I think this should go here, since I assume it counts as a conversion to/from 3.5. Please correct me if I'm mistaken.
Anyway, I could use some help with this. Maybe it's because it's late right now, but I just can't wrap my head around this math:
Downtime rules for gaining Capital
The Craft and Profession skills allow you to attempt a skill check once per week, earning an amount of gp equal to 1/2 your check result. If you were to divide that amount by 7, you'd get your earnings per day. However, that assumes you work 7 days per week, and most people take 2 days off per week for rest and worship, so that's only 5 days of actual work per week. Dividing your check result by 2 and then by 5 is the same as dividing by 10, which is why the downtime system has you divide your check result by 10 to determine gp earned per day. You can work 7 days per week (if you really need the 2 extra days for earning capital), but even mighty adventurers need a day off now and then!
Referring to dividing your total result for earning gp or Capital by 10 to get your final earnings. Now, keep in mind that the Forgotten Realms uses tendays rather than weeks to track time, so... For instance, if you have a building that has +80 to earn gp per day, and you take 10 as suggested, your result looks, at a glance, like 90 / 10 = 9gp/day. Of course, that really isn't that bad (90gp/tenday, if your building works all the time); but, the base math is also based on a 7-day week. Blast and bebother FR tendays for this reason, by the way, but here we are.
So, the rules say that the mechanic of dividing by 10 is due to that being the same as dividing your skill check result in half (as with Craft or Profession) and then dividing by 5 (the number of days worked in a week, assuming the standard 2-day weekend) to get your daily result. In my game, we've already decided that, based on this math, there are 2 possible "work weeks" in a tenday (rather than change all the numbers entirely). But, to get the actual amount earned, do we just double it to account for 2 "work weeks" of 5 days each? Is that right? Or does it take care of itself, e.g., by simply working for 10 days, it evens out since you're still earning the 5-day rate, but for two weeks in a tenday? That doesn't seem completely correct, but the algebra is making my head swim.
Does any of this, including my question/confusion, make sense? I know I'm missing something obvious, but right now all the numerals just look like squiggly lines fighting pointlessly to the death. Please help!
You have a number of choices. The "simplest" is just to assume that there are two work-weeks in a tenday, and double your results. However, that means that you're working with no weekends, which UCam specifically accounts for. A slightly fairer method would be to assume 4 work-weeks in a Faerunian month, so that in any given tenday you are working for 1-1/3 work weeks. The most realistic version, though, is just to roll each day a character works - if they choose not to take any "weekends", that's their choice. Teams and buildings also roll per day, but for every single day there is. Which will work out the same whether you're using "normal" weeks or tendays.
Anyway, strictly speaking the tenday earnings of a normal person in Faerun will be 43% higher than the weekly earnings of the same character in a "normal" world, because a tenday is 43% longer than a normal week.
Thanks for your reply. To be clear, it is buildings, specifically, of which we're speaking, not characters (although the mathematics remain effectively the same, I guess). A building's daily earnings check is still divided by 10, which number is based off of dividing the check result in half and then dividing by 5 for having worked 5 days out of a 7-day week.
So, assuming a standard 2-day weekend, wouldn't it be more realistic to divide by, say, 8 rather than 5 (for a character who works a normal tenday), or by 10 rather than 5 (for a building that works every day)? That amounts to less earnings per day, but realistically, lower wages/profit actually matches the economy of FR more closely, when you take into account the price of a cow, a goat, a meal, etc.
My problem is that the math is based off of a 7-day week, which assumes characters and buildings and whatever all work an average of 5 days, for the most part. The problem, mathematically speaking, is that 7-day weeks don't exist in FR, so that number can't be correct. But, I just can't figure out what to change to make it gel, for some reason. Every time I come at it, I know there's something off, but I can't get my head around it and I don't know why. :(
Checking each day for a character, for instance, still requires dividing by the number of possible workdays in a standard work-week in order to get the per-day earnings (if you follow the logic in the basic Craft and Profession skills). I guess that's easy enough; technically you could just divide by 9 instead of 5 (I said 8 above, as an example, but FR uses the principle of the "restday," so they only have a 1-day weekend). But what would you do for a building, to make it click? Divide by 10, because it "works" every day of a tenday?
Just saying there's 2 5-day work-weeks in a tenday doesn't seem right, because then you're applying economic math from a different setting with a different calendar to one that doesn't have them. Monthly earning rates and so on could be easily figured if I can just get the proper math for tendaily/daily earnings, so that's what I need.
Ah, I see where the problem lies.
Buildings don't stop earning capital over the weekend. They earn capital each and every single downtime day: whilst a character can earn 40% more by working a 7-day week, buildings don't ever stop (eg inns function all the time, you don't get kicked out - or kick out your patrons - 2 days out of every 7). The bonus they provide already accounts for this (as do the bonuses teams provide), so there is no "factoring in" you need to do for a tenday. Just roll every day.
That's part of it, yes. Here's how the UC downtime rules seem to break down:
- The earnings rate is explicitly based on the calculations for independent character earnings via Craft or Professions skill checks.
- Weekly (7-day week with a 2-day weekend = 5-day work-week) earnings for Craft/Profession are the check result divided by 2.
- Daily earnings for Craft/Profession are the weekly result (total check result / 2) divided by 5 (they assume weekends off).
- Simply saying there are 2 5-day work-weeks in a tenday has to be wrong, because that's applying the Golarion calendar to FR, where it doesn't exist. Tendays include a 9-day work-week and a 1-day weekend.
- So, substituting the math in the similarly-labeled locations, we get a character's daily FR Craft/Profession earnings with ([total check result / 2] / 9). That means FR characters earn less than Golarion characters, but it actually realistically matches the FR economy better, when you look at the prices of things.
- Here's where the problem starts: The daily earnings for a building use the same equation as for character earnings, even though it's explicitly stated that a building "works" every day and therefore checks for earnings every day. Buildings don't take weekends; the calculation for buildings' earnings is the same no matter what, even if you choose to close for a day or are only open a half-day sometimes, etc., etc.
- It cannot then be correct that an FR building's daily earnings equal ([total check result / 2] / 5), because that is assuming characters have a 5-day work-week, which is not true in FR.
- So, are a building's daily earnings ([total check result / 2] / 9) just like a character, regardless of the number of days the building is actually opened (if we're sticking to the provided mechanic)? This also means a FR building earns proportionally less than a Golarion building, but again, that matches the economy.
Example: Building gp modifier +90, taking 10, nets total check result of 100 / 18 = 5gp 5sp (rounded to nearest silver) per day.
Dividing by 18 is the same as dividing first by 2 and then by 9 (just like UC divides by 10, because that's identical to dividing first by 2 and then by 5).
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The "Standard" weekend doesn't exist in the Forgotten Realms. The good folk of Faerun have work that needs to be done every day, and any business that wants to stay in business recognizes that principle. I would just not halve the check result to get your earnings per tenday. Actually, no reason not to leave it just as it is. Halving the result has been the rule since 3.0, so if it ain't broke...