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Background
The MULE is of course the awesome macro mechanic for Terrans in Starcraft 2. It's also the name of one of the greatest multiplayer games as all time, so it's quite fitting that the name translates into Starcraft as well. =)
I've played over 500 games with Terran, and I've used the MULE extensively. I've made a lot of assumptions about the MULE, and heard a lot of rumors on its efficiency and its use:
"David Kim gets the MULE at 14/16"
"The MULE is as efficient as 3/6 SCV's"
"MULEs are way better than scans"
Now I'm sure some people have partially figured these things out already, but I've not personally found any definitive answers. I'm not saying they're not out there, but I was especially interested in doing my own research. I'll try my best to explain my methods along the way, and you may feel free to dispute them! I'll do more tests if needed.
PART 1 - MULE VS. SCV
STAGE 1
For this first test, I simply wanted to see what a MULE mines over one lifespan vs. an SCV in the same period of time, with the same mining distances in each case.
The MULE lasts 90 seconds, and it mined 270 minerals.
The SCV mined 90 minerals in 90 seconds.
In one lifespan, it's safe to say a MULE is about 3 times more efficient than an SCV.
STAGE 2
I wasn't convinced, simply because SCV's can't always be on the closest patches, while a MULE certainly can, so let's try this with the SCV's on patches of varying distances:
The MULE mines 270 minerals over one lifespan while on the closest patch, while the 3 SCV's mined between 240 and 255 minerals while placed on patches of varying distances.
This concludes that the MULE is actually slightly more efficient than 3 SCV's.
This also concludes that the use of a scan or supply drop effectively costs the Terran ~250-270 minerals over the course of 90 seconds. (Ouch.)
PART 2 - EFFICIENCY
So when should you get the Orbital Command? I'm not going to pretend to know the definitive answer to this question, however I will try to solve how long it takes for the MULE to become effective.
STAGE 1
Let's look at the facts:
The Orbital Command costs 150 minerals.
A SCV costs 50 minerals.
The Orbital Command takes 35 seconds to complete.
A SCV takes 17 seconds to complete.
A MULE mines around 270 minerals in 90 seconds.
A SCV mines around 90 minerals in 90 seconds.
SCV's cost 1 supply each.
From this you can determine that you can build ~2 SCV's in the time it takes to build an Orbital Command. Let's make a timeline, assuming you could build SCV's and an Orbital Command at the same time:
0:00 - Orbital Command Start
0:00 - SCV #1 Start
0:17 - SCV #1 Finish
0:17 - SCV #2 Start
0:34 - SCV #2 Finish
0:35 - Orbital Command Finish
SCV #1 can mine for 18 seconds before the command finishes, mining an estimated 18 minerals.
SCV #2 can mine for 1 second before the command finishes, mining an estimated 1 mineral.
Yield #1 + Yield #2 - Supply Cost - SCV Cost = Total Cost
(Supply cost is determined as ~18.75 minerals per supply.) (Cost of Depot + Lost Mining Time / 8)
18 Minerals + 1 Mineral - 37.5 - 100 = -118.5 Minerals.
It costs approximately 118.5 minerals to produce 2 SCV's in the time it takes to build an Orbital Command, which costs 150 minerals. Therefore it is 31.5 minerals cheaper (during construction time) to NOT build an Orbital Command.
This determines that it sets your economy back 31.5 minerals when you build the Orbital Command, assuming you'd otherwise be producing SCV's.
STAGE 2
Now that we know how much it 'costs' to build an Orbital Command, we can look back at how much a MULE can mine over the course of ONE lifetime, in comparison to that of the two SCV's which would otherwise be produced.
In one lifetime, we can recall that a MULE mines about 270 minerals. One SCV mines about 90 minerals at maximum in the same period of time, therefore two will mine a maximum of 180 minerals.
Using simple math, we can then determine that the Orbital Command's first MULE will gain the player 90 minerals over 90 seconds. Considering that the Orbital Command set us back ~32 minerals, it is accurate to say that when the first MULE is ONE-THIRD of the way through its lifespan, your economy will be equal to that of an economy without an Orbital Command.
Conclusions
In short, the Orbital Command pays for itself about 30 seconds after completion. This means, to me, that it certainly is an extremely worth early investment, assuming you are not killed within this short period of time.
It is also important to note the hidden pros/cons of the Orbital Command:
-If you choose to get it, you will have 2 less SCV's which have the ability to attack, while a MULE does not.
-MULEs have the same HP as an SCV, so if it is killed or interrupted through harassment, the early Orbital Command will hurt your economy initially to a greater extent.
-The Orbital Command also opens up the gameplay option of scans and supply drops.
-An early Orbital Command can slow or alter an early build order to a huge degree.
-Instantly creating an Orbital Command at an expansion instead of SCV's is, in general, much more efficient.
Let me know if you see any flaws in my math or logic, as I've stated already, I'll be happy to do additional tests.
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very nice effort, stuff like this is what will slowly decrypt the riddle that is SC2
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Cost of depot/8 makes a good assumption of cost per supply, but a depot does not cost 100 minerals.
Rather, it costs 100minerals+(build time)minerals because if SCVs mine 1 mineral/sec, and a depot costs 50 seconds to build, the SCV could have mined 50 minerals in that time, but didn't, thus the whole cost is 150 minerals.
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On March 07 2010 10:11 ghrur wrote:
Cost of depot/8 makes a good assumption of cost per supply, but a depot does not cost 100 minerals.
Rather, it costs 100minerals+(build time)minerals because if SCVs mine 1 mineral/sec, and a depot costs 50 seconds to build, the SCV could have mined 50 minerals in that time, but didn't, thus the whole cost is 150 minerals.
Great point, I'll have to add that =)
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United States4126 Posts
I'm in no way qualified to critique your mathematical analysis, but I'm happy to see the results of it 
It's interesting to know how long the MULE takes to pay for its worth.
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I've modified the calculations to include the cost of lost mining time into the 'supply cost' of the SCV's. If someone would like to check my math on that, it'd be great. =P
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Has anyone tested this, but do depots that have the added supply look any different than other depots when lowered? I find generally you can get away with the Mule if you OC at 15/16, and then save energy for Scan/Supply-blocked with your built up energy.
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On March 07 2010 10:25 Rothbardian wrote:
Has anyone tested this, but do depots that have the added supply look any different than other depots when lowered?
They do.
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In the hidden pro/cons, maybe you should mention the opportunity cost of getting the orbital command - in terms of what you can do with the 150 minerals (like getting a quick second barracks, or something along those lines.)
Great post overall, helps me clarify the usefulness of the mule.
edit:grammar.
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Added a variation of that as well, Comeh. Thanks.
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Very interesting, and carefully done.
Then it's definitely better to build an orbital command at the second expansion immediately. And compared to building two scvs, it's like you're getting one free scv.
So with high yield resources, it's (150-100-supply)+19 x rate, and you recover it at 1 x rate, so it should take 22 seconds on high yield resources. Also, can you save up energy so you can do a multi-mule drop on high yield resources?
I'm also curious about the value of an extra command center, which would be 400 + build time - supply cost, with an income of average mining rate x mineral patches + mule. With a mule you're breaking even in about a minute.
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United States703 Posts
Does the distance the SCV moves before you put down your supply depot count into the equation, or is it negated by the fact the other races also lose mining time to go to the build location? Terran usually op for the front door seal which is usually a bit farther then what the probe/drone move to plop down their building... Eh... its probably not worth throwing into the equation because then that varies from map to map. Just rambling I guess.
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On March 07 2010 10:51 NET wrote:
Does the distance the SCV moves before you put down your supply depot count into the equation, or is it negated by the fact the other races also lose mining time to go to the build location? Terran usually op for the front door seal which is usually a bit farther then what the probe/drone move to plop down their building... Eh... its probably not worth throwing into the equation because then that varies from map to map. Just rambling I guess.
I thought of this as well, but I figure it's a bit variable and probably doesn't matter enough to equate it. It might amount to maybe 5-10 more minerals for the ENTIRE depot, and not just the 2 supply that are being used, however this would further work IN FAVOR of getting the Orbital Command.
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neat stuff :S
ur format reminds me of my data management isu i did back in January
ohh the horrors >.<
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On March 07 2010 10:40 igotmyown wrote:
Also, can you save up energy so you can do a multi-mule drop on high yield resources?
you can, i cant remember exactly which one it was, but someone did a youtube video commentary, and one of the players put down a CC, then dropped 1 mule onto every high yield mineral patch
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Good shit...makes me want to do one for the queen...but I am a lazy bastard.
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Very nice man anyone who is thinking about getting orbitla command in part with their build will easily decide right here
queen guide by Monday gogo 
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For anyone interested in in-game numbers:
I compared 10sup 12rax 13refinery 15 orbital command to the same build without orbital command. I mined the same amount of gas in both builds (factory at first 100 gas, 2nd refinery at almost the same time--this matters for SCV saturation since I went past 16 SCVs on minerals).
The orbital command started at 2:37.
All times are in-game time.
Time/OC minerals/No OC minerals
4:00/1755/1705
5:00/2435/2285
6:00/3235/2995
Seems evident that the disparity only grows as the game goes on--partly because of saturation, I think--so you should make your OC as soon as you can without cutting SCVs for it to get the most out of it.
One note:
Instantly creating an Orbital Command at an expansion instead of SCV's is, in general, much more efficient.
This is certainly true if you want minerals, but quite untrue if, for instance, you floated it over to an island without SCVs inside and want gas. If you float over with SCVs inside, you should still probably produce 1 SCV before upgrading to an OC if you're mainly looking for gas.
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Time for me to create a ling timing rush on your MULEs
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Excellent ... some real number crunching reasoning.
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