teofpathfinder

World's best Pathfinder economic data visualization blog

Month: March, 2014

Wizards… how do they work?

Wizards… how do they work? No, I do not mean how do they get their magical powers. I mean how do they participate in the fantasy economy around them? Like any specialist, the wizard will be far behind in achievements if he tries to develop every spell on his own, hand-pick is own spell components, and make his own paper for his spell book. There are a variety of prices mentioned in the rules related to casters and wizards especially, and I am going to spend a couple posts discussing those rules, what they might imply about the Pathfinder wizarding world, and what rule changes might make the wizard prices align better with other fantasy settings.

I would like to start what Pathfinder has to say about a wizard’s costs and then his potential revenue sources.

* Recurring life maintenance costs. A wizard has a  cost of living,  the same as anyone else. The “Average” cost of living is 10gp/month, “wealthy” is 100gp/month, “extravagant” is 1000gp/month.  I think it is safe to assume that wizards worthy of the name certainly won’t fall below the “average” lifestyle in most settings. Note that “average” almost certainly isn’t the lifestyle of the typical inhabitant of most settings.
* One-time costs to record spells. A wizard needs a place to record his spells, typically a book. This takes:
    * One hour per spell level (with a DC15+spell level spellcraft check to understand the spell) in time to copy.
    * 0.15gp per spell level in cost of paper sufficient to record the spell (.15gp for 0 level spells, too).
    * 5gp for a 0-level spell or 10gp x spell-level-squared for suitable ink to copy the spell, unless the spell being recorded is one of the two spells automatically gained per wizard level. The automatic spells are free.
    * To borrow another wizard’s spells to copy them, the typical charge is half the copy cost. That is, 2.5gp for a 0-level spell or 5gp x spell-level-squared. Rarities will cost more.
    * Researching a new spell in addition to the ones gained by gaining wizard levels costs at least 1000gp per spell level and 1 week with mandatory spellcraft and arcana checks.   Each attempt requires a DC20 + 2 x spell level spellcraft AND arcana or the time is wasted. Each attempt takes 1 week for 0-3 level spell, 2 weeks for 4-6 level spell, or 4 weeks for a 7-9 level spell. Up to two research assistants are allowed to aid with the skill checks. The 1000gp base research cost is increased at GM discretion, perhaps based on the spell being researched and faciities available.
* Per casting costs
    * Casting from memory costs no gold because the spell components are effectively free unless specifically noted otherwise.
    * Casting costs from scroll are paid in advance to make the scroll and are 12.5gp x spell level x caster level + special component cost.
    * Casting costs from wands are paid in advance, in bulk (50 charges) for 7.5gp x caster level x spell level + special component cost per charge.
    
These are the costs listed as associated with being a wizard. On the typical day of a wizard’s life he probably has no marginal gold costs for using his powers.  Even when adventuring, he can avoid substantial use of scrolls with good planning. This observation about marginal casting cost is interesting because we have several Pathfinder rules about revenue sources available to wizards.
* Scrolls retail for 25gp x caster level x spell level,and can be sold to shops  for half that.
* Wands retail for 15gp x caster level x spell level, and can be sold to shops for half that.
* Spell casting services retail for 10gp x caster level x spell level + component

There are two interesting observations that come immediately from this. First, the raw material cost of scrolls is the same as the cost a retailer will buy them for. Second, the charge for spell casting services is less than the raw material cost to make a scroll.  What can we infer about the wizard markets in a standard Pathfinder setting?

    1. The magic item market (scrolls, wands, and the rest of the commercially available magic items) has retailers (strongly implied by the settlement rules), but it doesn’t have wholesaler or manufacturing firms or agents making money selling magic items. This inference comes from  the fact there is no money to be made between the wholesale price paid by retailers and the raw material cost.  The magic item creation section says that players cannot make money this way, and says to use the downtime system if you want to, but the 0gp margin has implications for more than just your wizard’s inter-adventure money woes.
    2. Wizards earning money in the market selling spell casting services are not going to be casting from than a scroll, since you certainly can’t operate with negative margins selling on a per-unit basis.  They might be casting from wands or permanent use magic items, which have a marginal casting cost lower than the price listed, and that would make sense to do so for spells needed immediately in large numbers.
    3. The cheapest way to acquire a new spell is to pay another wizard to lend you his spell book.  The most expensive way is to research it yourself.
    4. Time is the constraining resource for wizards, since money doesn’t limit spell casting once a spell is acquired.  
    
With these observations in hand, I invite you to think about the setting implications, because they are many and I am sure I haven’t thought of them all.  Here are a few I plan to discuss in future posts, but if you have any more ideas please leave them in the comments:    

* Why can’t anyone make money making or wholesaling magic items?
* Since you cannot make any money making them, who makes magic items and why?
* Why do casting services sell for more than marginal cost?
* Would or would not wizards cooperate on spell research when they are each other’s cheapest paths to new spells?
* Time is a major constraint on a community’s  aggregate magical capacity. How is this dealt with in terms of training new wizards?

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Crafting – What elements of the crafting rules are realistic? (Part 3)

As promised to havenofinspiration in the comments of my last post, this time I will show the “Thomas Edison” Approach to crafting.  Thomas Edison’s approach to invention was to try tons of things until something worked. He had a experimental laboratory where just kept trying variations on the invention until a commercially viable one was found.  In that spirit, how much time and money would it take a crafter to complete an ambitious project (both in gp and dc) if he had the backing of unlimited time and money?

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The top half of the figure shows the median amount of time it would take in log10 of weeks to complete the project of a given cost with the shaded area being the 10th to 90th percentiles.  The bottom half of the figure shows the same distributions for the amount of money in log10 of weeks. Remember, every skill check takes a week and every attempt costs one-third the retail price.  For reference, the red line in the gp half of the figure is the item costing its retail price in raw materials to make (e.g. 2 failures then a success).
The curves in blue show how a bonus +0 crafter would do making DC11 items with retail price from 10gp to 100gp. The curves in green show how a +10 crafter would do making DC21 items with retail price from 40gp to 400gp. In both cases, I chose these starting points because this starting price is the amount of value added a single take 10 success would create. For the +0 crafter, he will start spending more to make the item than its worth 50% of the time at about 40gp; for the +10 guy that happens at about 120gp.  However, the other half of the time, these crafters are still spending more (of much more) than the item is worth  to make it.  For very large projects (10 times the take-10 value-added per success), the median outcome is enormously expensive and the 10% to 90% range of outcomes is enormously wide.  For these big projects, you really have no idea what you are signing up for at the start (assuming you plan to chase success to completion).

This pattern looks realistic to me as a general representation that when we undertake a project out of our comfort zone (DC11+), we really have a wide variation in the time and effort it will take to complete it.   We often won’t know if success is just around the corner even after many previous failures (this attribute is modeled by the geometric distribution which is memory-less so previous success or failure doesn’t make subsequent success or failure more likely). A bad result on an ambitious project can be orders of magnitude worse than a good one.  This is a reminder that achievements like the moon landing were the products of good project management as well as high craft engineers.  Breaking a project into ten 10,000gp DC21 projects is much more likely to succeed on time and on budget than one 100,000 gp project of the same DC.

For players, I would say this re-iterates what I said in my previous post, with the possible addition of suggesting that you play a long-lived race if you care for your character to spend his retirement treasure on ambitious craft projects like writing the great novel of his or her respective cultural group. For GMs, an impatient patron who feels cheated by the artist contructing his glorious statue or precious steel-golem chassis are plausible adventure hooks, even if noone in particular is trying to do harm. Maybe the party needs to find a magic lathe to get that crucial additional bonus. Well… its an idea at least.

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.

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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.

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