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I know that there are a ton of Orbital Command posts so this is not to discuss their viability, just to clarify on some of the Math as I am unsatisfied with the calculations that others have done.
So how long does it take for an Orbital Command to pay for itself?
SCVs mine at 43 minerals/minute on average, cost 50 minerals, hold 1 supply, and take 17 seconds to build.
Supply Depots take 30 sec, cost 100 minerals, provide 8 supply.
Orbital Commands take 100 sec of SCV time (for Command Center), 35 seconds upgrade time, cost 550 minerals, and provide 11 supply.
Supply Depots cost 30 seconds build time (21.5 minerals of SCV mining time) plus 100 minerals = 121.5 minerals. With one Supply Depot providing 8 supply, the mineral cost per supply is 15.2 minerals.
They cost 550 minerals, plus 72 minerals worth of SCV mining time, minus 11*15.2 = 167 minerals of supply = 455 minerals per Orbital Command when using their supply.
Now the MULE mines 240 or 270 minerals (255 average) and it takes 85 seconds for the orbital command to regenerate the 50 energy to call down another MULE. Thus Orbital Commands mine at an average rate of 180 minerals/minute. This can be 190 minerals/minute if you only place mules on close mineral patches.
So 455 minerals investment / 180 minerals/minute * 60 seconds/minute = 152 seconds after completion plus 135 seconds of construction = 287 seconds = 4 minutes 47 seconds on average for an Orbital Command to pay for itself including supply.
For Comparison:
The return on investment for SCVs is thus 50 minerals + 15.2 minerals of supply / 43 minerals/minute * 60 seconds/minute = 91 seconds after completion + 17 seconds build time = 108 seconds or 1 minute 48 seconds for an SCV to pay for itself, including its supply cost.
Now for the ratio of the effectiveness of Orbital Commands compared to SCVs. 180 minerals/minute / 43 minerals/minute = 4.2 times the mining rate of an SCV. Orbital Commands have a return of investment of 287 seconds, while SCVs return on investment in 108 seconds. So Orbital Commands take 287/108 = 2.66 times longer to pay for themselves. Thus as an economical investment, Orbital Commands are 4.2/2.66 = 1.58 times better than SCVs. Orbital Commands are 1.58 times better of an economic investment than SCVs if you're using their supply.
I ignored the travel time for an SCV to get to the building placement location because this also happens for supply depots, and thus didn't feel like a significant enough difference for the difficulty of calculation. I also ignored the fact that you can be building additional SCVs at once with each Orbital Command, and SCVs speed up the return on investment, though this is limited by saturation and your maximum desired SCV count.
If you think that I've left some variable out that is important, let me know and I'll include it.
TL;DR: Orbital Commands return on their investment in 4 minutes and 47 seconds and are 1.58 times more efficient of an economical investment than SCVs.
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The ratio of Return on investments has nothing to do with ratio of efficiencies.. You're just comparing apples and oranges to make a point that orbital commands would somehow be more efficient then scv's... they're not...
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wow dude, great excuse to show what u learned in school today, to make urself look like an idiot.
User was warned for this post
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An orbital pays for itself after 2 mules
each mule gets about 270 minerals
and you will only lose mining time for 1 scv, which is minimal
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this is just a thread that says orbitals are good, but nothing else. anything else that your maths discovered is lost in the terrible mess of the explanation
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Did... the posters above me actually read his post?
No.
On January 16 2012 08:10 Simulacra001 wrote:
wow dude, great excuse to show what u learned in school today, to make urself look like an idiot.
You made an account JUST to say that?
Keep it up and you won't be on TL for much longer.
The numbers look about right to me after 1 reading, but you're leaving out the fact that with 2 Orbitals/CCs, it's 2x the SCV production as well so that's definitely a huge advantage that you overlooked.
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If I am not mistaken, he proves that it is better to build orbitals late game than replenish your scv count after heavy losses. Also, why blatantly discredit someone immediately?
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Interesting maths, I wonder if there's an intersection between where money allows for constant OC production and where it becomes a bad idea to continue building SCVs....
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On January 16 2012 08:10 Simulacra001 wrote:
wow dude, great excuse to show what u learned in school today, to make urself look like an idiot.
Some people just feel they have to contribute/show their skills the community no matter how "idiot" they look
But to the OP
I think there should be no discussion. OC is always great and pays itself quite quickly as long as you use MULEs effectively.
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On January 16 2012 08:02 Markwerf wrote:
The ratio of Return on investments has nothing to do with ratio of efficiencies.. You're just comparing apples and oranges to make a point that orbital commands would somehow be more efficient then scv's... they're not...
My general knowledge of economics is a little lacking, specifically about the official meaning of "efficiency" (I was relying on a coloquial understanding) so I went off of intuition that you're looking for how big your return is (long term mining rate) based on how much risk you take (minerals tied up for some amount of time), though perhaps this risk should include the initial investment in minerals and not just how long it will take to make it back. Is there another equation for efficiency that you would recommend?
On January 16 2012 08:39 Puph wrote:
If I am not mistaken, he proves that it is better to build orbitals late game than replenish your scv count after heavy losses. Also, why blatantly discredit someone immediately?
This is definitely one use that I had in mind. I didn't mention it in the post because I felt that the discussion about specific uses for Orbital Commands is already prevalent. This math was simply something that I worked out to help make build development a little easier for myself. I figured I'd share.
I put it under [D] because I wanted input about whether there was any error in the maths. General layout advice for clarity would be appreciated as well.
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On January 16 2012 08:10 Simulacra001 wrote:
wow dude, great excuse to show what u learned in school today, to make urself look like an idiot.
User was warned for this post
Says the guy who has one post on TL.net and is walking around calling people idiots.
Posts like this are always useful and encourage thinking about the game on a different level then just APM and basic strategy. I enjoyed it.
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not to be rude but even if this is interesting math its pretty much useless since the game is not about "when will this thing pay off." etc. (dont know how to explain what im trying to say)
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Seems like an interesting calculation for sure but as with most starcraft mathematical posts has limited application to the actual strategy of the game.
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On January 16 2012 11:18 Janders wrote:
not to be rude but even if this is interesting math its pretty much useless since the game is not about "when will this thing pay off." etc. (dont know how to explain what im trying to say)
The idea is closer to "can I successfully survive with 455 fewer minerals for the next 5 minutes?" If yes, then definitely build an Orbital Command.
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On January 16 2012 07:02 RFDaemoniac wrote:
If you think that I've left some variable out that is important, let me know and I'll include it.
SCV Saturation of the base, which changes the cost of the worker building time.
If the OC is used as an expansion, it gives access to additional mineral patches, which will lead to a faster payoff.
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Remember also that if your main is saturated (24 SCVs on minerals) then the mining per additional SCV is much lower.
One relevant use for this info is the amount of time it would take for a cheeky hidden expo (in a location that you cannot defend practically) to pay for itself. Assuming you just used mules at the new location and weren't worried about losing SCVs.
Also, unrelated, if we are talking about the value of late-game orbitals as a replacement for SCVs then you cannot take into account the supply included in the new orbital since one assumes you already have 200 worth of depots already
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I just realized that there is also a giant opportunity cost associated with building an orbital.
You can't just say, "great, I will ninja an expansion in the corner of the map, and I will be ahead as long as the expansion runs for about 5 minutes!" because for the majority of those 5 minutes, you have less units/tech/production, resulting in less defenses and reduced ability to pressure. In this sense, it probably takes quite a bit longer than 5 minutes for an orbital to truly "pay for itself" in terms of winning the game, and not purely in terms of minerals gathered.
However, to factor this opportunity cost into the calculations is... nearly impossible.
Edit:
Also, fucking pissed off at this shitty design of SC2 economics.
I'd say 1/4 of my games are <10 minutes, 1/2 are <15 minutes and 1/4 are <20 minutes with the few 20 + minute games pitifully scattered across my replays.
Yet, the game is such that it takes ~6 minutes (my estimate) for a Terran expansion to fully pay for itself, no wonder 1-base is so fucking strong across all leagues and this is definitely something that should be changed in HoTS; I want faster 100% return on investment expos please!
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Russian Federation164 Posts
HardMacro, isn't it almost the same for all races?
A bit off-topic: did any pro successfully played lategame with 150+ supply in army?
Like, sacrificing most SCVs to have 2 bases with 16 SCVs on minerals and MULEing like crazy of 3+ OCs on other expos. Say, 2 base x 16 on minerals + 3x6 on gases = exactly 50
Well, at least at the point when you bank 2k+ due to the lack of gas.
Since 3 OCs = 2 MULE/min, which is 500 miner/min + each expo ~700 miner/min
Now imagine how badly will a 150 supply army rape 120ish! :D
If you're a total baller, mine minerals off 1 base and have 166 suplly army ^_^
Replays, anybody?
edits: uhhh, I can learnz Englush -.-
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On January 16 2012 13:08 HardMacro wrote:
I just realized that there is also a giant opportunity cost associated with building an orbital.
You can't just say, "great, I will ninja an expansion in the corner of the map, and I will be ahead as long as the expansion runs for about 5 minutes!" because for the majority of those 5 minutes, you have less units/tech/production, resulting in less defenses and reduced ability to pressure. In this sense, it probably takes quite a bit longer than 5 minutes for an orbital to truly "pay for itself" in terms of winning the game, and not purely in terms of minerals gathered.
However, to factor this opportunity cost into the calculations is... nearly impossible.
Edit:
Also, fucking pissed off at this shitty design of SC2 economics.
I'd say 1/4 of my games are <10 minutes, 1/2 are <15 minutes and 1/4 are <20 minutes with the few 20 + minute games pitifully scattered across my replays.
Yet, the game is such that it takes ~6 minutes (my estimate) for a Terran expansion to fully pay for itself, no wonder 1-base is so fucking strong across all leagues and this is definitely something that should be changed in HoTS; I want faster 100% return on investment expos please!
This is silly.
The return on investment on your expo is not the same as building an orbital in isolation. The return kicks in pretty darn fast if you can saturate the min line quickly. For example if your gasses are up immediately then you double your gas income which makes a huge difference, ignoring the mineral aspect of things. Only terran can even consider the "return on investment" of an "expansion" which is still sitting in their main base.
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I mean orbitals not as expansions, but as an extra economic boost, akin to building only drones with inject or chronoboosting your nexus. In looking at efficiency, I realize that it should just be initial investment, which is 467 for orbitals (including supply) and 65.2 for scvs (including suppy), and considering that orbitals only mine at 4.2 times the rate of an scv, so scvs are clearly a better investment at any stage in the game. The only reason to consider additional orbitals would thus be to produce scvs faster, to oversaturate, and to ninja expansions. I think going to advocate building an orbital instead of supply depots whenever possible because supply depots do not generate income, but not to cut scvs until late game when you want a 160 supply army 
It's also worth considering that 2-3 orbital commands provide a free maphack... regardless of "it costs you 270 minerals to scan," if you build a couple orbital commands with the goal of scouting.
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EPT
