|
On February 11 2011 08:25 plagiarisedwords wrote:
I did my undergrad in economics and got top of my class so I know the theory you are basing this on fairly well. I have tried applying economics to Starcraft as well but generally find that it is not too useful. Mainly because starcraft is much more complex than many economics model allow for. The big problems are opportunity cost, risk and time.
The real concerns when playing starcraft is staying alive, and making sure you stay alive in the future too. This is based on what you do but also what your opponent does so is very hard to model. So optimality of revenue is a pretty small factor when deciding how many workers to build. What people care about is whether they can build it, stay alive and benefit in the long run or cut workers now and kill the opponent before their economy kicks in.
I have played with a few models but didn't post the results up on TL because the findings are so blatantly obvious to a diamond level plus player.
the human mind is too good at making calculations about risk and return, it is hard wired into our intuition to help is survive!
I'm not trying to model "the optimum amount of workers to win the game," all I did was show that to get the most minerals off of one base, you need 27 workers, not the previously-thought 24.
|
Not sure why people are so hostile, when all they'd usually do is lurk on the forums and never contribute anything of value; great work  . People need to quit nit-picking the 'practicality' of this information, since there are many things still to be discovered in SC2 and we've got to explore the whole scope of it.
|
All you guys who are reading this and responding with "OMG 1 BASE? 2 BASE IS BETTER" are yet to realise your error, because it's obvious 3 BASE IS BETTER LOL!
In all seriousness tho, natewOw, excellent post :D I'm sure a lot of people who read it will find it informative and I hope that they take away with them an insight into basic economic principles which will allow them to explore the issue further in a constructive manner.
In regards to optimizing your 'workers to base' count, I believe the point of this thread is to determine the potential maximum income per base, Yes it is obvious that having more bases will give you more income, but in a scenario of, for example, you have 5 bases, how many workers would you need to get a maximum possible income from 5 bases? (yes I am aware there is a supply cap, but it's not prudent for helping us understand these craftonomic theories). So please refrain from posting with comments like "just build more bases and don't saturate".
The above situation is more easily understood when you consider the 'worker to base' count of a 1-base scenario. Its relevant to early game, it's relevant to lategame when the map is mined out, and mid-game will just be a multiple of 1-base marginal revenues (assuming even worker distribution) depending on your base count.
I guess my only hang-up with your theory is that you've made the assumption that the game isn't going to immediately end and I'd be interested in modelling what happens when you change that assumption. Regardless I'd like to thank you natewOw for such a great post and inspiring me to explore some of these concepts myself :D
|
On February 11 2011 08:27 sl10 wrote:Not sure why people are so hostile, when all they'd usually do is lurk on the forums and never contribute anything of value; great work .
Honestly, people questioning the usefulness of this doesn't bother me. I never said I was introducing some earth-shattering fact that was going to change the shape of the game.
It's the people trying to tell me that 24 workers on one base gets you more income-per-minute than does 27, despite me showing empirical evidence that this is not the case.
|
If it would take 20 minutes or so for the extra 3 workers to pay off their cost, wouldn't the patches be mined out by then?
And 27 workers does generate more income than 24, common sense, but is that all that you're trying to prove?
|
On February 11 2011 08:29 natewOw wrote:Show nested quote +On February 11 2011 08:27 sl10 wrote:Not sure why people are so hostile, when all they'd usually do is lurk on the forums and never contribute anything of value; great work . Honestly, people questioning the usefulness of this doesn't bother me. I never said I was introducing some earth-shattering fact that was going to change the shape of the game. It's the people trying to tell me that 24 workers on one base gets you more income-per-minute than does 27, despite me showing empirical evidence that this is not the case.
How is it empirical? Your data is from a formula you don't even disclose, not actual in-game observations.
|
Dear natewOw,
First, thanks for undertaking this analysis--I am a bit of an economics geek myself, and I have been enjoying LaLush's (and now your) post and comments a lot. I think good analysis of this type can advance our understanding of the game considerably.
Some specific thoughts on your analysis:
-you've chosen to define MC and MR in terms of minerals/time. This is obviously fine. However, your argument that MC->0 as T->inf introduces a flaw in your analysis because given that the number of minerals available on any map is fixed, MR->0 as T->inf as well (i.e., if you have an unbounded amount of mining time, you can mine out the map with only one worker, or with just your original workers, or however you want to look at it). To the extent that this isn't really a practical consideration, then neither is the assumption that we should be calculating the limit of MC as T->inf. Why not just step back and say you've calculated the minimum worker count that produces the maximum revenue flow for a single base? (Note: this may not even be exactly true given LaLush's interesting finding that MR from distance mining may exceed MR from one-base at around 22 workers--I'd love to see this tested more.)
-you've chosen to estimate MR as a cubic function. LaLush and his predecessor chose to use an empirical estimate of MR (or related values). I'm not convinced yours is the preferable approach, particularly considering that your estimated function is concave and turns negative in the neighborhood of 20-30 workers. My prior on this is that it must be that MR->0 as workers->inf, and that MR cannot turn negative, or at least very negative. You need your estimated function to be most accurate in this range to prove your point, but its accuracy seems to be questionable in just that range. You write "...I generated predicted values of income per minute as a cubic function of the number of workers currently mining. Don't get too hung up on the method..." I'd actually love to hear the method you used--did you base it on some empirics you did, or that you got from another source?
I hope you take the feedback you're getting in stride, and that it prompts more of this brand of analysis from you and the rest of the community. I hope to add something in this vein at some point when I feel I have the time.
|
On February 11 2011 07:09 natewOw wrote:Show nested quote +I am wondering if you have the right definition for "Optimal Saturation". Here, you define optimal saturation as the maximum rate of mineral collection. You got it right, optimal saturation by my definition is the most minerals that can be collected per minute. I said nothing about build orders.
Nice response, but I wanted to ask you an idea about another economic concept. Your original argument says that the marginal cost goes to zero as T goes to infinity, and I thought it was a clever argument.
But what about the opportunity cost of the minerals to used to build the probe? That is, when you chose to build, you forgo the benefits of building a building or attacking unit, and those forgone benefits are a cost.
So how can the marginal cost of a probe go to zero, when it seems that the opportunity costs always exist (regardless of time)?
|
On February 11 2011 08:34 mucker wrote:Show nested quote +On February 11 2011 08:29 natewOw wrote:On February 11 2011 08:27 sl10 wrote:Not sure why people are so hostile, when all they'd usually do is lurk on the forums and never contribute anything of value; great work . Honestly, people questioning the usefulness of this doesn't bother me. I never said I was introducing some earth-shattering fact that was going to change the shape of the game. It's the people trying to tell me that 24 workers on one base gets you more income-per-minute than does 27, despite me showing empirical evidence that this is not the case. How is it empirical? Your data is from a formula you don't even disclose, not actual in-game observations.
I should have made this clearer in the post. It is from actual in-game observations. There's really no "formula", I just estimate more precise measurements of the marginal revenue increments, since blizzard's income meter only goes in increments of 20.
|
|
|
On February 11 2011 08:37 natewOw wrote:Show nested quote +On February 11 2011 08:34 mucker wrote:On February 11 2011 08:29 natewOw wrote:On February 11 2011 08:27 sl10 wrote:Not sure why people are so hostile, when all they'd usually do is lurk on the forums and never contribute anything of value; great work . Honestly, people questioning the usefulness of this doesn't bother me. I never said I was introducing some earth-shattering fact that was going to change the shape of the game. It's the people trying to tell me that 24 workers on one base gets you more income-per-minute than does 27, despite me showing empirical evidence that this is not the case. How is it empirical? Your data is from a formula you don't even disclose, not actual in-game observations. I should have made this clearer in the post. It is from actual in-game observations. There's really no "formula", I just estimate more precise measurements of the marginal revenue increments, since blizzard's income meter only goes in increments of 20.
So there is no magical "cubic" formula, and to put it simply, you pause the game and jot down on a piece of paper the minerals you have at a given time?
|
On February 11 2011 08:37 SolonTLG wrote:Show nested quote +On February 11 2011 07:09 natewOw wrote:I am wondering if you have the right definition for "Optimal Saturation". Here, you define optimal saturation as the maximum rate of mineral collection. You got it right, optimal saturation by my definition is the most minerals that can be collected per minute. I said nothing about build orders. Nice response, but I wanted to ask you an idea about another economic concept. Your original argument says that the marginal cost goes to zero as T goes to infinity, and I thought it was a clever argument. But what about the opportunity cost of the minerals to used to build the probe? That is, when you chose to build, you forgo the benefits of building a building or attacking unit, and those forgone benefits are a cost. So how can the marginal cost of a probe go to zero, when it seems that the opportunity costs always exist (regardless of time)?
I actually addressed this earlier, but even if you include opportunity cost within marginal cost, the marginal cost still converges to zero, because you are dividing MC by time, T. Thus, MC could include the cost of my dry cleaning, and it would still go to zero as the game time gets infinitely larger.
|
On February 11 2011 08:39 Nagano wrote:Show nested quote +On February 11 2011 08:37 natewOw wrote:On February 11 2011 08:34 mucker wrote:On February 11 2011 08:29 natewOw wrote:On February 11 2011 08:27 sl10 wrote:Not sure why people are so hostile, when all they'd usually do is lurk on the forums and never contribute anything of value; great work . Honestly, people questioning the usefulness of this doesn't bother me. I never said I was introducing some earth-shattering fact that was going to change the shape of the game. It's the people trying to tell me that 24 workers on one base gets you more income-per-minute than does 27, despite me showing empirical evidence that this is not the case. How is it empirical? Your data is from a formula you don't even disclose, not actual in-game observations. I should have made this clearer in the post. It is from actual in-game observations. There's really no "formula", I just estimate more precise measurements of the marginal revenue increments, since blizzard's income meter only goes in increments of 20. So there is no magical "cubic" formula, and to put it simply, you pause the game and jot down on a piece of paper the minerals you have at a given time?
Actually I jotted down the replay's estimation of the income-per-minute at X number of workers. Like I said, this only goes in 20 mineral increments and is no doubt an estimation, so I estimated more precise by making income-per-minute a function of workers, workers^2, and workers^3.
|
So why is there a diminishing return in MR between 7 and 8 workers if you assume your MC is 0?
|
United States7483 Posts
I understand your reasoning and logic behind your arguments, and why MR is measured by time, but I have to take issue with your units here, the marginal cost of an additional worker being 0 does not lead to optimal play.
I agree that you have shown that more than 24 workers on one base yields more minerals than exactly 24, but the units you are using makes it impossible to accurately determine if it's worth 'enough' more minerals per minute to make those extra workers while staying on one base. It's difficult to work around this however, with the way the game functions by using economic models.
|
You have two bases, It's possible, but the 27 gives you the lower bound. If you want to get the most minerals off ONE base, it's 27.
You could show that with 97% fewer graphs. Why does introducing marginal revenue and so on show anything more than the statement '27 workers gives you maximum income off one base'?
And the distance mining calculation was done better by Lalush.
|
On February 11 2011 08:09 natewOw wrote:
You now have 40 workers mining at the natural, but any amount of workers above 27 gets you nothing, and may even decrease your net income due to cluttering.
what do you mean by cluttering? There is no such thing as cluttering when workers mine cause they pass through eveything, including other workers.
just curious
|
OP spends an hour writing up some fancy econ post to show that 27 > 24 miners on 1 base and when he is confronted with the fact that this is useless in a real game (unlike Lalush's excellent thread on this topic), he then fills this thread with stubborn passive-aggressive bait posts (aka trolling). I don't see this thread lasting very long.
|
The optimal number of workers per base is 2 per mineral patch. When above 2 workers per patch you get diminishing returns per worker. I mean why would a player not want to have a worker pay for itself asap. If you have more then 2 workers per patch it takes longer for the workers to pay for themselves. I don't understand why people think it is anything else. The only reason to go above 2 per patch is if you can not safely expand(granted this happens a lot).
|
There is a HUGE flaw in the numbers that I think most people have just simply overlooked.
In the OP: "This is saying that the limit of the marginal cost function, as time gets infinitely greater, is zero. Thus, the expected marginal cost of producing an additional probe is zero."
If MC is zero, so then why is there a diminishing return on MR when there are 16 or less workers (assuming 8 mineral patches)? Does this make no sense to anyone else?
![[image loading]](http://i52.tinypic.com/xpomtj.png)
This would mean that the graph above would be completely false up to 16 workers. Am I missing something?
|
|
|
|
|
|
EPT
