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[SC2B] Gas Matters
April 26th, 2010 08:27 GMT
Don't get comfortable Aldaris. You're going to be chastising many a Protoss for not having enough gas for many years to come.
Don't let the extra geyser fool you. Things have changed in so far as concerns our favorite gaseous resource, vespane gas, and in quite a few far reaching and profound ways. And it's not just Aldaris who needs to be on his toes. Every race has been affected by the changes made to resource collection in general, not just vespane gas, and the consequences are large.
Although most will know this, here is a summary to the basic changes to gas collection:
- geysers now return only 4 gas a trip
- every main and expo in the map pool has 2 geysers
- geysers are 75 minerals (25 for zerg + the assumed 50 for the drone)
- geysers return no gas once depleted
So naturally this plays much differently in terms of teching, but with some interesting options. These changes make gas collection more graded, which in Brood War was accomplished by yanking miners off the geyser. That reduced the collection rate substantially, and it was only with real purpose that workers would be taken from gas.
Thus, in Brood War, gas, more or less throughout the game, had 2 gears: high or none. Yes, Terrans would pull SCVs in the opening but the majority of every match had 3 on gas once the mining structure was complete. But that's not so in SC2. There are debates about how heavily to invest in gas, when, and what the best combination is. To this end, I did a detailed analysis of gas collection rates with the 9 possible (read, reasonable) combinations of gas collection based on the number of geysers used (in parentheses) and the number of miners used.
Granted this analysis is limited in scope. While I strongly suspect there are no differences in gas collection rates between the races, my analysis was limited only to Terran, on Lost Temple at 6 o'clock. Of course, I am assuming that these are typical geyser positions and there are no differences between the gas collection rates between the races, and there were other moderate sources of error, namely a non-uniform starting place for the gas collection, but this is normed by the large number of data points and the absolute nature of gas collection. Thus, by linear regression, an approximation of the rate of gas collection can be ascertained, but more importantly, its relation to other methods of gas collection.
In the spoiler is the raw data table. If people want to analyze the replays from which I got these data, I can release those as well.
+ Show Spoiler +
Below are the individual data points as they stack up. Some error in imperfect data collection is visible but the overall pattern is fairly stable, and the conclusions are both rather intuitive and fairly reasonable. As noted above, the number of geysers taken is in parentheses and the number of miners collecting gas is beside it.
A few things to note before going on to the conclusions:
- The rate gas collection from 3(1) and 4(1) are identical. 3 miners saturates 1 geyser completely for all intents and purposes. In Brood War the rate of gas collection of 4 vs 3 was approximately 4 more gas for every 200, so the difference between 3(1) and 4(1) has not significantly changed between Brood War and SC2.
- The number of data points is uneven for each, although each has an acceptable minimum from which to draw conclusions.
- In order to better standardize the collection rates, measurement began after the first gas trip was concluded, which is why every line begins above 0. All are at 4 excepting 5(2) where both miners completed their first trips at identical times to start at 8.
So, with that out of the way, it is generally true that the graph validates the intuitions of most players and many conclusions carry over from Brood War. Despite how obvious many of these may seem to be, it is important to note every one of them because SC2 is a different game, and the changes to resource collection have been substantial. So, taking nothing for granted, to make everything prettier and easier to read, I will once again bullet the conclusions:
- With the exception of 4(1) and 3(1), having more miners on gas increases the gas collection rate. You do not see the line for 3(1) because it perfectly overlaps with 4(1).
- There is no significant difference between 2 miners on separate geysers and having 2 miners on the same geyser (see the lines for 2(2) and 2(1)).
- Possibly the most interesting conclusion from the graph is the difference between 3(2) and 3(1). The collection rate of 3(2) is significantly faster than that of 3(1). This would seem to make sense; miners have a brief idle period in 3(1) that is not realized in 3(2), allowing for faster gas collection.
- There are clear 'don'ts' for gas collection as relates to mineral economy; 4(1), 2(2), and possibly 1(1) waste a disproportionate amount of time or minerals per gas gained.
Now is an appropriate time for an aside. I chose the Lost Temple 6 o'clock because it has a fairly typical mining distance, but not all geysers are created equal. Some, like those on Metalopolis, have very short distances and can run at much greater efficiency than those on Kulas Ravine, for example. In instances where the distances are shorter, the difference in the rate of collection between 3(1) and 3(2) is more exaggerated because there is a longer layover for the 3rd miner and because 2 miners is already very efficient, but on those where the distances to the gas are longer the difference is mitigated somewhat by the shorter layover.
The exact collection rates, however, are far more useful to draw conclusions from. SC2 replays give vague and imprecise collection rates under the 'income' tab which are hardly of any significant utility to a player trying to decide when to pull miners off gas, how many miners are needed, and when to start a second geyser, especially in-game. The following are the collection rates based on linear regressions from data of the chart above. The b values have all been dropped because they don't mean anything aside from the consequences of my norming, and remember that the m value (the rate) is in vespane gas/second, but since vespane gas isn't collected continuously but rather in chunks of 4 these rates are only useful in so far as they are compared to other rates of the same units and won't give you measures in seconds on when you can most closely time your Orbital Command, for example. That having been said, here they are:
- 1(1) | 0.74 gas/second
- 2(1) | 1.50 gas/second
- 2(2) | 1.48 gas/second
- 3(1) | 2.00 gas/second
- 3(2) | 2.23 gas/second
- 4(2) | 3.05 gas/second
- 5(2) | 3.33 gas/second
- 6(2) | 3.94 gas/second
Several things stand out from this. First, as could be expected, having 2 miners on the same gas doubles the collection rate, and having 2 miners on 2 separate gas does the same. However, noticeably, having 3 miners on the same gas does not triple the collection rate, but having 2 on 1 gas and 1 on the other does (because of the aforementioned brief traffic jam on a saturated geyser). Having 4 gas on 2 quadruples the collection rate, but again upon saturation of 1 the collection rate does not gain as much, and further unto the saturation of a second. Perhaps more useful here would be to look at a somewhat unusual comparison, but paradoxically far more comprehensible to your average player, being seconds/gas. Essentially, we're just flipping the previous collection rates on their heads to get something far more useful out of it. The following is how many seconds there are between gas returns.
- 1(1) | 5.40 seconds
- 2(1) | 2.66 seconds
- 2(2) | 2.70 seconds (*this is not a significant difference from 2(1))
- 3(1) | 2.00 seconds
- 3(2) | 1.79 seconds
- 4(2) | 1.31 seconds
- 5(2) | 1.20 seconds
- 6(2) | 1.00 seconds
Now, a very compelling pattern emerges here, one that looks like an exponential function. I took this and graphed it. Now, naturally, the actual data is more accurate than the function, and several manipulations removed from the actual data we're really getting into abstractions here, but the below graph essentially tells us that the amount of time exponentially decreases with each added miner per the function (calculated via exponential regression) f(x)=8.02477326e^-.4418030032x
The graph bears some discussion. Naturally, the actual utility of the graph cuts off after 6, because geysers are saturated at 3. The fit also isn't perfect, especially because 3(2) is quite anomalous to the pattern and is also very difficult to precisely compensate for, but the graph does reflect the effect that adding additional miners has on the speed of gas returns.
What this means for actual play could be very significant, or not so much. Gas always seems to be in high demand, and its collection is far more limited than mineral collection, but the amount of options in adjusting collection rates and the varying methods of investment allow intriguing possibilites for opening timing windows or interesting transitions. Essentially, what the gas changes have meant to play thus far is that there no longer need be just two settings for a player's gas collection, that you can alter and adjust the rate of gas collection based on needs and especially transitions and openings. This graph shows the value of each miner relative to the next or the one before it, and perhaps can, with care, be used to calculate more precise timings and adjustments for gas needs.
With all of this information we can also calculate which early gas is most cost efficient per minerals invested. With this, we actually use the rate of gas collection because it's easier to think about (in my opinion). Below is a friendly table that will make everything prettier to look at.
Unfortunately the table is the organized more by the scrambled nature of my brain than any real organizing principle so things may not be immediately apparent. Some things, as with the other graphs and pretty pictures, should stand out immediately, though. Namely, the value of adding just one more miner to gas early is huge. For 40% of the initial investment, there is a 100% increase in returns. Also, there's hardly any reason to construct two early gas if only 2 miners will be dedicated to them. Most SC players know this of course, but I've seen it. The most interesting datum is the 3(1) v 3(2) contrast. For 75% of the investment, ~90% of the gas is returned. So, while 3(2) does mine significantly better than 3(1), it is probably not worth the investment. Some other conclusions may be gleaned, but this wouldn't be fun if I just told you everything, now would it?
The most important thing to remember is that this is an examination of a single race, on a single map, at a single starting position, in the beta test. Because also these data were largely meant to influence how the opening can play out and options for tech, I did not do any testing on the high yield geysers included in the map editor or any testing on the varying distances that the geysers are from the spawn location. While the conclusions from this examination can likely be extrapolated across many other situations, there is no guarantee that they can, and as much stock should be placed in this as it deserves.
And those are the gas matters.
EDIT: There seems to be a fair bit of confusion about the graph. Just so everyone is clear, I should have put a domain on it and cut it off after 6, or simply edited the image to go no further, but as it stands, my MSPaint skills are marginal at best. Of course, I never meant for the graph to mean anything before 1 or after 6, and some people were confused by this. I submit this as my correction.
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SCIENCE.
Seriously, very interesting. Kudos for going so in-depth into it. Your graphs got me thinking, I think SC2's release will hopefully add some really interesting graphs in their scores screen. The current ones are good but just two is not enough there's room for way more.
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1st!
im contributing
User was warned for this post.
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Nice article. Are there any positions on any of the maps where one of your geysers mines faster than the other geyser if you only put 2 SCVs/drones/probes in it? I'm guessing that your test position was fine since the 2(1) and 2(2) data were essentially the same.
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As a side, but very important note: on various maps, 4(1) > 3(1) (you can't maximize one geyser mining with 3 workers).
Edit: answering question above - yes, there are geysers which are closer to your main base and some are far. This is pretty crucial knowledge and you should always build your first Refinery / Extractor / Assimilator on the better spot.
/R
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Wow, fantastic writeup and really interesting. I love it when people does this kind of thorough reasearch, and then writes it up good and befitting standards of a scientific magazine. Very well done!
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Good read very interesting... quite a work of art you have there, maybe people will think about throwing more into gas for transitions.
Articles like this are really good, for the community, and perhaps for Blizzard.
Edit: Also got me thinking, I have played SC/BW but that was a while ago, are the gas distances also not static? and considering SC2, wouldn't there be a concern about this? because perhaps for some maps it would be really good to use 4 or even 5 workers on gas because of the distance?
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the 3(1) vs 3(2) makes since once you have the numbers written down and you can see them in action. small difference, but noticeable once you extrapolate that across several expos
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ahhhh... the power of science Gj, interesting stuff
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Very interesting article. Now all we need is someone to test all the starting positions and naturals on all maps to see how much extra gas the third worker mines for each geyser.
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Interesting, and impressing. I dont know how much use it'll be for me. But I like these kind of articles anyway, makes the game experience deeper.
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I appreciate the data collection but it seems to me that the conclusion is simply: double mineral investment = double gas collection rate.
I think the choice between 5(2) and 6(2) are potentially most interesting, but unfortunately most builds these days take the 2nd gas late and thus the 50 mineral difference would not be as significant as in early game.
I also can't see anyone taking 3(2) over 3(1) just to squeeze out a minor advantage.
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On April 26 2010 17:39 TossPro wrote:
1st!
im contributing
User was warned for this post.
hehe, epic fail 
anyways, really good read... all though I'm not quite there yet... just got my beta yesterday and I realize how much different it is watching the game than playing it o_O
in other words... I'm being owned >_<
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Good read i liked the graphs 
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Shit mate,
Awesome read. Very technical
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I am a top gold player on EU and I actually think I might go for some 4(2) action ! thanks you !
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good read, amazing how ppl think of these things, that's why TL.net is the best community!
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This is really awesome. I love looking at these numbers and come to some conclusions myself. Thank you!
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United Kingdom2674 Posts
A very interesting and informative article.
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What has science done..But really a good graph and calculations,maybe your major is on math :p
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Pretty nice article. I know one thing for sure I never have gas in sc2. It's funny it seemed you were promoting 3(2) the whole time until the end
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awesomeness became readable, really interesting
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I will definitely keep in mind the 3(2) > 3(1) information during my games.
Thanks for a great writeup + research!
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On April 26 2010 19:45 Vetlock wrote:
What has science done..But really a good graph and calculations,maybe your major is on math :p
I see no math or science done here. All he did was collect some data, put it in excel and use data analysis. No fundamental relationship or equation was derived.
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I guess that you can vary between three different distinctive rates of mining. These are roughly:
2 gas / second -- 3(1)
3 gas / second -- 4(2)
4 gas / second -- 6(2)
These have the highest investment return. Relative 98-100%.
The analysis was made for "Fast" not "Faster" speed of game, which should be noted I think.
Also without any reference to other aspects of game these gas rates mean almost nothing.
16 workers mine ab. 10 minerals / second
20 workers-- 12 minerals / second
24 workers -- 13.33 minerals / second
So the final minerals / gas ratio is 13.33/4 = 3.33
Ratio minerals/gas
Thor -- 3 / 2
Tank -- 6 / 5
Marauder -- 4 / 1
Banshee -- 3 / 2
Viking -- 2 / 1
Stalker -- 5 / 2
Immortal -- 5 / 2
Colossus -- 3 / 2
Sentry -- 1 / 2
Phoenix -- 3 / 2
High Templar -- 1 / 3
Observer -- 1 / 2
etc. etc.
I.e. Marauder takes 30 seconds to make.
To make 3 marauders continously you should have 12,5 min / s , 2,5 gas / s.
( 125 * 3 / 30 , 25 * 3 / 30 )
It means that you could go with 20-24 workers at minerals and 4(2) at gas.
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Honestly this is the sort of data every one should have gathered for themselves in the first few days, but it's nice to see it written down, I guess.
It's interesting that you mentioned the difference in geysers depending on maps, but didn't test the actual difference in collection rates from map to map. It seems like that would have a significant effect on the outcomes and therefore the conclusions.
For whatever it's worth, you get very similar/identical data using the in game "income" tool on replays.
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Very nice way of looking at it Nah. Great first post! Good way to know when you have enough for steady production of a particular unit or set of units.
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Nice read. I disagree with the last table, though: wouldn't it be reasonable to count the minerals the SCVs on gas won't be mining instead of how much they cost? Usually the decision is between SCVs on minerals or on gas. I guess cutting scv's would belong to "mineral matters".
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I notice sooo many players leave 2 on gas the whole game. And I have noted other people saying it too, this makes it seem far less fatal than it would in BW.
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Hm. I have some objections.
On April 26 2010 17:27 Arrian wrote:- Possibly the most interesting conclusion from the graph is the difference between 3(2) and 3(1). The collection rate of 3(2) is significantly faster than that of 3(1). This would seem to make sense; miners have a brief idle period in 3(1) that is not realized in 3(2), allowing for faster gas collection.
While I think the OP is probably correct in its rough estimate for 3(1) as 2 gas per second and 3(2) as 2.25 gas per second, I don't think this is very clearly visible in the graph at all. A faster rate would be visible in the graph as a different slope, not just a higher or lower line. I don't think the graph shows clearly whether the slope for 3(2) is really different from the slope for 3(1); it is more as if the 3(2) line is consistently about 5 gas higher than the 3(1) line. Part of this could be explained by measurement error, part of it may be because in the 3(1) test the second and third scvs has to wait for the first two to come out of the refinery, while in the 3(2) test only the third scv has to wait a while. So I don't think this argument is altogether convincing, although I do tend to believe the conclusion.
On April 26 2010 17:27 Arrian wrote:
Now, a very compelling pattern emerges here, one that looks like an exponential function.
Sorry, but this is nonsense. If the miners would not hold each other up, then the mean time between gas returns would obviously be inversely proportional to the number of miners; to be precise
#gas = r * #miners * #time, where the mining rate r = 0.75 gas/second
To calculate the time for a single return, substitute #gas = 4 to obtain #time = 4 / (r * #miners) = 5.33... / #miners. This imperfect model already fits the numbers quite well:
#miners | 5.33... / #miners
1 | 5.33
2 | 2.67
3 | 1.78
4 | 1.33
5 | 1.07
6 | 0.89
Now obviously the miners do hold each other up, an effect that presumably gets worse when you increase the number of miners. Thus, in reality the mean time between gas returns will be larger than the amount of time predicted by the inverse proportional model. (This is exactly what happens: the predicted numbers are smaller than the measurements, especially for #miners equal to 5 or 6.)
In contrast, in the proposed exponential model the mean time between returns drops ridiculously quickly as a function of the number of miners. For example, according to the exponential model the mean time between returns for 25 workers would be 0.00013; in other words you would collect 4/0.00013 = 31121 gas per second, while according to the inverse proportional model you would collect 25*r=18.75 gas per second, a much more reasonable figure. While an exponential model may give a reasonable fit if you just don't look at the graph beyond 6 miners, it is clearly a completely inappropriate model in this case, so you're just as well off just drawing any reasonable looking line through the data points.
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Good article. Nice calculations.
A good reminder to check the gas locations on your base, since one may be closer than the other
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Thank you mate, very interesting!
Don't have to search that out for myself now.
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Excellent article, thank you for writing it. Has anyone been building 2 refineries closer to the same time so that you can get 2 workers on each of them sooner than you put the 3rd on one of them? The early 75 minerals cost would be worth it for faster tech.
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is it just me or is the first graph actually missing the 3(1) chart
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+ Show Spoiler +On April 26 2010 21:52 shoop wrote:Hm. I have some objections. Show nested quote +On April 26 2010 17:27 Arrian wrote:- Possibly the most interesting conclusion from the graph is the difference between 3(2) and 3(1). The collection rate of 3(2) is significantly faster than that of 3(1). This would seem to make sense; miners have a brief idle period in 3(1) that is not realized in 3(2), allowing for faster gas collection.
While I think the OP is probably correct in its rough estimate for 3(1) as 2 gas per second and 3(2) as 2.25 gas per second, I don't think this is very clearly visible in the graph at all. A faster rate would be visible in the graph as a different slope, not just a higher or lower line. I don't think the graph shows clearly whether the slope for 3(2) is really different from the slope for 3(1); it is more as if the 3(2) line is consistently about 5 gas higher than the 3(1) line. Part of this could be explained by measurement error, part of it may be because in the 3(1) test the second and third scvs has to wait for the first two to come out of the refinery, while in the 3(2) test only the third scv has to wait a while. So I don't think this argument is altogether convincing, although I do tend to believe the conclusion. Show nested quote +On April 26 2010 17:27 Arrian wrote:
Now, a very compelling pattern emerges here, one that looks like an exponential function.
Sorry, but this is nonsense. If the miners would not hold each other up, then the mean time between gas returns would obviously be inversely proportional to the number of miners; to be precise #gas = r * #miners * #time, where the mining rate r = 0.75 gas/second To calculate the time for a single return, substitute #gas = 4 to obtain #time = 4 / (r * #miners) = 5.33... / #miners. This imperfect model already fits the numbers quite well: #miners | 5.33... / #miners 1 | 5.33 2 | 2.67 3 | 1.78 4 | 1.33 5 | 1.07 6 | 0.89 Now obviously the miners do hold each other up, an effect that presumably gets worse when you increase the number of miners. Thus, in reality the mean time between gas returns will be larger than the amount of time predicted by the inverse proportional model. (This is exactly what happens: the predicted numbers are smaller than the measurements, especially for #miners equal to 5 or 6.) In contrast, in the proposed exponential model the mean time between returns drops ridiculously quickly as a function of the number of miners. For example, according to the exponential model the mean time between returns for 25 workers would be 0.00013; in other words you would collect 4/0.00013 = 31121 gas per second, while according to the inverse proportional model you would collect 25*r=18.75 gas per second, a much more reasonable figure. While an exponential model may give a reasonable fit if you just don't look at the graph beyond 6 miners, it is clearly a completely inappropriate model in this case, so you're just as well off just drawing any reasonable looking line through the data points.
Your math is wrong. He clearly states in his article that he doesn't use his regression for unreasonable combinations, like oh... 25 workers on gas. Based on his assumption that the graph holds up to 3 workers per gas, and allowing for some variance, the exponential regression is just fine.
Take your math major and shove it up your ass, the first thing people do in "real" life is make a set of assumptions for each situation.
So no, YOU are making complete nonsense.
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On April 26 2010 23:34 Anti wrote:
is it just me or is the first graph actually missing the 3(1) chart
Read the entire thing next time? He says you can't see the 3(1) because the 4(1) lays over it.
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Oh, oops :3
I was thinking about gas usage the other day though, thanks for the article.
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ESCIENCE!
But seriously is there any game on the face of the earth that recieves this kind of dedicated research. Im sure Halo doesnt have statistical analysis on a professional level.
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On April 26 2010 23 begin_of_the_skype_highlighting 26 2010 23 end_of_the_skype_highlighting:43 Archerofaiur wrote:
ESCIENCE!
But seriously is there any game on the face of the earth that recieves this kind of dedicated research. Im sure Halo doesnt have statistical analysis on a professional level.
SSBM, GGXX, any competitive fighting game.
And this specific kind of analysis is ultimately quite pointless.
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This article is so unneccesary long it's unbelievable...
First of all the method and data is nice and all but really this could be summarized much easier. It is pretty safe to assume beforehand to that rate of gas income is constant while the gas geyser is running as we all know this from playing experience. Thus just putting 1, 2 and 3 workers on a geyser and just timing for a minute each and calculating how much you gas income you would get would suffice, doing the 2nd gas as well is completely unneccesary as it's obviously the same as the first.
So 4(2) is really the same as 2x 2(1)??, everyone could think of that beforehand..
The only interesting thing in here is how much less efficient the 3rd worker is then the first 2 ones using the geyser. The raw gas income is also slightly interesting.
The inverse graph is completely useless and add's nothing to the whole issue, that entire paragraph should be scrapped really.
Also the investment and income table at the end hardly makes sense as it counts the costs of workers which you would be having anyway. It neglects the oppurtunity cost of making the refinery as well which though different for each race can't just be neglected either.
The whole writing and setup of this piece is just not good. Needlessly trying to do complicated things which add nothing to the whole subject...
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There are a few geysers on the current maps where 4 miners is optimal. The far geysers on Kulas Ravine (at both the starting and the natural) bring in more far more gas with 4 then with 3. I don't have numbers handy here at work to show my proof.
The gas at the naturals on Scrap yard are the same way.
Great article, if you still feel ambitious running data for the spots I have mentioned would likely help the community a ton.
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Great article, not sure how to use the information just yet but glad to have it. Thanks for doing the leg works and including various graphs for reading it in different ways. I think this will be a goto reference for anyone doing highly polished tech timings.
Thanks for the work Arrian!
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very awesome read. Enteresting how it was like reading a Harvard student's essay or something! Very in-depth analysis as others said, its really good. I guess i should focus my attention to reading more about sc:bw stuff here from now on because it seems to be the only foriegn site active as of recently.
And im still enjoying Sc1, i've tried sc2 already...but i just didnt get quite with the new feel but it was entertainment and wasn't hard to play.
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On April 26 2010 23:59 Shikyo wrote:Show nested quote +On April 26 2010 23 begin_of_the_skype_highlighting 26 2010 23 end_of_the_skype_highlighting:43 Archerofaiur wrote:
ESCIENCE!
But seriously is there any game on the face of the earth that recieves this kind of dedicated research. Im sure Halo doesnt have statistical analysis on a professional level. SSBM, GGXX, any competitive fighting game. And this specific kind of analysis is ultimately quite pointless.
Don't forget EVE online, they've got a Ph.D. economist who does quarterly reports that are much more in depth than this.
I agree with other replies, reasonably good info but not very in-depth and way too verbose. The graphs all say the same thing, why not analyze minerals not mined when moving workers to gas? Or how about do a graph of mineral+gas income and overlay it onto a popular build order to give an example of what timing to move from gas to minerals or vice versa. That would have been a lot more informative.
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Nice analysation,
however I recently did those measurements myself and as your results differed from mine I have redone my experiments and I would like to share my findings.
My experiments were done on Blistering Sands on the southwest main on faster speed. I measured every race for the southern geyser and the northern geyser for protoss additionally to compare both.
Table in spoiler:
+ Show Spoiler +
My results have the following implications:
1. All 3 races gather at the same speed. (Requires creep for the zerg, but the hatchery is there anyway)
2. The northern geyser might be a little bit more efficient because of its distance. Even if it is insignificant building the northern geyser first has no drawback.
3. Maybe the most drastic: The diminishing returns of the 3rd worker are nearly non-existant on both geysers.
This should demonstrate the differences on different maps more clearly.
And in conclusion the statement 3(2) > 3(1) might not be generalizable and would require further research.
Edit: I just noticed I should have done 4 workers as well. :/
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2(1) and 4(2) seem to be the most interesting parts, at least on maps where 3 miners saturates your geyser. You get most of the maximum mining rate while still maximizing gas per miner.
So running with 4 on gas instead of 6 is more efficient provided your minerals aren't saturated... but in most cases once you get to that point gas is the limiting factor anyway so it's ultimately not very useful.
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The real question is how much more efficient is holding off on gas till you can build 2 geysers and then saturate them... or maybe even 4 after a quick expo. Do you get more gas by a certain point than if you had started one geyser a little early?
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On April 26 2010 23:37 itzbrandnew wrote:
Take your math major and shove it up your ass, the first thing people do in "real" life is make a set of assumptions for each situation.
Wow, that's a very well-balanced and constructive remark. I'm just pointing out where I think this article is weak. No need for the hating.
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Great effort, thanks for doing this.
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That's some very very interesting stuff. Thanks for the in-depth article!
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United States7166 Posts
good article but it does not account for something major that has been concerning me related to gas, and that is that all gas geysers are clearly not at equal distances, at least in your example!
* 1(1) | 0.74 gas/second
* 2(1) | 1.50 gas/second
* 2(2) | 1.48 gas/second
* 3(1) | 2.00 gas/second
* 3(2) | 2.23 gas/second
* 4(2) | 3.05 gas/second
* 5(2) | 3.33 gas/second
* 6(2) | 3.94 gas/second
how is this possible? 5(2) should be simply the rates of 2(1) and 3(1) added together..
clearly this means not all gas geysers are spread at an equal distance, which means if you have a 5(2) situation you should put the 3 workers on the further geyser, and the 2 worker geyser on the closer one. just look at how little the gain is between 4(2) and 5(2) in your data. and then look at the gain from 5(2) to 6(2), that's .61 gas/second increase when it should be .50 according to the difference between 2(1) and 3(1).
something's wrong with the data here, and if 4(2) and 5(2) are accurate than clearly the gain for adding another worker on that closer geyser is a very marginal gain in gas collection
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Yeah, as most said: interesting info, but a bit redundant...
Would like to have more info on those 4 miners geysers, is there a list somewhere?
Must be hard to find just by looking at their position...
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Hmmm, I kinda see what youre saying... sorta... There is a thor drop build I do where the timing is pefect if i use 5 workers on gas and then have my worker that built my factory go on to the second gas once it's done, but I don't think having a graph helps at all with finding timings like that.
Also other things come into play, if i feel they might cheese and i scout a little early I have to adjust the timing on when i make the 2nd refinery a little later to make up for lost minerals and then I consequently have to add a 3rd scv earlier to make up for the missed gas effectively giving me the same gas with a later refinery, but vs P i usually will take refinery earlier if I'm going to do this build so they don't gas steal it.
how is this possible? 5(2) should be simply the rates of 2(1) and 3(1) added together..
clearly this means not all gas geysers are spread at an equal distance
Yea.. I'd think it's pretty obvious... The geysers that are further away don't mine at 100% efficiency. There are a couple on the new 2v2 maps that are especially bad. I think one on the left of metalopolis is bad too. I was obsing a game vs 2 friends and noticed that one had faster gas income even though they had 6 on gas each. Just like in sc1 some geysers benefit from 4.
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Wow, great research Arrian! I'm a super noob down in the coppers, but because of how it seemed to look I always put 2 workers on a gas (it seemed like there was no downtime, so no reason to put 3 on it) so thank you for putting it simply for me (yes, having all the math set up on charts and graphs is "simply" for me lol).
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Very interesting, thnx for the report!
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This was my favorite line
What this means for actual play could be very significant, or not so much.
This could be extremely important......or not at all.
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iNcontroL
USA29055 Posts
nice
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It would have been easy to have the same mineral collection as is Brood War, but the new mechanics make us have to reanalyze everything. I personally enjoy that a lot in contrast to everything being standardized and those with the faster fingers reigning supreme. Great work and analysis, I hope more like this will come as SC2 is released and more people gain access to it.
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On April 26 2010 17:27 Arrian wrote:
So, just for kicks, if you were to put those together to get numbers for gas/s per mineral invested ( * 1000 )
1(1) 5.92
2(1) 8.57
3(1) 8.88
3(2) 7.43
4(2) 8.71
5(2) 8.32
6(2) 8.75
3 workers on one gas would seem to be the most investment-efficient way to mine... but why isn't it the same rate as 6(2)? Just discrepancy in distance between the two geysers? I guess this really just tells us, "saturate the closest geyser first". Kinda obvious, I guess, but I never really thought about it.
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If you want less error and more actually significant figures the best way is to just stick the appropriate number of workers in the gas and see how long it takes to mine out the gas (and of course assume that the mining rate is continuous). This also much more clearly reveals whether there is a difference between different situations since a small difference compounds over the long time it takes to mine out an entire geyser.
I definitely like the effort and SC2 needs more analysis on resource gathering especially with its implications on mapmaking.
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so 4 workers on 2 gas is more efficient than 6? Cool.
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Articles like this make me feel inadequate when it comes to math :/
At least there are kind people like the OP who spend their time and effort for the community :D
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United States889 Posts
On April 27 2010 00:20 Kickchon wrote:Nice analysation, however I recently did those measurements myself and as your results differed from mine I have redone my experiments and I would like to share my findings. My experiments were done on Blistering Sands on the southwest main on faster speed. I measured every race for the southern geyser and the northern geyser for protoss additionally to compare both. Table in spoiler: + Show Spoiler +My results have the following implications: 1. All 3 races gather at the same speed. (Requires creep for the zerg, but the hatchery is there anyway) 2. The northern geyser might be a little bit more efficient because of its distance. Even if it is insignificant building the northern geyser first has no drawback. 3. Maybe the most drastic: The diminishing returns of the 3rd worker are nearly non-existant on both geysers. This should demonstrate the differences on different maps more clearly. And in conclusion the statement 3(2) > 3(1) might not be generalizable and would require further research. Edit: I just noticed I should have done 4 workers as well. :/
Nice work
I don't think our results are in conflict because they all seem to vary appropriately based on the difference in geyser position. The differences in rates seem to be a function exclusively on that. And yeah, the 3(2)>3(1) seems to be heavily dependent on the geyser position, to the point where the mineral investment would almost always make 3(1) a better choice than 3(2)
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United States42262 Posts
Geysers are only 75!?? Then why have I been waiting for 100 every game.
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Would be interesting to add how many minerals/s a drone collects, anyone?
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On April 27 2010 02:06 KwarK wrote:
Geysers are only 75!?? Then why have I been waiting for 100 every game.
Yeah. I noticed that for Terran after a few games. I said to my friend, "Wtf; my reaper rush can come so much faster now."
Nice analysis. It's not too beneficial for my current loose build orders but I can see it being key with more development of precise build orders.
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nice information
it seems this is mostly a lesson in common sense, but a good lesson nonetheless
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Your definitely going to be one of the professors at starcraft university
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Nice,
I was thinking about 'What is the best gas strat' today =)
Thanks for write up!
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As others have said, there is no science or maths here, just some annotated arithmetic.
Furthermore it makes absolutely no sense to regress a function on a domain for which it is undefined. Quite a lot of pretentious nonsense in this article.
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Nice writeup. Enlightening, especially on the 3(2). Was this a single run or multiple tests on the same position?
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You know, I've been wondering about this kind of stuff for a while and I'm glad you took the time to write an article on it! This really helps out a lot, especially the table where you can compare them all. I'll put this to good use; keep up the good work
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Arrian, this is a great analysis; one direct practical conclusion would be knowing how much to invest on gas mining while trying to FE (several tier 1.5 units require gas - and determing just how many tier 1.5 units one should build to FE successfully!)
but instead of including a "minerals invested" vs "rate of gas"
the logically correct comparison should be rate of minerals mined vs rate of gas mined; with x workers on gas, (total workers - x) on minerals of course
i can help you with the analysis if you would like!
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Thanks for this. You put in a lot of effort, and it shows.
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I agree that most of this article was unnecessary fluff, but there was one very important discovery that I actually think I will incorporate into my play: the fact that the third worker doesn't add as much as the first two.
Basically, early game it might give a significant advantage (in regards to net wealth) to get two refineries with two workers on one and one or two on the other rather than one refinery with three, and keep the leftover workers on minerals until gas is needed more urgently.
The dividing of gas in sc2 was definitely a good idea; it makes getting gas an actual choice. For map makers, I think you should consider expansions or even mains with only one or possibly three geysers.
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It is not surprising that your rate of gas mining is proportional to the number of workers mining gas. Because your rate of collection is constant per worker, when you add an additional worker, you necessarily increase your rate of gas collection per time by some approximate exponential factor. For example, consider the graphs y = x for one worker, y = 2x for two workers, y = 3x etc. When you factor in build times for the workers and offset those linear functions by said build times you get something that looks like the exponential function. From kinematics you know there will be some max rate that is determined by the distance of the geyser from the main building, worker acceleration (do workers accelerate?) and speed etc.
Some specific comments:
The first graph is labeled incorrectly. Gas x time is not a graph of gas collection rates. The rate of gas collection per time is the slope at any point on the gas x time graph. I found the differently shaped graph points distracting given that you are trying to analyze the overall behavior of the graphs as opposed to comparing specific points between them.
The second graph isn't that helpful. Intervals of time to the geyser vs. workers on gas. It starts high and goes down. There's not a lot to say about it. A more useful graph would a graph of gas collection per second x workers/geyser b/c it can help you visualize what is significant about rates of resource collection: potential unit production. For example, if your gas collection per second is 20 gas/sec then you can calculate the optimal number of barracks to support continuous marauder production given that you know the marauder build time. I will leave this as an exercise for the reader
Also, it would be cool if you added your data files to the OP.
I hope you found my comments constructive ^_^ Thanks for taking the time to share your research and analysis!
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Your math must be incorrect:
4(2) | 3.05 gas/second
5(2) | 3.33 gas/second
6(2) | 3.94 gas/second
The Increase from 4(2) to 5(2) is .28g/s, and the increase from 5(2) to 6(2) must also be .28g/s, making 6(2) worth 3.61g/s.
The only thing that could change this is if the map / spot you chose had a different distances. I would recommend redoing the data on a map where the gases are equidistant from the Hive/Nexus/CC
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I'm laughing so hard at gasexpfunction.png (2nd graph). You interpolate from the data of 1,2,3,4,5,6 workers, and then add the caveat that that everything you've interpolated is meaningless. So essentially what you've done is intentionally introduced error to your data points by artificially fitting it to an inverse exponential, with no benefit. If you think about it, the real function should be like 1/x, but this is still meaningless, because as you discuss this formula only applies on the domain {1,2,3,4,5,6}.
If this seems harsh I apologize, the rest of the article was very interesting and it is great you are taking the time to do this.
e: oops I see this has been said about 5 times before.
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The first thing that popped in my head was the effect of geysers returning 0 gas once depleted would have on the game. Perhaps an analysis of this has been discussed earlier and I've overlooked it. Otherwise a very good read for any aspiring SC2 Pro :D
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very interesting statistics there.
glad to know that there is no question between 3 or 4 workers on one gas geyser anymore.
with that, we are one step closer in analyzing sc2 =D
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whoa, this is why i joined this forum
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Thank you for proving what most people "make an ASS out of U and ME"
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awesome research and write up i really enjoyed reading it! just felt as if it could've been summed up a lot quicker
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Good initiative from OP, and nicely exposed, but this article is missing the most useful thing it could hold : analysis of far away geysers vs close geysers.
Also, any good game has research like this. It is what makes playing them more than just a passtime, and what makes playing them fun and rewarding.
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HMMM, i guess blizzard makes up for the depleted mining by adding a second geyser. However, this is devolution by not being about to mine 8 gas per mine!!!
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so this means that a 5(2) is better than a 6(2) in the start of the game cause this seems a little hard to understand . . .
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Very interesting good to see hard data on the 3(2) > 3(1). Also 4(2) > 3(1)+ 1(1) .
The obvious questions I guess is are there any interesting fast 2 refinery builds to take advantage of this. Perhaps to speed up a gas heavy timing attack?
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Wow- really fantastic article. This is the kind of stuff I have been looking for! Thanks so much Great job-
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There are high-yield geysers in the editor, so once release I'm sure we'll see maps popping up all the time that have high-yield gas, completely changing the pacing of gas.
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On April 26 2010 23:43 Archerofaiur wrote:
ESCIENCE!
But seriously is there any game on the face of the earth that recieves this kind of dedicated research. Im sure Halo doesnt have statistical analysis on a professional level.
World of Warcraft theorycrafting blows SC theorycrafting away in terms of sheer volume and complexity.
At this point, it's complicated enough that the community uses mods, monte carlo simulations, and any other automation they can to determine optimal gear setups, talent specs, and DPS rotations.
It's amazing the level of dedication people have to figuring out things that aren't real.
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this was extremely well written !
the content was nice too, not sure how significant it may turn out to be due to all the things you mentioned at the end,
great post nonetheless!
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On April 26 2010 17:36 prOxi.swAMi wrote:
SCIENCE.
Seriously, very interesting. Kudos for going so in-depth into it. Your graphs got me thinking, I think SC2's release will hopefully add some really interesting graphs in their scores screen. The current ones are good but just two is not enough there's room for way more.
+1
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So if I have two refineries and 3 SCVs mining each, how long will it take before my government develops alternative energy sources?
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Great Analisys, so I guess I was right, thanks for the confirmation. GJ
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Is there any possibility of adding scv and drone mining lost to the minerals per gas rate comparison? Obviously a non-issue for protoss, but I would be particularly interested to see if the 3(2) and 4(2) come out as far ahead with mining lost taken into account.
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As for the maths, I think the WoW community does the most analysis out of all the blizzard games. They run simulations and derive equations used by blizzard and run cost/benefit analysis fairly regularly with every new mechanic introduced.
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On April 26 2010 21:52 shoop wrote:Hm. I have some objections. Show nested quote +On April 26 2010 17:27 Arrian wrote:
Now, a very compelling pattern emerges here, one that looks like an exponential function.
Sorry, but this is nonsense. If the miners would not hold each other up, then the mean time between gas returns would obviously be inversely proportional to the number of miners; to be precise
Yes, and that is what the OP 2nd's graph clearly shows. I think you may be confused. e^x is given by:
As you can see, the exponential function's value is proportional to its previous values. Considering e^-x it is inversely proportional to its previous values. It is this property of prior dependence that makes it particularly good for modeling growth and decay.
Also see this to convince yourself.
#gas = r * #miners * #time, where the mining rate r = 0.75 gas/second
To calculate the time for a single return, substitute #gas = 4 to obtain #time = 4 / (r * #miners) = 5.33... / #miners. This imperfect model already fits the numbers quite well:
#miners | 5.33... / #miners
1 | 5.33
2 | 2.67
3 | 1.78
4 | 1.33
5 | 1.07
6 | 0.89
This is a linearization using the number of workers and the average mining rate. Of course it fits the data! Because the number of miners is always an integer you aren't interested in the data between points so there is a strong argument for a simpler model. For something more complex ( mineral collection) a more sophisticated model would be desirable. Regardless, one model doesn't invalidate the other, they should both generally confirm the underlying truth of the system.
Now obviously the miners do hold each other up, an effect that presumably gets worse when you increase the number of miners. Thus, in reality the mean time between gas returns will be larger than the amount of time predicted by the inverse proportional model. (This is exactly what happens: the predicted numbers are smaller than the measurements, especially for #miners equal to 5 or 6.)
The miners to not "hold each other up." What you are describing is a constraint on the number of workers able to collect gas at a given time. If only one worker can collect gas, then the other workers cannot collect gas so they must wait for their turn. When this is happening the gas you mine per second is increasing albeit at a decreasing rate until you reach the equilibrium point.
In contrast, in the proposed exponential model the mean time between returns drops ridiculously quickly as a function of the number of miners. For example, according to the exponential model the mean time between returns for 25 workers would be 0.00013; in other words you would collect 4/0.00013 = 31121 gas per second, while according to the inverse proportional model you would collect 25*r=18.75 gas per second, a much more reasonable figure.
The exponential model is an inversely proportional model. The end behavior of 1/x and e^-x is the same as x->oo. Besides, the modeling function is a solution over a specific domain, who cares what it does at infinity?
While an exponential model may give a reasonable fit if you just don't look at the graph beyond 6 miners, it is clearly a completely inappropriate model in this case, so you're just as well off just drawing any reasonable looking line through the data points.
I don't follow your logic.
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On April 27 2010 16:24 space_yes wrote:Show nested quote +On April 26 2010 21:52 shoop wrote:Hm. I have some objections. On April 26 2010 17:27 Arrian wrote:
Now, a very compelling pattern emerges here, one that looks like an exponential function.
Sorry, but this is nonsense. If the miners would not hold each other up, then the mean time between gas returns would obviously be inversely proportional to the number of miners; to be precise Yes, and that is what the OP 2nd's graph clearly shows. Also see this to convince yourself. I think you may be confused. e^x is given by: As you can see, the exponential function's value is proportional to its previous values. Considering e^-x it is inversely proportional to its previous values. It is this property of prior dependence that makes it particularly good for modeling growth and decay.
lol
What you've written here is nonsensical. There's no "previous values" to a real function, and the only function that's inversely proportional to it's "previous values" is 1 (given a reasonable definition of what this even means, e.g. f(x) = a/f(x-c), c>0, for all x).
If a miner does a trip in 5 seconds, then two miners do two trips in 5 seconds, and k miners do k trips in 5 seconds, so miners do k/5 trips a second. Sticking with k miners, Let's call this rate R. If k miners do R trips a second, then it takes 1/R seconds for a trip to be done. Notice how we took the inverse? This shows that they are inversely proportional. (We've just discovered the obvious concept that period is the inverse of frequency.) The relevant function here was 1/x, not e^-x.
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4(2) interests me greatly.
I believe it could be worked as a middle gear for gas collection. All you'd have to do is set 3 workers to one gas until your 2nd geyser is set up and then take one off that gas. Then just put him on the nearest mineral patch after he's returned his gas and take another worker off the other far edge mineral patch after it delivers its crystal and drop him in that gas to increase gas collection rate while not hurting your resource collection rate.
Then you can fill your gas out to 3 workers each as you see fit.
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On April 27 2010 17:40 DarkChrono wrote:Show nested quote +On April 27 2010 16:24 space_yes wrote:On April 26 2010 21:52 shoop wrote:Hm. I have some objections. On April 26 2010 17:27 Arrian wrote:
Now, a very compelling pattern emerges here, one that looks like an exponential function.
Sorry, but this is nonsense. If the miners would not hold each other up, then the mean time between gas returns would obviously be inversely proportional to the number of miners; to be precise Yes, and that is what the OP 2nd's graph clearly shows. Also see this to convince yourself. I think you may be confused. e^x is given by: As you can see, the exponential function's value is proportional to its previous values. Considering e^-x it is inversely proportional to its previous values. It is this property of prior dependence that makes it particularly good for modeling growth and decay. lol What you've written here is nonsensical. There's no "previous values" to a real function, and the only function that's inversely proportional to it's "previous values" is 1 (given a reasonable definition of what this even means, e.g. f(x) = a/f(x-c), c>0, for all x). If a miner does a trip in 5 seconds, then two miners do two trips in 5 seconds, and k miners do k trips in 5 seconds, so miners do k/5 trips a second. Sticking with k miners, Let's call this rate R. If k miners do R trips a second, then it takes 1/R seconds for a trip to be done. Notice how we took the inverse? This shows that they are inversely proportional. (We've just discovered the obvious concept that period is the inverse of frequency.) The relevant function here was 1/x, not e^-x.
I am trying to use easy to understand terms. Something inversely proportional is given by 1/x.The OP function is of the form be^(ax) + c = e^-x = 1/e^x. Look at the definition of the exponential function. You must not understand something. With respect to "previous values" I'm referring to the last value for x i.e. a Maclaurin series polynomial of degree 5 (or whatever we need for that interval of workers and accuracy). The exponential function is used to model over a specific domain so how is that not a real valued function?
Here is the Taylor series expansion for e^x with a = 0:
Look very hard at that series before you post claiming nonsense and wikipedia exponential function until you understand.
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On April 27 2010 17:40 DarkChrono wrote:
The relevant function here was 1/x, not e^-x.
obviously you've not taken calculus
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I think he has the mean time confused with the rate of change of the mean time.
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On April 27 2010 18:14 hacpee wrote:
I think he has the mean time confused with the rate of change of the mean time.
lol
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On April 27 2010 18:17 space_yes wrote:Show nested quote +On April 27 2010 18:14 hacpee wrote:
I think he has the mean time confused with the rate of change of the mean time. lol
Just try to graph it yourself. You see that it is in fact 1/x. Do a thought experiment.
Lets say the interval to return gas with 1 worker is 1. The interval to return gas with two workers is 1/2. The interval to return gas with 3 workers is 1/3. The interval to return gas with 4 workers is 1/4. You see the pattern? 1/x is f(x) and 1,2,3,4,5,6,7,8 is x. The numbers match.
Usually, you get an exponential or inverse exponential when dy/dt=-y. I'm just not seeing which variable, as you increase the rate of change of it, will decrease the variable. Then again, its been 3 months since I did modeling with differential equations so I might not be the best person to see the relationship.
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All this math hurts my head. But I would like to object to the blub thing in that this well written article containing good information does not actually talk about gas USAGE at all.
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On April 27 2010 18:24 hacpee wrote:Show nested quote +On April 27 2010 18:17 space_yes wrote:On April 27 2010 18:14 hacpee wrote:
I think he has the mean time confused with the rate of change of the mean time. lol Just try to graph it yourself. You see that it is in fact 1/x. Do a thought experiment. Lets say the interval to return gas with 1 worker is 1. The interval to return gas with two workers is 1/2. The interval to return gas with 3 workers is 1/3. The interval to return gas with 4 workers is 1/4. You see the pattern? 1/x is f(x) and 1,2,3,4,5,6,7,8 is x. The numbers match.
Consider the Taylor series where a = 0 of degree 1.
If you do not know what this is do not respond to my post.
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On April 27 2010 18:36 space_yes wrote:Show nested quote +On April 27 2010 18:24 hacpee wrote:On April 27 2010 18:17 space_yes wrote:On April 27 2010 18:14 hacpee wrote:
I think he has the mean time confused with the rate of change of the mean time. lol Just try to graph it yourself. You see that it is in fact 1/x. Do a thought experiment. Lets say the interval to return gas with 1 worker is 1. The interval to return gas with two workers is 1/2. The interval to return gas with 3 workers is 1/3. The interval to return gas with 4 workers is 1/4. You see the pattern? 1/x is f(x) and 1,2,3,4,5,6,7,8 is x. The numbers match. Consider the Taylor series where a = 0 of degree 1. If you do not know what this is do not respond to my post.
a=0 of degree 1? What notation are you using?
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On April 27 2010 18:40 hacpee wrote:Show nested quote +On April 27 2010 18:36 space_yes wrote:On April 27 2010 18:24 hacpee wrote:On April 27 2010 18:17 space_yes wrote:On April 27 2010 18:14 hacpee wrote:
I think he has the mean time confused with the rate of change of the mean time. lol Just try to graph it yourself. You see that it is in fact 1/x. Do a thought experiment. Lets say the interval to return gas with 1 worker is 1. The interval to return gas with two workers is 1/2. The interval to return gas with 3 workers is 1/3. The interval to return gas with 4 workers is 1/4. You see the pattern? 1/x is f(x) and 1,2,3,4,5,6,7,8 is x. The numbers match. Consider the Taylor series where a = 0 of degree 1. If you do not know what this is do not respond to my post. a=0 of degree 1? What notation are you using?
You have not had calculus. There is only one parameter for a Taylor series and the degree is the number of times you take a linear approximation. Open a calculus textbook or use wikipedia.
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Look, to be clear, I'm not trying to talk over anyone here I'm merely responding to someone claiming I was spouting nonsense and unfortunately its hard to argue with someone who doesn't know what you're talking about. I hope you can empathize with that.
I tried to make my original post as clear to the non-math person as possible. It is not my intent to come across as a math genius here but I want to be clear that both 1/x and 1/e^x = e^-x (over a specific domain) are inversely proportional.
FYI: The Taylor series for e^-x where a = 0 is 1 + 1/x . There's a 1 but hey, we always fix the constant
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On April 27 2010 18:52 space_yes wrote:
Look, to be clear, I'm not trying to talk over anyone here I'm merely responding to someone claiming I was spouting nonsense and unfortunately its hard to argue with someone who doesn't know what you're talking about. I hope you can empathize with that.
I tried to make my original post as clear to the non-math person as possible. It is not my intent to come across as a math genius here but I want to be clear that both 1/x and 1/e^x = e^-x (over a specific domain) are inversely proportional.
Ok imagine this. If you have one worker, you return gas at one second. If you have two workers, you return gas in .5 seconds. If you have 3 workers, you return gas in .333 seconds. Does that make sense? Now plot y=1/x in matlab and plot the points (1,1), (2,.5), (3,.3333), (4,.25), etc.
Remember what we're plotting. We're plotting time between return of gas vs number of workers.
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On April 27 2010 18:59 hacpee wrote:Show nested quote +On April 27 2010 18:52 space_yes wrote:
Look, to be clear, I'm not trying to talk over anyone here I'm merely responding to someone claiming I was spouting nonsense and unfortunately its hard to argue with someone who doesn't know what you're talking about. I hope you can empathize with that.
I tried to make my original post as clear to the non-math person as possible. It is not my intent to come across as a math genius here but I want to be clear that both 1/x and 1/e^x = e^-x (over a specific domain) are inversely proportional. Ok imagine this. If you have one worker, you return gas at one second. If you have two workers, you return gas in .5 seconds. If you have 3 workers, you return gas in .333 seconds. Does that make sense? Now plot y=1/x in matlab and plot the points (1,1), (2,.5), (3,.3333), (4,.25), etc. Remember what we're plotting. We're plotting time between return of gas vs number of workers.
See my edit.
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The OP's 2nd graph was time to collect x number workers. You can use an exponential fit for that. I'm not saying you should, but I am saying you can.
Regardless, as I stated previously, you're only dealing with integer values for workers so you don't need the time for gas collection between worker values i.e. 1.5 workers so using an exponential model on such a small domain isn't necessary which others have already point out in their own words.
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On April 27 2010 19:00 space_yes wrote:Show nested quote +On April 27 2010 18:59 hacpee wrote:On April 27 2010 18:52 space_yes wrote:
Look, to be clear, I'm not trying to talk over anyone here I'm merely responding to someone claiming I was spouting nonsense and unfortunately its hard to argue with someone who doesn't know what you're talking about. I hope you can empathize with that.
I tried to make my original post as clear to the non-math person as possible. It is not my intent to come across as a math genius here but I want to be clear that both 1/x and 1/e^x = e^-x (over a specific domain) are inversely proportional. Ok imagine this. If you have one worker, you return gas at one second. If you have two workers, you return gas in .5 seconds. If you have 3 workers, you return gas in .333 seconds. Does that make sense? Now plot y=1/x in matlab and plot the points (1,1), (2,.5), (3,.3333), (4,.25), etc. Remember what we're plotting. We're plotting time between return of gas vs number of workers. See my edit.
1/x! from 2-infinity is 1/2, 1/6,1/12, etc. Nothing to do with 1/2, 1/3,1/4,1/5 etc.
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On April 27 2010 19:03 space_yes wrote:
The OP's 2nd graph was time to collect x number workers. You can use an exponential fit for that. I'm not saying you should, but I am saying you can.
Regardless, as I stated previously, you're only dealing with integer values for workers so you don't need the time for gas collection between worker values i.e. 1.5 workers so using an exponential model on such a small domain isn't necessary which others have already point out in their own words.
Try to model it. Thats just my advice.
y=e^-x is what you're saying the function is. What is y? What is x? How does that relate to dy/dx=-y(because that is the differential equation you need to solve for y=e^-x). Does it make sense?
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On April 27 2010 19:05 hacpee wrote:Show nested quote +On April 27 2010 19:00 space_yes wrote:On April 27 2010 18:59 hacpee wrote:On April 27 2010 18:52 space_yes wrote:
Look, to be clear, I'm not trying to talk over anyone here I'm merely responding to someone claiming I was spouting nonsense and unfortunately its hard to argue with someone who doesn't know what you're talking about. I hope you can empathize with that.
I tried to make my original post as clear to the non-math person as possible. It is not my intent to come across as a math genius here but I want to be clear that both 1/x and 1/e^x = e^-x (over a specific domain) are inversely proportional. Ok imagine this. If you have one worker, you return gas at one second. If you have two workers, you return gas in .5 seconds. If you have 3 workers, you return gas in .333 seconds. Does that make sense? Now plot y=1/x in matlab and plot the points (1,1), (2,.5), (3,.3333), (4,.25), etc. Remember what we're plotting. We're plotting time between return of gas vs number of workers. See my edit. 1/x! from 2-infinity is 1/2, 1/6,1/12, etc. Nothing to do with 1/2, 1/3,1/4,1/5 etc.
The series expansion is not a factorial. That was my exclamation point. I fixed the comment to make this more obvious.
For clarity the series is:
1 + 1/x
Go to the wikipedia page on the exponential functions and read it. Then Google how to use an exponential function to model growth or decay. If you haven't had calculus so you don't understand what a Taylor series then I can't help you 
My question to you: is 1/x^2 inversely proportional?
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On April 27 2010 19:08 hacpee wrote:Show nested quote +On April 27 2010 19:03 space_yes wrote:
The OP's 2nd graph was time to collect x number workers. You can use an exponential fit for that. I'm not saying you should, but I am saying you can.
Regardless, as I stated previously, you're only dealing with integer values for workers so you don't need the time for gas collection between worker values i.e. 1.5 workers so using an exponential model on such a small domain isn't necessary which others have already point out in their own words. Try to model it. Thats just my advice. y=e^-x is what you're saying the function is. What is y? What is x? How does that relate to dy/dx=-y(because that is the differential equation you need to solve for y=e^-x). Does it make sense?
![[image loading]](http://www.teamliquid.net/staff/Arrian/gasexpfunction.png)
y = interval between returns
x = number of workers
Look at the fitting function at the bottom of the graph it is of the form y = be^(ax). I'm not going to try and model it. Someone already did
Have you convinced yourself that y = f(x) = 1/x^2 is inversely proportional yet? Consider:
u = x^2 -> y = f(u) = 1/u
Now consider 1/e^x over a specific domain...
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On April 27 2010 19:16 space_yes wrote:Show nested quote +On April 27 2010 19:08 hacpee wrote:On April 27 2010 19:03 space_yes wrote:
The OP's 2nd graph was time to collect x number workers. You can use an exponential fit for that. I'm not saying you should, but I am saying you can.
Regardless, as I stated previously, you're only dealing with integer values for workers so you don't need the time for gas collection between worker values i.e. 1.5 workers so using an exponential model on such a small domain isn't necessary which others have already point out in their own words. Try to model it. Thats just my advice. y=e^-x is what you're saying the function is. What is y? What is x? How does that relate to dy/dx=-y(because that is the differential equation you need to solve for y=e^-x). Does it make sense? y = interval between returns x = number of workers Look at the fitting function at the bottom of the graph it is of the form y = be^(ax).
So that function will read.
So as the rate of change of the interval becomes larger(more positive) with respect to workers, the interval decreases. Thats how the differential equation reads. It doesn't make sense intuitively.
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I didn't make the graph but it does make sense. When you have 1 worker the time to collect gas is at its max and it decreases as you add workers b/c your collection rate is increasing. It is increasing at an increasingly slower rate! Because you are dealing with integer values for workers only, the exponential fit is unnecessary.
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On April 27 2010 19:41 space_yes wrote:I didn't make the graph but it does make sense. When you have 1 worker the time to collect gas is at its max and it decreases as you add workers b/c your collection rate is increasing. It is increasing at an increasingly slower rate! Because you are dealing with integer values for workers only, the exponential fit is unnecessary.
Here is why it doesn't make sense. If there are no workers, if it follows an exponential model, what is the interval?
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On April 27 2010 19:45 hacpee wrote:Show nested quote +On April 27 2010 19:41 space_yes wrote:I didn't make the graph but it does make sense. When you have 1 worker the time to collect gas is at its max and it decreases as you add workers b/c your collection rate is increasing. It is increasing at an increasingly slower rate! Because you are dealing with integer values for workers only, the exponential fit is unnecessary. Here is why it doesn't make sense. If there are no workers, if it follows an exponential model, what is the interval?
There can be no gas collection when there are 0 workers so there is no model The domain is 1-3 or 1-6 ^_^
EDIT: you could get around the problem of exponential fitting at e^-x = 0 by using a system of differential equations and an initial condition but hey we're really talking about 1,2, or 3 workers on gas it's not necessary
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I know it is disturbing to think that we can use e^x to model most kinds of growth or decay but eventually you will see how awesome of a function it is.
For example consider Euler's Identity:
e^(i * pi) + 1 = 0
pretty cool!
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On April 27 2010 19:47 space_yes wrote:Show nested quote +On April 27 2010 19:45 hacpee wrote:On April 27 2010 19:41 space_yes wrote:I didn't make the graph but it does make sense. When you have 1 worker the time to collect gas is at its max and it decreases as you add workers b/c your collection rate is increasing. It is increasing at an increasingly slower rate! Because you are dealing with integer values for workers only, the exponential fit is unnecessary. Here is why it doesn't make sense. If there are no workers, if it follows an exponential model, what is the interval? There can be no gas collection when there are 0 workers so there is no model The domain is 1-3 or 1-6 ^_^ EDIT: you could get around the problem of exponential fitting at e^-x = 0 by using a system of differential equations and an initial condition but hey we're really talking about 1,2, or 3 workers on gas it's not necessary
using a system of differential equations? So you would have two or more solutions?
As I said, the key is to try to model it using your own intuition. Then you will see that it can't be exponential decay.Yes, you can play with the coefficients and try to force an exponential function onto the 1/x function. They look pretty similar. However the relationship isn't exponential decay.
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Just curious: did you draw those graphs manually or you have some kind of tool ;P?
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On April 27 2010 20:07 hacpee wrote:
using a system of differential equations? So you would have two or more solutions?
You would have an infinite number of solutions
As I said, the key is to try to model it using your own intuition. Then you will see that it can't be exponential decay.Yes, you can play with the coefficients and try to force an exponential function onto the 1/x function. They look pretty similar.
There is a reason why 1/x and 1/e^x = e^-x look similar ^_^
However the relationship isn't exponential decay.
I'm not claiming gas mining intervals are governed by exponential decay, I am only affirming that e^-x can be used as a fit (model) to the data and that it maintains necessary characteristics of proportionality. I've stated numerous times it is unnecessary (especially if you already have a function to describe that data that isn't some sort of approximation) b/c you have integer only values for the workers over a small domain.
The key to modeling isn't intuition. You couldn't be more wrong. People refused to believe the world was round b/c their intuition told them they'd fall off it if that were the case. No one truly believed until Foucault's Pendulum.
Anyways, I need to sleep ^_^ ~~
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On April 27 2010 18:12 space_yes wrote:obviously you've not taken calculus
Speaking as a professional mathematician, you really need to keep your nonsense to yourself. You don't understand much of anything you've been saying in this thread yourself, some meaningless calculus newbie errors interspersed with "go read wikipedia if you don't understand".
On April 27 2010 16:24 space_yes wrote:
As you can see, the exponential function's value is proportional to its previous values. Considering e^-x it is inversely proportional to its previous values. It is this property of prior dependence that makes it particularly good for modeling growth and decay.
Not even coherent. An exponential function is proportional to it's derivative.
On April 27 2010 18:36 space_yes wrote:
Consider the Taylor series where a = 0 of degree 1.
If you do not know what this is do not respond to my post.
Possibly the most transparent attempt to win an argument by obfuscation. Totally irrelevant fluff.
Real calculus is defined on the reals, it works because the reals have a significant amount of useful properties which allow calculus. The reals are a field, a Hilbert space, a locally compact topological group, a continuum Using real calculus to analyse this is entirely meaningless. No algebraic, analytic or geometric representations have even been considered for this model yet, just some poor straw grabbing attempt to apply real variable calculus onto a problem for which it is completely unsuited.
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The whole discussion here is rather amusing, since when do we need differential equations, taylor expansions, the limit and series expansion definitions of e^x to discuss three bro's mining gas.
I thought you wanted to keep your post understandable for non-mathematicians. Now why would you then define how to compute the real number e? Which also doesn't have anything to do with the problem we are looking at here, since the simple inverse proportionality is enough to model it.
Are you trying to say that e^-x is decreasing over time and therefore can be used to model things? Well sure, but fitting a few datapoints to the function doesn't make things prettier, you could use just any function to do that.
I think you should tuck that mathematical schlong back into your pants.
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What are you ppl talking about?! ...Jezus Christ !
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On April 27 2010 21:29 freakclub wrote:
I think you should tuck that mathematical schlong back into your pants.
I tried, but it's four dimensional and noncompact.
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QuantumPenguin, I didn't mean yours, you have my permission to keep waving it around  We posted at the same time. I meant the one of space_yes, who has, as you pointed out, filled this thread with some serious mathematical bullshit.
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The key to modeling isn't intuition. You couldn't be more wrong. People refused to believe the world was round b/c their intuition told them they'd fall off it if that were the case. No one truly believed until Foucault's Pendulum.
The pendulum proves the earth rotates, not that it is round.
The proof for the earth being round is more in the lines of Galileo who argued that when ships arrives you'll first see the top and then gradually more and more of the ship.
Just thought I would give my incredibly relevant input to the totally overboard math discussion... IT'S 1 vs 6 workers on gas for christs sake - the minor faults in the OP aren't relevant at all...
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On April 27 2010 21:18 QuantumPenguin wrote:Speaking as a professional mathematician, you really need to keep your nonsense to yourself. You don't understand much of anything you've been saying in this thread yourself, some meaningless calculus newbie errors interspersed with "go read wikipedia if you don't understand". Show nested quote +On April 27 2010 16:24 space_yes wrote:
As you can see, the exponential function's value is proportional to its previous values. Considering e^-x it is inversely proportional to its previous values. It is this property of prior dependence that makes it particularly good for modeling growth and decay.
Not even coherent. An exponential function is proportional to it's derivative. Show nested quote +On April 27 2010 18:36 space_yes wrote:
Consider the Taylor series where a = 0 of degree 1.
If you do not know what this is do not respond to my post.
Possibly the most transparent attempt to win an argument by obfuscation. Totally irrelevant fluff. Real calculus is defined on the reals, it works because the reals have a significant amount of useful properties which allow calculus. The reals are a field, a Hilbert space, a locally compact topological group, a continuum Using real calculus to analyse this is entirely meaningless. No algebraic, analytic or geometric representations have even been considered for this model yet, just some poor straw grabbing attempt to apply real variable calculus onto a problem for which it is completely unsuited.
My first TL troll! Cool! ^_^ At least you took the time to take my posts out of context and do some googling. A professional mathematician too? Wow @_@ I'm so intimidated !! You can specifically state that you're not trying to come across as a math expert but people still try and make you out to be some evil asshole by first claiming you're spouting nonsense, and then when prove you're not, claim you're obviously just trying to show off! lolz
Not even coherent. An exponential function is proportional to it's derivative.
Did you intend this as a joke? All elementary functions are 'proportional to their derivatives' and d/dx of e^x is e^x... Anyways I don't want to feed the troll any more than I already have -_-~~
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They're talking about bad maths, 3xist.
Stuff interpreted wrong, bad vocabulary transmitting the wrong idea, unnecessary complications for a topic that doesn't require them, mistakes, and show offs.
To sum it up: using a continuous graph (of an interpolated function) for this was a bad idea.
Most of the stuff up here in this page, you'll understand if you ever read take a Calculus I course / read a book on the subject / read wikipedia and research a bit.
It won't help you on getting more gas efficiency in SCII though.
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Great arcticle, I love it!
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SO, gas issue still exist on SC2?
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On April 28 2010 01:42 brocoli wrote:
They're talking about bad maths, 3xist.
Stuff interpreted wrong, bad vocabulary transmitting the wrong idea, unnecessary complications for a topic that doesn't require them, mistakes, and show offs.
To sum it up: using a continuous graph (of an interpolated function) for this was a bad idea.
Most of the stuff up here in this page, you'll understand if you ever read take a Calculus I course / read a book on the subject / read wikipedia and research a bit.
It won't help you on getting more gas efficiency in SCII though.
So can you explain why it is or isn't 1/x? Because you seem to know how to explain it better. No I am not being sarcastic.
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hacpee, you got it right in you earlier posts. space_yes doesn't know anything about maths, just don't listed to that rubbish.
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On April 28 2010 00:53 space_yes wrote:
All elementary functions are 'proportional to their derivatives'
This is not true. If it were true, then every elementary function would be a solution to some differential equation df/dx = kf, for k in R, which of course is not true. The exponential functions up to equivalence by scalar multiplication, i.e any e^kx for k in R, are clearly in bijection with R. Moreover, you could have proven this to yourself in two seconds by differentiating any other elementary function, or by reading a definition of proportionality which is obviously something you also don't understand.
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Yeah ignore everything I said about the Taylor series expansions, it adds unnecessary confusion and doesn't support my argument.
For anyone who is following this the Taylor series centered at a = 0 of degree 2 is given by:
f(a) + f'(a)(x - a) <-- notationally a is very common but not necessarily standard here, different texts use different variables
So e^x:
1 + x
and e^-x is:
1 - x
And for degree of 1 you have 1 and -1 respectively.
credit: Cascade
I pulled an all nighter doing homework so there were some errors in my posts.
So everyone is clear before you PM: I have consistently stated the exponential model is unnecessary and my original op was critical of its use. I don't know why everyone is hating on the OP's modeling function be^(ax) so hard. Its not that big of a deal. The OP probably used excel for an exponential fit and obviously didn't derive 5.4/x.
Regardless of how you decide to model gas collection it should generally confirm the underlying behavior of the system assuming your error bounds on your model are reasonable and your step size isn't do big (if its a linearization). Because the period for returning scv is inversely proportional to the number of SCVs an exponential fit is inappropriate given that nothing is being doubled or halved during a fixed interval of time.
After re-reading my comments from last night and considering some user PMs I want to emphasize it wasn't my intent to exclude anyone from the discussion by unnecessarily elevating the discourse so my apologies if you felt that this occurred or that I derailed the thread...I get excited talking about math and I was nerdraging about being called nonsensical (even if someone my points weren't correct or hard to understand).
Additionally, due to a specific TL user request I promise the community I will not post my mathematical analysis while high.
EDIT: for clarity, pm suggestions
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lol, space_yes got trolled.
His math is sound enough despite the dubious utility for analyzing sc2 gas mining. His vicious argument style and monumental nerdrage interferes with helping lesser nerds understand.
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very good read, people have really been going all out on the technical aspect of the game. however i dont think my zerg playstyle would allow for less than 6 drones on 2 gas from the start.
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science. stats. graphs
i find it hard to argue <3
very nice
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interesting to read this once. but i think this wont affect the playstyle anyway. i mean everybody should know the 3(2) > 3(1) thing since you see that the 3rd probe is always idel for a sec.
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On April 28 2010 03:23 QuantumPenguin wrote:Show nested quote +On April 28 2010 00:53 space_yes wrote:
All elementary functions are 'proportional to their derivatives'
This is not true. If it were true, then every elementary function would be a solution to some differential equation df/dx = kf, for k in R, which of course is not true. The exponential functions up to equivalence by scalar multiplication, i.e any e^kx for k in R, are clearly in bijection with R. Moreover, you could have proven this to yourself in two seconds by differentating any other elementary function, or by reading a definition of proportionality which is obviously something you also don't understand.
Yes, proportional is not correct and actually this was not what I was trying to express. See my edit above. PM me if you want to continue this discussion. I worked it out so you know I understand
f(x) = e^x
f'(x) = e^x
f'(x) = kf -> e^x = ke^x where k = 1
f(x) = sin(x)
f'(x) = cos(x)
f'(x) = kf -> cos(x) = k * sin(x) where there is no constant k that makes this equation true for k in R
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On April 27 2010 18:00 space_yes wrote:Show nested quote +On April 27 2010 17:40 DarkChrono wrote:On April 27 2010 16:24 space_yes wrote:On April 26 2010 21:52 shoop wrote:Hm. I have some objections. On April 26 2010 17:27 Arrian wrote:
Now, a very compelling pattern emerges here, one that looks like an exponential function.
Sorry, but this is nonsense. If the miners would not hold each other up, then the mean time between gas returns would obviously be inversely proportional to the number of miners; to be precise Yes, and that is what the OP 2nd's graph clearly shows. Also see this to convince yourself. I think you may be confused. e^x is given by: As you can see, the exponential function's value is proportional to its previous values. Considering e^-x it is inversely proportional to its previous values. It is this property of prior dependence that makes it particularly good for modeling growth and decay. lol What you've written here is nonsensical. There's no "previous values" to a real function, and the only function that's inversely proportional to it's "previous values" is 1 (given a reasonable definition of what this even means, e.g. f(x) = a/f(x-c), c>0, for all x). If a miner does a trip in 5 seconds, then two miners do two trips in 5 seconds, and k miners do k trips in 5 seconds, so miners do k/5 trips a second. Sticking with k miners, Let's call this rate R. If k miners do R trips a second, then it takes 1/R seconds for a trip to be done. Notice how we took the inverse? This shows that they are inversely proportional. (We've just discovered the obvious concept that period is the inverse of frequency.) The relevant function here was 1/x, not e^-x. I am trying to use easy to understand terms. Something inversely proportional is given by 1/x.The OP function is of the form be^(ax) + c = e^-x = 1/e^x. Look at the definition of the exponential function. You must not understand something. With respect to "previous values" I'm referring to the last value for x i.e. a Maclaurin series polynomial of degree 5 (or whatever we need for that interval of workers and accuracy). The exponential function is used to model over a specific domain so how is that not a real valued function? Here is the Taylor series expansion for e^x with a = 0: Look very hard at that series before you post claiming nonsense and wikipedia exponential function until you understand.
Don't get me wrong, it's great that you're taking an interest in math, but the ability to be honestly critical of your own (and others) arguments is an essential skill. It's ok to be wrong, even though it's the internet.
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On April 28 2010 04:59 space_yes wrote:
Yes, proportional is not correct and actually this was not what I was trying to express.
I guess you are meaning that all elementary functions have derivatives that can be expressed in terms of the original function, which is not strictly true. However there is something similar I have just found:
http://en.wikipedia.org/wiki/Pfaffian_function
Quite cool.
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Slightly off topic, but I don't think it serves much purpose to go into the whole discussion again.
Am I the only one who gets the feeling that the psychology involved in discussing math topics on an open forum is much more interesting than the actual "maths" itself? Reading through the thread just raises so many questions: what on earth drives people to write some of these responses? Why do we get so worked up over issues that are so unimportant in the grand scheme of things? It's also amazing how responses to a single post can vary so much in their assessment. For your enjoyment, I've collected some excerpts - decide for yourself who you agree with.
Brilliant
prOxi.swAMi: SCIENCE. Seriously, very interesting. Kudos for going so in-depth into it.
Clearout: I love it when people does this kind of thorough reasearch, and then writes it up good and befitting standards of a scientific magazine.
v3chr0: Good read very interesting... quite a work of art you have there
mfZOR: Shit mate, Awesome read. Very technical
Archerofaiur: seriously is there any game on the face of the earth that recieves this kind of dedicated research.
LiquiDLegend: Very in-depth analysis as others said, its really good.
RonNation: it seems this is mostly a lesson in common sense, but a good lesson nonetheless
Reborn8u: Your definitely going to be one of the professors at starcraft university
Korpze: My mind has been blown.
stork4ever: whoa, this is why i joined this forum
bay: Wow- really fantastic article. This is the kind of stuff I have been looking for! Thanks so much
So so
BladeRunner: reasonably good info but not very in-depth and way too verbose.
Zalan: Yeah, as most said: interesting info, but a bit redundant...
Toran7: Articles like this make me feel inadequate when it comes to math :/
crate: I definitely like the effort and SC2 needs more analysis on resource gathering especially with its implications on mapmaking.
Osmoses: I agree that most of this article was unnecessary fluff, but there was one very important discovery that I actually think I will incorporate into my play
Rubbish
QuantumPenguin: As others have said, there is no science or maths here, just some annotated arithmetic. Furthermore it makes absolutely no sense to regress a function on a domain for which it is undefined. Quite a lot of pretentious nonsense in this article.
shoop: Sorry, but this is nonsense. If the miners would not hold each other up, then the mean time between gas returns would obviously be inversely proportional to the number of miners...
Markwerf: This article is so unneccesary long it's unbelievable
DarkChrono: I'm laughing so hard at gasexpfunction.png (2nd graph)
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On April 28 2010 06:20 DarkChrono wrote:
Don't get me wrong, it's great that you're taking an interest in math, but the ability to be honestly critical of your own (and others) arguments is an essential skill. It's ok to be wrong, even though it's the internet.
You have to be wrong to learn ^_^.
I guess you are meaning that all elementary functions have derivatives that can be expressed in terms of the original function, which is not strictly true. However there is something similar I have just found: http://en.wikipedia.org/wiki/Pfaffian_functionQuite cool.
Yes and that Pfaffian function you came across is pretty cool.
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Very very nice article, but i am wondering about one thing
* 1(1) | 0.74 gas/second
* 2(1) | 1.50 gas/second
* 2(2) | 1.48 gas/second
* 3(1) | 2.00 gas/second
* 3(2) | 2.23 gas/second
* 4(2) | 3.05 gas/second
* 5(2) | 3.33 gas/second
* 6(2) | 3.94 gas/second
it should be true in my opinion that
5(2) = 2(1)+3(1)
but result is different.
2(1)+3(1) = 1.5 g/s + 2.0 g/s = 3.5 g/s
while 5(2) = 3.33 g/s
Is this because of fact that one geyser is closer than second one ? Or is this just small deviation in data ?
Btw, i am curious how it is with minerals, especially how long should i wait in seconds to get minerals spend on worker back.
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* 4(2) | 3.05 gas/second
* 5(2) | 3.33 gas/second
* 6(2) | 3.94 gas/second
If you put a third worker on one geyser you get +0.28gas/second, but if you put a third worker on the second geyser you get another + 0.61gas/second, which doesn't make sense to me.
Anyone has an explanation for this?
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On April 28 2010 08:21 shoop wrote:
Rubbish
QuantumPenguin: As others have said, there is no science or maths here, just some annotated arithmetic.Furthermore it makes absolutely no sense to regress a function on a domain for which it is undefined.
Everything I said here was true. Even if one were to pretend that the graph has some meaning for a real number of workers (which it doesn't), the interpolation is still wrong, as every natural number of workers n for n > 6 has gas return interval equal to the gas return interval of n=6.
You do also realise that only one of the data points is even remotely close to its graphical position, right? That picture is just meaningless.
Edit: Oh, I thought you were classifying my post as rubbish, until I saw you'd self-quoted there My apologies.
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On April 28 2010 18:01 QuantumPenguin wrote:
Edit: Oh, I thought you were classifying my post as rubbish
I think you're quite right, actually But given how this thread developed I thought it would be better not to go into right and wrong too much anymore. After all, I already said what I think. I'm still thinking if I can come up with a good psychological theory to explain the way threads such as this often develop. It's crazy.
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On April 27 2010 00:00 Markwerf wrote:
This article is so unneccesary long it's unbelievable...
First of all the method and data is nice and all but really this could be summarized much easier. It is pretty safe to assume beforehand to that rate of gas income is constant while the gas geyser is running as we all know this from playing experience. Thus just putting 1, 2 and 3 workers on a geyser and just timing for a minute each and calculating how much you gas income you would get would suffice, doing the 2nd gas as well is completely unneccesary as it's obviously the same as the first.
So 4(2) is really the same as 2x 2(1)??, everyone could think of that beforehand..
The only interesting thing in here is how much less efficient the 3rd worker is then the first 2 ones using the geyser. The raw gas income is also slightly interesting.
The inverse graph is completely useless and add's nothing to the whole issue, that entire paragraph should be scrapped really.
Also the investment and income table at the end hardly makes sense as it counts the costs of workers which you would be having anyway. It neglects the oppurtunity cost of making the refinery as well which though different for each race can't just be neglected either.
The whole writing and setup of this piece is just not good. Needlessly trying to do complicated things which add nothing to the whole subject...
Congrats on proving that you're a moron. Do you want to confess to murdering JonBenét Ramsey now, too?
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On April 26 2010 17:27 Arrian wrote:
Granted this analysis is limited in scope. While I strongly suspect there are no differences in gas collection rates between the races, my analysis was limited only to Terran, on Lost Temple at 6 o'clock. Of course, I am assuming that these are typical geyser positions and there are no differences between the gas collection rates between the races, and there were other moderate sources of error, namely a non-uniform starting place for the gas collection, but this is normed by the large number of data points and the absolute nature of gas collection. Thus, by linear regression, an approximation of the rate of gas collection can be ascertained, but more importantly, its relation to other methods of gas collection.
There is a slight advantage to gas that will be placed on a "pure" horizontal or vertical pattern. When I play Z I try at times to take that little extra inch to get a kind of benefit overtime with an xtra hatch placed in this "optimal" way. After a few comparisons I won about 30-60 gas in two minutes with that hatch instead of letting the original hatch be the gathering point.
Shame I actually play T but I think that on some maps that has geysers placed diagonally some Z's could undergo a few bo's optimized for those type of maps, given if that xtra hatch would be part of a viable plan, that is. ^^
Excellent post, it just adds up with the little things I found myself!
Little edit what I pretty much did on my part (but too lazy to share) was to make up a list of gathering gas with a 1(1), 2(1) and 3(1) for every different timing of a building, unit, upgrade and research, then grouped up the stats.
I'm finally and slowly starting to think WHEN should I really take that gas, but what you just showed here simply gives me more to ponder and to readjust.
I did notice after writing down my "gas over time" that it wasn't possible to have a beginning estimate of over 20 seconds for example and then think "it will be the double harvested in 40 seconds" because, just as you said yourself, the chunky way the gatherers are bringing the resource to our main building; that's why I ended up doing an estimate for every specific timing that exists (only for Terran; I didn't have the courage to do the different ones for the two other races). Besides I didn't want a deeper understanding of "how gas works", I only wanted to plug in the amount gained over the given times to implement them into the relative timings and triggers. But you just showed us that deeper understanding would have important things to know :-)
If I ever feel like playing Z again (was Z on bw), I might give a try of some bo's with an xtra hatch but I'll just place it as close as possible to geysers that are originally put in a diagonal. I remain certain that it could be a considerable advantage over time against another race that won't be too fancy about making a CC/Nexus just for a geyser.
Last edit: I profusely apologize for making this so long but I just realised that the "triple" gas gained by doing 2(1st) and 1(2nd) can become a very very little difference if you play on a map where the geysers are positioned further away (LT is in his case of observations the shortest distance you can profit from) because the pause coming from a scv/probe/drone as the 3rd one being in one gas becomes nearly non existent.
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very informative, you actually went through the process of showing statistics with the graphs and all.
great work =]
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Great read to start the day off. ;-)
Thanks for the effort!
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Very informative! this shall come in handy lol
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This is a great article. Keep up the good work!
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The biggest question I have is is there any difference between a 1(2) and a 2(1) because honestly the fact that the 2(1) jumps so much higher than the 1(1) is blowing my mind. Is this the same rate that a 1(2) would have though? It could possibly change my entire starting strategy!
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I think gas consuption needs to be balanced early game by race. Terran seems to be very "eco-friendly" as far as this goes, whereas zerg requires a much more vasp/min ratio.
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U should work for newspaper. Or like Randy in SP. Nice article, but too much information and effort to have little point in the end.
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Very informative analysis. Till now I had only two starting options for gas. Either 3 on 1 or 6 on 2. Now, however, I might go with 2 on 1 or 5 on 2 if gas isn't desperately needed.
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From what I have seen in the game, the rate at which you collect gas still works pretty well with various build orders.
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super hot article. that really shows how dedicated the starcraft fans are!!!! :D
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i'm glad someone actually did this! thanks for going through this trouble
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wow nice job, you definitely used your effort into this
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Someone should doublecheck me on this because if it's true then I'm honestly surprised that this data's gone this long undisputed. I ran a bunch of tests on blistering sands comparing 2 drones to 3 on an extractor and I found the 3rd drone to be just about as valuable as the 2nd. The 3 drones mined ~155gas/minute (2.58/s) and the 2 drones mined ~105gas/minute (1.75/s). This is considerably different than OP's data: 3(1) | 2.00 gas/second and 2(1) | 1.50 gas/second.
I ran the test a few times for 5 minutes each, but that should be accurate enough. I'm not sure if the discrepancy with OP is because of the geyser location, human error or some other unknown factor, but considering how a lot of the different trials in OP don't add up correctly, I'd say the data's a bit questionable. If you watch 3 drones mine a geyser, the wait period is practically nonexistant so I'm a little skeptical.
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On May 02 2010 01:00 Fu-Fo- wrote:
U should work for newspaper. Or like Randy in SP. Nice article, but too much information and effort to have little point in the end.
Yo, this guy is putting together a data and drawing a conclusion and all you can say is that it wasn't a big enough impact? How would he know what the impact would be if he hadn't done the data collection. Maybe there could have been a big discovery here. Like if Edison hadn't actually ever make a light bulb, it still wouldn't have been a waste because there was possibility of him actually making something happen. Now we know that there is a subtle difference between gas collection rates. G-d, just thank this guy for doing this on his own time for you. If you want it done better, shut up and do it yourself
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On May 02 2010 01:00 Fu-Fo- wrote:
U should work for newspaper. Or like Randy in SP. Nice article, but too much information and effort to have little point in the end.
I dunno, I kind of like that he didn't make his point clear. I kind of feel that he's trying to get us to think of what we could do, now that we have all of this information on hand. This is the kind of information players will need to come up with truly innovative and creative builds.
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Appreciate the information you found. Even though the outcome may not have been a crazy breakthrough, it did clear the air of a lot of uncertainty I had regarding the two vespene geyser system in SC2.
I'm sure in due time there will be some sort of minuscule timing window where it may be effective to abuse. Then again its probably all map, race, and circumstance dependent.
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On May 04 2010 17:35 Beakyboo wrote:
If you watch 3 drones mine a geyser, the wait period is practically nonexistant so I'm a little skeptical.
This IS strange: if it is because of geyser location, then either your geyser is further away than the OP's, or it is closer. Since you mine more gas per second with two drones than the OP did, it appears that your geyser is closer. But if it's closer, then the third drone should have at least as large a delay before it can get into the geyser, so the effectiveness of three drones should be decreased even more than in the OP. The only explanation I can think of is that your extractor is in fact further away AND you tested with a faster game speed.
As you may have noticed reading the previous posts in this thread, I think the analysis in the OP is in fact pretty bad, even though it is long and looks complicated and most people seem to love it to bits. I'm in favour of the following heuristic, which is safer, simpler and relies more on common sense than blindly adopting the figures from the OP: "if I see a drone waiting at the geyser, I'm not mining at optimum efficiency so I should consider placing more extractors". Sorry if that sounds simplistic. It's either that or test and memorize how far away the geysers are on all maps.
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the graph is missing the line for 3(1)
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Great article and imba mathing skills!
You're awesome!!!
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Very good analysis and everything =D Makes me think about how i start in SC2 beta nao.
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this stuff reminds me of my physics labs. Exel ftw!!!
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well after reading the whole thread im a little confused.... because in sc2 everything is so gas expensive.. ur going to want to saturate ur gas pretty quick. ontop of that all this talk about 4/2 5/2 pretty much only matter around 25 food or so and only lasts for like 5 food or so.. so in the grand scheme it really isnt important. u need SOOO much gas that if this article was about a 4th miner per gas node it would be much more interesting.
its even funny cause i see shoutcasters saying oh hey this guy has 4 guys on gass what an idiot. when the fact is on far gas it makes a difference.
im always gas starved and i play platinum. forces you to expand and get more tech building i guess.
ever notice with only 3 guys on a gas node u run outa mineral nodes earlier then gas even when they start at the same time.
woulda been nice if u guys had ANY data on what really matters... 4th miner.
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amazing stuff, but u lost me at exponential function
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Am I missing something? What is everyone fawning over? Seems like the OP only gave us two useful pieces of info:
1) In normal circumstances, any miner beyond #3 is a waste (duh... we can see the next guy waiting in line)
2) 3 miners on 2 geysers is slightly more efficient than 3 miners on 1 (not as obvious, but also not as helpful)
Everything else is chaff. I mean what role does an exponential regression function or "return on investment" have in a game of starcraft? "Sorry teammate, I would like to tech to mutas to counter his banshees, but if I put another drone on the gas I'm not getting an optimized return on investment."
If you're concerned about optimizing return on investment, never make any probe beyond the first 6 you get. Investment = free... therefore Return = ∞ ... there's some info that'll really help you climb the ladders.
Moral of the story: Never underestimate the power of a chart and mathematical jargon to impress those who don't understand it...
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I am very much a fan of these statistic threads
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Couldn't you just say that 2.67 workers saturates a geyser?
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Hmm... Very interesting information gathered. I must say that most of the points proven in your post were assumed. However, having statistical data to back it up is nice.
The most interesting was the 3(1) vs. 3(2). I highly doubt I will utilize this information (75 extra minerals to get to start harvesting on the second gas isn't worth its value), I can see how it could possibly open up for some different opening builds.
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Very good analysis. I would agree "conclusions are both rather intuitive and fairly reasonable." Although it seems you didn't graph 3(1), perhaps it is hiding behind 3(2).
Props for your time and conclusion.
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So we're all sticking to 3 on each, it seems. That's quite the in-depth analysis, it's good to know we've had it right all along
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Great post, very thorough and informative (dare I say overkill?)
I think it may be helpful to add a third column to that last table, for (gas/s per min investment)
The numbers would be as follows
1(1) .00592
2(1) .00857
3(1) .00889
3(2) .00743
2(2) .00592
4(2) .00871
4(1) .00727
5(2) .00833
6(2) .00876
Naturally, saturation 3(1) and 6(2) is the most efficient investment. it's notable that 4(2) and 5(2) are very close behind saturation in terms of investment efficiency,
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EPT![[image loading]](http://www.teamliquid.net/staff/SilverskY/SCIIConceptBanner.jpg)
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