Income and population mechanics

[Olm]

Originally Posted by shatner

Also, are you sure the base income for that province is population/100? I ask because if the base number weren't 52.6 than it'd explain the difficulty we're having.

Thats what the manual says. Don't know if CBM changes that.

[Olm]

Loaded an old SP game of mine to check how its without CBM.
Turns out I had chosen zero scales for that.
Without any scale effects income is Pop/100 rounded down.
For one scale effect it seems like ((Pop/100 rounded down)*scale modifier) rounded down.
I check now on multiple scale effects.

[shatner]

Originally Posted by Olm

I cannot reproduce the income in my provinces.
I am always somewhat higher than the game, regardless if I just add up all scale effects (Order 2 + Growth 2 = 12%+4%=16%) , add up one scale and multiply sequentially (Order 2 + Growth 2 = 1,12*1,04=1,165) or multiply even within one scale (Order 2 + Growth 2 = 1,06*1,06*1,02*1,02=1,169).
Has CBM changed more than just scale effects (basic income)?
Its even for provinces with no unrest and no admin.
Or any Idea how it is really done?

Example: Pop 5260, Basic Income 52,6 Scales: Order 3 Growth 3 Heat 1 Sloth 1, 100% tax no unrest.
Ingame Income: 57

1st case: 18%+6%-4%-5%=15%; 52,6*1,15=60,49
2nd case: 1,18*1,06*0,96*0,95=1,141; 52,6*1,141=60,01
3rd case: 1,06³*1,02³*0,96*0,95=1,153; 52,6*1,153=60,63

Nothing near 57. I am puzzled.

We are more in the region of a scale Effect of 8%: 57/52,6=1,084
I also tried rounding to full digits, doesn't do the trick either.

Another province with the same scales has 9080 pop, basic income 90,8, actual income 101.
So actual scale effect for this province is roughly 11% (101/90,8=1,112).
Am I missing something?

You're remark about rounding to full digits got me thinking and, after a little trial-and-error, I think I've found a pattern that matches both examples: A) base income of 52.6 and B) base income of 90.8

1) Reduce base income to a whole number
a) 52.6 => 52
b) 90.8 => 90

2) Multiply the first positive scale (order's +18%) and reduce to whole number
a) floor(52 * 1.18) = floor(61.36) = 61
b) floor(90 * 1.18) = floor(106.2) = 106

3) Multiply the next positive scale (growth's +6%) and reduce to whole number
a) floor(61 * 1.06) = floor(64.66) = 64
b) floor(106 * 1.06) = floor(112.36) = 112

4) Multiply by the first negative scale (heat's -5%) and reduce to whole number
a) floor(64 * 0.95) = floor(60.8) = 60
b) floor(112 * 0.95) = floor(106.4) = 106

5) Multiply by the second negative scale (sloth's -4%) and reduce to whole number. Since there are no other income modifiers, this is the final income for the province for this turn.
a) floor(60 * 0.96) = floor(57.6) = 57
b) floor(106 * 0.96) = floor(101.76) = 101

That "reduce to whole number" and sequential multiplication really reduces the efficacy of positive scales and heightens the effects of negative scales!

[Corinthian]

Also, are you sure the base income for that province is population/100? I ask because if the base number weren't 52.6 than it'd explain the difficulty we're having.

Do you have a fort or unrest in the province? If so it would increase or decrease the gold income from the province.

As for overtaxing, keep in mind that you can invest the money you get from overtaxing in order to reap further dividends down the line. Using the money to build a fortified city in a province with 20k pop and neutral scales will net you 50g/turn for every turn after its completion. This in addition to whatever other utility you can get from the fort. And if thats not your fancy, how about investing the money in troops for taking lands from your enemies? Who cares that your capitol is worn down, you can just use the money to take some other poor schmucks capitol.

[Olm]

Who had the idea of doing it that way? It's ugly!
It even depends on the sequence you apply your boni. So one now has to check what the correct sequence is by examining lots of provinces and searching for the combination that works everywhere.
Perhaps I will do that another day.......

[JonBrave]

Originally Posted by Squirrelloid

Money now is worth more than money later.

Are you currently (or were you previously) involved in running one of the world's major economies?

[shatner]

I ran a few more numbers to determine the effects of administration from forts as well as over/under-taxing

As stated in the manual, forts offer an (admin/2)% boost to income. This boost appears to happen before any scales are factored in. Over/Under-taxing happens at the end as is a straight multiplier of the final income amount (rounded down). The scales are applied in the following order: order, production, temperature, growth. Therefore the income formula goes like this

1) floor(Population/100) = base income
2) floor(base income * (admin/2))% = F income
3) floor(F income * (order)%) = FO income
4) floor(FO income * (production)%) = FOP income
5) floor(FOP income * (temp)%) = FOPT income
6) floor(FOPT income * (growth)%) = FOPTG income
7) floor(FOPTG income * (tax rate)%) = final income

Examples:
Pop(29770), Admin(30), O/P/T/G(0,0,0,0), Tax(100%) = 341
Pop(29770), Admin(30), O/P/T/G(0,0,0,0), Tax(150%) = 511
Pop(30450), Admin(60), O/P/T/G(18,12,-15,-2), Tax(100%) = 433
Pop(30280), Admin(50), O/P/T/G(-18,12,-15,6), Tax(100%) = 311
Pop(30480), Admin(60), O/P/T/G(18,-12,-15,6), Tax(100%) = 368

[Squirrelloid]

income modifiers are definitely multiplicative.

-12% is actually multiply by .88, etc...

Multiplication is communicative and distributive, so there's no need to multiply by some first and then others as Elmokki does.

(x*.95*.95)*1.05*1.05 = x*.95*.95*1.05*1.05

So long as given modifiers multiply without flooring occuring inbetween, you can do all the multiplication operations at once.

[Squirrelloid]

Originally Posted by JonBrave

Are you currently (or were you previously) involved in running one of the world's major economies?

=P

Its a basic fact of economics. Or to phrase it another way: Would you rather have $10 now or $10 next week?

[Nightfall]

Originally Posted by Olm

I am playing MA Man in CBM and follow the advice to maximize money.
I have Order 3 Growth 3 Sloth 1 Heat 1 Misfortune 1.
I try to have a Forrester patrol each province with a halfway decent income, and overtax them to 110%
Seems to work great. But how could I really maximize the gains? Where is the break even between killed population and more income?
Any experience?

So as to your original question, based on shatner's work.

So for the capital of man, you actually get around:

300 * 1.25 -> 375 * 1.18 -> 442 * 1.06 -> 468 * .95 -> 444 * .96 -> 426 base * 1.2 -> 511 from 20% overtax

For an extra 85 gp a turn, although in order to minimise failed patrols I'd probably use 2 Foresters.

That costs you two capital hires, 40 gp and 3 gp per turn in upkeep (As I understand it upkeep rounds up.

Assuming you don't overtax, on just turn twenty your capital will be worth:

300 * (1.009^19) -> 355 * 1.25 -> 443 * 1.18 -> 522 * 1.06 -> 553 * .95 -> 525 * .96 -> 504

So each turn that extra 82gp gets eaten away, slowly at first until it's essential no bonus at turn 20.

Even in your capital, which is by far the most favourable province to do this in, you make probably an extra 1000gp before you start losing money.

I'm not sure it's worth being 2 mages and about 300 research points down.