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Home » Stars! 2.6/7 » The Academy » pop management, 50% "cutoff" (Includes a pretty graph!)
pop management, 50% "cutoff" Sun, 18 May 2014 06:36 Go to next message
mrvan is currently offline mrvan

 
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Perceived wisdom seems to be that there are three 'cutoff' values for pop:

25% - max growth rate
33% - max absolute growth
50% - balance between growth and economy

The 25 and 33% are logical, but whence the 50%? Since I'm a visual person, I graphed growth rate, absolute, and marginal effect of adding 3% more pop:


[img]http://i.imgur.com/rNV3ASj.png[/img] (edit: what's up with images here?)

The blue line is the pop growth, assuming a 20% growth race on its homeworld. The blue line shows overcrowding starting at 25% of capacity. (secondary axis)
The red bars are total pop increase, which plateaus at the 33% mark as expected.
The yellow bars are marginal pop increase, i.e. how much extra pop growth will removing 30k colonists cause (multiplied by 10 for visibility). It grows steeply from 33% until around 50% and then maxes out.

What I never quite realized is how flat the abs growth plateau is. From 25% to 33% capacity is a change from 50k to 52671, moving further to 42% capacity reduces this to 50236. So, all values from 25% to 42% are within 2500 colonists (5%) of max growth.

After that it drops more quickly: Increasing up to 51% has a much stronger effect because the marginal starts to pick up: 43538 or around 7000 colonists (83% of max growth). Going even further to 66% you only have half of total pop growth left.

For me, this means that
(1) I don't need to be as precise with pop management as I have been trying to, and building an extra freighter to get 35% down to 33% is probably not worth it;
(2) factory allocation is more important than pop management within that range, i.e. as long as there is a good green neighbour, it is probably best to keep at 25% until HW factories catch up, and then let population grow with factories until around 40%; and
(3) the 50% 'cutoff' doesn't make a lot of sense to me, as the curve is pretty smooth from 40% to 67% (ie each 10k pop gains you 1% production and costs you 1 or 2% pop growth). It makes more sense to me to keep it at 40% longer until the nearby breeders are at capacity (also allowing for some germ export), and then backfilling as soon as it reaches around 67%.

What do other people think?




[Updated on: Sun, 18 May 2014 06:37]

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Re: pop management, 50% "cutoff" Sun, 18 May 2014 06:57 Go to previous messageGo to next message
nmid

 
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50% is just an easy number to remember, but real top line is 42% as you found out. I use 25% for fastest growth, 33%-40% for increasing resources while growing..and then 45% because it doesn't lead to a major dip in growth imo and I am comfortable with that number.
However as you noted, having a floating pop between 33%-42% is best and keeping to ur factories at 33% cap, so your factories don't idle in the migrant population zone.
From my phone



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Re: pop management, 50% "cutoff" Sun, 18 May 2014 17:18 Go to previous messageGo to next message
skoormit is currently offline skoormit

 
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50% is a common compromise hold level for me because I don't have to think much to calculate it. To hold at 42% I have to get out the calculator or keep notes on my hold levels or something, and I have enough MM as it is. 45.45% is another common hold level for me, because it's half the planet value * 10k (assuming OBRM). Saving time and mental cycles makes me a sharper player. More than worth the marginal loss in pop growth.




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Re: pop management, 50% "cutoff" Sun, 18 May 2014 17:26 Go to previous messageGo to next message
iloverushandledzepp is currently offline iloverushandledzepp

 
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what % capacity does over pop happen at?


Drill on the sun?! I'd rather freeze on Pluto than fry on the sun! What? How much minerals did you say? Well, Since you put it that way...

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Re: pop management, 50% "cutoff" Sun, 18 May 2014 17:29 Go to previous messageGo to next message
skoormit is currently offline skoormit

 
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iloverushandledzepp wrote on Sun, 18 May 2014 16:26
what % capacity does over pop happen at?


"overpop" normally means "over 100% capacity." At that point, colonists start dying off.



What we need's a few good taters.

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Re: pop management, 50% "cutoff" Sun, 18 May 2014 19:12 Go to previous messageGo to next message
nmid

 
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iloverushandledzepp wrote on Mon, 19 May 2014 02:56
what % capacity does over pop happen at?


Overpop between 100%-300% produce only half the colonist resources.
Post 300% pop, you get 0 colonist resources.



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Re: pop management, 50% "cutoff" Mon, 19 May 2014 13:16 Go to previous messageGo to next message
Altruist is currently offline Altruist

 
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mrvan wrote on Sun, 18 May 2014 12:36
For me, this means that
(1) I don't need to be as precise with pop management as I have been trying to, and building an extra freighter to get 35% down to 33% is probably not worth it;


Well... if I may link to a post of my own: Colonisation

There is also a subchapter called "Why not letting your HW grow straight to 42% before colonisation?"

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Re: pop management, 50% "cutoff" Mon, 19 May 2014 15:40 Go to previous messageGo to next message
mrvan is currently offline mrvan

 
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Altruist wrote on Mon, 19 May 2014 13:16
mrvan wrote on Sun, 18 May 2014 12:36
For me, this means that
(1) I don't need to be as precise with pop management as I have been trying to, and building an extra freighter to get 35% down to 33% is probably not worth it;


Well... if I may link to a post of my own: Colonisation

There is also a subchapter called "Why not letting your HW grow straight to 42% before colonisation?"


I agree - given that there is another decent world nearby. For me the realization was that if max production (in absolute numbers) from one breeder was the goal, there is not much difference between 25 - 33 - 42 percent. Of course, 25% reaches the same absolute number with much less pop, so of course the percentage is much better.

(the specific context for my graphing exercise was the current challenge where you have a 50 year delay on the AI, so you can't really get any planets initially, hence pop is either on the planet being productive or on a freighter making room for growth).

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Re: pop management, 50% "cutoff" Tue, 20 May 2014 07:53 Go to previous messageGo to next message
m.a@stars is currently offline m.a@stars

 
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mrvan wrote on Mon, 19 May 2014 21:40
the current challenge where you have a 50 year delay on the AI, so you can't really get any planets initially,

Are you sure about that? pop*cough*drop Twisted Evil



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Re: pop management, 50% "cutoff" Tue, 20 May 2014 16:44 Go to previous messageGo to next message
mrvan is currently offline mrvan

 
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I considered that, but it seemed a waste of a very valuable resource for something that I can't really hold on to until I get good techs. But then again the other people are reporting much faster numbers than mine so I must be doing something wrong Smile

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Re: pop management, 50% "cutoff" Wed, 21 May 2014 04:22 Go to previous messageGo to next message
m.a@stars is currently offline m.a@stars

 
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mrvan wrote on Tue, 20 May 2014 22:44
I considered that, but it seemed a waste of a very valuable resource for something that I can't really hold on to until I get good techs.

Not against good players you wouldn't, but these are AIs. Hit over head

It won't be easy, but... Pirate



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Re: pop management, 50% "cutoff" Wed, 21 May 2014 23:39 Go to previous messageGo to next message
magic9mushroom is currently offline magic9mushroom

 
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nmid wrote on Sun, 18 May 2014 20:57
50% is just an easy number to remember, but real top line is 42% as you found out. I use 25% for fastest growth, 33%-40% for increasing resources while growing..and then 45% because it doesn't lead to a major dip in growth imo and I am comfortable with that number.
However as you noted, having a floating pop between 33%-42% is best and keeping to ur factories at 33% cap, so your factories don't idle in the migrant population zone.
From my phone


42% just happens to have the same growth as 25%. There's nothing especially worthy about that hold level; it's definitively NOT the maximum resource integral. I would ask you, and anyone else, to PLEASE stop spreading misinformation like this.

The proper hold levels are:

Alternative is green over 1/3 hab of breeder: 25%.
Alternative is green under 1/3 hab of breeder: somewhere between 25% and 1/3.
Alternative is yellow: 1/3 of cap (slightly over 33%).
Alternative is sitting in space: a touch under 50%.

The reasons for these are as follows:

- If the pop would be working (ie, on a planet, green or yellow) then all that matters is maximising growth. The marginal pop-growth of a green drops to 1/3 of max immediately upon reaching 1/4 of cap, then slowly drops to 0 as the pop level rises to 1/3 of cap. Yellow die-off is minute and thus does not appreciably affect the hold level; technically, however, it's a sliver over 1/3 dependent on the yellow's kill rate.

- If the pop would not be working (ie, held in freighters in space) then you need to maximise the resource integral - the total resources you get out of the planet in the long run. The exact optimal hold here varies - the tangent to the graph is at exactly 1/2 of cap, but that ignores the resources lost while growing *to* a higher hold level, so in reality it's slightly less. The exact value is situational, because of the discrete nature of Stars! turns; technically I believe it ends up as "the largest hold, less than 50%, that grows to 100% in an exact number of turns". But you're looking at ~100 resources lost by just setting it to 50%, so in practice that's probably the best reward for effort.


Note that all of this flies out the window when considering IS because IS pop grows in space and this forces you to consider resource integral whenever over 25% or on planets under 50% hab. IS optimal hold levels actually vary with planet quality because of this.


EDIT: Ooo, we have a graph! (Don't worry about the image not embedding, you can't embed images on these forums.) I assume the "marginal" is in fact x(-10) and not x10?

The graph makes it easier to explain the 50% hold. See, maximising the resource integral is the same as minimising the total resources you didn't get compared to instantly being at 100% - this is equal to (time you aren't at 100%) * (resource loss per turn you aren't at 100%). The time taken for a hold to fill is inversely proportional to growth, and the resource loss per turn is proportional to (100% - hold%), so we want to minimise (100%-hold%)/(growth at hold%), which is the same as maximising (growth at hold %)/(100%-hold%). This means we want a line, drawn from the right edge of your graph at (100% hold, 0 growth) and passing through some point on the growth curve (and thus intersecting it at (hold%), (growth at hold%)), to be as steep as possible - you can see from your graph that the point giving the steepest such line is around 50%, and indeed if you compute it mathematically it's exactly 1/2.


[Updated on: Thu, 22 May 2014 05:12]

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Re: pop management, 50% "cutoff" Thu, 22 May 2014 05:08 Go to previous messageGo to next message
nmid

 
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magic9mushroom wrote on Thu, 22 May 2014 09:09

42% just happens to have the same growth as 25%. There's nothing especially worthy about that hold level; it's definitively NOT the maximum resource integral. I would ask you, and anyone else, to PLEASE stop spreading misinformation like this.

lol, magic has pulled me up on this a number of times earlier Mad.

I agree with him that it's not a max integral.
My point was that it lets me have more pop on the ground, while I can continue with my same cargo/shipping plans that I had for 25%. Just makes life a little easier.

When I'm going for max growth, I keep my pop between 25% to 32% even if I have factories built for 42/45/48% caps.



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Re: pop management, 50% "cutoff" Thu, 22 May 2014 05:16 Go to previous messageGo to next message
magic9mushroom is currently offline magic9mushroom

 
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nmid wrote on Thu, 22 May 2014 19:08
lol, magic has pulled me up on this a number of times earlier Mad.

I agree with him that it's not a max integral.
My point was that it lets me have more pop on the ground, while I can continue with my same cargo/shipping plans that I had for 25%. Just makes life a little easier.

When I'm going for max growth, I keep my pop between 25% to 32% even if I have factories built for 42/45/48% caps.


I was taking issue with this:

nmid wrote on Sun, 18 May 2014 20:57
real top line is 42% as you found out

However as you noted, having a floating pop between 33%-42% is best and keeping to ur factories at 33% cap, so your factories don't idle in the migrant population zone.
From my phone


...which implied there was something special about 42%. There's not, besides the aforementioned coincidence. You certainly CAN hold there, and I've no issue with people preferring it for convenience, but it's not the "real top line". That's the 25%/33.33%/~50% holds. The OP's question was, after all, asking what was theoretically optimal about the 50% hold, not what hold is most convenient.


[Updated on: Thu, 22 May 2014 05:17]

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Re: pop management, 50% "cutoff" Thu, 22 May 2014 06:23 Go to previous messageGo to next message
nmid

 
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Ah, thanks for pointing that out.
You're quite right.



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Re: pop management, 50% "cutoff" Thu, 22 May 2014 08:50 Go to previous messageGo to next message
magic9mushroom is currently offline magic9mushroom

 
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Oh yes, forgot another little tidbit about IS. The optimal hold for most races is a static hold (hold at X% until enough pop to fill world), but for IS it's actually a moving hold (you change the amount of pop on the ground every turn). This is because dropping pop down to the planet affects growth less, on a percentage basis, the bigger the rest of the orgy is.

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Re: pop management, 50% "cutoff" Thu, 22 May 2014 11:14 Go to previous messageGo to next message
mrvan is currently offline mrvan

 
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@magic
Thanks for the detailed explanation of the resource integral. IIUC, what you are optimizing is total amount of resources from one planet over time, assuming that you hold at X% to fill freighters until you have enough pop to fill to 100%. Is that correct?

My scenario was that you don't have good breeders anymore, so pop goes off to marginal worlds that only contribute to long term growth, while you also need some resources to research/build the stuff you need to reach said long term. In your advise, you say hold at 33%, which is of course the way to fill those marginal worlds asap.

My reasoning for a hold around 42% (I agree there is no magic at 42% like there is at 25/33) would be that you want the planet to produce a good number of colonists while also having good resources/mines. I was surprised at how little absolute growth you lose around 33%. 33% is still optimal, of course, but in absolute terms you only lose 5% of max absolute pop growth, while gaining around 25% production. Of course, the optimal value for jointly maximizing production and pop growth depends on the relative weight of either. Moving further to 50% you gain another 19% over the resources at 33%, but at a cost of 15% of colonist production. This is presumably optimal as you point out for the capacity of this planet, but in most cases I would want to keep one breeder around to top up the nearby good worlds anyway, so considering the resource integral in the context of only a single planet is not so useful.

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Re: pop management, 50% "cutoff" Thu, 22 May 2014 17:22 Go to previous messageGo to next message
magic9mushroom is currently offline magic9mushroom

 
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mrvan wrote on Fri, 23 May 2014 01:14
@magic
Thanks for the detailed explanation of the resource integral. IIUC, what you are optimizing is total amount of resources from one planet over time, assuming that you hold at X% to fill freighters until you have enough pop to fill to 100%. Is that correct?


Right.

Quote:
My scenario was that you don't have good breeders anymore, so pop goes off to marginal worlds that only contribute to long term growth, while you also need some resources to research/build the stuff you need to reach said long term. In your advise, you say hold at 33%, which is of course the way to fill those marginal worlds asap.


Right, because they're still working. It's only when the alternative is "not working at all" that the optimum jumps to 1/2.

Quote:
My reasoning for a hold around 42% (I agree there is no magic at 42% like there is at 25/33) would be that you want the planet to produce a good number of colonists while also having good resources/mines.


'Course, that 9% would still be producing the same amount of resources/mines if you shipped them off to a marginal green.

Quote:
33% is still optimal, of course, but in absolute terms you only lose 5% of max absolute pop growth, while gaining around 25% production.


Except that you don't actually "gain" that production since the pop would be producing resources wherever it is.

Quote:
Of course, the optimal value for jointly maximizing production and pop growth depends on the relative weight of either. Moving further to 50% you gain another 19% over the resources at 33%, but at a cost of 15% of colonist production. This is presumably optimal as you point out for the capacity of this planet, but in most cases I would want to keep one breeder around to top up the nearby good worlds anyway, so considering the resource integral in the context of only a single planet is not so useful.


Right. 50% is only optimal once you've filled your yellows and little greens, as it's used for topping off the breeders themselves.

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Re: pop management, 50% "cutoff" Fri, 23 May 2014 13:59 Go to previous messageGo to next message
mrvan is currently offline mrvan

 
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I agree with your points and I guess getting better at stars! is to some extend to make those kind of optimization decisions intuitively. Thanks for the detailed explanations.

My thinking was that it is more efficient to have people working in a place with sufficient factories, but I guess it is always long term optimal to have them make new factories somewhere else.

BTW is there a good thread on pop considerations for AR, as I guess it is quite different there because production is multiplied by the hab value ?

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Re: pop management, 50% "cutoff" Sat, 24 May 2014 03:51 Go to previous messageGo to next message
XAPBob is currently offline XAPBob

 
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1% or less is the target for AR.

Seriously, you want to spread as thin and evenly as possible to abuse that sqrt!

Same colonist count on every planet, upgrade bases to stay <25% if possible.

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Re: pop management, 50% "cutoff" Sat, 24 May 2014 06:02 Go to previous messageGo to next message
magic9mushroom is currently offline magic9mushroom

 
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mrvan wrote on Sat, 24 May 2014 03:59
I agree with your points and I guess getting better at stars! is to some extend to make those kind of optimization decisions intuitively. Thanks for the detailed explanations.

My thinking was that it is more efficient to have people working in a place with sufficient factories, but I guess it is always long term optimal to have them make new factories somewhere else.

BTW is there a good thread on pop considerations for AR, as I guess it is quite different there because production is multiplied by the hab value ?


More importantly, production is not proportional to pop but to sqrt(pop). This means AR should always flagpost all greens and yellows, as their most productive colonists are the first few and as such they receive direct returns from colonising everything in sight. XAPBob isn't quite right, though, you do want to keep a lot of pop on breeders early on (as it maximises both pop growth and resource efficiency).

I could run an optimisation calc on filling a single world for AR (I don't believe one's actually been done). More than a single world, though... I think it's actually close to irrelevant, strange as that may sound. Once everything reaches 33%, putting extra pop on breeders loses growth (but AR isn't as dependent on breeders to grow pop thanks to their hab-invariant population caps), but putting it on bad worlds loses resource production. And shuffling pop around has its own cost in the thrice-damned pop deaths from warp travel. In any case, there's not as much at stake since a world at 33% has 58% of the full world's resources instead of 33%.


[Updated on: Sat, 24 May 2014 06:07]

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Re: pop management, 50% "cutoff" Sat, 24 May 2014 06:11 Go to previous messageGo to next message
XAPBob is currently offline XAPBob

 
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You of course need some planets to be anle to build ships, and growth vs reaources need thought for a non 3i AR. Colonist deaths complicate matters as well.

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Re: pop management, 50% "cutoff" Sat, 24 May 2014 06:18 Go to previous messageGo to next message
magic9mushroom is currently offline magic9mushroom

 
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XAPBob wrote on Sat, 24 May 2014 20:11
You of course need some planets to be anle to build ships,


Not just that. Because habitability is in the AR resource formula (and outside the square root, at that!), before crowding sets in it is most efficient to keep more colonists on the higher value worlds - in every possible sense: growth, resources, and indeed shipbuilding. The optimal proportion isn't to keep 100% of the pop on high-value worlds like it is for non-ARs, but they should still keep most of their pop on breeders until all the breeders hit 25%.

EDIT: Oh, and there's a confounding variable for AR optimising filling worlds (probably why nobody's done it) - resources now are more important for an AR than resources later because of Energy tech factoring into their resource equation. If you get an Energy tech level just a couple of years earlier, the increased resources from other worlds will massively outweigh the resources lost from the hold's "inefficiency".


[Updated on: Sat, 24 May 2014 06:23]

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Re: pop management, 50% "cutoff" Sat, 24 May 2014 06:55 Go to previous messageGo to next message
XAPBob is currently offline XAPBob

 
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I've spent too long looking at 3i AR Rolling Eyes Embarassed

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Re: pop management, 50% "cutoff" Sat, 24 May 2014 07:28 Go to previous messageGo to previous message
magic9mushroom is currently offline magic9mushroom

 
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I know the feeling. When I started preparing for Lowtek I had to teach myself how to deal with hab that wasn't ALL PLANETS ARE PERFECT.

(Not 3i AR, though.)

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