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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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EPT
