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| Re: Overall AR economy formula |
Thu, 08 April 2010 22:07  |
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 Marduk |
 | Ensign |
Messages: 345
Registered: January 2003
Location: Dayton, OH | |
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I ran through a few numbers and I think the best balance is to weight populations proportionally to the hab value (assuming the same orbitals, at least). So if you have 500k pop to split between four systems at 100%, 75%, 50% and 25%, I would suggest putting 200k at the 100%, 150k at the 75%, 100k at the 50% and 50k at the 25%. (500k pop/250% total hab = 2k pop/% hab at a system.) Resource production is not that far off from the maximum possible and pop growth remains good.
Having different orbitals at different systems only affects this in terms of crowding affecting growth and smaller population caps possibly affecting resource production. If crowding is becoming a problem then it is time to upgrade the orbital; if crowding is a problem and the orbital is a death star, it's not really a problem. Regarding where to fill first when filling is required, I'm inclined to fill the high value systems first. Their production is better and by the time filling is an issue managing pop growth should not be as critical.
Let's see... say you have a 100% system and two 50% systems, all with ultrastations, total pop one million. For simpler example math you have chosen a 10% PGR, have an En/10 coefficient and are at energy 10. I would advocate distributing the population so:
100% - 500k pop, 707 resources, 71 mines and 50k pop/year
(2x) 50% - 250k pop, 250 resources, 50 mines and 12.5k pop/year
Total 1M pop, 1207 resources, 171 mines, 75k pop/year.
If you split the pop up at 333k per system (334k at the 100%), your resources will be 1154, you'll have 174 mines, and you will breed 66.7k pop/year.
Hmm, now I'm noticing something about squares - it looks like the optimal distribution would have one-quarter the population at a world with half the hab value... let's see:
100% - 668k pop, 817 resources, 81 mines and 52.5k pop/year
(2x) 50% - 166k pop, 203 resources, 41 mines and 16.6k pop/year - roughly one quarter of the pop at the 100% world
Total 1M pop, 1223 resources, 163 mines, breeding 85.7k pop/year.
So equal distributions of pop that do not factor in hab are great for mining and poor for resources and pop growth. My sort-of-simple plan weighting to hab values is pretty good for mining and resources, and so-so for pop growth. If you are willing to do slightly more complicated math weighting to the squares of the hab values you can trade mining for resources and population. Compared to equal distributions of pop, 6.3% less mining for 6% more resources and 28.5% more pop growth. The nice thing is that because it is weighted to hab values, growth over time will only slowly de-optimize the distribution. Run some freighters around every several years to reset the populations to near-optimal levels and you should be fine. If the micromanagement doesn't drive you crazy. 
For anyone interested in a formula for weighting by squares of habs and too lazy to figure it out themselves, add up all the squared hab values (e.g.: 1 for 100%, 0.64 for 80%, 0.25 for 50%, 0.16 for 40%) and divide your total pop by that value to figure out how much pop should go to a 100% world. For other hab values, multiply the 100% number by the square of the hab at a system and you'll get the amount of pop it should have.
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