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Optimal Number of Peons to Maynard
by Richard “richlol” Serrano
To request the .doc file containing a better version of these results, send your request to:
serrano@berkeley.edu
Objective
The goal of this paper is to find the optimum number of peons to transfer (maynard) from a main base to the nearest expansion.
Method
+ Show Spoiler +I created a single player instance where I had 2 Terran command centers—one in the main base with 9 mineral patches and one at the nearest expansion with 7 mineral patches—and a select number of SCVs to begin with sitting next to the main base’s command center. These SCVs are in the “Stop” command next to the minerals they are going to mine. The number of SCVs present next to the main command center is equal to the number of SCVs most commonly found at the event of a maynard transfer. Through various replays and opening build orders, i.e. Stylish’s terran BOs and vods, the most common number of SCVs was averaged to 27, so I will be using this number. The map used was Python 1.3 at the 9 o’clock position. The nearest expansion is north of it. The distance between the command centers is 25 tiles, or if using buildings as measurement, 8 and 1/3 command centers.
To determine the effectiveness of the maynard transfers, the net gain of minerals will be recorded in 30-second intervals up to 2 minutes. The control group will be an instance where 0 of 27 SCVs will be transferred to the expansion. Different numbers of SCVs will be transferred in every trial, such as 1 SCV transferred, 2 transferred, 3…to 27 SCVs max. Three trials were run for each number of SCVs transferred and the results were then averaged for each trial for more precision in the results.
27 SCVs were lined up next to the mineral patches they are going to mine. To increase consistency between trials and minimize error, game speed was reduced to the slowest speed while distributing SCVs to mine at time=0. SCVs were equally distributed between the mineral patches during each trial as quickly as possible grouping them in 9 groups of 3 with each group going to a different mineral patch. For trials with transfers, respective SCVs were hotkeyed and sent to unique mineral patches at the expansion immediately after sending SCVs at the main base to mine. As soon as the last SCV was sent to the expansion, game speed was brought to the fastest setting and the stopwatch simultaneously began to record time.
No additional SCVs were produced during these trials.
Results
+ Show Spoiler +I will revise this table so that it's accurately formatted later on. I hope you can still see the parameters. There is the time elapsed (seconds) on the top (30, 60, 90 ,120). On the left side is the number of SCVs transferred. The other numbers are the corresponding mineral gains for respective SCV transfers at those recorded time intervals. SCVs Transferred Elapsed Time (Seconds) --30----60----90----120 0 516 1056 1600 2200 1 520 1056 1608 2184 2 596 1152 1704 2258 3 568 1162 1710 2352 4 554 1152 1760 2384 5 584 1240 1912 2608 6 584 1224 1860 2560 7 600 1297 1992 2712 8 624 1284 1990 2712 9 612 1342 2081 2784 10 600 1296 2016 2774 11 624 1372 2106 2824 12 600 1344 2109 2792 13 610 1312 1820 2680 14 584 1200 1750 2480 15 545 1145 1644 2436 16 524 1008 1554 2298 17 516 1015 1506 2256 18 516 1010 1448 2136 19 490 985 1465 2108 20 448 908 1407 1956 21 434 910 1416 1934 22 418 850 1398 1884 23 414 865 1380 1844 24 380 838 1368 1808 25 364 840 1324 1820 26 346 810 1316 1810 27 280 740 1240 1770 Diagram 0: Minerals Mined per SCVs Transferred at 30, 60, 90, and 120 seconds Diagram 1: Minerals Mined at 30 Seconds per SCVs transferred Diagram 2: Minerals Mined at 60 Seconds per SCVs transferred Diagram 3: Minerals Mined at 90 Seconds per SCVs transferred Diagram 4: Minerals Mined at 120 Seconds per SCVs transferred
Analysis
+ Show Spoiler +From the data and the graphs, we can see that the minerals mined reaches a peak when about 12 SCVs are transferred to the expansion. This number is even more definitive as time progresses and we can see more evident differences in minerals (diagram 4). 12 SCVs transferred is significant because this number surpasses the ratio of the SCVs currently at the main base. With 12 SCVs transferred to the expansion with only 7 mineral patches, this is a ratio of 12/7 or 1.714. At the main base, only 15 SCVs remain for the 9 mineral patches, this is a ratio of 15/9 or 1.667. In this study, there were 27 SCVs and 16 mineral patches (9 patches at main and 7 at expo). To spread the SCVs equally, we divide SCVs by the number of patches: 27/16=1.6875. To find how many SCVs we want to transfer, simply multiply the number of mineral patches at the expansion by this ratio: 7*1.6875=11.8125, or about 12. The data and the graphs support this finding. Transferring any more than 12 SCVs will theoretically decrease overall effectiveness because it is transferring an amount that surpasses what is expected to be efficient; that is, the highest efficiency is achieved when there are equal SCV to mineral ratios per patch.
What this means is simple: just like you would spread your SCVs out equally amongst all your mineral patches in your main base, similarly, to reach maximum mining efficiency when maynarding, you want to spread out all your SCVs equally among all your patches including your expansion.
For example, if you have 30 SCVs, 10 mineral patches at your main base and 5 mineral patches at your expansion, to reach maximum effectiveness, allocate SCVs such that each mineral patch (main base+expo) has the same number of SCVs on it. In this example, maynarding 10 SCVs to the expansion will leave 20 at the main base, leaving each mineral patch with an equal number of SCVs mining it.
Notes
+ Show Spoiler +Keep in mind that these results are specific to the conditions of the trials that were run. This means that other factors can also affect the effectiveness of maynarding workers(SCVs, Drones, Probes). The longer the distance between the sending and receiving base, the less effective the overall process of maynarding (I will extend this post to cover this when I get more time after finals). The number of workers at the main base must also be significant enough such that transferring a number of them will increase yield. It makes no sense to maynard when you have 7 SCVs on 9 mineral patches. Therefore, another factor not covered here is the minimum number of workers one must have before maynarding becomes effective. SCVs were also not being produced by either command centers during this period. Early speculation however indicates that this affects the results negligibly. More on this later.
Consider this as a general guide when you don't exactly know how much to transfer.
TL;DR version
To reach maximum mining efficiency when maynarding, you want to spread out all your SCVs equally among all your mineral patches including those in your expansion such that each mineral patch you are mining has the same number of SCVs.
Let me know what you guys think, this is all empirical preliminary data, but I think it was a lingering question everyone had that had to be definitively answered. Hopefully I can add on to this later.
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This looks pretty awesome. I look forward to your post-finals post!
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Belgium9947 Posts
Like mentioned in your notes you kinda oversimplified things imo, not splitting up in races, for instance, is already a pretty big mistake.
For example, it's race related too. Terrans want to transfer less than equal amount of scvs cause they'll be building things in their main too, so need extra scvs there for optimal mining scvs spread. Of course you prefer this to building at your nat, cause then you'd have to transfer more to your nat (loses mining time) and then build there. This actually means for instance, in a TvZ, your specific post 1rax cc build order (fast ebay or not, etc) determines the optimal number of scvs you bring.
In PvZ, the maynard often occurs after a Forge-FE build, in which case you want to leave more peons in your main cause you get your gas there faster. If you do a Bisu Build, you transfer one more probe because you're gonna get your second gas faster than when you do a citadel zealot speed +1 attack timing rush.
Zerg can, because of the hatchery-larvae mechanic, transfer a lot less than optimal drones, because they can cycle larva for overlord/ling usage to the most efficiently mining hatchery and can relay drone production to the least efficiently mining hatchery.
I know these are just specific examples. The only thing I want to prove here is that it's impossible for you to make an analysis that encompasses all details and will be superior to a good player's judgement of how many to transfer.
That said, I can only encourage mathematical analysis of in game mechanics. However, when it's done, you should refrain from 'trying to get practical results too easily'. The analysis itself should help people get an idea of how it works, and what they need to consider, rather than to try to come to a specific result people can practically use.
Just my 2 cents.
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Wow! Thanks so much for your hard work. I do appreciate the effort. And i am sure that the rest of TL will as well.
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To reach maximum mining efficiency when maynarding, you want to spread out all your SCVs equally among all your mineral patches including those in your expansion. For 27 SCVs, maynard 12 to your expo.
The wording here is unclear. Do you want to have the same number of SCVs per patch per expansion, or the same number of SCVs per expansion?
Good work though. Since I'm a Zerg player, it should be pretty useful since I can't be producing drones the entire game like Protoss/Terran can.
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On May 15 2009 10:28 RaGe wrote:
That said, I can only encourage mathematical analysis of in game mechanics. However, when it's done, you should refrain from 'trying to get practical results too easily'. The analysis itself should help people get an idea of how it works, and what they need to consider, rather than to try to come to a specific result people can practically use.
Just my 2 cents.
You hit it pretty much on the head. There are too many factors involved to make a definitive conclusion as to how many exactly to maynard. Build orders, gas, race mechanics, and others all affect the decision of how many to transfer. Trying to cover all of these would probably require an entire library to cover, so basically what I tried to do was provide an intuitive answer that would make sense, at least generally, for those people who are wondering how many to transfer at any given point in time 
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On May 15 2009 10:32 APurpleCow wrote:Show nested quote +To reach maximum mining efficiency when maynarding, you want to spread out all your SCVs equally among all your mineral patches including those in your expansion. For 27 SCVs, maynard 12 to your expo. The wording here is unclear. Do you want to have the same number of SCVs per patch per expansion, or the same number of SCVs per expansion? Good work though. Since I'm a Zerg player, it should be pretty useful since I can't be producing drones the entire game like Protoss/Terran can.
You want to have the same number of SCVs per mineral patch. If you have 30 SCVs, 10 patches at main base, and 5 patches at nat, you then want to maynard 10 to your expo, leaving 20 at your main. This spreads workers out evenly such that every patch, regardless of whether or not its your main or expo, has the same number of SCVs mining it (2).
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You should do one with Zerg as well, doing a standard 12hatch, 11pool FE opening and one for Protoss doing their standard FE.
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I believe the optimum for a zerg 12 hatch is 1-3 drones depending on how many lings you are making. 1 for 6 lings 3 for 2 lings. What I decided to make a general rule just based off of heuristic experience is keep enough at the main for 9 mineral patches + the 3 for the gas. Since with a standard 3 hatch build, your gas should come up soon after 12 hatch finishes morphing. After finals(in a week or so), I plan on doing some trial runs with zerg maynard with variations based on build timing, so if the OP doesn't do it, I'll post my results when I'm done.
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On May 15 2009 10:39 richlol wrote:Show nested quote +On May 15 2009 10:32 APurpleCow wrote:To reach maximum mining efficiency when maynarding, you want to spread out all your SCVs equally among all your mineral patches including those in your expansion. For 27 SCVs, maynard 12 to your expo. The wording here is unclear. Do you want to have the same number of SCVs per patch per expansion, or the same number of SCVs per expansion? Good work though. Since I'm a Zerg player, it should be pretty useful since I can't be producing drones the entire game like Protoss/Terran can. You want to have the same number of SCVs per mineral patch. If you have 30 SCVs, 10 patches at main base, and 5 patches at nat, you then want to maynard 10 to your expo, leaving 20 at your main. This spreads workers out evenly such that every patch, regardless of whether or not its your main or expo, has the same number of SCVs mining it (2).
The thing is, that although the ratios will be same with, say, 18 SCVs in main and 14 in natural, if you keep producing non-stop out of both, after 10 SCVs you'll have 23 SCVs in main and 19 in your natural, where your SCV/min ratio will be 2,555 in main and 2.714 in your natural, and your natural ratio will just keep growing faster the whole game. So in reality you need to transfer a lot less SCVs than your study suggests.
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awesome article ! looking forward to your results.
-Cheers
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On May 15 2009 10:39 richlol wrote:
You want to have the same number of SCVs per mineral patch. If you have 30 SCVs, 10 patches at main base, and 5 patches at nat, you then want to maynard 10 to your expo, leaving 20 at your main. This spreads workers out evenly such that every patch, regardless of whether or not its your main or expo, has the same number of SCVs mining it (2).
That's it right there. In other words: marginal product of an SCV should be roughly equal across all expansions (however many you have). Granted, there is some travel time from trasfer, so you want to leave 1-2 extra scvs mining in main base.
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Calgary25980 Posts
Good quantitative analysis.
I would have also liked to see some qualitative analysis on where this analysis should be taken further, and why it isn't entirely correct in a real game.
Thanks!
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Don't take this the wrong way, but this seems a bit overblown or unnecessary.
I think it should be easily proven that you take the total amount of workers, subtract however many needed for gas/building (gas at main and expo) from that total, and divide the remaining workers keeping workers per mineral ratio constant over all patches (main and expo). It doesn't make much sense that you would want a higher worker per mineral ratio at your main versus at an expansion. If I'm making some kind of grave mistake someone correct me.
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A pretty important issue to keep in mind is how well does the expansion/main get saturated (maximize minerals mined over time, not per miner):
If you are mining an expansion with exactly 1 mineral patch it takes exactly 2 scvs/probes/drones to fully saturate.
However, if its a 9-patch expansion it takes much more then 18 (I would say almost 30...?) to saturate the expansion.
Basically with an increased amount of mineral patches and a different layout, miners will spend more time looking for a patch. If the minerals are really close, they will have spend less time going from patch to patch looking for one that isn't being mined. However, they will have more patches in proximity to search.
Soooo, this obviously has to be taken into account
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but good post and research anyways. Thanks richlol!
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On May 15 2009 23:49 InsideTheBox wrote:
Don't take this the wrong way, but this seems a bit overblown or unnecessary.
I think it should be easily proven that you take the total amount of workers, subtract however many needed for gas/building (gas at main and expo) from that total, and divide the remaining workers keeping workers per mineral ratio constant over all patches (main and expo). It doesn't make much sense that you would want a higher worker per mineral ratio at your main versus at an expansion. If I'm making some kind of grave mistake someone correct me.
As I've already said, even if it's good right at the moment to have similiar saturation, main normally has more mineral patches. So after 5 more SCVs in both bases, your natural will actually be more saturated and your main will have too few SCVs. That's why you should leave more SCVs in your main than the results show.
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Belgium9947 Posts
On May 15 2009 23:49 InsideTheBox wrote:
Don't take this the wrong way, but this seems a bit overblown or unnecessary.
I think it should be easily proven that you take the total amount of workers, subtract however many needed for gas/building (gas at main and expo) from that total, and divide the remaining workers keeping workers per mineral ratio constant over all patches (main and expo). It doesn't make much sense that you would want a higher worker per mineral ratio at your main versus at an expansion. If I'm making some kind of grave mistake someone correct me.
You forgot that theres a distance between main and natural, resulting in mining time loss when workers are transferred.
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On May 16 2009 00:44 RaGe wrote:
You forgot that theres a distance between main and natural, resulting in mining time loss when workers are transferred.
That's what I said above. This is important if you have a relatively short time horizon you care about - in the very long run you just want the same number of SCVs per patch.
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I hate all these calculations. YOU MUST USE YOUR GUTS!!!!!!!!
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On May 16 2009 01:03 citi.zen wrote:Show nested quote +On May 16 2009 00:44 RaGe wrote:
You forgot that theres a distance between main and natural, resulting in mining time loss when workers are transferred. That's what I said above. This is important if you have a relatively short time horizon you care about - in the very long run you just want the same number of SCVs per patch.
Did you read what I said o_o or were you planning on cutting SCVs after maynarding?
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I read it, but had not fully "internalized" it. You make a good point - the ratio of main/expo scvs will get closer to 1 as you keep making workers from both CCs.
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On May 16 2009 01:15 MiniRoman wrote:
I hate all these calculations. YOU MUST USE YOUR GUTS!!!!!!!!
YALL HEAR???
Word son word.
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isn't it with zerg, longer distance to expansion, more drones you maynard. Mainly because larva system.
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Typically expansions have less mineral patches so the SCV to mineral patch ratio increases faster with the production of a single SCV than a main base with more mineral patches. So in a real-game scenario you want to maynard less SCVs than stated in my original post. I mentioned this in the Method section, that no SCVs were produced during these trials. But when I get time after finals, I will include more factors like production of SCVs, travel time between CCs, how these affect how many to maynard, and how these can be optimized to short term vs long term gains.
In reality of course when more of the conditions (ie SCV production, SCVs on gas/construction, etc) are factored in, the optimal amount to maynard is less. But again, like I said earlier, these trials were bound to very specific conditions to provide someone a very basic understanding of how to maynard.
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Very nice effort done. This'll be handy for most of us.
Nothing else to say since what I could say, you probably know (Experiment constants etc)
Anyway, good job! ;p
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On May 16 2009 00:44 RaGe wrote:Show nested quote +On May 15 2009 23:49 InsideTheBox wrote:
Don't take this the wrong way, but this seems a bit overblown or unnecessary.
I think it should be easily proven that you take the total amount of workers, subtract however many needed for gas/building (gas at main and expo) from that total, and divide the remaining workers keeping workers per mineral ratio constant over all patches (main and expo). It doesn't make much sense that you would want a higher worker per mineral ratio at your main versus at an expansion. If I'm making some kind of grave mistake someone correct me. You forgot that theres a distance between main and natural, resulting in mining time loss when workers are transferred.
The effect of travel time/distance was negligible during these trials as you can see that even in the short term (@30 seconds), there was no net loss of minerals from transferring SCVs up until about 17-18 SCVs. Following from this, what probably played a bigger role in the loss of minerals at that point were other factors such as the oversaturation at the natural (17) and a lack of SCVs at the main (10).
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On May 15 2009 10:28 RaGe wrote:
Like mentioned in your notes you kinda oversimplified things imo, not splitting up in races, for instance, is already a pretty big mistake.
no, he did the calculations with scvs and terran is the only race that matters
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I just grab a bunch and move em.
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Nice thread.
If you consider that
- 3 scvs might already be mining gas
- some scvs might be building buildings
- one scv is already making the cc
- When producing scvs from the natural cc the scv/miningpatches ratio will increas faster than in the main.
This will generally lead to a decreased amount of transfered SCVs to your expansion.
In you test, 11 SCVs transfered seems optimal whereas in reality, considering the points above, a number of 7-8 is more accurate.
I've tried different ammounts of SCVs transfered over a number of games when I used the standard opening in singleplayer, and I've looked at the replay alot to find out which ammount gives me the fastest growing economy.
So my aswer to how many SCVs is the optimal number to send when you do 1rax 2suply FE is 7-8 SCVs.
If the expansion is faster, transfer less SCVs, if it's later transfer more.
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you should look for the ratio. the ratio is all that matters. for example:
what is the optimal ratio of farmers z:y when the total amount of mining farmers equals z and x farmers remain in the main with a mineral patches after y farmers are transferred to the natural with b mineral patches.
z is the amount of farmers you have devoted to mineral mining. it does not include building, scouting, gas mining or any other non mineral mining farmers
y is the amount you maynard.
the ratio of z to y should be the same for each race, yes? even though the variables themselves will be different.
obviously, we are not factoring in the distance to the expo and i am not a proponent of counting all your scvs before maynarding. but the fact is.. there IS an optimal number and knowing that is helpful.
so for Terran we supposed the total amount of SCVs was 27 and through testing we found that 7-8 miners should be transfered, yes? assuming we dont need to make subtractions from that 27 and that they are all mining minerals then our ratio is 27 to 7 or ~25%.
Can we say that if zerg has 16 mining drones when he maynards he should only send 25% or 4 drones?
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