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Growth Rate

Thu, 12 February 2004 05:26

Captain Zed

Crewman 3rd Class

Messages: 6
Registered: February 2003
Location: bedfordshire

Hi all
Does anyone know what formula is used in the growth rate of planets, how is the slow down in growth calculated as it nears 100% capacity

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Re: Growth Rate

Thu, 12 February 2004 06:22

iztok

Commander

Messages: 1209
Registered: April 2003
Location: Slovenia, Europe

Captain Zed wrote on Thu, 12 February 2004 11:26

Hi all
Does anyone know what formula is used in the growth rate of planets, how is the slow down in growth calculated as it nears 100% capacity

You can find it if you search google's rec.games.computer.stars for keywords "Formula for growth rate". You can also look at the site http://www.starsfaq.com/download.htm#utils, but the "SB Possey's Stars Spreadsheet" is rather unavailable.
BR, Iztok

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Re: Growth Rate

Thu, 12 February 2004 08:36

mazda

Lieutenant

Messages: 655
Registered: April 2003
Location: Reading, UK

The nominal growth of ( pop x growth rate x hab ) is modified by a factor :-

(1 - %capacity)^2 * 16/9

At a capacity of 25% this factor = 1
Below a capacity of 25% this factor is greater than 1 and is ignored.

So you could say the growth figure is

min((1 - %capacity)^2 * 16/9 , 1) * ( pop x growth rate x hab)

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Re: Growth Rate

Thu, 12 February 2004 08:41

Captain Zed

Crewman 3rd Class

Messages: 6
Registered: February 2003
Location: bedfordshire

Thanks to you both, that solves that little problem Very Happy

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Re: Growth Rate

Thu, 12 February 2004 18:51

Captain Maim

Lt. Junior Grade

Messages: 492
Registered: March 2003
Location: USA, Mesa, Arizona

Through the magic of trial and error I've found (as an easy rule of thumb) the optimal population growth (yeilds to absolute most people while leaving the most people on the surface) is (for AR starbases or for non HE 100% worlds) 349,900 people for non OBRM and 369,500 for OBRM races.. The best pop is really much closer to 35% than it is to 33%.. But the other brake point of 25% is pretty much right.. I just use the 35% though.. (I did one for AR Deathstars but it's a moot point as you can't set waypoint to 1,039,500 [or there abouts])

Formula's good too though.

Rule 1: "Pillage, THEN burn!"

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Re: Growth Rate

Fri, 13 February 2004 03:52

mazda

Lieutenant

Messages: 655
Registered: April 2003
Location: Reading, UK

Well simple differential of the expresion leads to cap = 1/3 or 1 at a maxima/minima.
At cap = 1, i.e. full, the growth is 0, so pretty clearly a minimum.
So at cap = 1/3 the growth is a maximum.

Any idea why you get 34.99 % for non-OBRM and 33.59% for OBRM ?
Seems a large gap just for rounding errors.
Of course, you can't see where the maximum is, as the result is quoted to the nearest 100 (or even nearest 200).

M

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Re: Growth Rate

Fri, 13 February 2004 07:23

Kotk

Commander

Messages: 1227
Registered: May 2003

The 25% is theoretically best to take planets above 30% value. 1/3 cap is theoretically better instead of 25% for taking yellows or small greens. 50% cap is theoretically best to fill up all planets beside breeders. OTOH ... life show that its small frame while the small greens stay small so using 1/3 cap gives little to none actual effect.

I have dropped using 1/3 cap. I suggest keeping breeders at 25% until all planets are taken and after that at 50% to fill up HW, the smaller planets and to have some spare pop just for case.

Less pop uselessly in air, less calculations what is that ideal 1/3 and less MM. People with bad pop MM are usually novice players. People with too perfect MM are usually weak warriors. Wink

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Re: Growth Rate

Fri, 13 February 2004 07:48

mazda

Lieutenant

Messages: 655
Registered: April 2003
Location: Reading, UK

Unless you are shipping the pop to another equally good, close planet then I'd be tempted to stick at 33%.
You'll get more pop and more resources than 25%.

What significance is there in holding at 50% ?

M

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Re: Growth Rate

Fri, 13 February 2004 08:27

overworked

Lt. Junior Grade

Messages: 403
Registered: November 2002
Location: Pittsburgh, PA

mazda wrote on Fri, 13 February 2004 07:48

50% hold is a spot where the population generated is not that much less than what you get at 33%, but you get to operate more factories and mines. Basically trading off some population generation for better resources and mineral generation. And those resources are generally doing research mid-game to get ready for a major warship build using the accumulating minerals.

It's also a fairly easy ballpark pop figure to keep a planet at.

And, if I have a few operational breeders I take my HW to 50% hold once it has a "green queue" with 33% capacity of population.

- Kurt

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Re: Growth Rate

Fri, 13 February 2004 11:01

Kotk

Commander

Messages: 1227
Registered: May 2003

mazda wrote on Fri, 13 February 2004 14:48

Unless you are shipping the pop to another equally good, close planet then I'd be tempted to stick at 33%.
You'll get more pop and more resources than 25%

The difference is more obvious if we divide the people on 1/3 filled world into two parts:
Lets say 1/3 of 100% value world is 369,000
The 275,000 from it is the 25% of max that grow at your pop growth rate
The rest of them the 94,000 grow like at 30% world.
So they are the bad guys and they are logically better to carry away while you have something to colonize. Expansion is usually more important than having 90 more resources at HW.

Quote:

What significance is there in holding at 50% ?

Its later... when you are filling worlds to 100% (lets say because of good mineral conc) you are actually stopping them from growing at all.
Say you got pop for 2 planets and have 4 planets then what is better:
1) Have 3 worlds held at 1/3 and one filled to full.
2) Have 4 worlds at 50%
Occurs that second option is better. However letting them to grow over 50% (say to 60%) is no good, best overall growth is when you keep breeders at 50%.

[Updated on: Fri, 13 February 2004 11:04]

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Re: Growth Rate

Fri, 13 February 2004 12:13

Captain Maim

Lt. Junior Grade

Messages: 492
Registered: March 2003
Location: USA, Mesa, Arizona

I got my figure not through equations but through actually zeroing in on the highest pop yield to the 100 pop.. In other words, I measured it using the game itself. Rather than follow some formula. Try it! You can get more pop at those values than you can at the traditional. I also measured till I couldn't even get 100 more. So that's how I got that.

Rule 1: "Pillage, THEN burn!"

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Re: Growth Rate

Fri, 13 February 2004 13:54

Kotk

Commander

Messages: 1227
Registered: May 2003

Yes of course... i try to explain it once more...
Keeping HW cap above 25% while you have something to colonize is simply slowing your overall growth despite HW output is bigger.

Lets get OBRM race with 19% growth and find 100% breeder.

275,000 people grow there 52,200 or 19%
369,500 people grow there 55,000 or 14.9% (its like at 79% world)

Correct?

Simple math show that the additional 94,500 grow only 2,800 or only 3% (or like at 16% world). That pop grows quicker almost anywhere else.

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Re: Growth Rate

Sat, 14 February 2004 03:01

Captain Maim

Lt. Junior Grade

Messages: 492
Registered: March 2003
Location: USA, Mesa, Arizona

Fair enough... Though you do get more RU with 33%..
16% planets? Really? Explain.. Also.. How is this detail useful?

Rule 1: "Pillage, THEN burn!"

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Re: Growth Rate

Sun, 15 February 2004 07:12

Kotk

Commander

Messages: 1227
Registered: May 2003

2,800 divided by 94,500 is 0.0296296 so its 2.96% lets say 3%.

16% world will grow below 25% cap at rate 16% * 19% = 3.04% lets say 3%.

This detail means that if you have some 17% or better worlds available for colonization then that additional pop that you have above 25% at HW floor is growing there quicker than on your HW.

Actually i did not want to go so deep in math initially. What i wanted initially to say was that 33% cap give nothing in practice.

Lets take testbed 19% HG with territory of 35 planets. 25 are habitable, 10 are reds forever.

With 5 years we reach 25% cap, then colonize 25 years with 2 privateers + maria per colony and all is taken. Year is 2430 and time to kill someone.

Now lets restore the turn 0 to other directory and try different strategy. With 7 years we reach 33% cap at HW colonize again 25 years (that one maria of additional pop we get per year does improve nothing). Year is 2432 and time to kill someone.

So what we did ... we simply lost 2 years of time on "all" our colonies and that somehow shows in 2450 result as 3-4K less econ.

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Re: Growth Rate

Sun, 15 February 2004 20:27

Captain Maim

Lt. Junior Grade

Messages: 492
Registered: March 2003
Location: USA, Mesa, Arizona

Hmm.... ok.

Rule 1: "Pillage, THEN burn!"

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Re: Growth Rate

Mon, 16 February 2004 06:26

mazda

Lieutenant

Messages: 655
Registered: April 2003
Location: Reading, UK

I see what you are saying.

A planet held at 33% isn't growing all of it at 16%.
25% of it is growing at 19%, and the next 8% is growing at somewhat less than 6%, so if you can ship it somewhere else where it will grow better then do so.

This covers the expansion phase.

After expansion, where you start filling planets you suggest to go to 50% hold (presumably you get a better resource integral whilst filling other planets than holding 33%. i.e. takes perhaps a year or two longer, but you have more resources over that period).
Is it massively different for races with and without factories ?
(ignoring IS)

For races with no factories I would feel there is less resources gained by holding at a higher level, and so you might gain more by growing at a better rate.

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Re: Growth Rate

Mon, 16 February 2004 06:46

iztok

Commander

Messages: 1209
Registered: April 2003
Location: Slovenia, Europe

Hi!

Kotk wrote on Sun, 15 February 2004 13:12

Actually i did not want to go so deep in math initially. What i wanted initially to say was that 33% cap give nothing in practice.
... snip test ...
So what we did ... we simply lost 2 years of time on "all" our colonies and that somehow shows in 2450 result as 3-4K less econ.

At first I couldn't believe, so I opened my spreadsheet and did some work. I assumed all planets 60% habitable, germ conc 50, 2 years of travel time. Despite the 33%-held HW breeded 60k pop for new colonies (57k with 25% hold), produced 5k more resources and 3000kT more minerals, the overall pop, resource output and sum of produced resources at turn 32 (when the last colonizer fleet from 33%-held landed) were much better with 25% hold. Please check the following table:

turn 32 data    33%held   25%held
-------------+---------+---------
sum pop          5.34M      6.2M
res output       12.4k     14.4k
sum res           102M      133M

Because of so surprisingly big difference I've double checked all calculations and couldn't find any errors. I've thought of making a testbed, but to get so many green planets I assumed I'd need a HE. But with the HE I've already proven the best results are obtained with breeders held at 25%. So other races can't be any different.

BR, Iztok

[Updated on: Mon, 16 February 2004 09:26]

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Re: Growth Rate

Mon, 16 February 2004 10:41

vonKreedon

Lieutenant

Messages: 610
Registered: March 2003
Location: Seattle, WA USA

I think that one needs to include a couple of non-math factors into this issue.

One is the level of MM you take on if you stay at 25% AND are maximizing the growth on other planets to get the total best growth. If I keep my HW at 33% (actually high 34%) to maximize raw numbers of pop produced and exported then I don't worry about any of the planets I am exporting to, they just take pop with no attempt to keep them at 25% or 33% to make sure that they produce more pop than my HW produces between the 25% and 34% hold rates. Also, the pop produced at 34% tends to fit very nicely in two Privateers and two colonizers. Saves me time that I can use for other things like laying MFs or having a life.

Another thing is early game tech research. My HW typically reaches the 33% hold level early and soon after builds all of the factories/mines for that level. Now I'm only researching and I have more resources to do so. A question, is the overall research better done by starting earlier with 25% or by having more resources with 34% hold?

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Re: Growth Rate

Mon, 16 February 2004 16:18

Kotk

Commander

Messages: 1227
Registered: May 2003

mazda wrote on Mon, 16 February 2004 13:26

After expansion, where you start filling planets you suggest to go to 50% hold (presumably you get a better resource integral whilst filling other planets than holding 33%. i.e. takes perhaps a year or two longer, but you have more resources over that period).
Is it massively different for races with and without factories ?
(ignoring IS)

For races with no factories I would feel there is less resources gained by holding at a higher level, and so you might gain more by growing at a better rate.

I am suggesting that the 50% is not only giving more overall econ but again giving more overall growth.
It is because growing breeder from 33% to 50% is not actually lowering the absolute value of growth on that particular breeder much. However putting that 17% of pop above 33% to other planet to fill it to 100% is immediately stopping all growth at that other planet to 0%.
Keep in mind with -f races their general nature! Any "filling places up" style pop management should take place after the leftover neighbours start to be too hard to shot down and take over, not earlier. Wink

vonKreedon wrote on Mon, 16 February 2004 17:41

One is the level of MM you take on if you stay at 25% AND are maximizing the growth on other planets to get the total best growth.

Nope... what i gave was example testbed where i breed only from HW at 33% and 25% cap and IGNORE all other planets letting them just to be. 25% is giving superior results even ignoring rest of the MM beside expanding from HW. No tricks involving lotcha MM. 25% cap is superior with MM or none. My common play style is to keep most above 80% planets as breeders and ignore the caps at the rest of the planets just dropping 2 privateers of pop on each and forgetting them until i have so lot pop that i start to fill my planets up.

Quote:

A question, is the overall research better done by starting earlier with 25% or by having more resources with 34% hold?

One goes to war not earlier with HG than at 2430...2435. At 2430 the 25% cap gives both superiour tech and resources thanks to secondary breeders that are colonized earlier and start to play their researcher role earlier ... and so on. Wink

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Re: Growth Rate

Mon, 16 February 2004 21:35

vonKreedon

Lieutenant

Messages: 610
Registered: March 2003
Location: Seattle, WA USA

Cool, good information well presented. Many thanks to Kotk and Iztok. I guess I will alter my SOP.

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Re: Growth Rate

Wed, 18 February 2004 05:17

mazda

Lieutenant

Messages: 655
Registered: April 2003
Location: Reading, UK

Yes, thanks Kotk.

I did a small test last night where I took the HW up to 25%.
Then I colonised a nearby (50% hab) planet, filled it up to 20% capacity, and then let the HW grow past 35%.
I also repeated the test but took the HW up to 33%, colonised the nearby planet and then grew the HW past 35%.

In the first case (25% hold) I ended with more pop on both planets (!) and had more total resources over the exercise.

So, all in all, no obvious reason for holding at 33%.

M

[Updated on: Wed, 18 February 2004 05:19]

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