Having too much time on my hands and being rather curious on what the effects and workings are of growth rates in the long run in EU2, I have made the following analysis.
The province population growth percentage expresses the growth on the basis of a decade because otherwise you get really small percentages.
A handsoff game has lead me to the following observation, the game actually calculates the population growth on a monthly basis for a province. This monthly increase is determined by the percentage given for the province divided by 120, the number of months in a decade. A province that has a growth rate of 12% will have the following monthly growth rate: 12/120=0.1% per month. Over the course of a decade this leads to the following population increase factor: (1+0.001)^120=1.127.
In the handsoff game this was confirmed. Starting with a province of 1000 inhabitants with a growth rate of 12%, I ended up with 1127 inhabitants after exactly 10 years of gameplay. Now if growth was based on a decade basis a population of only 1200 would be expected after a decade.
Take notice of the effects of compounding, like with interest that accumulates on a bank's deposit account. When growth is determined on a monthly instead of yearly, or in this case decade's basis significant differences can emerge.
I will now express the general formula for the increase of population used in EU2:
P(end) = P(start)*(1 + (PGR/120)/100))^n
P(end) = Population at the end of the period in the province.
P(start) = Population at the start of the period in the province.
PGR = Province Growth Rate, this is given in the view province screen.
n = The number of months over which you wish to calculate growth of the province population.
Given the abovementioned observation the formula yields the following result: 1000*(1+(12/120/100))^120=1127.42
Being rounded to an integer value this fits the observation nicely
Now how is the growth rate determined? The following factors are of influence:
- Stability: giving a range from +1% growth at -3 stab till +7% growth at +3 stab, each additional stab point thus increases growth rate with 1 percentage point.
- The colony modifier: this is a +5% additional growth, this applies for any province not having reached the 5000 inhabitants yet.
- The Center of Trade Modifier: +5% for any province that has a CoT in it, for provinces neighboring a CoT this modifier is +2%.
- The Governor: + 1% for any province in which a major is promoted to a governor.
[edit, I forgot to add that a manufactory gives +2% growth as well]
- Then there is also a fixed penalty for a province which can vary from -1% till -14%. This penalty will decrease at certain population levels, 1000, 2000 and it will disappear completely at 5000 inhabitants. Nations that have their capital on the same continent/region as the province that is penalized don't receive a growth penalty. For example African nations will not suffer any growth penalties in African Colonies.
The other penalties are due to war/rebel related activities
- 3% of having a province occupied by an enemy force, this is when someone else has taken over control of your province.
- 5% when a province is looted, happens when an enemy army is in the province at the end of the month, the effect lasts for 13 months.
- 5% when a province is under siege.
- 5% if enemy troops are currently present in the province.
I have drawn up the following table which shows the growth factors over the long run at different growth rates. The lefthand collumn gives the growth percentages and the upper row the number of years.
Please note that the growthfactors in the lower right corner should be ignored, since at 5000 inhabitants the colony bonus disappears, 13% is the maximum possible percentage afterwards.
Studying this table I have noticed the following at what I estimated as the standard growth percentage of about 4%, leaving some margin for stab losses and wars which cause lower growth then the default 7% at +3 stab at which I run my nations most of the time. Over the entire EU2 period this would mean a that your population increases by a almost a factor 5. Compared with the growth of the world population during the EU2 history this very high. The world population grew at a much lower average rate of annually 0.0025% giving a growth factor of 2.17.
Now I know that the population of a province represents only that of the most important city and that populations of those cities tended to grow at a higher rate due to migration to the cities. But in EU2 this rate still too high IMHO especially when the CoT bonus is taken into account. I had a colony as portugal in India in the early 15th century with the natives having joined the population. Around 1550 I got a random CoT popping up, after 200 years in 1750 the population had reached a staggering 150.000.
Concluding, I would propose to make some cuts in the growth percentages of provinces. Firstly to cut the base growth rate by stability in half, each additional stab point should only give a o.5% increase instead of 1%. Secondly reduce the CoT presence bonus, propably cutting it back to 2% or 3% and 1% for neighboring provinces.
Overall the average growth rate in a province should be around 2.5%-3.5%, it should start out a 2.5% in the beginning of the game and increase as the game progresses. This can be achieved by increasing growth rate with 0.1% for each infrastructure tech level.
I am not too sure about the precise effects in the game, escpecially when it comes to the tax gains from a province which depend to a large extend on the population size. Perhaps the size population brackets for the taxvalues should be decreased. Also a higher number of population tax brackets would required to make more populous provinces profit from their bigger populations.
This is rather a long post and I may have made some errors especially since I wrote a great part of it last night. I may carry out some changes later on.
[edit] Drats, that table looked really nice in a texteditor, I wish I knew how to get it more tidy.
The province population growth percentage expresses the growth on the basis of a decade because otherwise you get really small percentages.
A handsoff game has lead me to the following observation, the game actually calculates the population growth on a monthly basis for a province. This monthly increase is determined by the percentage given for the province divided by 120, the number of months in a decade. A province that has a growth rate of 12% will have the following monthly growth rate: 12/120=0.1% per month. Over the course of a decade this leads to the following population increase factor: (1+0.001)^120=1.127.
In the handsoff game this was confirmed. Starting with a province of 1000 inhabitants with a growth rate of 12%, I ended up with 1127 inhabitants after exactly 10 years of gameplay. Now if growth was based on a decade basis a population of only 1200 would be expected after a decade.
Take notice of the effects of compounding, like with interest that accumulates on a bank's deposit account. When growth is determined on a monthly instead of yearly, or in this case decade's basis significant differences can emerge.
I will now express the general formula for the increase of population used in EU2:
P(end) = P(start)*(1 + (PGR/120)/100))^n
P(end) = Population at the end of the period in the province.
P(start) = Population at the start of the period in the province.
PGR = Province Growth Rate, this is given in the view province screen.
n = The number of months over which you wish to calculate growth of the province population.
Given the abovementioned observation the formula yields the following result: 1000*(1+(12/120/100))^120=1127.42
Being rounded to an integer value this fits the observation nicely
Now how is the growth rate determined? The following factors are of influence:
- Stability: giving a range from +1% growth at -3 stab till +7% growth at +3 stab, each additional stab point thus increases growth rate with 1 percentage point.
- The colony modifier: this is a +5% additional growth, this applies for any province not having reached the 5000 inhabitants yet.
- The Center of Trade Modifier: +5% for any province that has a CoT in it, for provinces neighboring a CoT this modifier is +2%.
- The Governor: + 1% for any province in which a major is promoted to a governor.
[edit, I forgot to add that a manufactory gives +2% growth as well]
- Then there is also a fixed penalty for a province which can vary from -1% till -14%. This penalty will decrease at certain population levels, 1000, 2000 and it will disappear completely at 5000 inhabitants. Nations that have their capital on the same continent/region as the province that is penalized don't receive a growth penalty. For example African nations will not suffer any growth penalties in African Colonies.
The other penalties are due to war/rebel related activities
- 3% of having a province occupied by an enemy force, this is when someone else has taken over control of your province.
- 5% when a province is looted, happens when an enemy army is in the province at the end of the month, the effect lasts for 13 months.
- 5% when a province is under siege.
- 5% if enemy troops are currently present in the province.
I have drawn up the following table which shows the growth factors over the long run at different growth rates. The lefthand collumn gives the growth percentages and the upper row the number of years.
Code:
[FONT=courier new] [COLOR=white]
%\years 10 50 100 150 200 250 300 400
-12 0,89 0,55 0,30 0,17 0,09 0,05 0,03 0,01
-11 0,90 0,58 0,33 0,19 0,11 0,06 0,04 0,01
-10 0,90 0,61 0,37 0,22 0,14 0,08 0,05 0,02
-9 0,91 0,64 0,41 0,26 0,17 0,11 0,07 0,03
-8 0,92 0,67 0,45 0,30 0,20 0,14 0,09 0,04
-7 0,93 0,70 0,50 0,35 0,25 0,17 0,12 0,06
-6 0,94 0,74 0,55 0,41 0,30 0,22 0,17 0,09
-5 0,95 0,78 0,61 0,47 0,37 0,29 0,22 0,14
-4 0,96 0,82 0,67 0,55 0,45 0,37 0,30 0,20
-3 0,97 0,86 0,74 0,64 0,55 0,47 0,41 0,30
-2 0,98 0,90 0,82 0,74 0,67 0,61 0,55 0,45
-1 0,99 0,95 0,90 0,86 0,82 0,78 0,74 0,67
0 1,00 1,00 1,00 1,00 1,00 1,00 1,00 1,00
1 1,01 1,05 1,11 1,16 1,22 1,28 1,35 1,49
2 1,02 1,11 1,22 1,35 1,49 1,65 1,82 2,23
3 1,03 1,16 1,35 1,57 1,82 2,12 2,46 3,32
4 1,04 1,22 1,49 1,82 2,23 2,72 3,32 4,95
5 1,05 1,28 1,65 2,12 2,72 3,49 4,48 7,39
6 1,06 1,35 1,82 2,46 3,32 4,48 6,05 11,02
7 1,07 1,42 2,01 2,86 4,05 5,75 8,16 16,43
8 1,08 1,49 2,22 3,32 4,95 7,38 11,01 24,51
9 1,09 1,57 2,46 3,86 6,05 9,48 14,86 36,55
10 1,11 1,65 2,72 4,48 7,38 12,17 20,06 54,51
11 1,12 1,73 3,00 5,20 9,02 15,62 27,07 81,29
12 1,13 1,82 3,32 6,04 11,01 20,06 36,53 121,22
13 1,14 1,91 3,67 7,02 13,44 25,75 49,30 180,76
14 1,15 2,01 4,05 8,16 16,42 33,05 66,52 269,55
15 1,16 2,12 4,48 9,47 20,05 42,42 89,76 401,92
16 1,17 2,22 4,95 11,01 24,48 54,45 121,12 599,28
17 1,19 2,34 5,47 12,78 29,89 69,89 163,43 893,54
18 1,20 2,46 6,04 14,85 36,50 89,71 220,51 1332,22
[/COLOR] [/FONT]Please note that the growthfactors in the lower right corner should be ignored, since at 5000 inhabitants the colony bonus disappears, 13% is the maximum possible percentage afterwards.
Studying this table I have noticed the following at what I estimated as the standard growth percentage of about 4%, leaving some margin for stab losses and wars which cause lower growth then the default 7% at +3 stab at which I run my nations most of the time. Over the entire EU2 period this would mean a that your population increases by a almost a factor 5. Compared with the growth of the world population during the EU2 history this very high. The world population grew at a much lower average rate of annually 0.0025% giving a growth factor of 2.17.
Now I know that the population of a province represents only that of the most important city and that populations of those cities tended to grow at a higher rate due to migration to the cities. But in EU2 this rate still too high IMHO especially when the CoT bonus is taken into account. I had a colony as portugal in India in the early 15th century with the natives having joined the population. Around 1550 I got a random CoT popping up, after 200 years in 1750 the population had reached a staggering 150.000.
Concluding, I would propose to make some cuts in the growth percentages of provinces. Firstly to cut the base growth rate by stability in half, each additional stab point should only give a o.5% increase instead of 1%. Secondly reduce the CoT presence bonus, propably cutting it back to 2% or 3% and 1% for neighboring provinces.
Overall the average growth rate in a province should be around 2.5%-3.5%, it should start out a 2.5% in the beginning of the game and increase as the game progresses. This can be achieved by increasing growth rate with 0.1% for each infrastructure tech level.
I am not too sure about the precise effects in the game, escpecially when it comes to the tax gains from a province which depend to a large extend on the population size. Perhaps the size population brackets for the taxvalues should be decreased. Also a higher number of population tax brackets would required to make more populous provinces profit from their bigger populations.
This is rather a long post and I may have made some errors especially since I wrote a great part of it last night. I may carry out some changes later on.
[edit] Drats, that table looked really nice in a texteditor, I wish I knew how to get it more tidy.
Last edited:
