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Introduction:
Sometimes in a game I wonder if I can afford to make an expansion. It costs the initial investment and it takes some time after it is completed before it returns sufficient minerals to pay for itself.
This can also be presented as "if the expansion can survive for X seconds I will be in a better position by expanding" (hidden expansion). This same argument can be flipped around to "if the game is finished before X seconds then I shouldn't expand" (all-in one base strategy).
So I decided to calculate it for myself and present the findings.
Some assumptions:
* No Maynard transfer (this calculation is mostly for the 3rd base where Maynarding is not always feasible)
* MULE resturns 255 min per trip (between 6 and 7 returns as it depends on the mineral patch layout)
* MULE harvested minerals are added gradually over its entire duration
* All time figures are in game time
* SCV harvesting speed 1 min / game sec
* The building SCV starts mining as soon as the CC is done
* Linear increase in harvesting as a function of the number of SCVs
I tested 2 different scenarios; without Orbital Command and with Orbital Command.
Scenario 1: Without Orbital Command:
Production: Total mineral cost, Total time, Total minerals harvested
Command Center: 400min, 100sec, 0min
+SCV: 450min, 117sec, 17min
+SCV: 500min, 134sec, 51min
+SCV: 550min, 151sec, 102min
+SCV: 600min, 168sec, 170min
+SCV: 650min, 185sec, 255min
+SCV: 700min, 202sec, 357min
+SCV: 750min, 219sec, 476min
+SCV: 800min, 236sec, 612min
+SCV: 850min, 253sec, 765min
+SCV: 900min, 270sec, 935min
+SCV: 950min, 287sec, 1122min
Scenario 2: With Orbital Command:
(use MULE whenever available):
Production: Total mineral cost, Total time, Total minerals harvested
Command Center: 400min, 100sec, 0min
+Orbital Command: 550min, 135sec, 35min
+SCV: 600min, 152sec, 103min
+SCV: 650min, 169sec, 188min
+SCV: 700min, 186sec, 290min
+SCV: 750min, 203sec, 409min
+SCV: 800min, 220sec, 545min
+SCV: 850min, 237sec, 698min
+SCV: 900min, 254sec, 868min
+SCV: 950min, 271sec, 1055min
+SCV: 1000min, 288sec, 1259min
Conclusion:
In both cases it takes about the same time for both scenarios to return the investment, which is about 260sec in game time, corresponding to 3min 7sec in real time.
It may seem odd that the Orbital Command isn't favourable, but this is primarily due to the higher investment cost. The Orbital Command is returning minerals at a much higher rate, so as usual it is a great idea to build it immediately as it doesn't affect the payback time.
TL;DR: Don't build an expansion if you can't keep it for 3 min (real time)
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*claps* *standing ovation*
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Bear in mind that a CC also gives supply, so its effective cost includes both the opportunity cost of the SCV tied up building it minus the cost of supply that it gives.
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100 out of 10 times you are going to maynard, soooooo....
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Thnx for the work.
Interesting but also useless. I mean, this way of thinking cant be used when playing a match.
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On April 16 2010 23:20 JTPROG wrote:
100 out of 10 times you are going to maynard, soooooo....
Just not true- On scrapyard for example its not uncommon to take gold minerals, the island minerals, or one of the blocked off minerals, before your "natural" (because its so damn hard to defend). Its hard to maynard to the islands...
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Aotearoa38208 Posts
You can at least take 5 workers to the island via loading them into the CC 
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The problem with those calculations is that they ignore opportunity cost. You do not at all break even after 3 minutes because instead of building the expansion, you could have invested your minerals otherwise, for instance in a bigger army or additional tech, which can either save you resources (by protecting your economy from attacks/harrassment) or cost your opponent resources (either by attacking/harrassing him or by scaring him into investing more resources into defense and less into his economy).
However, the opportunity cost varies greatly based on the current situation and is very difficult to calculate, thus it is unfortunately impossible to state in simple terms how long an expansion needs to break even. However, thanks to your calculations, we now at least know that it's always more than 3 minutes real time if your assumptions are fulfilled.
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Nice calculations, but shouldn't all the mineral numbers be moved back a step?
Command Center: 400min, 100sec, 0min
+SCV: 450min, 117sec, 17min
You are assuming here that the SCV can mine while it's still building. Instead it should be
Scenario 1
+SCV: 1000min, 288sec, 935min
...
Scenario 2
+SCV: 1000min, 288sec, 1055min
also noting when you drop the mule would be a nice addition. Good work nevertheless.
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On April 16 2010 23:20 JTPROG wrote:
100 out of 10 times you are going to maynard, soooooo....
I agree that this is always the case for the natural and usually the third. It is not a hard and fast rule, but more like something I've thought about.
The reason for me not to include it is that it is impossible to model Maynarding as it depends on the saturation, distance and number of SCVs transferred, so it will be impossible to get some good benchmark numbers. Island expansions cannot easily transferred to either.
Regarding the whole idea of Maynarding across the map, then I've just seen way too many replays (SC1+2) of people giving away free workers and the location of their hidden expansion by transferring workers right through a camping army.
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On April 16 2010 23:42 caution.slip wrote:
You are assuming here that the SCV can mine while it's still building. Instead it should be
This is the SCV building the CC that is mining during the construction of the first SCV.
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Well there are too many things simplified or neglected here to give a usefull number.
First of all the scv building it is not mining so thats a oppurtunity cost of 100 minerals if you are not saturated. If you are this oppurtunity cost lowers.
Second point is that the scv provides 11 supply. A depot gives 7 supply and costs 100 minerals + a oppurtunity cost of 35 minerals (if not saturated).
Combining points 1 and 2 you will get a real cost of 400 + 100 - 11/7 * 135 = 288
This will be slightly lower when you are saturated as the opportunity cost decreases.
Also maynarding has to be included in the time as it's 99% of the case happening.
Mining speed goes up linear up till 16 mineral workers per base and then tops with max speed at 24, with 20 minerals workers being already about 95% of max mineral mining on one base.
Given that by the time a expo finishes your mineral workers are virtually always above 16 maynarding matters alot as extra workers on the expo are way more efficient then extra workers on your main.
To calculate this you need to know the exact efficiency decrease of workers more then 16. The maynarding time can probably just be averaged for 12 secs or so given all maps.
Anyway getting a more exact payback time for a CC isnt too difficult to calculate with some extra data, the number itself will still be relatively useless as the oppurtunity cost of not making other stuff in the meantime (tech, units, etc.) is very hard to determine and gamespecific. In a situation where it's useless to attack and safe to expand this oppurtunity cost is 0 (like when he invested alot in static defense) in any other situation it's not 0 though and extremely hard to determine.
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Should I upgrade to an OC before I lift off, or should I use the CC to carry SCVs to my island expansion? I'll try to compare the two.
Assumptions:
80 second travel time. OC saves its starting energy and lands at the expansion with 100 energy, drops two mules upon landing.
SCVs above saturation only harvest 10% as much.
Transferred SCVs have an opportunity cost of 0.1 minerals/second while in transit.
A MULE is equal to three SCVs in minerals/second.
Blue Minerals
+ Show Spoiler +
Scenario 1: Carry 5 SCVs:
Production: Total mineral cost, Total time, Total minerals harvested
Carry 5 SCVs for 80 seconds: 40min
Command Center: 440min, 180sec, 0min
+Orbital Command: 590min, 215sec, 175min,
+SCV: 640min, 232sec, 311min
+SCV: 690min, 249sec, 464min
+SCV: 740min, 266sec, 634min
Breaks even at 276sec
+SCV: 790min, 283sec, 821min
+SCV: 840min, 300sec, 1025min
Covers the production cost of transferred SCVs at 305sec
+SCV: 890min, 317sec, 1246min
+SCV: 940min, 334sec, 1484min
In this scenario, the last 2 SCVs we load up will bring us under saturation, so they have a full carrying cost of 1min/sec each.
Scenario 2: Carry 10 SCVs:
Production: Total mineral cost, Total time, Total minerals harvested
Carry 10 SCVs for 80 seconds: 244min
Command Center: 644min, 180sec, 0min
+Orbital Command: 794min, 215sec, 350min,
+SCV: 844min, 232sec, 571min
+SCV: 894min, 249sec, 809min
Breaks even at 255sec
+SCV: 944min, 266sec, 1064min
+SCV: 994min, 283sec, 1336min
Covers the production cost of transferred SCVs at 293sec
+SCV: 1044min, 300sec, 1625min
+SCV: 1094min, 317sec, 1931min
Mineral line is saturated
Scenario 3: Flying Orbital Command:
Production: Total mineral cost, Total time, Total minerals harvested
Command Center: 400min, 100sec, 0min
+Orbital Command: 550min, 135sec, 0min
Land at 215sec
+SCV: 600min, 232sec, 102min
+SCV: 650min, 249sec, 221min
+SCV: 700min, 266sec, 357min
+SCV: 750min, 283sec, 510min
+SCV: 800min, 300sec, 680min
Extra MULE dies at 305sec
+SCV: 850min, 317sec, 816min
Breaks even at 321sec
+SCV: 900min, 334sec, 969min
Gold minerals:
+ Show Spoiler +
Assume that energy from other OCs will be used the same way each time.
Scenario 1: Carry 5 SCVs:
Production: Total mineral cost, Total time, Total minerals harvested
Carry 5 SCVs for 80 seconds: 40min
Command Center: 440min, 180sec, 0min
+Orbital Command: 590min, 215sec, 245min,
+SCV: 640min, 232sec, 435min
+SCV: 690min, 249sec, 650min
Breaks even at 252sec
+SCV: 740min, 266sec, 888min
Covers the production cost of transferred SCVs at 274sec
+SCV: 790min, 283sec, 1149min
+SCV: 840min, 300sec, 1435min
+SCV: 890min, 317sec, 1744min
+SCV: 940min, 334sec, 2078min
In this scenario, the last 2 SCVs we load up will bring us under saturation, so they have a full carrying cost of 1min/sec each.
Scenario 2: Carry 10 SCVs:
Production: Total mineral cost, Total time, Total minerals harvested
Carry 10 SCVs for 80 seconds: 244min
Command Center: 644min, 180sec, 0min
+Orbital Command: 794min, 215sec, 490min,
+SCV: 844min, 232sec, 799min
Breaks even at 235sec
+SCV: 894min, 249sec, 1133min
Covers the production cost of transferred SCVs at 266sec
+SCV: 944min, 266sec, 1490min
Mineral line is saturated
+SCV: 994min, 283sec, 1849min
+SCV: 1044min, 300sec, 2211min
+SCV: 1094min, 317sec, 2575min
Scenario 3: Flying Orbital Command:
Production: Total mineral cost, Total time, Total minerals harvested
Command Center: 400min, 100sec, 0min
+Orbital Command: 550min, 135sec, 0min
Land at 215sec
+SCV: 600min, 232sec, 143min
+SCV: 650min, 249sec, 309min
+SCV: 700min, 266sec, 500min
+SCV: 750min, 283sec, 714min
Breaks even at 288sec
+SCV: 800min, 300sec, 952min
Extra MULE dies at 305sec
+SCV: 850min, 317sec, 1142min
+SCV: 900min, 334sec, 1357min
After 215 game seconds, the CCs that loaded up SCVs are returning more minerals than the OC, constantly. Before that, the OC can only return more minerals (in the short term) by using a MULE at an established base before it lifts off. The numbers look even worse for the OC when gold minerals are considered. Also, 80 seconds of flying time is fairly long, and shorter times will favor the CC because less energy can regenerate.
Supply depot construction and MULE usage by older OCs should all be constant across these scenarios. Because SCV production may resume at an older base in order bring the mineral line back over saturation, I've marked when a CC covers the cost of producing the SCVs it carried.
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When you create a OC before flying, you use it just before you lift off offcourse. You don't fly and then drop the mule as you will be stockpiling energy.
Offcourse that whole calculation is totally reliant on how being able to mine at your existing base(s) compares to mining at the expansion which in your assumptions is the 'SCV above saturation only harvest 10% as much'. Considering there is nothing to base this assumption on or whatsoever the whole analysis is a bit useless.
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So according to this, it takes about 4 minutes game time to break even with a 1base eco after expanding. If this is true, than it takes about just as long to set up expansions as it does in bw (i think?). If blizz made timing pushes and massing stronger and faster, then they should make expanding just as fast. Time to file new balance proposal hahah
Edit: Never mind...making cc/nex/hatch build times go down would not make timing pushes weaker by enough...
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EPT
