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Okay, because of the 50 character max in the title, I cannot say exactly what I want to say in the title alone.
Hello. This is my first post on this forum.
I bought Starcraft back in 98, but I have recently started playing again. I have noticed dramatic increases in my decision-making and APM since I started about two months ago. I'm not a pro, by any means (currently a D on ICCUP, with a little over 50% win ratio, half-way to D+, and my B.Net stats are similar), but I do enjoy playing Starcraft.
One thing that bugged me was trying to figure out how many SCVs to use (I play Terran) for their maximum return on investment. If I was only concerned with efficiency, I would use only 1 per mineral patch, and if I was only concerned on the speed of mining, I would use 3+ per patch (maybe more).
I wanted to determine what the best rate mining was for the minimum input. For this, I needed to run a few trials.
I tested this on a number of different maps, with a variety of numbers of SCVs. I tested with 1.0, 1.3, 1.6, 1.9, 2.2, 2.5, 2.8, and 3.1 scvs per patch.
The results I obtained were interesting. They were different than I expected, which is why I wanted to share this.
1.0 scvs/patch mined 59 minerals/scv per minute.
1.3 scvs/patch mined 54 minerals/scv per minute.
1.6 scvs/patch mined 50 minerals/scv per minute.
1.9 scvs/patch mined 47 minerals/scv per minute.
2.2 scvs/patch mined 45 minerals/scv per minute.
2.5 scvs/patch mined 43 minerals/scv per minute.
2.8 scvs/patch mined 41 minerals/scv per minute.
3.1 scvs/patch mined 41 minerals/scv per minute.
I ran 8 trials of each, and these are heavily rounded averages. I used the more precise numbers in the calculations later on.
Now, that is how fast they return minerals. Note: about 3 scvs/patch mines approximately double what 1.0 scvs/patch mines. To determine what is really best, the cost of the scvs, plus appropriate Supply Depots and the Command Centre must be taken into consideration.
Assuming 9 patches of minerals (which is very common on most currently popular maps (excluding fastest, which I do not like playing)), the costs of mining with said number of scvs is
1.0 scvs/patch is 838 minerals
1.3 scvs/patch is 1025 minerals
1.6 scvs/patch is 1150 minerals
1.9 scvs/patch is 1338 minerals
2.2 scvs/patch is 1525 minerals
2.5 scvs/patch is 1713 minerals
2.8 scvs/patch is 1838 minerals
3.1 scvs/patch is 2025 minerals
Now, you may think I'm nuts with these calculations, but I've taken into consideration that there is a supply cost to having this many scvs, as well as the cost of the command centre. Although you do not pay for the first one, IMO it is more important knowing how much an expansion will cost.
Now, comparing the rate of mining compared to the cost, it comes out as follows
1.0 scvs/patch returns 63% of its cost per minute
1.3 scvs/patch returns 63% of its cost per minute
1.6 scvs/patch returns 61% of its cost per minute
1.9 scvs/patch returns 60% of its cost per minute
2.2 scvs/patch returns 59% of its cost per minute
2.5 scvs/patch returns 58% of its cost per minute
2.8 scvs/patch returns 58% of its cost per minute
3.1 scvs/patch returns 57% of its cost per minute
This is where I thought it would be different. They are all very similar. I thought there would actually be a peak somewhere around 2.5, which is why most people argue that it is the best.
Now, considering a real-game situation:
If your opponant has his main and natural, and his mineral line is saturated (3+ workers/patch), that is a huge investment. To get roughly the same rate of mining as your opponant has, you need to have your main, natural, and 2 more expansions with 1.0 scvs/patch.
Multiple bases have some benefits, such as more space, better map control, etc. Also, if you are harassed, it does not hurt your economy as badly as if you had all of your workers in a smaller area. This also frees up your max supply better (ie. you use 40 scv, your opponant uses 60), so you can have a larger army in total. You also have the ability to make twice as many comsat/nuclear silos (for those who actually make them.....) as your opponant. You can also produce workers at twice the rate of your opponant (yes, Zerg is different, but a similar principle applies to them too, they have a maximum rate of building units in total, instead of just workers).
The main downside I see is that you are more open to attacks, because you have to spread yourself out more. Unless you can somehow contain your opponant, you will be at their mercy.
So, because of this, I believe there must be a medium somewhere. Only mining out of two bases at a time hurts in some ways, but it is easier to defend. Mining out of more bases gives you a better economy for a lower cost, and allows you to build a bigger army but you are more spread out.
Maybe this is why that "2.5 workers/mineral patch" is a rule of thumb. It is somewhere inbetween. Also, 2.5 scvs/patch allows you to transfer a few workers to a newly made expansion without hurting your current economy. That is a huge benefit.
It appears that between 2 and 2.5 workers/patch is actually ideal. It has benefits, and drawbacks compared to either extreme, but it is not as severe. Instead of continuing scv production after 2.5, you should start another CC (if you haven't already, and you probably should have).
This information also means - if you get a good containment on your opponant, FLAUNT IT. Go out and build another command centre (or 2, 3, 4+) if you can, and have only 1 scvs/patch mining. If they break containment, you've still probably had an excellent return on investment (it only takes about 100 seconds of mining at each one to pay for itself, anything after that is helping your economy in a huge way).
I've played a couple of long macro games, where this kind of mentality has either won or lost the game for me. Now I know why.
Anyways, I thought I would share this revelation with some other SC players.
As a side note - why is there no love for the Wraith? I love that unit. It is an awesome sniper unit. I typically use 6-10 every game, for economy/supply harassment, and sniping dropships, science vessels, overlords, guardians, shuttles, carriers, battlecruisers, reavers, sieged tanks, arbiters, etc..... They are so useful as snipers, to run in, hit something scary, then retreat. Is this impractical in higher levels of play?
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I think your numbers have to be wrong
1.0 scvs/patch mined 59 minerals/scv per minute.
1.3 scvs/patch mined 54 minerals/scv per minute.
1.6 scvs/patch mined 50 minerals/scv per minute.
1.9 scvs/patch mined 47 minerals/scv per minute.
2.2 scvs/patch mined 45 minerals/scv per minute.
2.5 scvs/patch mined 43 minerals/scv per minute.
2.8 scvs/patch mined 41 minerals/scv per minute.
3.1 scvs/patch mined 41 minerals/scv per minute.
you're saying that SCVs are no less efficient between 2.8 and 3.1? Also, are those multiples of 9 SCVs?
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While this is good work(assuming it was tested well), the reason such scrupulous analysis is unnecessary is because it's fine to get too many SCVS because at any given moment, in any given game, you will be planning on expanding soon and then you can transfer scvs to your new expansion.
The exception I suppose is if you are developing an all in timing attack BO and you are sure you won't be expanding.
Still nice to see this stuff.
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appreciate the arduous process you went through.
tho its very likely youd have to do this some more times to truly sell anyone on the finding.
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Sick first post man, good work.
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As for the difference between 2.8 and 3.1 - those are rounded. It is 41.2 and 39.7 respectively. These are extrapolations from the graph of logistic equation of best fit of the points plotted (which were obtained through calculations of the results). II figured that the logistic equation would be the best choice, because there will be a maximum rate that the minerals can be mined at. 3 scvs/patch is nearly at the limit. A logistic equation does match the points well.
The reason I showed by the 0.3 incriments is that they were generally closer to whole numbers, and I wouldn't have to clutter the post with decimals.
I found that there is little difference for the rate of mining/cost between 1 per patch and 3 per patch. I did not expect this. However, having more expansions means that your economy will continue steadily for a longer period of time, whereas your opponant will have to build at a new location to continue mining.
In a real game situation, there are a lot more variables. At least I know that whether I sit and turtle in a single base, I can keep up if my opponant has two. At least for the time being.
Yes, more testing would be needed before it would be conclusive, but it gave me enough information to make my decision on it.
"Knowledge is useless unless you pass it on." That's a quote that my High School math teacher taught me.
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On March 22 2009 14:34 lMPERVlOUS wrote:
In a real game situation, there are a lot more variables. At least I know that whether I sit and turtle in a single base, I can keep up if my opponant has two. At least for the time being.
Interesting work overall. I've examined this statement for a minute or two, trying to figure out what you meant. Won't your opponent having 2 Command centers (or Nexus' or Hatches) quickly enable them to outproduce you in peons? I can only see this statement being true of zerg, who are capable of powering out the same number of drones from one base as a two base person.
However, this also does not account for the linearity of vespene, which ensures that you will be unable to maintain parity with an opponent who has one expansion additional to yours. I guess I'm basically questioning your statement that turtling enables an economic equality beyond a very brief one. And even then, with the way maynarding works, they will likely being to out produce you within a minute, as they should have an equal number of scvs/probes to you.
(Also, is there a point beyond which there is no return on investment for additional miners?)
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conclusion: more expos -> zerg is the awesomest race ^_^
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nice work. maybe also take consideration that a base saturated with miners takes heavier loss from storm/reaver/siege/lurker (anything with splash dmg ) drops. so more all the more reason to expo all over if you can.
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Yes, if your opponant has two Command Centres to your one, they can outproduce your workers quickly, which puts you into a new level of trouble. Pumping out workers is a short term solution to being contained by your opponant. If you don't break it, you're going to be out-macro-ed later on.
And this does not take into consideration the gathering of Vespene. This hurts your ability to make units higher up in the tech tree, as well as making necessary upgrades.
It would only last a few minutes at maximum, before your opponant starts to completely outproduce you. As I said, it is "for the time being".
By the look of the curve, there is very little return on investment after 3.7-4.0 scvs/patch, basically a negligible amount. This is based on the extrapolation of the curve though, so I do not know exactly. A logarithmic curve will approach a limit, but never reach it. This makes sense for this situation, because the minerals can only be mined so fast, it has a limiting factor to it.
Bah, Terran is by far the most awesomest race. We've got tanks, guns, and BATTLECRUISERS (not that I've used them in more than 1 game, and even then.....). Plus, we've got COMSAT, allowing us to check out anything we want. What is cooler than that? NOTHING!!!!!
Yea, I did cover that (under the "less affected by a harassment" comment I made in the original post). However, it is more likely that you will be unable to stop a harassment.
It is a tradeoff - yes, you are less affected, but it is more likely to happen. It really seems that a balance of 2.0-2.5 scvs/patch is ideal.
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a logistic equation would be a terrible fit for this data if you think about it logically. If it gets to 4-5 scvs/patch, it's clearly going to be much less... it's not going to stay at some maximum
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Okay, yes, a logistic equation is a horrible fit for the "rate per scv", but the actual rate per scv is a logistic equation divided by the number of scvs.
The "rate in total" is a logistic equation. I was not very clear about that. The "rate in total" has a limit to how fast it can be mined.
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There is already a long project result about this on Chinese Forums
I think somebody can translate it to English
The result is workers = minerals patch x 3 - 1
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On March 23 2009 02:52 emucxg wrote:
The result is workers = minerals patch x 3 - 1
thanks, I'll remember this
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workers = minerals patch * 3 - 1
I found that even when you went to 3.1 scvs per mineral patch, the rate of return of minerals still increases.
I compared the cost of the system to the rate of return, and I found that the ideal number of workers is actually at 1.0 per pach (but I do not know how it would work with less, my feeling is that it is actually equal to 1.0 per patch).
Looking at real game situations, that is impractical, because it is more difficult to defend, and it takes time to build an expansion. Also, having extra workers at a mining area is not a bad thing.
However, there are benefits to it having a lot of expansions.
For instance - I played an EPIC game of TvT on Python a while ago. I put a fairly early contain my opponant, and limited him to 3 bases (I destroyed his fourth). I proceeded to make an expansion at every spot save 1, and I only had at maximum 1.0 scvs/patch at any of them (other than at the very beginning when I only had 2, I had close to 3.0 per).
I had 8 small bases to his 3 big ones. We both had a similar amount of SCVs mining at any given time (I actually had less). I had a larger army, and I was able to recover my losses faster.
The whole game led to him trying to move out with his army, or he would harass me and kill off my expansions, only to have me rebuild them. I had units all over the battlefield, enabling me to shoot down his Dropships before they could do too much damage, and also it allowed me to react to where he was attacking, allowing me to push him back. I lost a lot more units than he did during the game.
Eventually he mined out, and I was able to stop him from expanding, and when his final units died, I officially won the game.
This game is what spiked my interest in the "ideal mining" subject. I had a better economy, I was able to sustain it longer, and I was able to have a larger total army, because I spread myself out more. For a large portion of the game, I had 10 factories pumping units constantly. At one point, I had 12 factories pumping units. He made about as many factories, but I killed most of them early on, and he did not have more than 6 pumping units at any given time.
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Knowledge is useful if you can use it!
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Haven't figured out what ur formula is
May be follow the tactic idea is the most important thing, you can have that much scvs if you want to make a rush.
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I did some tests myself some time back to figure out how many SCVs were necessary to get maximum out of an expansion. Never used it to anything because in a game you always produce SCVs so when you expand you can move like 24 SCVs there straight away.
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On March 23 2009 20:23 rrsszzcc wrote:
Haven't figured out what ur formula is
May be follow the tactic idea is the most important thing, you can have that much scvs if you want to make a rush.
I don't have a formula. I tried to make one, but there really isn't one.
Basically, no matter how much you spend on your economy (until about 3.0 workers/patch), you get a similar return on investment.
The most efficient setup is to have 1.0 workers/patch, and you can have more units because you use less workers to keep up the same economy. As Terran, you gain the ability to use more Comsat or Nukes. As Zerg you gain the ability to produce units faster. Your economy is more stable against harassment, because it hurts a smaller portion of your economy than it would if you hit one of your opponants expansions. You can also outlast your opponant, because your opponant will mine out quicker.
However, you are more spread out, which means you are more vulnerable to harassment and counterattacks. Also, it takes longer to see a return on investment than simply adding SCVs at each current expansion.
This is why I believe that there is no "ideal" number of workers - it depends on the map, you, your opponant, and other factors. Knowing that you get a similar return on investment, you make your own decision on what is better - 1.0 workers/patch, 3.0+ workers/patch, or something inbetween.
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This is just off memory. I read a post here some time last year or the year before that (back when I lurked and didn't even have an account) of a guy trying to figure out the same thing. What he came to was 5 scvs/3 min patches. I don't remember what they were, but I do remember his arguments were valid and sound. Of course, he said that you should always keep producing for when you get an expo, but for max efficiency it's 5/3.
This is the number I've gone by if I ever get into late game. Maps with 10 min patches get 17 scvs, and since my multitasking isn't too great I'd just set rally points from other cc's there and queue up 16/17 scvs.
Also, probes mine a teensy bit faster than scvs. Dunno if this would factor into your calculations or not.
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Put data into excel. Run regression and find variance!
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well you still have to build more to transfer to other bases, and who actually has time to check how many SCVs are in each base?
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On March 24 2009 00:37 Garnet wrote:
well you still have to build more to transfer to other bases, and who actually has time to check how many SCVs are in each base?
Unless you are a pro, you dont count your workers. (I remember that they count their workers and not overmake them)
And i just pump workers no-stop until i think i have enough of them, you'll need extra workers to transfer them into new expos anyway
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On March 22 2009 14:09 inReacH wrote:
While this is good work(assuming it was tested well), the reason such scrupulous analysis is unnecessary is because it's fine to get too many SCVS because at any given moment, in any given game, you will be planning on expanding soon and then you can transfer scvs to your new expansion.
The exception I suppose is if you are developing an all in timing attack BO and you are sure you won't be expanding.
Still nice to see this stuff.
This isnot as useless as you might think, because this tells you how many SCVs you want to leave behind after a maynard transfer. In other words, if you are getting ready to expand, you should build SCVs to the optimal number and then add however many SCVs you want to have transferred to the expansion once it goes up. Then stop.
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On March 23 2009 23:17 lMPERVlOUS wrote:Show nested quote +On March 23 2009 20:23 rrsszzcc wrote:
Haven't figured out what ur formula is
May be follow the tactic idea is the most important thing, you can have that much scvs if you want to make a rush. I don't have a formula. I tried to make one, but there really isn't one. Basically, no matter how much you spend on your economy (until about 3.0 workers/patch), you get a similar return on investment. The most efficient setup is to have 1.0 workers/patch, and you can have more units because you use less workers to keep up the same economy. As Terran, you gain the ability to use more Comsat or Nukes. As Zerg you gain the ability to produce units faster. Your economy is more stable against harassment, because it hurts a smaller portion of your economy than it would if you hit one of your opponants expansions. You can also outlast your opponant, because your opponant will mine out quicker. However, you are more spread out, which means you are more vulnerable to harassment and counterattacks. Also, it takes longer to see a return on investment than simply adding SCVs at each current expansion. This is why I believe that there is no "ideal" number of workers - it depends on the map, you, your opponant, and other factors. Knowing that you get a similar return on investment, you make your own decision on what is better - 1.0 workers/patch, 3.0+ workers/patch, or something inbetween.
Sure there is no ideal number, but I always make it depend on the supply used or a certain time period such as start mechanics push.
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In most of the maps, the formula may be Amount of scv = amount of minerals multiplied by something,then + or- something For the best invest-returning ratio.
Although it really depends.
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Hey! This is a very interesting thread on ideal mining. I am a College student and I am currently working on an economics assignment regarding mineral mining in Starcraft. I have decided to do some research on the internet first and have coincidentally found this great thread and this equally great community (P.S. I was really ignorant about the existence of teamliquid bcos I started SC like.... 4 weeks ago!? LOL!? Srry 'bout dat)
I have collected data through in-game experiments and they are VERY similar to yours posted here. However I was not quite convinced with your half-way-done explanation regarding the need for 2 to 2.5 workers / mineral patch. After the end of my assignment and having collected data from in-game experiments, i THINK i have found a explanation for having that amount of workers / mineral patch by using the Short-Run Average Cost (SRAC) idea, which has been accepted by my economics tutor. I am SO EAGER to post my findings bcos I feel this might be quite a contribution to this community (perhaps? :p)....
glhf!
(pssstt.... the notice on bumping this old thread made me feel like i'm not suppose to be here, especially with the 'you better have a good reason' warning.... LOL!)
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Oh and yes.... I am not able to post a new thread due to the trail period of 3 days....
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some chinese did a research of ideal mining, i hope this helps u
credit playsc.com
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luckily i read chinese.... cool.... he investigated into the marginal increase of minerals gathered per worker. Thx. These data are useful in confirming my own experimental data. But the outcome of these data are not explained (in economics).
great job... he used the uncertainty of measurement.... O.O
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good luck with your findings, i'm eager to hear what you come up with
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On March 23 2009 03:31 lMPERVlOUS wrote:
workers = minerals patch * 3 - 1
I found that even when you went to 3.1 scvs per mineral patch, the rate of return of minerals still increases.
I compared the cost of the system to the rate of return, and I found that the ideal number of workers is actually at 1.0 per pach (but I do not know how it would work with less, my feeling is that it is actually equal to 1.0 per patch).
Well, the normal 2.5-3 SCVs per patch saturation simply approaches the problem from another angle - as the number of SCVs increases, the rate at which the patch is being mined approaches 100%, therefore giving you more resource. However, you're interested in the rate at which the individual worker mines. If you want to achieve optimal results for that, yes, the optimal number is exactly 1 per patch since the next worker added will lose mining time due to wander because all patches are already taken. Having a high amount of bases however, is mostly dictated by need for gas - which is why Zergs get so many bases with relatively low drone counts on minerals - they just need gas that much more. Incidentaly, this situation replicates itself in TvT in nearly the same manner once you go past 3 bases total - you need more gas for production as you already have tons of spare minerals.
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However, you're interested in the rate at which the individual worker mines. If you want to achieve optimal results for that, yes, the optimal number is exactly 1 per patch since the next worker added will lose mining time due to wander because all patches are already taken.
You are right that 1 worker / patch gives the most mineral gathered for each worker, but that is not our aim. The aim is to find the way to gather the most amount of minerals in the shortest time with the least cost. That IS the idea of ideal mining. The stats of how much each worker mines according to how many workers / patch are just data that are used to derive the answer for our main question.
However, do not be confused. 1 worker / min patch may give you the most minerals gathered by each worker but it does not let you gather the most minerals in the shortest time with the least cost!
good luck with your findings, i'm eager to hear what you come up with
Thanks! That will be 12 hours more...
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Yes, I am also interested in hearing followup from this.
One thing though - it's complicated..... There really may be no "ultimate" or "right" answer, because of all kinds of factors:
Benefit/Cost ratio
Effect on supply cap
Ability to defend
Linear production of vespene
Point in time of the game
Number of available expansions
etc.....
I'm just glad that someone is finding some use from this. I've learned a lot about the economies in Starcraft, and I like Zerg best because of their flexible economy. This information helped lead me to switching to Zerg.
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btw i've posted a new thread so do check it out... http://www.teamliquid.net/forum/viewmessage.php?topic_id=109458
One thing though - it's complicated..... There really may be no "ultimate" or "right" answer, because of all kinds of factors:
Yes.... you are so right..... the most efficient number of workers in theory does not reflect the best way to do things in a real game bcos of many different circumstances. But we can take the ceteris paribus assumption in THEORY 
Sadly I did not include zergs in my research but, again, IN THEORY, using the Short-Run Average Cost (SRAC) curve, the zergs need less workers to be efficient as the hatchery is less costly. More in the thread linked above.
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Very informative, I'll keep the workers=mineral patches x 3-1 in mind.
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