I feel this would be tedious. I will produce some document with details if you ask me too.


There exists a simple way to verify that something strange is happening.
Let us say that we want the prices not in "copper pieces", but in "half copper pieces", so that there is 384 half copper pieces (192*2) in a gold coin.

Then the price of gold should be twice that of what it is now : 1729.06 * 2 = 3458.11 (accounting for rounding errors)
And the price of ore should also be twice what it is now : 0.75 * 2 = 1.5
(some adjustment might make these slightly off, but not by much)

So to make that change we change 192 by 384 in both K4 and L8.
When we make that change, we observe that L8 is now 3 (actually 2.989...) which is not twice, but four time the original amount.
As 4 is the square of 2, this would be consistent what I wrote about L8 somewhat depending on 'copper pieces squared'.

We can observe the same behaviour with 'third copper coin' (576 per gold coin): we get an ore price that is around 9 times the original price.

I sincerely hope I made my concern clearer to you.









Alexis Smolensk said...

Wandrille,

You are in essence correct - except where you say the price is such-and-such more than it "was".

"Was" when? What is this "was" you speak of. It is, yes, 9 times more than a baseline amount that we are using to calculate the price of ore across the whole system - but that baseline amount refers to no actual price that exists anywhere; only the final result actually has any application in the system - and it is the difference of this final result in this market vs. that market that matters, not the difference between the final result versus the "pre-result."

I know this will seem illogical to a mathematician; but I will argue that this is economics, not math. Which should elicit a math.

An engineer, a chemist and an economist are trapped on a desert island and the only available food consists of thousands of cans of food that have washed ashore with them. They set out to decide how to open them. The engineer proposes that perhaps some kind of force could be applied using rocks, mass, velocity or perhaps pressure. The chemist suggests that perhaps they could use the salt water of the ocean to erode the seals on the cans so that they could be weakened, making force and pressure more practical.

The economist begins this argument: "First, let's assume we have a can opener . . ."

Wandrille Duchemin said...

Alexis,

again I am sorry, my words were bad and instead of:

"but four time the original amount."

There should have been:

"but four time the price in copper piece."

So that, if I rephrase: "if a pound of ore is worth 10 copper piece, then the same pound of ore is worth 40 half copper piece"

You argue that this is economics.
But I argue that what I am speaking about is not economic reasoning behind your model (and by model, I really mean that: "a description of a system using mathematical concepts and language" without any need for it to be accurate). What I am speaking about is the soundness of the equations you present.

I don't know if that is useful but, to draw on your joke, the economist could be answered:
"We have a can opener, but it opens can by making them explode..."



Alexis Smolensk said...

Ah well.

Again, you're right. It absolutely isn't logical. Except that it works - at least in excel.

Wandrille Duchemin said...

If you allow me a play on word: it does not work, it seems to work.

Anyway, I feel I have made my point.
I hope these comments might be useful if anyone were to adopt the same strategy as I to try to understand how your system works, or even you.
If at some point you tinker on your system and it starts behaving strangely, please think about it.

I would just conclude by writing that according to something similar to Gresham's law, one should melt all his half-copper coins in order to make copper coin out of it.
(And then, quickly run to the nearest change to change these into gold coins while there are still some left.)

Alexis Smolensk said...

Ah. Now I understand the apologies and the reassurances.

Very well, I'd like to examine "works," "does not work" and "seems to work."

Does the system:

- formulate prices for goods and services based on the origin of things? check.

- are the prices reasonable for players to pay in a campaign? check.

- allow for tweaking and adjustment by the user in an easy and practical manner? check.

- account for every possible product that a DM or player could ever want to fix a price for? check.

- has the system survived ten year of continuous, weekly playtesting? check.

- is the system applicable to any sort of campaign or RPG genre? check.

- does the system logically fit Wandrille's reformulation of the algorithm? no.

At this point, being the internet, I'm supposed to make a cheap slur; but I'm not going to do that. I don't know why your reformulation doesn't work or doesn't fit; I do know that when I create a list of products based on this design and put it in front of players, they love it. They love that they can watch me calculate a price to something on the fly, that they want and isn't accounted for already; they like that they can tailor make houses and fortifications and identify things by their value and recognize that there is a difference in that value as they move from place to place. For me, this is how I defined "works." No other definition, certainly not one based on any mathematical proof I don't fully understand (I admit it, I'm not a mathematical genius), matters to me.

Point in fact, I also feel I need to point out that "melting all his half-copper coins" to any significant degree would mean operating a forge, a fairly overt venture with a significant physical footprint, requiring space, time, cost to build, fuel and workers, particularly if none of the party happens to have any skill as a puddler. You should know that destroying the king's image stamped on a coin for the purpose of melting coins down has been considered a serious crime going back to the Romans; it has often been considered tantamount to treason. There's also the reality that selling a large amount of raw material in my world requires legal recognition, the sort of tiny door that guilds control, so they're bound to wonder where the copper is coming from; that could be a problem. But if your character in my world wants to give that a shot, I'm open to creating an adventure around that.

Alexis Smolensk said...

Continuing the comment above,

As I look at that proof, I "think" I sort of kind of get the problem. Since everything is a multiplier of a multiplier, when you increase the base numbers (half-copper, third-copper), the system gets wildly out of control and ceases to work logically.

Fair enough. It recommends using ONE fixed base currency in the resolution of the base price for things, regardless of what that base currency is called, sized or whatever. I have never, ever, tried to calculate prices through the algorithm in silver pieces or half-copper or anything else - so I've never, ever encountered this particular problem. A silver piece in my game is always 12 c.p.; and since the system is never calculated in silver pieces, no problem.

I am completely unclear on why this is a "concern." Clearly, you're asking the system to do more than it was designed to do. Sorry it is failing you there. I would expect it to fail you there.

The weather system I put out last year was a total failure at depicting actual weather. The combat system in the game is a total failure at depicting actual combat. None of this is a "concern."

I guess I am saying, do it as I do it and it will work for you. Fuck around with it and yes, it won't work.

As near as I can tell, if you decided to set your absolute measuring formula at 384 half-copper per gold ounce, AND NEVER CHANGE IT, then the system would still work exactly as I designed it.

I hope this helps you understand my position on this matter.

Wandrille Duchemin said...

I would first like to apologize: in my third comment the unit for L8 should read:
( Oref * cp * cp )/ (oz. gold * oz.gold * lb. of ore)

instead of:
( Oref * cp * cp )/ (oz. gold * oz.gold)

I forgot to type it.

Now, with regards to your comment(s).
I get that your system works for you. You have been using for a long time and it satisfies you so, why would you change it if you don't want to?

referring to my first comment, I first I thought this merely was some typo in your excel formula. As you explain, it is not a typo and you are happy with it.
I understand that now and about that "seems to work", I am sorry for kind of forcing on you my own definition of "works".


Two small bicker:

* Concerning the last item on the 'check-list', I would argue that:

"- does the system logically fit Wandrille's reformulation of the algorithm? no."

would, in my view, be better put as:

"- does the system fit Wandrille's standards? no."

Or something like that, because what bother me is not "Wandrille's reformulation" of the algorithm, it is the system as you present it. But that is my problem, no?

"Wandrille's reformulation" of the algorithm (or one could call it a slight variation as only two or three formulas change), satisfies my standards along with many of the points you mention (but again, it is 99% your system).
Will it survive for as long as yours? only time will tell, but for now it works for me.

* I would also point out that I am not a mathematical genius as well. In fact many of my peers would laugh at me if I styled myself a mathematician (I would laugh at myself).

Well, these two points are really quite silly.


I feel that this "melting half-coppers" stuff is a good example of why I should refrain from humour outside of my native language (or at all). Nevertheless, you were kind enough to describe the process and obstacle, I will digress a little.
Were I, as a character to think about getting some precious metal from a kingdom's coinage, and were the rest of the party agreeing that this is what they want to do,
I would not do this in the said kingdom. I would look for another country, preferably at war, or in conflict with the kingdom whose coin I want to melt.
There I would seek some authority and propose to supply their own coin industry with the metal I get from the melting of the coin of their concurrent. Or I could propose to help them set up a clandestine workshop making cheap (ie. with less precious metal) versions of the concurrent kingdom before smuggling them there in order to devalue their money (as was done during the second part of the 100 years war).
It would be quite hard to both operate discreetly and also to gain the confidence needed in the other country, but I would find it interesting.
However I think to recall that you don't have different coins systems in your world so that plan might not be applicable.


Anyhow, thank you for taking the time to understand my point and answering. I understand your position and won't bother you with that anymore.

Alexis Smolensk said...

Wandrille,

My having put the thing out there will promote, I hope, someone who has the skill to come up with an algorithm that will satisfy both of us. Wouldn't that be nice? I've hit my limitation.

I only hope that when they do, they can put it into English clear enough that I can reprogram my pricing table.

Wandrille Duchemin said...

As I wrote in my e-mail, here is a link to a googledoc sheet:
https://docs.google.com/spreadsheets/d/1FSEJ8i6OWh3kVGUaYjj4SDuqdlOeUvQouhil6vHDZXs/edit?usp=sharing

The links allows editing, so one can play around with parameters.
(I made a copy of the original document anyway)

On the top left part of the document, there is the system you present on the wiki.

On the bottom left part of the document, I detail a dimensional analysis of your system, and I do the same for a variation of the system I propose.

On the top right part of the document, I expand that variation.

On the center of the document, I use a graph to dynamically compare the unchanged and changed system.

On the bottom right part of the document I discuss the changes a bit further and propose ways to adapt the changed system to a world where some prices have already been fixed (as many a DM already has some sort of price table).

I hope this will be useful.