| A few thoughts (and numbers) about IS pop growth... |
Sun, 13 February 2005 07:26 |
|
 Robert |
 | Lt. Junior Grade |
Messages: 393
Registered: November 2002
Location: Dortmund, Germany | |
|
A few thoughts (and numbers) about IS pop growth...
Some basics about growth first:
The formula to calculate the growth is pop_on_surface * modified_growth_rate
The modified growth rate (for capacity >25%) is growth_rate * ((max_pop - pop_on surface)/(0.75 * max_pop))^2
Example: you got OBRM and are non HE or AR or JoaT so the max_pop is 1.100.000
If your growth rate is 19%, then for a planet with 33% cap -> 363.000 pop on surface is:
19 * ((1.100.000 - 363.000)/(0.75 * 1.100.000)^2 = 15,1% (or something close), means
you grow by 0.151 * 363.000 = 54.900 pop
IS has the advantage that pop always growth in fleets like a planet with 50% value and infinite capacity.
In the order of events IS growth in fleets happens before production and growth on planets, which means
that IS can grow the same pop twice - this is because if the freighters are full, the excess population
is dropped to the surface before growing again.
Ok, so far the basics...
Now some numbers (I love numbers):
For now lets assume you got a 100% world with 500.000 pop, and as many freighterspace as you want.
500.000 pop on surface gives 50.000 pop growth and 500 resources (just dropping it all)
363.000 pop on surface gives 54.900 pop growth and 363 resources (33% capacity = 15.1% growth)
275.000 pop on surface gives 52.200 pop growth and 275 resources (25% capacity = 19% growth)
25% always gives max. relative growth, while 33% gives max. absolute growth.
What we can see first is that we got a trade-off between growth and resources. Some people claim
(Jason Cawley was one of them) that you should not maximize the growth, you should try to maximize
the "resource integral" over time - and presented some formula that showed that keeping pop at 47%
once all planets are filled up is best - I dont want to go into such detail, I will just show some
numbers here 
So - this has been quite boring, but lets do the same for IS now:
500.000 pop on surface gives 50.000 pop growth and 500 resources (just dropping it all)
363.000 pop on surface gives 54.900 pop growth and 363 resources (33% capacity = 15.1% growth)
additionally the 136.400 pop in freighters reproduce and grow by 12.900, so the overall growth
is 67.800
275.000 pop on surface gives 52.200 pop growth and 275 resources (25% capacity = 19% growth)
additionally the 225.000 pop in freighters reproduce and grow by 21.300, so the overall growth
is 73.600
We see that for IS keeping planets at 25% gives both, max relative and max absolute growth:
73.600 pop with 500.000 pop total.
Seems great, but is it really?
Compared to the 33% hold level you got another 5.600 pop, but you got 88 less resources
in production that turn. this means the "invest" pays off after 15.7 turns. Thats twice what
a HG with 12/9/x factory settings gets (or half, because it is worse).
So, decide for yourself if you like the 25% or 33% hold levels for IS - it is up to you (and depends
on the situation I guess).
Ok, now lets have a look at the interesting part...!
What if we fill the freighters in a way that the excess pop drops on the surface and fills it to
exactly 25% or 33% ?
The numbers are:
put 350.000 on the surface, 150.000 pop in freighters, fill the freighter up with some minerals you
can spare. The pop in the freighters grows by 14.250 pop, dropping on the surface and filling it up
to 364.000 - growing again by 54.900 -> total growth 69.100 (compared to 67.800 not using the
"overpop" trick).
put 250.000 pop on surface, the other 250.000 in freighers, fill them up again. The 250.000 in freighers
grow by 23.750 and fill the surface up to 273.700, growing again by 52.200 -> total growth 75.700
(compared to 73.600 not using the "overpop" trick).
So, comparing again the growth for 500.000 pop on a 100% world for
a) normal races
b) IS races
c) IS with overpop
is
a) b) c)
50.000 50.000 50.000 (for dropping everything)
54.900 67.800 69.100 (for 33% hold levels)
52.200 73.600 75.700 (for 25% hold levels)
I will not comment on the numbers and everyone should decide on his own how relevant they are...
Picking 500.000 pop has of cource an influence on the results, max growth you can have with 3.8 mio
pop in freighters, growing by 363.000 and then again by 55.000 -> 418.000 pop... but I had to
pick some number to start with.
Maybe this helps someone to understand the pop-bonus of inner strength races a bit better,
simply have fun
Robert
[Updated on: Sun, 13 February 2005 09:39]
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