Colonization Growth Rates

Tactics and Action Reports.
Post Reply
reuelkb
Posts: 3
Joined: Thu Apr 08, 2010 6:39 pm

Colonization Growth Rates

Post by reuelkb » Sat Feb 05, 2011 12:38 am

Hello everybody! Been lurking around here for a while, but it has come to my attention that if I don't make myself known, my account will be heading for the chopping block.
So, here I am, and since I'm here, I figure I'll make a post that I've been meaning to make for a bit, but simply never got around to.

So, I wanted to figure out how many colonizers I should send to a planet based on its hazard rating. To answer this question, I thought it important to figure out how population growth is modeled, and thus I ventured forth in an attempt to solve the mystery. I looked at the wiki and searched the forums, and none of the model I've seen worked, likely because the model has changed since then. However, Martinl's model in the thread 'Colonization Economy Changeded' appeared to be close, and so I used that as a baseline (referring to his equation near the end of the thread).

After many hours of plugging and chugging, here's my result:

GR = 1 + 1.2(1+RacialBonus+TechBonus)*(1-Haz/MaxHaz)^1.85

Civilian growth starts when the population exceeds 10,000. What seems to happen is that, at that point, 1000 Imperials are converted into civilians (except for the Zuul of course) and the civilians and imperials each grow at their own rates from then on.

Civilian growth rate appears to be: CGR = 1 + 0.3(1+RacialBonus+TechBonus)*(1-Haz/MaxHaz)^1.85

Note the 0.3 instead of the 1.2, but everything else is the same.

Another thing I've found is that at least for GM and AA, the Hivers get 50% more effect from those technologies. So, instead of giving you a 10% increase in growth rate, the Hivers get a 15% in growth rate (and 9% instead of 6% for AA). I haven't tested it, but I assume that the 50% bonus applies to the other pop growth techs. The Hazard bonuses, however, are the same.

Here are the Racial bonuses (default MaxHaz):

Human: 0 (600)
Hiver: +0.8 (650)
Liir: -0.2 (600)
Morrigi: -0.15 (550)
Tarkas: +0.1 (625)
Zuul: 0.7 (675)

I've found that these values model the actual population growth very accurately. There is some small amount of error as the populations get near the millions, but I assume that
this is because the climate hazard that we see is truncated to what is being used behind the scenes (a climate hazard of 323.3322 would show as 323.33 on the interface).
Of course, I can't confirm that, but it's the only explanation I have.

For low haz worlds, the hivers seem to be the kings of growth, but, at the GM tech level, the Zuul catch up at around CH = 350.



So, to help me figure out how many colonizers I should send, I should first figure out how additional colonizers would benefit me, and the primary way they do, is by maturing the colony quicker.

If your growth rate is 2 for example, you save an additional turn by sending a second colonizer with your primary one. You save a second turn by sending another two, a third turn by sending four more, etc. So you have to figure out how much an additional turn is worth to you.

On high hazard wolrds, another turn can be very beneficial, since the costs for maintaining the colony are so high. You also get more bang for each colonizer.

At a GR of 1.2, two colonizers will net you four turns, three colonizers will net you seven turns, and ten colonizers will net you 13 turns, etc.

For example, a Zuul with GM and with a planet of CH = 50 with have a GR = 2.873. At that level, it takes 21 colonizers just to save you three turns, which might not be worth it to you.

I hope this will be of use to anybody, and if anyone sees any errors, let me know!

Edit:

For reference, I've uploaded Growth rate tables in addition to a pair of tables that shows you how many turns are gained based on how many colonizers you sent. You can use this as a set of guidelines to help you decide how many colonizers are appropriate. Do note that the Liir are a special case in that their colonizers terraform the planet somewhat.

http://www.filedropper.com/sotsgrtables

I'll also look into whether a deployed gate for the hivers is responsible for their growth bonus, as I hadn't thought of that. Regardless, most of their planets would likely have a gate, so you can still effectively count them as having the bonus regardless.
Last edited by reuelkb on Sun Feb 06, 2011 4:47 pm, edited 1 time in total.

phaethon
Posts: 2
Joined: Wed Feb 02, 2011 10:22 pm

Re: Colonization Growth Rates

Post by phaethon » Sat Feb 05, 2011 5:43 pm

Heck of a first post!

User avatar
Coyote27
Posts: 2958
Joined: Fri Dec 29, 2006 5:13 am

Re: Colonization Growth Rates

Post by Coyote27 » Sat Feb 05, 2011 7:34 pm

Not gonna check the math, but it sounds about right to me. Good work! :thumbsup:
"In the absence of any orders, go find something and kill it." -Erwin Rommel

The Apprentice
Posts: 2967
Joined: Tue Mar 10, 2009 5:50 am

Re: Colonization Growth Rates

Post by The Apprentice » Sat Feb 05, 2011 11:44 pm

Regarding Hivers, at one point a KP person said that the presence of a deployed Gate adds a bonus to growth (simulating the easier access to the world for material and pop).

Did you, by chance, check if the Hiver growth was effected by this? Could it explain why they are getting more growth from those techs?

And, to echo another.... heck of a first post! :thumbsup:
Feel free to call me App- it's shorter.

Wyrdfire
Posts: 263
Joined: Wed Dec 07, 2005 3:40 am

Re: Colonization Growth Rates

Post by Wyrdfire » Sun Feb 06, 2011 8:51 am

This is very well thought out. Thank you. Despite a wealth of previous posts about this, it is something I have been confused about for a very long time, and I had let it boil down to some very simple rules of thumb which I really couldn't modify per situation.

Mathematical accuracy notwithstanding, this is gold:
If your growth rate is 2 for example, you save an additional turn by sending a second colonizer with your primary one. You save a second turn by sending another two, a third turn by sending four more, etc. So you have to figure out how much an additional turn is worth to you.

I have used the same reasoning for Overharvest, but I had not considered how it is applicable to colony ship production too. Me saying "I generally send about 10 colony ships" sounds kind of silly in that light. Everything comes down to this: your colony will "pop" some number of turns after they raise that imperial flag. At that point it will have full infrastructure, full climate, and it will be producing some number of credits or IO per turn. You can spend some money up front to reach that point sooner. So, how much sooner, and how much should that be worth to you (in credits) now?

[edited: cut the rest now that it's been read, in order to not distract from the original post]
Last edited by Wyrdfire on Fri Feb 11, 2011 6:35 am, edited 1 time in total.

reuelkb
Posts: 3
Joined: Thu Apr 08, 2010 6:39 pm

Re: Colonization Growth Rates

Post by reuelkb » Sun Feb 06, 2011 5:02 pm

I've edited my post with a link to some growth tables per race.

I'll also look into the Hiver gate situation.

I didn't go into Biome colonizers too much since by that point, maximizing efficiency isn't as important.

Liir colonizers also complicate things a little bit with their terraform bonus per colonizers. At low CH, this doesn't matter too much, but at high CHs, this can make a significant difference.

At a CH=425 for example, their GR=1.098 which is about equal to 1.1.

Looking at the bottom table, if the cost of one colonizer was worth an additional turn (and at that level, it is), then you can plop down 40 colonizers and gain 38 turns. But this will reduce the CH by 200, making the CH 225. At that, GR=1.4, where the population increase from the 40 colonizers only give you 10 turns. Of course, the terraform bonus will save you additional turns as well, so it's trickier to know where the sweet spot is if you measure 1 turn being worth 1 colonizer. I may look into that later.

I may do an analysis of OH later on. The Zuul though, should probably always OH since they get 40 base IO per overharvested resource rather than the 10 IO that most of the other races get.

Wyrdfire
Posts: 263
Joined: Wed Dec 07, 2005 3:40 am

Re: Colonization Growth Rates

Post by Wyrdfire » Sun Feb 06, 2011 10:19 pm

I would just like to reiterate how great this is. Thanks again.

User avatar
ivra
Posts: 1346
Joined: Fri Sep 17, 2010 1:33 pm

Re: Colonization Growth Rates

Post by ivra » Mon Feb 07, 2011 12:48 am

Yep, me too! I think you just found(ed) (ambiguousness intended) the holy grail of SotS. :thumbsup:

Using your tables I can find out how many colonizers is the optimal number (ok, close to optimal) to send in any given case. A planet costs a specific amount of money each turn to develop. I just have to compare this cost with the cost of producing a certain number of colonizers. Since the first turns of a colony development costs roughly the same, I can just take the cost and multiply it with the number of turns I want to gain. Then I can compare that to the cost of producing the number of colonizers necessary to gain that many turns. As long as the cost of the colonizers is lesser than the development cost of these gained turns, it is a good deal. When the cost of colonizers becomes higher than the development cost of the gained turns I have reached the break point and should settle for gaining one less turn.

At least this is my understanding of it.
A lot of these road signs go missing every year as the tourists collect their trophies. It makes me wonder if this road sign is indeed the most wanted souvenir of Norway...

User avatar
Coyote27
Posts: 2958
Joined: Fri Dec 29, 2006 5:13 am

Re: Colonization Growth Rates

Post by Coyote27 » Mon Feb 07, 2011 5:04 am

Well, you also have strategic concerns to take into consideration too, as getting a planet to the point of being able to produce ships quickly can be worth quite a lot if you need to defend it in a hurry. That can be motivation to send more colonisers than would be most efficient money-wise.
"In the absence of any orders, go find something and kill it." -Erwin Rommel

Redeyes
Posts: 38
Joined: Thu Jan 20, 2011 2:09 pm

Re: Colonization Growth Rates

Post by Redeyes » Tue Feb 08, 2011 12:31 am

ivra wrote:At least this is my understanding of it.
Pretty much, but remember that a credit is always worth more this turn than a guaranteed (income is never guaranteed) credit X turns later!

Wyrdfire
Posts: 263
Joined: Wed Dec 07, 2005 3:40 am

Re: Colonization Growth Rates

Post by Wyrdfire » Fri Feb 11, 2011 10:11 pm

Reuelkb, the pdf you uploaded is great. Thanks! I'd like to look at the overall development times on my own. Is it correct to say that this would let you calculate the time T until the colony is full?

[Size] x 100M = [Principle] x [GR] ^ T

[Principle] = [Colonist/Ship] x [Ships]

I understand that as time goes on you'll be trimming the hazard down, and that the hazard should be cleared before the world is actually full, but I still think it would be interesting to look at.

Could someone correct me if I am wrong? I'm really just trying to figure out, in general, how long a world takes to fill up. I suppose the planet size would not affect how many ships I send out. Your IO should be based on current pop and as far as I know it takes the same amount of production to cut 1 hazard off a size 1 world as a size 10 world. I'm just terrible at figuring out the timeframes on my own.

User avatar
ivra
Posts: 1346
Joined: Fri Sep 17, 2010 1:33 pm

Re: Colonization Growth Rates

Post by ivra » Sat Feb 12, 2011 1:04 pm

In principle you are right. The only shortcoming I see is using [GR] as a constant. When the CH shrinks, the GR will grow. But your formula should give you an upper case for the number of turns T. T will probably be lower.

I tested these tables in a recent Hiver game I played. Hivers are an ideal test candidate since their travel time is always one turn, and because they can always colonize the lowest CH planets first. When calculating the cost of building colonizers and comparing that to the reduced cost of spending fewer turns terraforming a colony, the result was a little surprising. The result showed that it was cheapest to send only one colonizer to all planets with a CH < 200. The cost of 1-4 extra colonizers needed to trim off a turn in terraforming was higher than the cost of the planet. This test was done during an actual game so I researched more and more bio techs as the game progressed. When the time came to colonize planets with 150<CH<200, I had already some basic terraforming techs (GM, AA and eventually ET).

I think the need of these tables is highest when you have to colonize a high CH planet early in the game. When colonizing a low CH planet, other concerns like how quick you need that planet to get self sustained may be more important than the overall cost.
A lot of these road signs go missing every year as the tourists collect their trophies. It makes me wonder if this road sign is indeed the most wanted souvenir of Norway...

Wyrdfire
Posts: 263
Joined: Wed Dec 07, 2005 3:40 am

Re: Colonization Growth Rates

Post by Wyrdfire » Sun Feb 13, 2011 11:52 pm

Thanks, Ivra. I understand that GR will increase as hazard goes down, but I am more interested in the upper bound than in solving the equation explicitly (just due to the level of complexity). It is too bad... when colonizing a planet, I'll just leave it at 50-50 or move the terraforming percentage up in sort of a general way the higher the hazard is. I'd like to have a better understanding of that part of the game, but it seems beyond me.

The experiment you added with Reuelkb's data has a very meaningful result. The hazard limit for "cheaper to send only one colonizer" is an important cut-off. This thread just gets better and better :thumbsup:

ZedF
Board Ninja
Board Ninja
Posts: 12582
Joined: Sun Aug 27, 2006 7:13 pm

Re: Colonization Growth Rates

Post by ZedF » Mon Feb 14, 2011 3:29 am

Probably worth a note in the strategy forum archive page, even. :)
Zed's TARs (sample):
Fractious Allies -- Hiver vs. Hiver, with allies
Who Let The Bugs Out -- Hiver vs. Tarka and Zuul
Tarka Ascendant -- Tarka vs. Hiver and Zuul

Strategy & Tactics Forum Archive -- More posts on strategy, tactics, and TARs

User avatar
BlueTemplar
Posts: 3131
Joined: Wed Aug 29, 2007 9:15 am

Re: Colonization Growth Rates

Post by BlueTemplar » Fri Feb 18, 2011 5:55 pm

Wow, this is so great! I've thought about it myself, but it seemed too much of a chore to do all the calculations and tests, and use the exact results in the game, so I settled for the 2x colonizers = 1 less turn rule of thumb.

A reminder about terraforming:
The maximum usable infrastructure % is (pop/100)^1/3. I'm not certain but I think at these levels it's usually better to put the more IO in infrastructure building as you can (up to the previous limit).

So here's a rule of thumb table showing how much of the infrastructure you're expected to be able to use next turn based on the current turn population and a doubling of that population every turn (for an average example, 2x is Tarkas with GM on a ~100 CH world) :

Pop--------Inf_Rounded
100------------1
200------------1,25
400------------1,6
800------------2
1 600----------2,5
3 200----------3
6 400----------4
12 500---------5
25 000---------6,5
50 000---------8
------------------------- (note that the values are repeating themselves)
100 000-------10
200 000-------12,5
400 000-------16
800 000-------20
1 600 000-----25
3 200 000-----30
6 400 000-----40
12 500 000----50
25 000 000----65
50 000 000----80
100 000 000--100

*approaching steps*
"Damn, quick, hide all the charts and tables, Mecron is coming!" :mrgreen:

Post Reply

Return to “T.A.R.”

Who is online

Users browsing this forum: No registered users and 1 guest