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Background
Most TvP games today feature the Terran going for a 1 Factory, 2 Factory or 1 Factory & 1 Starport opening. The standard build orders for the 1 Factory build try to maximize the mineral mining rate for faster CC and the like and as such tries to optimize the amount of SCVs on Gas in the early phase. Anything more agressive like 2 Factory or 1 Factory & 1 Starport requires more gas and thus 3 SCVs on Gas all the time after its completion. A regular Protoss player exploits and is most often able to read the Terran on how he will tech depending on the amount of SCVs on Gas.
Afterall by the time the second Factory will go up or a Starport is being built proper marine and SCV micro can deny the scouting information, but he will still know something fishy is going on if he saw 3 SCVs on Gas and will prepare accordingly.
The question is, how many minerals do you gain from putting SCVs back to minerals and then back on gas. And is there any more "optimal" way of managing your SCVs?
Definitions
* We let t denote the ingame Starcraft time-unit that is independent of the game speed and s denote real time in seconds that is dependent of the game speed.
The following holds approximately at the fastest game speed: 1 s = 1.6 t or 1 t = 0.625 s equivalently. Henceforth we will stick to the ingame time unit.
* Let m/t denote the gathering rate of minerals per time-unit and m/s the gathering rate of minerals per second.
Assuming that any worker could have 0 travel path from the CC to a mineral patch the maximal gathering rate is then 1.5 m/t or 1.5*1.6 m/s = 2.4 m/s. The reality is different and as it turns out; at the standard mineral distance one SCV will gather 0.68 m/t which is about 45% of the maximal mining rate one mineral patch can deliver.
Data
The data is taken from a future post of mine that will discuss optimal mining in detail. It represents the amount of minerals mined per time unit on a "general" 9 mineral patch main @ Python. I will not go into detail of what the different data represents or how I obtained it but will rather just present the results.
Also note that the almost horizontal section around 13 (1.5 SCVs per patch) to 23 (2.5 SCVs per patch) is due to worker wandering. Also note that 1
This represents the marginal benefit to the mining rate of adding one SCV. For example if we have 12 SCVs mining then our mining rate would be 8.1 m/t as seen in the upper graph. Adding an additional SCV would increase this rate with about 0.8 to 8.9 m/t. Which is the mining rate of 13 SCVs.
One can readily see that you gain an negible amount mining by adding SCVs when you have 12 to 22 SCVs mining. And you gain the most between 0 to 9 and then 22 to 26. After 26 you've fully saturated your mineral patches and gain nothing from additional SCVs.
Mechanics
Max Mineral Mechanic: (16 Fac - 1 Gas)
The current widely used mechanic consists putting 3 SCVs on gas at the rafinery completion and then building a Factory on 16 supply. At 16 supply you will have 1 SCV scouting, 1 building another supply and 1 on gas (removing 2). Then at 20 supply when the Factory is complete you will have 17 SCVs mining and you transfer 2 SCVs to gas again, totalling you 15 mining SCVs.
Max Gas Mechanic: (16 Fac - 3 Gas)
This consists of always having 3 SCVs on gas and thus only having 11 mineral SCVs at 16 supply.
Optimal Mechanic: (16 Fac - 1 Gas, 17 - 2 Gas, 18 - 3 Gas)
The difference between this and the mineral mechanic is that you take away 2 SCVs on gas at the start of the Factory but then each new SCV built is being put on Gas instead of on minerals up to 3 SCVs on gas.
Results
Max Gas vs. Max Minerals.
Max Minerals has a total mineral gain of 33.2 + 17 + 0.2 + 3.1 = 53.5
Max Gas vs. Optimal
Optimal has a total mineral gain of 33.2 + 16.9 + 0 + 0 = 50.1
Conclusion
The "Optimal Mechanic" is obviously optimal because not only does it give you more gas if you would decide to change gears and change your build order instead of say expand but also does it allow you to fool your opponent into thinking you're going for a gas heavy build, or at best leave him in the dark.
Any comments are appreciated!
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A terrible terrible day for protoss.
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if i understood this right, taking 2scvs off gas, until factory is done only gives you a plus of 3 minerals in comparison to your optimal solution? i find that sort of hard to believe, that would mean that the scvs that are built in the time the factory is made, only mine 3 minerals until its done?
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Wurzelbrumpft. That's correct. The reason is worker wandering in SC.
Ideally one SCV will mine one mineral patch at 45% capacity. Meaning two SCVs will mine one patch at 90% capacity, but not really because of wandering. This means, whenever one SCV arrives at a busy patch he won't always wait for the other SCV to finish but rather go to a nearby patch and try to mine it. At some SCV populations this is even amplified as you can see in the first graph around 13 to 22 SCVs. There wandering is really high and those additional SCVs spend much of their time wandering instead of mining. In fact you can see how many mineral patches at these populations are idle not being mined on.
Edit: Of course these 3 minerals won't always be 3 minerals but on average. Sometimes it can be less, sometimes more.
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GrandInquisitor
New York City13113 Posts
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Yeah, but what about if you micro all your SCVs individually to minimize wandering? 
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This was interesting, can you do it for P too? IE the economic impacts of various scout times and or build orders?
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A great read for when I occasionally screw around in TvP.
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I liked this post
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intrigue
Washington, D.C9934 Posts
pretty nifty! the limiting resource in the speed of standard 1fact cc the minerals though, so though it's less efficient it is probably better in the long run (getting your nat up faster) to do it the standard way. the timings of this could definitely confuse your opponent though.
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I would just like to know the number of trials that you took to produce the mining rate vs no. scv graph data. (I know you will post it later, but I cannot wait xd).
Thanks.
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Muff2n: I mined the 9:clock main with said number of SCVs for 2 queued battlecruiser building time. That is 2*133 time units. Then I used http://www.teamliquid.net/forum/viewmessage.php?topic_id=92971 to see how the 9:clock compares to other mains and factored that in. The reason why I used battlecruisers is that in general using a timer is inaccurate I've found and watching replay time likewise. The only accurate and reproducable result I could find was the battlecruiser's building time.
Intrigue: The mineral loss is negible on average (3 minerals)
Xe(-_-)ro: The races have different gathering rates because of different acceleration and mining animation. Roughly one worker on one patch has for P: 0.72 m/t, Terran: 0.68 m/t and for Z: 0.70 m/t. So, roughly, what is said above holds for protoss too however there are small subtle differences. Assuming it takes 60 time units to go from one main to another on a map the costs for scouting as protoss at 9 supply is 0.72*60 for one main, 0.30*60 for the other main, 0.11*60 for the third. At 13 supply it is 0.30*60 then 0.11*60 then virtually 0*60.
okum: That's really hard in practice.
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wow thanks, very interesting read
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great read, now i can fool my protoss opponents even more
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Well I have been keeping putting scvs back on gas once I have 13. If my bo needs to fast cc anways, they I'll wait until when i dump all 3 scvs back on minerals I will nw have a total of around 18. Then any more that pop get gas again. Now I dont know how much this has been 'earning me' but I do notice that less scvs wander at the start, so it does have a feeling of increased total resource mining.
What seems a little odd to me is that I need 27 scvs to max out a mineral patch! 3 to 1, I always believed it was 2:1.
I would be very interested if you could repeat the data takings 1-2 more times for comparison.
But thanks for this info.
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I don't get it 
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nice work. i didn't know it was just 3 minerals. i'll be trying your optimal mechanic from now on.
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On July 19 2009 18:23 Muff2n wrote:
Well I have been keeping putting scvs back on gas once I have 13. If my bo needs to fast cc anways, they I'll wait until when i dump all 3 scvs back on minerals I will nw have a total of around 18. Then any more that pop get gas again. Now I dont know how much this has been 'earning me' but I do notice that less scvs wander at the start, so it does have a feeling of increased total resource mining.
What seems a little odd to me is that I need 27 scvs to max out a mineral patch! 3 to 1, I always believed it was 2:1.
I would be very interested if you could repeat the data takings 1-2 more times for comparison.
But thanks for this info.
What I didn't explain in this post is that wandering depends on how many mineral patches you have. The more mineral patches clumped together the higher wandering. Since all mains have 9 tight mineral patches it makes no difference. However if you have an expansion with 8 mineral patches in groups of 4 then you will attain max at 2 SCVs per patch. Because then you will have about 93% of the max and no wandering.
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O.o so for 9 you need 3x as many (root 9), for 4 you need 2x as many (root 2) and therefore logically you need root 1 for a lone patch which is ... 1x. Damn! Thought I was onto something 
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I didn't actually manage to read this until now.
Great analysis and report Sub!
Depending on what build I do I would take SCVs off accordingly, so I have tried this way before, but I didn't know it was optimal regardless of your factory followup. Thanks.
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I very well could be wrong, but it seems like some unnecessary data was presented to merely confuse us.
Such as why did you give us the ingame "time" compared to actual seconds? What relevance does this actually hold? Instead you just assign them both variables, causing that many more things for the reader to remember, and instead making it more likely for the reader to skip over the actual math and just accept your conclusion.
A lot doesn't make sense (to me at least, and I very well could be wrong as stated at the beginning of my post). Such as how do you explain that the marginal benefit from an additional SCV at 12 --> 13 is 0? Mathematically, it would mean that the mineral lines are saturated at 13, but all of a sudden mineral rate actually increases again? Wandering has no relevance concerning these details.
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On July 20 2009 18:45 FabledIntegral wrote:
I very well could be wrong, but it seems like some unnecessary data was presented to merely confuse us.
Such as why did you give us the ingame "time" compared to actual seconds? What relevance does this actually hold? Instead you just assign them both variables, causing that many more things for the reader to remember, and instead making it more likely for the reader to skip over the actual math and just accept your conclusion.
A lot doesn't make sense (to me at least, and I very well could be wrong as stated at the beginning of my post). Such as how do you explain that the marginal benefit from an additional SCV at 12 --> 13 is 0? Mathematically, it would mean that the mineral lines are saturated at 13, but all of a sudden mineral rate actually increases again? Wandering has no relevance concerning these details.
If you'd read the thread a bit more careful, you see the answers are there.
He uses the ingame time because, a follow-up message says, any other time measures were found to be too inconsistent. Is there another reason why he used ingame time? No, you're reading too much into it.
He explained the marginal benefit by worker wandering. It is also explained why. Why don't you explain why wandering would not explain this phenomenon? And yes, it is apparently a phenomenon, you can test it yourself as well and show your findings, perhaps in this same thread. It'd be great to have more people come up with the same numbers, then we know this for sure-er. Or if you get different numbers, that would be interesting too.
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On July 20 2009 18:45 FabledIntegral wrote:
I very well could be wrong, but it seems like some unnecessary data was presented to merely confuse us.
Such as why did you give us the ingame "time" compared to actual seconds? What relevance does this actually hold? Instead you just assign them both variables, causing that many more things for the reader to remember, and instead making it more likely for the reader to skip over the actual math and just accept your conclusion.
A lot doesn't make sense (to me at least, and I very well could be wrong as stated at the beginning of my post). Such as how do you explain that the marginal benefit from an additional SCV at 12 --> 13 is 0? Mathematically, it would mean that the mineral lines are saturated at 13, but all of a sudden mineral rate actually increases again? Wandering has no relevance concerning these details.
Well the time compared to seconds discussion was added so people would have a grasp of how many minerals per second those minerals per time unit correspond to. It is quite irrelevant for the result.
12 -> 13 isn't 0 it is almost as good as 11 -> 12. Mathematically it does not mean that the mineral lines are saturated at 13 because then the average mining rate is only about 9 m/t (or 9/9 m/t = 1 m/t per mineral patch if you wish) while the maximal gathering rate is 13.5 m/t (or 13.5/9 m/t = 1.5 m/t). The marginal benefit may very well be close to 0. Note it is not 0 over time but over, say, a build time of 1 SCV the additional SCV will bring close to 0 minerals in average. This is simply because of wandering. If you add additional SCVs to your mineral line they will start wandering. It's simple as that. As you can see the mining rate starts climbing up at around 23 SCVs which means that wandering is large enough for those "wandering SCVs" to efficiently pick up idle patches.
You can test these facts out yourself and feel free to do so. Thanks for the criticism, more of that!
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If a mod could either hard delete this or ban users with a terran icon from reading this thread that would be great .
jkjk this is a good analysis I didn't know that there was only a 3 mineral difference, very interesting
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This is an amazing idea and really helpful. Hopefully it gets added to liquipedia.
really nice work
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Each spot mines slightly differently on python, and even within that, there are faster patches at each base, there was a post about this a while ago. How many times did you test this? And isn't the main purpose of scv off gas to have more workers when the CC/FE is done for transfer? You don't need the extra gas anyways.
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On July 16 2009 23:41 okum wrote:Yeah, but what about if you micro all your SCVs individually to minimize wandering?
I guess this is not general knowledge but people already micro them into empty patches. So in a way i guess people already knew that doing that would get them more minerals also a bit of common sense i guess ( if they mine more they get more minerals...) This also works for all races obviously.
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I believe the y axis of your graph should not be labeled dm/dt but rather marginal dm/dt or something like that. As I understand it, the reimann sum of your graph should end up resulting in that quantity you call dm/dt, correct?
I found this confusing on first read simply because you referred to how the dm/dt remains roughly horizontal, I was confused by the plot, which, obviously, was not horizontal, though it was labeled dm/dt. Whatever you choose to label this marginal dm/dt which is really the derivative of the function (dm/dt) with respect to the number of scvs ( d(dm/dt)/d(scvs) ), it should not ALSO be dm/dt.
Other than the notation, I found the results of your paper (yes, i called it a paper, that's how good I thought it was) both academically exciting and practically applicable.
TL peepz are geniuses
edit: Actually, now I see what you did there. The horizontal section referred to the previous plot. Sorry about that.
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Shenanigans!
1s = 1.6 t.
Saturated patch
1.5 m/t * 1.6 t / 1s > 1 > 0.9375 m/s
Your mineral rate per second should increase on fastest vs fast or normal or whatever.
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This is all very good in theory, however most of the progamer terrans I watch still pull scvs off gas when they fast expend:O
I guess it's a Korean thing.
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On July 24 2009 03:49 CharlieMurphy wrote:
Each spot mines slightly differently on python, and even within that, there are faster patches at each base, there was a post about this a while ago. How many times did you test this? And isn't the main purpose of scv off gas to have more workers when the CC/FE is done for transfer? You don't need the extra gas anyways.
If you read my main post I actually refer to this post you speak of. I take an "average" efficiency of the mineral patches on the 9-o-clock patch and multiply this with a constant to get an average over all Python mains.
I tested each odd SCV count twice as is said in the main post.
On July 24 2009 04:32 GreEny K wrote:Show nested quote +On July 16 2009 23:41 okum wrote:Yeah, but what about if you micro all your SCVs individually to minimize wandering? I guess this is not general knowledge but people already micro them into empty patches. So in a way i guess people already knew that doing that would get them more minerals also a bit of common sense i guess ( if they mine more they get more minerals...) This also works for all races obviously.
My "data" assumes that all workers are uniformly distributed among the patches and not biased towards any single patch. That is, say you remove some SCVs in a real game on gas then you end up with two free patches, then one of course micros idle SCVs onto these patches. This is an assumption I tacitly make.
On July 24 2009 06:15 Eggplant wrote:I believe the y axis of your graph should not be labeled dm/dt but rather marginal dm/dt or something like that. As I understand it, the reimann sum of your graph should end up resulting in that quantity you call dm/dt, correct? I found this confusing on first read simply because you referred to how the dm/dt remains roughly horizontal, I was confused by the plot, which, obviously, was not horizontal, though it was labeled dm/dt. Whatever you choose to label this marginal dm/dt which is really the derivative of the function (dm/dt) with respect to the number of scvs ( d(dm/dt)/d(scvs) ), it should not ALSO be dm/dt. Other than the notation, I found the results of your paper (yes, i called it a paper, that's how good I thought it was) both academically exciting and practically applicable. TL peepz are geniuses edit: Actually, now I see what you did there. The horizontal section referred to the previous plot. Sorry about that.
If you speak of the lower graph then it is correct that it's not the precise derivative of the m/t graph but just marginal m/t. Which should properly be labled as you say d(m/t)/d(SCVs). The first graph is just m/t whose Riemann sum is the amount of minerals mined during the time in the x-axis. Afterall, the x-axis has SCV as label and since you have constant SCV production it's just is t multiplied by 20, the building time of an SCV. So in short, m/t remains "roughly" horizontal on the first graph and d(m/t)/d(SCVs) remains roughly around 0 in the corresponding interval as you can see on the second graph by the big drop in the middle. I do agree that the notation is kind of faulty here but I don't believe most TL members are mathematicians so I don't want to confuse them with unnecessary notation.
On July 24 2009 11:30 igotmyown wrote:
Shenanigans!
1s = 1.6 t.
Saturated patch
1.5 m/t * 1.6 t / 1s > 1 > 0.9375 m/s
Your mineral rate per second should increase on fastest vs fast or normal or whatever.
I don't see what 1.5 m/t * 1.6 t / 1s should mean, or what you're trying to show. And yes the mining rate is of course fastest on the fastest speed.
Thanks for the comments!
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Here's an example, stasis last 70 t, or 70 /1.6 = 43.75 s (70 t *1 s/ 1.6 t).
If you stasis one saturated patch, they lose 70 t * 1.5 m/t=105 m
If you stasis one saturated patch on fastest speed, they lose 0.9375 m/s * 43.75 s = 41 m
So they lose less minerals in one stasis on fastest as opposed to normal speed, according to your numbers.
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On July 25 2009 03:50 igotmyown wrote:
Here's an example, stasis last 70 t, or 70 /1.6 = 43.75 s (70 t *1 s/ 1.6 t).
If you stasis one saturated patch, they lose 70 t * 1.5 m/t=105 m
If you stasis one saturated patch on fastest speed, they lose 0.9375 m/s * 43.75 s = 41 m
So they lose less minerals in one stasis on fastest as opposed to normal speed, according to your numbers.
Oh yes. Of course. The wrong think in my post was 0.9375 m/s doesn't equal 1.5 m/t. It should be 1.5 m/t = 1.5*1.6 m/s = 2.4 m/s. I'll change it. It doesn't change anything in the main post, however, since all the calculations are based on m/t. Thanks for being observant!
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