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The Cost of Repairs - Tank vs Planetary Fortress
In my obsessive hunt for obscure stats and numbers related to Starcraft 2, I decided to look at one of my more recent interests: Repairing stuff. I did some calculations on what it costs to repair something and what effect it has to lay siege to a PF that's being repaired, something that I've seen both in pro-games as well as my own attempts at playing.
I've posted this as a blog rather than on the strategy forum since it's a mostly theoretical analysis with limited in-game applicability. Nevertheless, it satisfies my own needs.
Repairs 101, powered by Liquipedia
First order of business is to check out how much repairs cost. Liquipedia has the answer. I didn't verify the results myself, so I'm putting my faith in the dedicated LP-editors. Treat it well, Liquipedians!
Repairing a mechanical unit or structure has a cost proportional to the health repaired. Repairing something from zero to hero costs 25% of the original cost to build. As an example: A half-health Helion is patched up to mint condition for the mere cost of 12.5 minerals. Orbital Commands and Planetary Fortresses use the combined cost (CC + upgrade) as their cost.
As an intermezzo, this price makes me wonder even more why so many Terran pros don't send a few SCVs with their mech army of doom. Not only does your push have more success if it stays up and running, it's also way cheaper to repair than to replace. A late-game mech Terran won't be mineral-starved, so you can afford to take a few SCVs away from mining duties.
Then there's the time factor. LP says that repairing a unit/building to full health takes the same amount of time as building it, if it starts at 1 health and is repaired by 1 SCV. Time requirements are proportional to health deficit (unit at half health rather than near-death: half the time needed) and inversely proportional to SCV count (twice as many SCVs repairing: half the time needed).
Sieging up the PF
Now we come to our test-case, sieging a Planetary Fortress. The scenario is not that uncommon, you have a composition with tanks and manage to get position on one of your opponents outlying bases. His army is out of position / contained / unable to engage for other reasons and you start shelling the PF. Your opponent wisely puts SCVs on repair duty.
Now a PF costs 550 minerals and 150 gas and takes 160 seconds to build (100 for the CC, 60 for the upgrade). A single sieged tank does 50 damage to a PF per shot, every 3 seconds. Because of armor, the actual damage dealt is 47 per shot or 15.667 damage per second. This is 1.044% of the maximum health of the thing, which means that repairing up a sieged PF costs you 1.44 minerals and 0.392 gas per second when a single tank is firing. This corresponds to the constant harvesting rate of roughly 2.5 SCVs (depending on things like saturation).
Now we compute the time required to repair. 1.044% of the PFs health is reduced per second by a single tank. The repair-rate for 1 SCV is 1/160 = 0.625%. So to keep up with the damage being dealt by the tanks, we need 1.67 SCVs repairing instead of mining
Concluding remarks
A single Siege Tank attacking a Planetary Fortress that is being repaired costs the player income corresponding to around 4.2 SCVs, some to compensate for the repair costs and some to compensate for lost mining time. The costs are directly proportional to the number of tanks: Twice the tanks, twice the costs.
Obviously, mech upgrades increase the repair costs. At +1 attack you're looking at roughly 4.6 SCVs, at +2 it's 5.1 and at +3 it's 5.5 SCVs per tank.
The real-world usefulness of this information is limited, but it does show that sieging up a Planetary Fortress for an extended period can be a non-trivial drain on resources to the point where it may be more beneficial to give up the location and start building a new CC back at home to be flown out once the area has been retaken.
 
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Thanks for this! ~5 SCVs is a number that I can keep in mind while watching.
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why is this in blogs? It's actually pretty useful
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Wow, actually an insightful strat post, really gj!
So to keep up with the damage being dealt by the tanks, we need 1.67 SCVs repairing instead of mining
I think the opportunity cost should be calculated in here as well. That is, the amount of minerals per second that these two SCVs could be mining instead. Obviously that's something difficult to calculate, given that it depends on the worker saturation of the expansion, but I think you could make some assumptions here.
Splash damage plays a role here too, doesn't it? So after a few vollies you are actually going to start losing SCVs as well.
but it does show that sieging up a Planetary Fortress for an extended period can be a non-trivial drain on resources to the point where it may be more beneficial to give up the location and start building a new CC back at home
I think I disagree with your conclusion here.
I think there's actually two senarios which should be accounted for here. First, the case you presented in which your army is within striking distance of PF and your opponent is out of position. While you may be able to cause them to expend resources and take SCVs off mining by hitting their PF, if the opponent is out of position it's likely there are much more valuable and softer targets nearby, such as productions structures. Hitting ebays and production structures is going to do far more damage to your opponent. I would argue even hitting the SCVs at the expo is going to do more damage than sieging the PF. So realistically, the longer your opponent is sieging your PF, the better as their are essentially wasting time they should be using to hit higher value targets.
Further, even though you may be losing SCVs by defending the PF, Terran in the mid to late game are going to have abundant MULES, which means any economic damage may be somewhat mitigated as many harvetsters lost repairing the PF can be replaced with speed. Expos however, cannot be replaced easily. Further reasoning to defend the PF instead of giving it up.
There's another instance to consider here as well, dropping siege tanks on a nearby highground to hit the PF. Of course if you were to siege with 3-4 tanks the mineral requiremens should increase proportionally correct? So to repair a PF versus 3 sieged tanks would take the equivalent minerals and gas of 8 mining SCVs? That's a bit more substantial.
But I still think it's minimal, given that unless the sieging player has very good micro, they are probable going to lose those tanks after a while (3 tanks by themselves could easily be cleaned up by a single banshee etc.) Losing even just one of those three tanks would be 150 minerals 125 gas. Three times the cost rate of repairs would be 4.32 minerals and 1.176 gas per second. Not accounting for destroyed SCVs or lost mining time, that would mean your attack would need to last for at least 113 seconds to just break even with mineral costs.
Now consider the cost of a lost SCV, 50 minerals to replace + the opportunity cost of lost mining income while the replacment SCV is built. Easily 50+20 (rough estimate, obviously again this all depends on saturation). Kill one SCV and that could easily cost your opponent between 70-80 minerals. Clearly this is still the better target than the PF. So again, if your opponent is targeting the PF I would argue it's better to keep it alive for longer less they shift their attention to higher value targets.
So realistically, unless your opponent has only one mining expo or you are trying to reduce their map control, killing PFs over other targets really makes no sense IMO.
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On March 30 2012 23:34 TheToast wrote:Wow, actually an insightful strat post, really gj! Show nested quote +So to keep up with the damage being dealt by the tanks, we need 1.67 SCVs repairing instead of mining
I think the opportunity cost should be calculated in here as well. That is, the amount of minerals per second that these two SCVs could be mining instead. Obviously that's something difficult to calculate, given that it depends on the worker saturation of the expansion, but I think you could make some assumptions here.
I've calculated the cost of repairing in terms of "keeping X SCVs occupied". This cost comes from 2 components, the resource cost of repairing and the time cost. The translation from resource cost into number of SCVs depends on saturation, the time cost, when expressed in SCVs is precise.
I could do it the other way around, express the total cost in terms of resources lost. This would make the contribution from the resource-component fully accurate but would introduce uncertainty in the cost of the time-component.
Splash damage plays a role here too, doesn't it? So after a few vollies you are actually going to start losing SCVs as well.
I'm not sure actually. A PF is rather big. Certainly, if you have SCVs on the opposite side of the PF compared to the tank, you won't get them splashed. I don't know if the point-of-impact of the tank shell is the center of the PF or the point on the building closest to the tank. This matters for splash when you do a full surround. Of course, an attentive player will focus-fire SCV clumps with his tanks when possible.
Show nested quote +
but it does show that sieging up a Planetary Fortress for an extended period can be a non-trivial drain on resources to the point where it may be more beneficial to give up the location and start building a new CC back at home
I think I disagree with your conclusion here. I think there's actually two senarios which should be accounted for here. First, the case you presented in which your army is within striking distance of PF and your opponent is out of position. While you may be able to cause them to expend resources and take SCVs off mining by hitting their PF, if the opponent is out of position it's likely there are much more valuable and softer targets nearby, such as productions structures. Hitting ebays and production structures is going to do far more damage to your opponent. I would argue even hitting the SCVs at the expo is going to do more damage than sieging the PF. So realistically, the longer your opponent is sieging your PF, the better as their are essentially wasting time they should be using to hit higher value targets.
Depends on the map and situation. Just to make an example, Korhal Compound. The opponent has his main army at his natural choke or at the Xel'naga and you circle around and siege up his fourth. In this case there are no softer targets available (as these are in the main / natural) and you may be able to get into position in such a way that you cut off access to the fourth for your opponent.
Further, even though you may be losing SCVs by defending the PF, Terran in the mid to late game are going to have abundant MULES, which means any economic damage may be somewhat mitigated as many harvetsters lost repairing the PF can be replaced with speed. Expos however, cannot be replaced easily. Further reasoning to defend the PF instead of giving it up.
So that depends on the situation. If you know that it may take some time before you can break his siege on your PF, it may be more efficient to start building a new CC in your base and fly it over once you've broken the siege rather than continuing to repair your PF.
There's another instance to consider here as well, dropping siege tanks on a nearby highground to hit the PF. Of course if you were to siege with 3-4 tanks the mineral requiremens should increase proportionally correct? So to repair a PF versus 3 sieged tanks would take the equivalent minerals and gas of 8 mining SCVs? That's a bit more substantial.
The resource cost is around 2.5 SCVs of mining per Siege Tank at +0 attack upgrade, not counting the fact that you lose resources by pulling SCVs from the mineral line to repair. The total cost would rise to around 4.2 SCVs per tank. So for 3 tanks you'll suffer a cost of 7.5 SCVs worth of harvesting and around 5 SCVs need to continuously repair.
But I still think it's minimal, given that unless the sieging player has very good micro, they are probable going to lose those tanks after a while (3 tanks by themselves could easily be cleaned up by a single banshee etc.) Losing even just one of those three tanks would be 150 minerals 125 gas. Three times the cost rate of repairs would be 4.32 minerals and 1.176 gas per second. Not accounting for destroyed SCVs or lost mining time, that would mean your attack would need to last for at least 113 seconds to just break even with mineral costs.
Now consider the cost of a lost SCV, 50 minerals to replace + the opportunity cost of lost mining income while the replacment SCV is built. Easily 50+20 (rough estimate, obviously again this all depends on saturation). Kill one SCV and that could easily cost your opponent between 70-80 minerals. Clearly this is still the better target than the PF. So again, if your opponent is targeting the PF I would argue it's better to keep it alive for longer less they shift their attention to higher value targets.
So realistically, unless your opponent has only one mining expo or you are trying to reduce their map control, killing PFs over other targets really makes no sense IMO.
Yeah, you're right. There's a reason why I posted this in Blogs rather than in Strategy, because the practical value of the results is very limited. Usually you don't want to sit stationary outside a PF just shelling it. However, it does happen sometimes and it is a very easy way to constantly damage your opponent as you require 0 APM once the siege is setup, allowing you to micro on other fronts.
The main reason why I posted this was because I saw a PF being shelled and repaired and started wondering how much of a resource-drain it actually was.
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Just answering your question of why more Terrans don't send SCVs with their mech army.
Simple answer really. Splash damage, both friendly and not friendly.
SCVs are notorious for finding their way in front of your mech units because they simply move faster than tanks or thors.
No matter what race you're against, if you're using mech there's going to be splash damage.
SCVs are not half as meaty as your mech army is, and they die VERY fast to splash making their usefuleness as in combat repair squads very limited. There are exceptions to this obviously and most of those revolve around heavy Thor compositions.
Also, repairing mechanical units that originally cost gas to build also cost gas to repair so it isn't as cheap as you're making it sound.
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This is actually really cool information. Well done figuring everything out ^^
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On March 31 2012 00:37 Vindicare605 wrote:
Just answering your question of why more Terrans don't send SCVs with their mech army.
Simple answer really. Splash damage, both friendly and not friendly.
SCVs are notorious for finding their way in front of your mech units because they simply move faster than tanks or thors.
No matter what race you're against, if you're using mech there's going to be splash damage.
SCVs are not half as meaty as your mech army is, and they die VERY fast to splash making their usefuleness as in combat repair squads very limited. There are exceptions to this obviously and most of those revolve around heavy Thor compositions.
Also, repairing mechanical units that originally cost gas to build also cost gas to repair so it isn't as cheap as you're making it sound.
But that is what APM should be spent on then! The rest of SC2 is mechanically easier so that you can micro, for example where SCVs are standing at all times. A higher skill player should be able to keep their SCVs in the right spot to repair giving him an advantage.
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On March 31 2012 00:37 Vindicare605 wrote:
Just answering your question of why more Terrans don't send SCVs with their mech army.
Simple answer really. Splash damage, both friendly and not friendly.
SCVs are notorious for finding their way in front of your mech units because they simply move faster than tanks or thors.
No matter what race you're against, if you're using mech there's going to be splash damage.
SCVs are not half as meaty as your mech army is, and they die VERY fast to splash making their usefuleness as in combat repair squads very limited. There are exceptions to this obviously and most of those revolve around heavy Thor compositions.
Also, repairing mechanical units that originally cost gas to build also cost gas to repair so it isn't as cheap as you're making it sound.
I agree to some extent when you're using a sortof mobile mech army (Thor/Helion), but if you're slow-pushing tanks, I like to keep 3-4 SCVs on a separate hotkey in the back to repair up anything that takes damage. It takes a bit of babysitting to keep them alive, especially at my level (diamond), I more often than not forget about them at some point. But I'd think the pros should have the spare APM.
As for repairing and gas-cost. True, it costs gas, but it's still less than what it would cost to rebuild the unit (25% of the build cost for a full repair). So not only is it cheaper than rebuilding, it's also much more beneficial to have that Thor or Tank up there with your push at full HP because of repair than it is to have it rolling out of the factory back home.
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I am toss, and what is this  .
Seriously though, this is something i will be looking out for in the future when i watch pro terrans. I really don't know why more pros use this advantage given to terran to combat the issue of replacing a mech army.
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EPT
