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### Crafting – What elements of the crafting rules are realistic? (Part 2)

In my last post I left off with a figure showing how the likelihood that a crafter will complete a project requiring multiple successes drops precipitously as DC increases. This is a straightforward result of making multiple rolls with low likelihoods of success. This is realistic in the sense of showing how undertaking a challenging project is uncertain in how long it will take to complete and how much money (how many bad failures) you will need to spend along the way.  This is a typical finding in large real-world projects where the true size (GP) and challenge (DC) of the project are not known at the start.  A DM wishing to make a new project more realistically challenging might add a random element to the DC, so for example, crafting a clockwork sword robot might be DC30+1d4 where the 1d4 is only rolled after the first attempt.  Perhaps what makes Manuals of Golem Crafting so useful is that they spell out exactly how to manage a golem-body building project so it is DC30 and 20000gp in retail cost.

For a project of known DC and skill bonus (i.e., for a fixed target number) there is still a great deal of variation in possible results.  The figure below is a histogram showing out of 10,000 trials of a +7 crafter on a DC18 infinite cost project, how many trials were able to complete a given gp in value before failing miserably.  Only a very small number of attempts would have suceeded at creating a 200gp project.  Students of statistics may recognize this as a geometric distribution, which makes sense since the canonical process for generating geometric distributions is the count of the number of dice a player needs to roll before getting a success.  In our case, we are getting this shape from the number of successes rolled before a bad failure with some variation thrown in from the fact that different successes are worth different amounts of craft value.

The mean result is completing only 68gp and the variance is 7,335gp^2. This is a distribution where most efforts don’t get very far but the lucky few can complete big projects.  Is that realistic for a worker who isn’t quite comfortable with what he is doing and has to “try his luck” to make progress?  I think so.  From a different point of view, half of the time, a project to make an item worth 42gp retail will fail (median 41gp), so a craftsman will have to use twice as much raw materials, 32gp (66% of the value), to complete the items on average. This craftsman will on average take about 3 weeks  to finish the 48gp item. The rules say earnings are half the crafting checks, but with only 16gp in difference between the raw material cost and retail price, this crafter cannot be getting his 3 weeksx17.5(av. skill check/week)x 0.5(gp/skill check) = 26.25gp  out of only 16gp.  So what gives? Some might say this just means the rules are an inconsistent mishmash, but I think that the more interesting implication is that, when being practiced to earn wages, the crafters work by taking 10 on the most difficulty item they can make. Crafters who find themselves rolling d20s for their work are probably:

– Have no choice. For example the ship will sink if the patch is not repaired.
– Practice to learn
– Undertaking an ambitious project at the behest of a client/patron
– Did not know it would be so difficult when they started
– Doing it for the inherent value or pleasure of doing it (hobbyist)

Realistically, at very low-skill levels (below 0 net bonus) it is unclear how a crafter could earn a living in the trade at all.  A crafter with a -1 net skill bonus supposedly can earn 4.5gp a week by taking 10 on his check, but it is is a stretch to imagine how this person could crediby do so. Below a 0 bonus, taking 10 doesn’t even allow the crafter to aid another crafter, and on his own the -1 crafter can only make items worth 5.4gp more than their raw materials per week if the craft difficulty table is assumed to allow items with a DC of 9. If only DC 5 is available, the -1 crafter can only make items worth 3gp more than the raw mateials.  There is no room for the crafter to actually make his supposed earnings. I think it is realistic to assume that noone in Pathfinder is making his living by a skill with less than a 0 bonus, and most of those who are working with a 0 bonus are either apprentices or making very simple items.

All in all, the roll of randomness in crafting doesn’t seem especially unrealistic to me.

### Crafting – What elements of the crafting rules are realistic? (Part 1)

The primary goal of the designers in making Pathfinder’s crafting rules was probably not to realistically model pre-industrial manufacture. Simplicity and fun should come before realism, for example. All the same, this post is going to look at the attributes of the crafting rules and discuss what results of the mechanics are realistic or unrealistic because that was a point of discussion of an acquaintance.

### Overview of the system

The craft system in Pathfinder allows the character to transform unspecified raw materials into another product. As written, the value of the finished good of ordinary quality is three times the value of the raw materials. Each good has a difficulty level and price associated with it, and these are crucial quantities to the formula because they govern whether a craftsman can make the item and how long it will take the worker. To make progress at producing a good, the craftsman’s skill check for the effort must meet or exceed difficulty level for the good. A good is finished when the product of the skill check and the difficulty level meets or exceeds the price in silver pieces. Skillful or hurried craftsmen may elect to increase the difficulty of the good by increments of five to speed production. Failing a skill check badly results in wasted raw materials and a ruined product. Simple failures result in no progress for the week. The skill check can be influenced by many modifiers including: craftsman’s skill, tools, settlement modifiers, assistants, and local conditions.

### Ratio of the prices of raw materials and finished product

The good produced has a list price in the rules that is denominated in gold pieces and the price of the raw materials to make that good are one-third of that price. I don’t know whether this ratio is appropriate for pre-industrial production, though perhaps one day I will research that question. The Pathfinder rules themselves provide for examples of these deviations in the settlement modifiers that raise or lower the prices of certain goods without increasing the price of th raw materials.

The existence of a single ratio for all domains of production is defensible, if unrealistic simplification because even in a pre-industrial setting there will be some producers of raw materials with more or less market power in times of calm (e.g. economic equilibrium) than the craftsmen. It might also be that the skill is particularly in demand and the produced good is much more valuable than the raw materials. The raw materials might come from a monopoly source (e.g., a single mine) or the craftsmen might have a strong guild that can control input prices. As a general rule, this is a reasonable simplification, and I would assume that one-third is the setting-wide average ratio of raw material to finished product price. For all these reasons it is not realistic to have the same ratio apply to all trades.

The GM should feel confident from a realism point of view about raising or lowering this ratio in the face of social circumstances or shocks to the supply of materials because the factors are not rare today nor were they unusual in the past. Local famines were frequent before the agricultural revolution and improved transportation made regional food markets inexpensive. The shock of a bad harvest would move up the supply chain easily. Less universal examples include kobolds capturing a key mine supplying iron for the production of weapons or the discovery of a huge cache of gems sold by adventurers for the production of jewelry.

### Role of randomness in production

There are two ways that randomness and uncertainty bear on the Pathfinder craftsman’s work: unforeseen events and craft skill rolls.

I already mentioned an example of the first – mining accidents making quality iron harder to come by. If only low quality iron were available, this might apply an unforeseen -2 to the skill check and might slow down an experienced craftsman. This kind of randomness in the production process is fun and realistic.

For a sufficiently skilled craftsman, there is no randomness in the transformation of inputs to products. While the societal modifiers might raise or lower the prices, a sufficiently skilled will create a definite amount of product. This isn’t completely unrealistic in the sense that an experienced worker might be able to perform predictable amount of work on a well-understood task, but this breaks down quickly if the product is something new, challenging, etc. This brings us to whether a series of d20 rolls against a target number is a reasonable way to model the time it takes and ultimate success of a project.

While each d20 roll is itself a uniformly distributed random integer from 1 to 20. However, the actual craft process has three possible outcome’s for a week’s roll: success, failure, and bad failure (fail by more than 4). Within a successful roll there is also a distribution of results because a better roll will mean more hypothetical value added than a roll that barely passes. The progress is equal to the product of the DC and the total roll with modifiers in silver pieces.  When the full value has been reached through these successes, the work is finished.

To show how much the process can vary for a craftsman who is not taking 10, I have created a figure showing the distribution of time taken and value created before a bad failure by a +7 craft bonus worker on an “infinite cost project’. The dark blue line shows the median time taken and value added and the gray area is the 90th percentile to 10th percentile of outcomes. As shown below, the 50%of  crafting attempts needing an 11 to pass will not make not make it past 2 weeks of attempts before ruining the raw materials. In that time,the median +7 craft process will create about would be able to complete a 40gp item.  Past 11, there is a quick drop off productivity with 50% of craft attempts not being able to complete anything of value if a 16 is needed. Large projects are ambitious even if the target is only an 11, only 10% of projects needing an 11 will accrue four average successes (about a 160gp item).

To return to the topic of realism, the crafter making taking some risk in his effort with a somewhat ambitious project (target roll 11) can expect to have a decent chance of having to start over or at least have a “one-week job” (based 40 gp price) take two weeks even if things go reasonably well (median result).  Very challenging might take many attempts (10 or more) to complete or worse, be effectively impossible,  to complete something that could have taken only  a small fraction of the time for a craftsman with moderately higher skill.  This kind of variation is not uncommon in work, but the distribution of the difference between a 50% outcome and a 90% outcome is an outcome of the game mechanics rather than something inherent to real life which might have a much wider variance in typical outcomes.

### Is the craft (or profession) skill a good way for PCs to get gold?

About a year ago, some friends of mine debated in email whether the Pathfinder craft skill rules were overly lucrative for PCs, unrealistic, and inconsistent. Off the cuff, I agreed only with the second of these contentions, but I am going to start this blog off with an exploration of these three points.

According to the skill rules, a craftsman practicing his trade earns half the result of a craft check in gold for the week of work. On average, the PC’s earnings in a week will be (10.5 (mean of d20) + skill modifier)/2 in gold. If a steady income and output of product were desired, taking 10 would yield nearly the same results. Out of his earnings, a craftsman must pay his cost of living. For the sake of evaluating aggressive assumptions, I assume that the PC is living as thriftily as possible with the “Poor” cost of living 3gp/month. A fourth level PC can earn 8.5gp per week without spending any feats or being particularly smart, saving 35.25gp in a 4.5 week month. The craftsman will have manufactured more than this in valuable goods; but, as will be discussed in more detail later in this series, the craftsman only manages to receive a portion of the value he creates.

I think the an appropriate comparison of these earnings is against the potential money to be gained by adventuring instead. The crafting rules are quite clear that you cannot do on the same day because killing orcs is hard work, and would leave you unable to properly apply yourself to your day job. Anyone using official Pathfinder materials may have noticed that the Golarion is a very wealthy and magic-rich world, and indeed the rules on character creation for characters beyond first level show that a PC’s expected earnings per level are generous compared to the home-grown campaigns I have played in.

The figure shows how many years it would take three hypothetical PCs of differing craft skill levels to earn the amount of treasure appropriate to gaining the wealth commensurate with the next level. The red, blue, and green lines represent PCs with a craft skills of +3, +7, and +11 above their levels, respectively. Only at first level would it take these PCs less than a year (between 4 months and 8 months depending on skill level). The time requires increases exponentially and is measured in decades even at low levels.

Practically speaking, the events of many campaign plots will advance past characters who spend decades crafting. Even in a sandbox campaign, human characters of moderate level would incur age penalties before they could gain significant magical equipment. Most plots do not allow for the kind of downtime required to earn the kind of wealth acquired from adventuring according to the Pathfinder suggestions. In a very low-treasure world, crafting might provide a significant income, but in a low-treasure campaigns that is also low-magic, it might still be difficult to turn mundane earnings from blacksmithing into a vorpal blade. It does raise the question of what elven communities do with all their accumulated wealth from long years of experienced artisans working in the community, but that is a digression for another post.

In most campaigns, downtime spent crafting will not significantly affect power level compared to the treasure handed out by the GM.

### Introduction

Welcome to the Te of Pathfinder. There is plenty of good blogging on RPGs, economics, and data visualization these days, but surprisingly few combining all three topics. I plan to use this blog as a way to explore the setting and word-building implications of the Pathfinder rules, fantasy economics in general, but other gaming topics are sure to intervene. I will try to include some data visuals to illustrate my points. I chose this name as a bit of an homage to and play on another blog, Tao of D&D. If the Tao is the way a game should be played, then perhaps Te is more about the attributes that will arise from a game so played. It remains to be seen if this blog will live up to that, but I have to try.