Income and population mechanics

[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?

[shatner]

I agree, it's puzzling. The only formula I've gotten to work so far was
1) Round income down to nearest 10: 52.6 becomes 50
2) Sequentially multiply by negative modifiers first: ((50 * .95) * .96) = 45.6
3) Sequentially multiply by positive modifiers: ((45.6 * 1.06) * 1.18) = 57.03648
4) Round result down: 57

And that's just me throwing those numbers into the formula-blender and taking whatever output looks right. I'll need more data points to test this or any other formula before I can be confident we've reverse-engineered the solution.

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.

[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.

[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.

[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!