The economics of expansion?

On a small map where battles are quick and visous probably not much return, if at all on the last one or two planets. On medium to large probably a lot of return especially with ports and refineries. On huge maps initially yes but towards the end each planet conquered would be minimal again because you would have such a huge eco going by then each added planet would add very little.

Of course this is just off the top of my head, dont have the numbers to back it up. 

good question! i don't think ive ever done a formal analysis on this specific situation. here's my first attempt, kinda crude but it shows some interesting stuff. 

quicky calculation based on quick-buy button resource conversion rates and the rate of return of an expansion asteroid with 3 resource rocks that is directly adjacent to your homeworld.

premises:

1) the tax income at full population from the asteroid is approximately 0.6 creds/sec. it takes several minutes to get to this level though. it will ramp up from 0.1 at initial settlement to 0.6 at full pop. assume that it takes 5 minutes to reach 20 population (its full level). 

2) the resource income of each rock is .47 resources/sec. the total income from this is 1.41 resources/sec. it takes 30 seconds and 250 credits to build each extractor.

3) the underdevelopment penalty will subtract 2.4 creds/sec for 45 seconds while the upgrade builds. this total cost is 108 credits.

4) the cost of building the infrastructure upgrade is 450 credits, 100 metal, 75 crystal. 

5) i will use the BUY rate conversion for resources on the black market since presumably we are not dealing with surplus situations in the early game and you will directly spend your resources. the BUY rate is used because it signifies resources you did not have to buy to make up for a shortfall. the analysis would be rather different if the SELL rate were applied, just something to be aware of. 

cost analysis:

your outlay in cost is 450+750+108= 1308 credits

in addition you pay 100 metal and 75 crystal. assume conversions rates of 1 resource = 5 credits (median black market price on quick buy button), this amounts to 875 credit equivalent. 

the total cost, all things considered, is 2183 credits. 

benefit analysis:

the population based income really needs to be handled with integral calculus. i don't wanna do anything that complicated and lack the proper function of growth(time) anyway. i'm going to make alot of simplifying assumptions about this. bear with me.

assume linear growth at a constant rate for 6 minutes. .1 cred/sec for minute 1, .2 cred/sec for minute 2, etc. this is close enough to the truth that i'm satisfied by it but really its a damn crude approximation. oh well.

population based income then will produce 126 credits in the first 6 minutes and an additional 36 credits per minute each minute thereafter.

extractors follow a similar model except it hits its plateau after only 90 seconds, not 6 minutes. you will produce 84.6 resources in the first 90 seconds followed by a steady stream of 84.6 resources per minute each minute thereafter. using the 5:1 conversion rate this is a credit equivalent of 423 credits in the first 90 seconds and then 493 credits per minute.

conclusions:

clearly the resources are what you really want from the roid, the population income sucks. ignoring the population income since it is so low and takes so long to develop compared to the resource income, the amount of time it takes to make up your initial outlay of 2183 credits is... 3.57 minutes (about 3 minutes 34 seconds). 

not too bad actually, those resources are worth alot if you consider what you'd have to pay to buy them from the black market. the roid is clearly a good initial investment. that pays dividends pretty quickly, only have to wait 3 and half minutes to see positive net revenue on it. 

bigger planets take longer to develop obviously, but have potentially greater rewards due to non negligible income from population. feel free to apply my analysis technique (crude as it is) to a more complicated situation, like developing a terran world for population income. you'll probably get a similar result but over a longer time frame. higher initial outlay and longer time to recoup investment but result will be a larger net gain once it goes positive. what i'd be most curious to find out is which is most efficient credit for credit in terms of building revenue. 

Pretty hard to do "cost analysis" of not expanding in a vacuum....it is a multi-variable problem.  The value of everything you do is determined by the map and what your opponent is doing.  The nearest thing would be an analysis of time required to recoup investment on an economic structure, planetary upgrade, or cost of colonization.  If you suspect the enemy is capable of burning down the investment before the time when it starts generating you profit, you probably shouldn't build or colonize it.

Experienced players have an organic sense of this, but I've never seen a chart with this kind of data.  It would certainly be interesting if someone with way too much time on their hands feels like punching the numbers into a spreadsheet and sharing.

Just about every game I've played I see people making decisions about how much colonizing they think they can do before they either attack, dig in and defend, or help an ally.  Later in the game people automatically colonize worlds they siege not for the economic advantage of owning them but for the tactical advantage of denying their opponents a world while gaining a new front line base for repair structures and factories.

Transitive beat me to it while I was typing and was kind enough to detail the methodology for the masses....

Good analysis of a 3 extractor roid.  I have done similiar analysis in the past for things like tradeposts and refineries (with certain assumptions made for avg trade length or extractor coverage) and have seen analysis done for things like population upgrades and civic upgrades that affect credit, trade, or resource income.  Now we just need someone who is really curious to make a big spreadsheet and analyze all the planets, upgrades, structures, and civic techs!

This is primarily a time value of money analysis problem, the kind you might expect in an introductory economics course.  A lot of people have tried to answer this very question for several games just on the basis of rate of return or payback period.  It doesn't work out well because there are so many factors to consider.  While payback period is a decent measurement (it's what transative is talking about), it's not the whole picture. 

The concept is simple:  500 credits now is worth more than 500 credits several minutes down the road.  If I'm going to invest in something, I want to get more than I paid for it.  Therefore, it's not enough to simply look at payback period, but effective payback period.  That is to say: when do I get the value of my investment to pay itself off?  Just earning the equivalent amount I payed is not full payback, an investment needs to pay the principle plus interest.  The answer the question fully, we need to know just how much interest is actually needed (and you'll probably want to fit opportunity costs in there, too).

I had the same sort of idea Ryat speaks of, i.e. on an exceedingly small map where you start out right next to each other ("point blank" type maps), a strat of not expanding at all, rather just pumping frigs and attacking, might be viable (or, perhaps just expanding to an asteroid).  On really big maps it always pays to expand, at least initially.  Then there is the "in between" situation.

Thanks to transitive for the quick and dirty roid analysis.  Sounds intuitively right, anyway.

Yes I agree with Cykur on colonizing to get "forward basing."  Much more of a strategic decision than an economic one, and something I do every game.

Hmmm....and here I thought Transitive's analysis was helpful for the masses to make better informed decisions!   You have opened my eyes! 

Hey!?  HELP!!  I needs the Opportunity Cost...err....the Investment Value of ..... an Assailant!  Can someone analyze for me whether it is better to make ships or should I invest that money in economic structures and upgrades???  I needs the WHOLE PICTURE!  K Thanks!

Without having done the analysis, I would like to comment on a few things I have seen.

People like How and Tyr sometimes will get the HW pop upgrade (assuming vanilla or non-quickstart Entrenchment) if they know they have time on their side (I've watched replays to see what they did in games I have been in with them, regardless of the side I am on). They know it will help them get the credits they need longer term. This is especially important for Vassari who cannot get trade until level 4 which requires at least a HW and 2 roids, assuming you want a port on each planet plus assailants.

If they don't go the planet upgrade, they generally will pump out ships as someone with a bigger (and better teched) fleet will kill the person with a better econ, but a smaller fleet due to getting that econ. This works as they don't have to replace ships as quickly as the better econ player due to greater DPS per second. So then it comes down to who can produce ships vs kill them quicker - the econ guy has to overpower the military one. This gets harder when teamwork comes into it via feeding.

I have also seen players sit back and let the credits/resouces roll in and just do a bit of colonsing, but build little in the way of research centres etc... Then have like 5000+ credits and 1000+ metal etc... but haven't done much with it. They then chose to get a fleet or layout econ depending. This can be very dangerous as they can support with a feed, support with a produced fleet for 2v1 or go and invest in econ.

The point here is that a formula works, but gets VERY complicated when there are lots of variables (like Cykur said). Since expansion and military are inextricably bound up, it is very hard to determine.

Another equally valid question is should I up my fleet level and buy new ships now, save credits for a bit and have more (due to less tax at the next rate), but less produced ships if I wait, or should I wait and increase my econ a bit and let that help me buy some ships in a little while (which goes back to AoK's original question)...

Well we are beyond the homeworld upgrade debate since quickstart is now standard, so I can reveal something about it: I have always been for upgrade. I based my decision on a simple analysis where I assume starting near enemy, about 2 jumps, with both going for military.  Of course if one made msitake went civil he will die.

Sure it may take a while to pay back the upgrade (23 minutes by some estimates), BUT the advantage it gives you is negligable, you can calculate it to be 3 Assailants.

But it gets smaller, because by the time you fight your opponent, even on close map, will be about 10 mintue mark, since neither of you will forgo the starting asteroid.  By that time you have recouped probably 33% of the cost, so you are down to 2 assailant advantage. 

However, if you are attacking, you are at a disadvantage of at least 2 assailants, due to the distance of your frigate factory to the enemy.  So if you have not taken the upgrade and attack, your opponent who took the upgrade will have same amount of units in play.  The 2 extra you have gotten are lagging behind.

Now most players will not even dare to attack an enemy on their turf without an advantage that they know will guarantee a victory!  Attacking someone with an equal size force is a recepie for disaster. You need 50% more force for a decisive victory.

On top of this, feed makes the biggest difference in early conflict.  2 assailants are just nothing.  Maybe if each of your allies forgoes the homeworld upgrade and gives you the money isntead, then it can add up to a difference, but then your team is at an economic disadvantage for the rest of the game.

Only place I would forgo the upgrade would be in the very rare chance where your homeworld is directly linked to the enemy.

As far as other expansion questions, it is a work in progress for me.  But I have rough estimates of cost vs benefit on most things. But I learn something new everyday almost.  And I am not willing to disclose any of it

You'll find population growth rates defined in /Reference Data/Planet[Type].entity file, where the type is asteroid/ice/volcano/etc. The segment of code looks like this:

There is some research to boost population growth, but overall there's not much.

Awww comon astax. You can tell me.... I'll buy you a cup cake!!!!

Always good to get the numbers out Bob. I'm not sure that it takes 30 minutes for 280 increase though.... I wonder if there is some other rule here - same as when looking at the damage output numbers in the files and how they don't equal DPS straight out....

Checked it out in game, the population increase averages out at about 1 every 8 seconds. The Vasari have a T2 civ tech that increases population growth by 20/40%, which properly reduces the growth time to around 6 seconds per pop.

Population growth seems fast on a planet because 1) Few pay attention to it 2)The homeworld starts with most of its population right off.

The Organic AI artifact will increase population growth by an additional 20%.

Each unit of population gives .025 credits of income by default. (from gameplay.constants)

Income rates are boosted 15% across the board on normal income settings.

thanks for the data Bobucles. 

based on the .125 per second growth rate, it should take the homeworld exactly 12 minutes to go from 190 population to 280 population (this is the increase gained from building the population upgrade at the beginning of the game). 

ithe amount of cred/sec gained after 12 minutes is 2.25 creds/sec. this is 135 credits per minute. what this more or less means it that our intuitions about the recoup time on homeworld population upgrade has been pretty accurate. it takes at least 15 minutes to break even on the credit outlay, and thats not counting the resource cost of it. considering most of us buy 100 crystal from the black market to afford it (but had metal to spare), you can basically just increase its total cost by 500 creds. 

so bottom line, homeworld pop upgrade starts to return positive value after approximately 20 minutes, depending on how you count certain things. since basically every game of Sins ever played lasts longer than 20 minutes it seems like a no brainer to get this upgrade as early as possible (usually within the first 30 seconds of the game). 

Keep in mind Bobucles that when you upgrade your planet you dont just upgrade your population space but also its growth factor as well. I believe that the Terran population growth can get up to like .8 or .9 (numbers not solid), even the roids get a mild bump(something like .125).

I think darvin is really hitting at the heart of the matter. Expanding is only one of many ways to increase your income. In the long run, it's usually the best way (especially for resource income), but it is very detrimental in the short run, all economic investments are essentially this tradeoff between short run and long run, but expansion is just the mother of all these choices (the largest short term drain, but usually also the largest net gain). Therefore, factors like choke fortification, enemy strength, and myriad others all weigh in on whether or not it's a time to grow militarily, or grow your economy. Either way, there are further decisions as to what is the best way to grow in either realm. This decision is essentially, as darvin pointed out, a largest net present value problem. However, it's even more than just weighing adding a colony or a tradeport, because it's not the case that doing a then b has the same present value as doing b then a. So your entire strategy is based on thousands of unconscious (and some conscious) decisions about how to best maximize your NPV at end game. Add to this the complexity of shifting military to economy and the math is essentially impossible (this is the main reason that AI is notoriously poor in RTS games).

The big benefit in not upgrading immediately is that it allows you to rapidly get additional labs up and immediately deploy a critical technoloy or ship prototype.  This could be volcanic or ice colonization if you don't have an asteroid (aka the bugged start), or you want to make a few extra ships to expand and dig in sooner.  Ever wonder how someone beats you to a critical chokepoint?  Those few extra ships they built allowed them to expand a little faster and voila, they have the critical chokepoint between your empires first.

Most of the time the upgrade money is used for immediately rolling out your LRF or carrier cruiser to pursue a rushing strategy.  This is all situational on the map and player, but you can see the advantages of having a counter class ship deployed very quickly.  Advent vs Vasari might immediately deploy carriers with the expectation of early fights against Assailants.  TEC vs TEC might immediately deploy LRM with the expectation of rushing and hoping the other guy made cobalts for his first ships.  As Astax pointed out earlier, the advantage is not too large in number of ships, but if you used your upgrade money to invest in military labs so you can immediately counter the other guys fleet, it can be crippling and allow a rush to succeed.

That said, it is pretty safe to do the 4th planetary upgrade, especially if you are Vasari since you only need 1 lab for Assailants.  As long as you are paying attention and see an early rush attack before it hits you, you usually have time to react and get a repair bay or two up.  You just have to fight defensively a little bit until your economic advantages start pushing the tide back in your favor.

Well put!  This is exactly why I don't make handy charts to help people make informed decisions....probably why Astax doesn't share his top secret "time to profitability" data either (not because he is stingy).  It would just lull people into a false sense of security with crude tools that are, at best, a poor reflection of the true depth and complexity of game.  Much better to wax poetic on the myriad intangibles than to rudely define them as base subsystems and pretend they exist apart from any other factor within a game.

This stratagy works on Point Blank. I do it all the time even on hard. Haven't tried unfair. I've also done this on Quickstrike. Build cap and frigates (or another cap) Rush. Kill cap ship factory, frigate factory, constructors, cap ship, then mop up. keep building frigates and rally at enemy homeworld Does not work to just rush frigates.

I use these maps to get most of the achievements. Cheesy. I know.

That said, this is a great topic. I've been trying to come up with a decent expansion plan. Too much and you get caught with your pants down by not having the fleet to properly repel incursions. One thing to keep in mind is there is a big difference between most multiplayer games and single player games. Most MP are quick start and FAST credit and resource rates. A normal SP game you might build extractors, a cap ship factory, and 2 research (scouts too) I don't have the exact numbers but by then over half your credits are gone. At that point you might need a colonizer and then you can build 2 or 3 light frigates. Your tapped out by then.

Starting out, the extractors are a must. After that it's up to interpretation. Astax has 2 replays here 1v1 part1 and 1v1 part2 that I thought were excellent examples of expanding and trade port building. From what I observed the return from the investment into 2 or 3 planets was quick. But that was quick start and fast economy settings.

Hack, you should checkout my starts in Entrenchment with Quick Start enabled.  I have found it very useful to queue up a civ lab and weapons lab ASAP and have terran population and assail techs upgrading simultaneously.  When my terran has about 5 pop left, I upgrade again.  I have found in Entrenchment that very few players are willing to rush an experienced player, so the tactic pays off enormously.  Heck, I might even colonize the Ice or Volc first if it's closer than the roid.  Entrenchment allows you to do some wacky s*it, and completely get away with it early game.

The initial expansion may be a closely guarded secret, but what about later on? You have to then factor in a huge chunk of lost allegience into your returns. The first planets may be "sure things", but when is it worth picking up a fringe world?

I know - the only game I've played with you really is that one with that yellow newb noob. I watched it more to see what happened from reds point of view since he had so many carriers when we went to fight him. That was funny. "Hack - help. I have no fighter cover...") "Coming - this should be OK with my cover and your ships"... "Crap - how did he get that many fighters???"

I have taken to throwing down one of each most games unless I am on the hard edge (i.e. all enemy on one side of me meaning I will be facing 2v1) since it allows me to get the assailants I need out (vital to a Vassari expansion plan) and be 1/2 way to getting artic/volcanic tech.

Hopefully will catch you on the weekend... I'm still trying to work out what whacky stuff I can do. Some good ideas from you, Cykur and Astax for me to ponder...

Yeah, that kindof sucked.  I was in the econ slot and wasn't expecting to fight anyone.  Jumping into a 5 bar fleet kind of ruined that; I was kind of surprised he had expanded all the way across the map.  Took me about a minute to scuttle 5 trade ports and build mil labs and factoriess to start spamming fleet.

Luckily, the guy didn't know how defenseless I was, and let me build in peace.

Lol - go team work!!!!

Thank you Transitve, for doing the analysis.  Very well presented, and thought out.  I was a little surprised by your results, since I had done a previous analysis with quite different results.  I would like to make a couple observations, and point out (what I believe is) one small error.  (Obviously, my old analysis of asteroids must include an error too).

assuming the asteroid adjoins the home world, and has 90% allegiance .  (Therefore 90% income.  Planets farther out decline to 80%, 70%, 55%, 40% and everything farther than 6 jumps away [or thru wormholes] earn only 25%).  Also assumes 3 mines, many have only 2 (which would increase the payback period by 50%).

I don't know where you got the 493!?  It is supposed to be 423 also.  Meaning 2183/423 = 5.16+.5= 5.66 minutes.  Still a very good return on your investment, compared to most income opportunities in the game. [.5 represents the extra half minute for extractor ouput to plateau]

Also, I have usually used the average 4:1 conversion rate, and sometimes 3:1!  Using these lower rates results in longer payback periods.  I calculated 6.4 and 7.7 minutes respectively, using those converstion rates on your figures.