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According to Table 6-15
Subsistence Cost of Living is 4sp per week.
Unskilled labor on a success ears 5cp per day.
That means if you have an unskilled laborer who works 7 days a week, it means they earn 35cp a week, which ends up being 5cp short of being able to pay for a single family members subsistence cost of living.
Even worse, if you do it by month, for 30day, they would earn 15sp, which is 5sp less than the 20sp for a month of subsistence.
I know that's not the focus level-wise for most characters, but it seems to show a potential problem with the floor level of the economics numbers. Also, why should a Trained craftman at 3rd level get the exact same income as an Expert craftman of that level. I understand that is the first level they expect to see that skill rank appear. But it really significantly seems like that rank should make a difference in their income. At that point they can do things they couldn't do before, that should open doors to greater profit.
Honestly, I think subsistence should be more like 3sp a week, and 12sp a month, or 140sp a year to allow an unskilled laborer to live at such a basic level.
AS it stands, unskilled workers can't even subsist.
It takes a full income for a 2nd level person to live a comfortable life (requiring the complete job income to do it) A 3rd level person could with full level appropriate job could afford to support two people at a comfortable living.
None of these offer any spare, to deal with how changing jobs, by current rules leaves you without income for a certain number of days.
Fine living would require a 9th level Master, 10th level Expert, or 12th level Trained job.
Extravagant living would require 13th level Legendary or Master, 14th level Expert, or 17th level Trained job.
Those upper levels aren't necessary bad targets, but it is worth thinking about are those approximately the levels you might imagine a nearby wealthy noble would be who is living an extravagant lifestyle? I imagine there might be ways to boost one's income a little via having some amount of capital, but I'm trying to start with what they have listed now.
Definitely agree with this here. Though Unskilled Labor should be low paying the fact that you are not able to subsist on it alone is pretty bad. Especially for the fact that you'll never have a guarantee of work every day.
Using standard downtime in Pathfinder First Edition the general assumption is that you're working for 5 days per week with two days off for rest, family, and religious reasons.
I think your estimate is pretty on the mark though I would go a step further and make subsistence cost 2 silver 5 copper per week. Using that estimate you can subsist on a meager lifestyle working 5 days per week. It also has the side effect of it taking 10 silver per month or 120 silver per year making nice round numbers.
Using that income you could also easily argue that a married couple with one or two children could also subsist on an unskilled labor wage for both parents, though any time between work might be a bit rough on them.
I'd say this (somewhat) accurately represents the real world and the fact that many people must rely on government assistance, assistance of family and friends, and charitable organizations for survival.
I'd say this (somewhat) accurately represents the real world and the fact that many people must rely on government assistance, assistance of family and friends, and charitable organizations for survival.
I'd agree that subsistence may often involve living off of the excess, discards or charity of those wealthier than you in an urban area. The subsist off the streets downtime action specifically refers to it. However, I don't see having subsistence costing more than a subsistence job can pay making sense as a built in core mechanic. And technically, smart people would choose not to have a job, as subsisting on the streets gives you a net profit vs. being employed.
Granted, it was true that people (non-good) with power have been known to create situations where they could control the economy, and they elevated the prices of items core to the cost of living to insure that costs always exceeded the reasonable amount of pay one could generally make.
Again, this included an attribute of (non-good) people controlling the economy to benefit themselves, and gain the equivalence of slaves by wielding their economic power.
I think that base assumption shouldn't be included as a core assumption in the base income and cost of living of the game that in theory included good realms where fair business is expected.
If you want to raise the price of subsistence in Cheliax or some areas in the Shackles to more than an unskilled laborer can make, fine, I can see enough reasons to readily accept it. I have trouble with it being the core expectation of the game for your default areas.
(Ok, I said non-good. But lets be honest. In most circles I'm in; people would say that creating a non-win situation, and using resources to advertise it as a great opportunity would be considered an actually a rather Evil act, since it is fundamentally a one-way trap.)
@Gloom: 25cp per week does seem like a convenient price point for subsistence. I believe you are correct about P1 tending to assume a 5 workday week, although I think medieval settings a 6 or even 7 workday week, especially for the poor seems quite viable. But as you say, two unskilled workers might be able to pay for a child if a child gets a bit of discount on their cost of living due to size/age/needs.
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A level 0 laborer probably does a mix of level 0 and level 1 tasks with Labor Lore, with some days off as they have to scrounge for jobs assuming there are limited gigs or firings and hirings and not a steady employment. They also fail a fair amount, making the lower value. So maybe every week our level 0 tries 4 level 1 tasks, 2 level 0 tasks, 1 day of failing to find work, let's call it 2 success/2 fail on level 1, 1 success/1 fail level 0, so 5 silver. Better bank that silver because that was a slightly above average week in terms of luck on successes, and some week I might fail all the level 1 tasks if I'm really unlucky, or fail to find jobs more often. Sometimes I might go hungry for a while too and start heading towards starvation if my luck stays down.
A level 0 laborer probably does a mix of level 0 and level 1 tasks with Labor Lore, with some days off as they have to scrounge for jobs assuming there are limited gigs or firings and hirings and not a steady employment. They also fail a fair amount, making the lower value. So maybe every 2 weeks our level 0 tries 4 level 1 tasks, 2 level 0 tasks, 1 day of failing to find work, let's call it 2 success/2 fail on level 1, 1 success/1 fail level 0, so 5 silver. Better bank that silver because that was a slightly above average week in terms of luck on successes, and some week I might fail all the level 1 tasks if I'm really unlucky, or fail to find jobs more often. Sometimes I might go hungry for a while too and start heading towards starvation if my luck stays down.
Thanks Mark for your reply, but unless I misunderstand the rules, the 1st level peasant tries to get a 1st level job. He has to wait 4 days (in order to line up or find a level equivalent job, right?) So by trying to get a level 1 job he burns at least 3 days income and makes the roll. If he succeeds, unless I'm mistaken, he rolls and finds he'll be getting 1sp/day income. It isn't absolutely clear if he gets paid for that last day or not. If so, he gets one sp, and he'll have 3 more SP coming the next three days if he works every remaining day of that week and I guess will be able to pay the 4sp for a that week. He also will be good to pay the next week's pay as long as the job lasts, until it is over a few day/weeks or months down the line. He better save up. If you don't get the one day's pay for the first 4 days of getting the job, he'll be 1sp short for his cost of living, that week. Hopefully he had some banked. But as long as that job lasts he will be good for a while.
If he failed, however, he gets 2cp in what is presumably severance pay? It really isn't enough to pay the bills so even if he isn't fired, he probably has to go elsewhere and try and find another job, meaning 4 more days of being paid nothing. At this point he's gone over a week and at most got 2cp.Honestly, I appreciate being reminded that someone could try to get a level 1 job, even if they are unskilled worker. But I really feel like an unskilled worker should have hopes of being able to generally barely rake in a subsistence living based on doing a untrained job, which is likely what they frequently will do, unless forced into a situation they have to support someone else.
You also pointed out to me that I completely forgot to factor in that they would need to make rolls to succeed at even their level 0 job periodically, meaning they'd have days rather than getting 5cp, they'd occasionally just get 1cp. (At which point I'm sure they'd try to get a different job, since there's no penalty for not changing jobs,since it says if you're only going to work 1 day at a time, you need to do a level 0 task) If unskilled labor is a daily check then if they get a 50% chance of success then the weekly income would drop from 35cp to 23cp assuming we are being generous. If a single success is normally enough to last for a week then it would mean that income would probably tend to be something more like 31cp per week.
Actually, with that in mind, it makes me really like the idea of subsistence being more like a 25cp/week level for someone. Especially since most people living on subsistence like that may not have that much in capital to help them earn extra income or get bonuses to their income checks.
But anyway, your indication of failing 2 income rolls for level 1 jobs would push him back 8 days of pay. And as you pointed out, you were probably being generous with their number of successes. that means every failed check would cut his income by around 38cp, and would be especially traumatic at the start, or if they miss more than one check in a row. And at 50% success rate, getting adjacent failures isn't an unreasonable occurrence to need to plan ahead for.
Anyway, I wanted to say, I still like the fact that there is now somewhat of a baseline of expected income and productivity that gets associated with people of a certain level/experience/proficiency. I appreciate it as a much better starting point than we had in 1st edition.
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Level 0 jobs are still trained jobs (just in this case of labor trained in like Labor Lore). We messed around with the lead-in days for the final so you wouldn't have all that set-up necessarily as a commoner. We generally assume that you periodically do get the option to take some tasks that are better than the baseline over a longer period of time as long as they are available in your settlement (the commoner might even get to gamble on a level 2 or 3 task very rarely, though it might start to get a bit too high in that case). You might also have a situation where commoners alternate a little bit of work with Subsisting on the streets, and I imagine the most unfortunate might be at a point where they are below subsistence some days (going hungry won't kill them right away, and needing to sometimes sleep on the streets or outside the walls somewhere can make them fatigued, so it's not a good situation, but it happens).
Level 0 jobs are still trained jobs (just in this case of labor trained in like Labor Lore). We messed around with the lead-in days for the final so you wouldn't have all that set-up necessarily as a commoner. We generally assume that you periodically do get the option to take some tasks that are better than the baseline over a longer period of time as long as they are available in your settlement (the commoner might even get to gamble on a level 2 or 3 task very rarely, though it might start to get a bit too high in that case). You might also have a situation where commoners alternate a little bit of work with Subsisting on the streets, and I imagine the most unfortunate might be at a point where they are below subsistence some days (going hungry won't kill them right away, and needing to sometimes sleep on the streets or outside the walls somewhere can make them fatigued, so it's not a good situation, but it happens).
Are you saying that you changed the rules for the lead in time so that you don't have as much 0 income time? That would definitely have some impact on one's income potential, if that is the case. I know a little thread talking about things we know. If you wanted to give us a definite on something having to do with income rolls, I'm sure there are lots of people who would be interested to hear. :)
I really have to stress, that in general I liked the shift to an expected productivity per level over the old system that people doing magic crafting, trap crafting, gun crafting, operated under one system, and mundane crafting operated under a different one at a completely different order of magnitude, and job pay operated on yet another different one of a couple systems. All very different ranges for what didn't' really seem like strategically sense-able reasons.
While this one some people might say it over-simplify some types of work's income ability, I still feel like it gives us a better framework to build from, in the long run. Thanks!
I had not considered how civilized 0th-level people survive under Pathfinder 2nd Edition Practice a Trade rules. I had assumed that 0th-level people were children supported by their parents. Other 0th-level people could be goblins living in sewers beneath Magnimar, but they would roll on Survive in the Streets rather than Practice a Trade.
I had looked at the Practice a Trade activity and TABLE 4–4: SKILL INCOME and realized that a 1st-level character could not earn the 2 sp per day required to live comfortably. Even a 2nd-level character would have trouble, due to jobs lasting only a few weeks and needing 4 days and a re-check to find another one. I figure that most townsfolk have a non-adventurer feat called Steady Employment that increases job duration.
Let me model the income of a 0th-level character practicing a trained trade. Let's give the character a +2 trained proficiency bonus to the Lore check and no other bonus, to represent an average person and medium DC 11 to represent an average job. Set the duration of the job to 90 days. In seeking a 0-level job, the character first spends 4 days seeking the job and then rolls on Lore:
1 chance out of 20 of critical failure for immediate firing and no pay.
7 chances out of 20 of failure for too little pay to survive on; hence, immediately quitting after 1 day of 1 cp pay.
10 chances of success for 90 days of work at 5 cp/day pay.
2 chance of critical success for 90 days of work at 1st-level pay, 1 sp.
The average money is (1/20)(0 sp) + (7/20)(0.1 sp) + (10/20)(90 days)(0.5 sp/day) + (2/20)(90 days)(1 sp/day) = 31.535 sp.
The average time is (1/20)(4 days) + (7/20)(5 days) + (12/20)(94 days) = 58.35 days.
The average pay rate is (31.535 sp)/(58.35 days) = 0.54 sp/day = 3.78 sp/week.
Suppose that 0th-level character tried for a 1st-level job instead. The search time goes up to 5 days and the DC goes up to 13.
1 chance out of 20 of critical failure for immediate firing and no pay.
9 chances out of 20 of failure for too little pay to survive on; hence, immediately quitting after 1 day of 2 cp pay.
9 chances of success for 90 days of work at 1 sp/day pay.
1 chance of critical success for 90 days of work at 2nd-level pay, 2 sp.
The average money is (1/20)(0 sp) + (9/20)(0.2 sp) + (9/20)(90 days)(1 sp/day) + (1/20)(90 days)(2 sp/day) = 49.59 sp.
The average time is (1/20)(5 days) + (9/20)(6 days) + (10/20)(95 days) = 50.45 days.
The average pay rate is (49.59 sp)/(50.45 days) = 0.98 sp/day = 6.88 sp/week.
If I drop the job duration down to 30 days, the 0th-level job pays 0.47 sp/day and the 1st-level job pays 0.81 sp/day. If I drop the duration down to 10 days, the 0th-level job pays 0.34 sp/day and the 1st-level job pays 0.53 sp/day.
The NPCs have no reason to seek out 0th-level jobs if 1st-level jobs are available. However, sometimes even the 1st-level jobs don't pay a subsistence wage of 0.57 sp/day.
I’m posting from my phone, so can’t really look up exact details, but level zero jobs were an exception to the normal setup time. I’m pretty sure that it was always 1day. It also later indicated that if looking for making money from working only one day, that level zero jobs was normally your option.
So even for a level 0 worker, I don’t think there is a four day setup time for the level zero job.
Also, as I recall, the level 0 job setup time was specified as 1 day, and the statement that you could make money workin 1 day at a level zero job, that you get your first income amount after the setup time. The first day on a level 0 job.
But yes, level 1 doesn’t get you to comfortable level. I think there should be a poor level, reflecting healthy enough food intake, but probably having a lack of privacy.
I see substance as minimum food, poor taste, potentially makeshift shelter, little safety or concept of stability or privacy.
Poor (not listed) as a fairly communal shelter with little or no privacy, but with basic food, and at least a touch of safety or stability.
Comfortable, implies a reasonable degree of privacy and security, with a distinct concept that you can meet more than your basic needs.
Charlie in the chocolate factory was in my opinion at a poor level. They had their own place but it was crowded. The had a tiny amount that was extra the used on basic nicety. They probably were not far above subsistence but not comfortable.
I’m posting from my phone, so can’t really look up exact details, but level zero jobs were an exception to the normal setup time. I’m pretty sure that it was always 1day. It also later indicated that if looking for making money from working only one day, that level zero jobs was normally your option.
So even for a level 0 worker, I don’t think there is a four day setup time for the level zero job.
Also, as I recall, the level 0 job setup time was specified as 1 day, and the statement that you could make money workin 1 day at a level zero job, that you get your first income amount after the setup time. The first day on a level 0 job.
The paragraph from the Playtest rules is:
You need to spend a minimum number of downtime days to locate and secure the job, prepare to practice your trade, and get started on the task. This number depends on your level and the level of the task. You must spend 4 downtime days for a task of your level. Reduce the number of days by 1 for each level lower than you the task is, to a minimum of 1 day. Conversely, increase the number of days by 1 for each level higher than you the task is. After this base downtime, you earn your initial amount of money, and you can continue at the task to keep earning more. The success entry explains how this works. Note that if you want to earn money for working just 1 day, you need to pick a task that requires only 1 day of preparation. A 0-level task always requires 1 day.
I confess I am confused by the 2nd-to-last sentence, "Note that if you want to earn money for working just 1 day, you need to pick a task that requires only 1 day of preparation." One day of preparation and one day of earning money is still 2 days.
Thus, the sentence after it about 0-level tasks I skip because I don't know whether it is affected by the part that confuses me. The Practice a Trade rules were not part of the playtest chapters that I reached, so I did not need to master Practice a Trade.
But yes, level 1 doesn’t get you to comfortable level. I think there should be a poor level, reflecting healthy enough food intake, but probably having a lack of privacy.
I see substance as minimum food, poor taste, potentially makeshift shelter, little safety or concept of stability or privacy.
Poor (not listed) as a fairly communal shelter with little or no privacy, but with basic food, and at least a touch of safety or stability.
Comfortable, implies a reasonable degree of privacy and security, with a distinct concept that you can meet more than your basic needs.
Charlie in the chocolate factory was in my opinion at a poor level. They had their own place but it was crowded. The had a tiny amount that was extra the used on basic nicety. They probably were not far above subsistence but not comfortable.
The phrase "subsistence level" makes me think of having barely enough food, shelter, and clothing to stay alive. To me that suggests that anyone living at subsistence level probably has developed a condition such as fatigued or stupefied. Drained condition seems appropriate, since starving people are vulnerable to disease. On the other hand, subsistence does mean having enough, so perhaps that is enough to avoid harmful conditions. 5 cp a day can pay for floor space in an inn to sleep and 2 poor meals a day according to TABLE 6–14: SERVICES on page 188. Most subsistence-level people will have their own hovel and save the 3 cp.
An adventurer on downtime would want at least a bed in an inn (1 sp), a poor meal for breakfast (1 cp), another poor meal for lunch (1 cp), and a square meal and a mug of ale for dinner (4 cp). That is 1.6 sp a day. A permanent resident could probably find cheaper bed space than the common room of an inn. So I expect a modest standard of living between subsistence and comfortable that costs 1 sp per day. It would be nice to have modest living at 7 sp per week squeezed into TABLE 6–15: COST OF LIVING between subsistence at 4 sp per week and comfortable at 14 sp per week.
Read A Christmas Carol. Throughout most of history workers were expected to work 6 10 hour days as a usual.
Only in recent history (20th Century) was the 40 hour work week the norm.
Since the Playtest Rulebook measures the working time only in days, we cannot see the difference between an 8-hour day and a 10-hour day. I played Pathfinder 1st Edition with a strict 8-hour workday, limiting daily crafting to 8 hours, though the characters could use the other 8 waking hours for other activities, such as drinking in taverns or having a quick 15-minute delve in a nearby abandoned castle.
The six-day workweek makes a big difference whether the impoverished laborer can earn 3.5 sp by working 7 days a week or only 3 sp due to a mandatory religious day every week.
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I know that's not the focus level-wise for most characters, but it seems to show a potential problem with the floor level of the economics numbers. Also, why should a Trained craftman at 3rd level get the exact same income as an Expert craftman of that level. I understand that is the first level they expect to see that skill rank appear. But it really significantly seems like that rank should make a difference in their income. At that point they can do things they couldn't do before, that should open doors to greater profit.
I have been mathematically deconstructing the skill income table to see how the numbers work. I figured out the basics. Mark Seifter revealed in Trickle down Alchemy Economics comment #16, "it's a piecewise-defined function on a logarithmic y axis," which confirms some properties I had deduced. Loreguard participated in that discussion, so is already familiar with it.
TABLE 4–4: SKILL INCOME (page 153) is the same as TABLE 4–3: CRAFTING PROGRESS PER DAY (page 148). This clever idea resolves the PF1 intra-party problem of inactive PCs during downtime. While the party crafter is spending weeks crafting magic items between dungeon delves, the other party members can pick up jobs via Practice a Trade and match the crafter in production. Then they earn enough money to pay the crafter for his work.
I think Paizo derived the numbers for the tables from the cost of high-level items. Let me demonstrate. I took the most expensive items from the Treasure lists (page 349-353) or the most expensive armor at 1st level, and made a table of how long to craft them at the fastest always-successful rate.
1st level: (1/2)(175 sp item)/(1 sp/day) = 88 days.
2nd level: (1/2)(350 sp item)/(2 sp/day) = 88 days.
3rd level: (1/2)(600 sp item)/(4 sp/day) = 75 days.
4th level: (1/2)(1,000 sp item)/(6 sp/day) = 84 days.
5th level: (1/2)(1,600 sp item)/(10 sp/day) = 80 days.
6th level: (1/2)(2,500 sp item)/(14 sp/day) = 90 days.
7th level: (1/2)(3,600 sp item)/(20 sp/day) = 90 days.
8th level: (1/2)(5,000 sp item)/(30 sp/day) = 84 days.
9th level: (1/2)(7,000 sp item)/(40 sp/day) = 88 days.
10th level: (1/2)(10,000 sp item)/(50 sp/day) = 100 days.
11th level: (1/2)(14,000 sp item)/(75 sp/day) = 94 days.
12th level: (1/2)(20,000 sp item)/(100 sp/day) = 100 days.
13th level: (1/2)(30,000 sp item)/(150 sp/day) = 100 days.
14th level: (1/2)(45,000 sp item)/(250 sp/day) = 90 days.
15th level: (1/2)(65,000 sp item)/(350 sp/day) = 93 days.
16th level: (1/2)(100,000 sp item)/(500 sp/day) = 100 days.
17th level: (1/2)(150,000 sp item)/(700 sp/day) = 108 days.
18th level: (1/2)(240,000 sp item)/(1,000 sp/day) = 120 days.
19th level: (1/2)(400,000 sp item)/(1,500 sp/day) = 134 days.
20th level: (1/2)(700,000 sp item)/(2,000 sp/day) = 175 days.
Paizo developers appear to aim at 90 days to craft level-appropriate items. For some reason, the prices shoot up beyond the usual increase at the highest three levels and that increases crafting time.
The slope of the skill income series 1 sp, 2 sp, 4 sp, 6 sp, 10 sp, etc. is interesting. Magic item prices are a geometric progression with multiplier 1.4678, which is the 6th root of 10. Roots of 10 gives more round numbers in a progression than other ratios, and 1.4678 is reasonably close to the 1.414 ratio for experience points. However, the low end of item costs, the mundane items, are determined by historic and PF1 legacy prices, so Paizo apparently did not feel as free to make them follow the 1.4678 ratio. The rapid increase in prices from 175 sp half-plate armor to 600 sp +1 magic light or medium armor over just two levels requires a 1.85 multiplier between levels, which the skill income progression approximates by multiplying by 2. The next two rations, 6/4 = 1.5 and 10/6 = 1.67 are still high, but after that the progression does a good job of following the 1.4678 ratio.
Basing the progression on magic item costs leaves out the effect of proficiency. If a developer started with the calculation (1/2)(item cost)/(90 days) = crafting progress per day, then he would create a single list of silver pieces per day without proficiency factored in. That list would be assigned partial columns in tables 4-3 and 4-4: the 1st and 2nd level entries would be in the Trained column, the 3rd through 6th level entries would be in the Expert column, the 7th through 14th level entries would be in the Master column, and the 15th through 20th level entires would be in the Legendary column, based on the assumption that a serious crafter would max out crafting proficiency.
Then the developer needs to fill in the rest of the table. In the crafting progress table, everything to the right of the single line of entries is left blank. In the skill income table, everything to the right of the single line of entries copies those entries. Thus, a character with legendary proficiency working a 2nd-level job (unlikely, but characters can take jobs below their level) would the same skill income numbers as a character with trained proficiency working the same job. The only difference is that the legendary character would find the job faster and be much more likely to roll a critical success. That seems odd, but the game lacks a compelling reason to do otherwise.
The numbers left of the initial line of entries is trickier. At 3rd level the trained skill income equals the expert skill income. At 13th level and higher, the trained skill income is exactly half the expert skill income. Starting at 17th level, that is roughly true for the comparison between expert and master, too. The comparison between master and legendary never reaches that ratio, but at 20th level master skill income is 75% of legendary skill income, and at 21st level (used for critical success at 20th level) it is 70%. That fits the level-based paradigm: with a 1.4678 ratio between levels, a ratio of 2 is the equivalent of 2 levels. At the maximum difference, a higher rank of proficiency is worth a +2 to effective income level.
The general principle in a row is that at low levels the Trained, Expert, Master, and Legendary numbers are the same, and at the highest levels the Trained, Expert, Master, and Legendary numbers double with each step to the higher proficiency. What happens inbetween? The increase by level slows down to a ratio of 1.3 until the lower proficiency's income is half the higher proficiency's income, and then the increase returns to a ratio of 1.4678. Rounding makes the actual ratios a mixture of 1.25 and 1.33 and an occassional more outlandish ratio rather than 1.3 exactly.
However, the jump from 5 sp at trained 4th level to 9 sp at trained 5th level is an enormous ratio of 1.8 where the pattern calls for a 1.3 ratio. I can't find any justification for that jump.
Like Mark Seifter said, it is piecewise. Each column is a combination of geometric progressions that have ratio 2, then 1.4678, then 1.3, and finally 1.4678 again.
Loreguard asked, "Also, why should a Trained craftman at 3rd level get the exact same income as an Expert craftman of that level." It is because the developer's mental gears had a conceptional glitch. The obvious places to piece in the slower 1.3 geometric progressions are at 3rd level, 7th level, and 15th level where the proficiencies are abandoned for better ones. However, ratios occur between levels, so the new 1.3 ratio does not affect the first entry. Thus, at 3rd level trained income equals 3rd level expert income. The trained income gets better at rate 1.3 and the expert income get better at rate 1.4678 at the next level. For the proper effect, the 1.3 ratio ought to have been applied a level earlier.
The skill income has another oversight. At 1st level, 1 sp per day is enough to finish the unfinished 87.5 sp of crafting on half-plate armor in 88 days. Thus, the crafter spends 88 days of time (plus 4 days of preparation) in order to save 87.5 sp on the armor. Except that he has to pay for room, board, and crafting space during that time. I cannot see that costing less than 1 sp per day. Subsistence living would leave the crafter too weak. Thus, the crafter will spend 88 days of time and 88 sp in living expenses in order to save 87.5 sp. That is useless. Even if the crafter can live off of 5 cp per day, he would have to spend 44 sp in order to save 87.5 sp.
Thus, in order to cover expenses properly so that the crafter can finish the crafting in the expected 90 days we have to also let him earn an extra 1 sp per day. This makes more sense with Practice a Trade than Craft, since all value from crafting goes into the item, but we might as well use the same numbers with both. At 5th level, which earns 10 sp/ay, the 1 sp/day is less than rounding error, so we can ignore expenses at 5th level and higher. But 4th level and below needs an increase.
For example, imagine using the following chart for trained skill income and crafting progress. Expert crafting progress is always twice trained crafting progress, master crafting progress is always twice expert crafting progress, and legendary crafting progress is always twice master crafting progress.
Oth: 1 sp/day
1st: 2 sp/day [44 days crafting at trained]
2nd: 3 sp/day [59 days crafting at trained]
3rd: 4 sp/day (8 sp/day expert) [38 days crafting at expert]
4th: 5 sp/day [50 days crafting at expert]
5th: 6 sp/day [67 days crafting at expert]
6th: 8 sp/day [79 days crafting at expert]
7th: 10 sp/day (40 sp/day master) [45 days crafting at master]
8th: 12 sp/day [52 days crafting at master]
9th: 15 sp/day [59 days crafting at master]
10th: 20 sp/day [63 days crafting at master]
11th: 25 sp/day [70 days crafting at master]
12th: 33 sp/day [76 days crafting at master]
13th: 45 sp/day [84 days crafting at master]
14th: 60 sp/day [94 days crafting at master]
15th: 75 sp/day (600 sp/day legendary) [55 days crafting at legendary]
16th: 100 sp/day [63 days crafting at legendary]
17th: 125 sp/day [75 days crafting at legendary]
18th: 150 sp/day [100 days crafting at legendary]
19th: 200 sp/day [125 days crafting at legendary]
20th: 250 sp/day (2000 sp/day legendary) [175 days crafting at legendary]
A 1st-level character making 175 sp half plate spends 87.5 sp up front on materials, and works 44 days to cover the remaining 87.5 sp via crafting progress. He sleeps in a corner of the shop and that costs 1 sp/day. Thus, he spends 87.5 sp in materials, pays 44 sp in expenses, and takes 44 days. That meets Paizo's expectations that someone who spends 131.5 sp on a 175 sp item requires 44 days to finish crafting it. Likewise, a 2nd-level character making a 350 sp expert shield pays 175 sp for materials, takes 59 days to finish the shield, and spends 59 sp on expenses. Paizo's intention was that a 2nd-level crafter who spent 234 sp (175 sp + 59 sp) would need 58 days to finish crafting the shield.
The beginning of my curve is linear because I wanted to use whole silver pieces and the increase was too small to add anything besides +1 sp. Later, I switched to a multiplier of 1.28. Since 1.28 is smaller than 1.4678, my curve does not keep a steady crafting time. Whenever the character increases his crafting proficiency, the time drops to 45 days, half of the intended 90 days, since his rate doubled. Then the crafting time gradually works its way back to 90 days before it is cut in half by the next proficiency increase. And I aimed for the 175 days crafting time that the original table had at 20th level.