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Hey TL, first time posting a thread here so I apologize if what I post isn't quite what you're used to. First I'll give a little run down of what this thread is about, and then I'll get into explaining how it works and why it's important.
Work done by: Bored.322 Magannon.463
Intro: Basically what I'm going to show you is the amount of damage that worker harass actually does, and how you can calculate exactly how much damage you've done by using an equation that I've come up with.Long story short I did some number crunching to come up with an equation which shows how much economic damage is done per worker lost. I tested this in a few build order testers and the results for one and two base play is 99% accurate. Why I really find this is important is it shows the cost efficiency of worker harass via hellions, drops, etc.
While I haven't included it in the equation or any of the other parts of the document, I believe I have come up with the pattern for three base play too although I haven't quite tested it and I am not happy with the result I got (I believe it was error on my play-testing). For this reason, I will keep it out and if the thread gets some attention I'll try and work out the kinks.
EDIT: This doesn't work for three bases for those wondering. It'll need some tweaking.
The Equation: 50x+(0.5x)(x+1)(11.33333)((((-1)^(b))-1)/2))^2)+(1/8)(7+(-1)^x+8x+2x^2)(11.33333)(((-1)^(b)+1)/2) where x=WORKERS and b=BASES
How to use the Equation: There are two simple ways of using this equation. i. Submit the values into a calculator. ii. Copy/paste the equation into Wolframalpha and modify the X value to be the number of workers killed and the B value to be the number of bases.
Warning: (Fairly easy) Math + Show Spoiler + How Does it Work? The equation is actually quite simple, and can be broken down into 4 easy parts. For the sake of keeping things brief I'll explain how this works on just one base, although it follows the same pattern if you were to also examine two base play.
i. 50x This is quite simple, it's the base 50 minerals lost to replace each worker.
ii. (0.5x)(x+1) This part is a little bit more complicated. What this does is compensate for the fact that you can't build all of your workers at once. For example let's say you lose two workers. You're going to lose 2x 11.33 minerals worth of mining every 17 seconds (the time it takes to create one worker). Since there are two workers this goes on for a total of 34 seconds since you have to queue one after another. You can't just double the amount of mining lost though, since the amount of missing mining time will start at 2x, but then become 1x once the first worker is created.
Where does this (0.5x)(x+1) come from though? It's actually quite simple. Rather than count minerals lost, it will count cycles. Each cycle will equate to 17 seconds, but that's not represented in this calculation (and that's okay). When you have one missing worker, you miss one 17 second cycle. 1. When you have two missing workers, you miss two cycles, and then one cycle. 3 total. Three workers missing and you'll have three, then two, then one. 6. If you continue the pattern you get 10, then 15, 21, 28 etc.
The (0.5x)*(x+1) is just a way of determining how many cycles you'll miss until you stabilize your economy.
iii. 11.333 The previous segment tells you how many cycles you've lost. A cycle is the time it takes to create a worker, 17 seconds. IIRC workers are said to mine at close to 40 minerals per minute. 40*(17/60) = 11.333 minerals per cycle. Multiplying the amount of minerals/cycle by the amount of cycles will yield the amount of minerals lost through lost mining time.
iv. ((((-1)^(b))-1)/2))^2) What in the name of all that is Starcraft is this? Well all it really is, is a way of saying "based on the number of bases, do or do not ignore this."
If you say you have one base (b=1) you get: =((((-1)^(1))-1)/2)^2 =((-1-1)/2)^2 =(-1)^2 =1 So multiply the equation by one and carry on.
If you say you have two bases (b=2) you get: =((((-1)^(2))-1)/2)^2 =((1-1)/2)^2 =(0^2) =0 So multiply the equation by zero and carry on.
The reason this is important is that the equation is divided into segments. The first part shows one base, the second two base, and eventually there will be a third and possibly a fourth. If you have two bases you will have a different equation for the amount of cycles lost and you'll have to zero out the equation for one base.
It could have been done separately to give two much simpler equations, but I decided I want to combine the two so that I could just input the data into a program and calculate how much mining time would be lost.
Why is this important? Well it can't really be used in game, but it can be used beforehand to tell if the effectiveness of a drop play is worth it, or how much damage you'd have to do in order for it to be worth it. Let's say you're using hellions against someone who is on two bases. A lot of people will say "4 hellions should kill 6-8 workers in order for them to be worth it" with a lot of people starting to go towards the higher end of the spectrum (from what I've noticed at least). Well if they're on two bases then 5 workers killed will set them back at around 386 minerals. HOWEVER this assumes that their reaction is instantaneous in terms of building workers again. Chances are that they're going to be microing a bit and trying not to lose more, so in all fairness it's probably safe to round up to 400 which basically pays for the 4 hellions alone.
The other part to this, is that you're just setting them back 386 minerals, this doesn't even account for the amount of minerals that it's putting you ahead. If they're already in the process of building workers than the most current worker won't be used to put them a head but rather put them behind one full cycle. This means you're already pushing them back 17 seconds of building + 386 minerals.
Results: I've run a series of tests on multiple build order testers. What I've noticed is that I'm getting results that are up to 99% accurate. Now these are controlled experiments (I'll detail the process momentarily) and my reaction times are instant in the way that I've set it up, so I expect to see that the amount of damage done will actually EXCEED the amount that my equation will give you, but that equation is merely the minimum.
I don't have any footage/pictures available to me at the moment, should someone really want them I will redo them and post them, but I can give you my method. First, I went onto a build order tester and started as terran. I hotkeyed each SCV individually from 1-6.
- 1:00 - Sent the hotkeyed SCVs to mine. To be as consistent as possible I sent 1 SCV to the patches from left to right at a rate of one move command per second.
- 3:00 - I pulled off 1-4 SCVs after they had returned their yield and recreated the same amount.
- 6:00 - I let all of the SCVs finish their mining round and then stopped them.
From this, you would finish with two different amounts of minerals. The totals are irrelevant, the difference is the important part. I would make note of the difference, and divide it by the expected amount from the equation to determine how accurate it was (You could also use experimental error, although it'll basically give you the same number).
Final Thoughts With that, I leave you what I've been working on for a couple of hours. There may be some factors which I didn't take into consideration, and with that I would like to hear your feedback. Keep in mind that this doesn't cover opportunity costs, it merely shows the actual damage.
Could this change how we view economic harassment? Could this change how effective we think we have to be with our harassment? Could this change how people do their builds in order to be the most efficient in their harassment?
These are some of the questions I leave with you, thank you for your time and thanks for sticking it out to the end.
Cheers, Bored.322.
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This is very cool but during a game I really don't care I just like to bbq drones.
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On August 30 2012 10:54 Maxd11 wrote: This is very cool but during a game I really don't care I just like to bbq drones.
Admittedly it isn't very useful for when you're IN a game, but it can help you figure out how much damage you should be doing in order for you to be working effectively. But yes flaming drones are a funny sight, although it's not one I particularly enjoy since I play zerg :[
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The Equation: 50x+(0.5x)(x+1)(11.33333)((((-1)^(b))-1)/2))^2)+(1/8)(7+(-1)^x+8x+2x^2)(11.33333)(((-1)^(b)+1)/2) where x=WORKERS and b=BASES ]
Oh god I laughed until my sides hurt
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On August 30 2012 10:55 Bored wrote:Show nested quote +On August 30 2012 10:54 Maxd11 wrote: This is very cool but during a game I really don't care I just like to bbq drones. Admittedly it isn't very useful for when you're IN a game, but it can help you figure out how much damage you should be doing in order for you to be working effectively. But yes flaming drones are a funny sight, although it's not one I particularly enjoy since I play zerg :[ How do you modify the equation for each race to factor in chrono boost/the facts that zerg can (theoretically) replenish all their workers at the same time using larvae?
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On August 30 2012 10:58 Aild246 wrote:Show nested quote + The Equation: 50x+(0.5x)(x+1)(11.33333)((((-1)^(b))-1)/2))^2)+(1/8)(7+(-1)^x+8x+2x^2)(11.33333)(((-1)^(b)+1)/2) where x=WORKERS and b=BASES ]
Oh god I laughed until my sides hurt
It's messy, yes, but it gets the job done. It's hard to make math equations look nice without using images of it arranged nicely. Wolframalpha is good at it, but I won't have an account for it for about a month or so which makes it hard to display it nicely.
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LOL
User was banned for this post.
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On August 30 2012 10:59 Maxd11 wrote:Show nested quote +On August 30 2012 10:55 Bored wrote:On August 30 2012 10:54 Maxd11 wrote: This is very cool but during a game I really don't care I just like to bbq drones. Admittedly it isn't very useful for when you're IN a game, but it can help you figure out how much damage you should be doing in order for you to be working effectively. But yes flaming drones are a funny sight, although it's not one I particularly enjoy since I play zerg :[ How do you modify the equation for each race to factor in chrono boost/the facts that zerg can (theoretically) replenish all their workers at the same time using larvae?
I'm working on a method for larvae, but chronoboost is a little bit easier. Chrono boots is something that increases build speed by 50% for 20 seconds. This means it does 1.5 seconds of build time for 20 seconds, resulting in 10 seconds of reduced build time each time it's used. If CB is saved purely for the nexus during times of economic recovery I could factor in 10 seconds of reduced build time every 25 seconds, which would effectively reduce the 11.333 to a lower number. If people are interested I can try and work a way to calculate that.
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On August 30 2012 11:01 giuocob wrote:. . . LOL
You can use a calculator or any other computational program, that's just the most convenient in my opinion.
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Why is it that everyone is being so negative? Appreciate this guys work, dont just mock specific parts of what he said.
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Once again, shows that SC2 is fucking complex..
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is there an equation for how much economic dmg is done when a players is not mining?
ie situation you want to go into his mineral line and you opponent is dancing with his harvesters
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Ok, it is a good start, but I think the approach is a bit too simple to be really useful.
- You assume that the defending player would not build workers otherwise, which is almost always not true, making your formula almost always inaccurate. If you want to get a useful formula, you kindof have to include that.
- You should probably mention that your odd/even number of bases in the formula only works on 1 or 2 bases. plugging in 3 bases will handle it as if you had one base. Maybe better to just provide one formula for 1 base, and the other for 2 bases, instead of messing around with the (-1)^b...
- I think you need to take into account that a mineral at 5 minutes is worth more than a mineral at 8 minutes, so spending 400 minerals for hellions to set someone back 400 minerals 2 minutes later should be counted as a loss for the aggressor. And even if you dont include the resources to build the factory and rector (yes, you would build them later anyways), you now need to spend the resources for them earlier, which is a big deal.
So the approach definitely works, but you need to think it through more for it to actually be useful imo. good luck.
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this is nice. you seem to have put a lot of effort into it.
if i'm understanding it correctly, your equation tells how many 'potential' minerals worker harass is taking away from an opponent? the problem you'll find is that effectiveness of harassment is not only a measurement of whether the harassing units 'paid' for themselves in the form of worker disruption. there are a whole lot of other factors to consider in order to evaluate how successful harassment needs to be. for example, differences between build orders. in a TvT where both players open up CC first into a similar mid game, you can, relatively easily, weigh the benefits of any given harassment. if however, one player where to open with a blue-flame hellion drop, it wouldn't be so easy to assess whether damage from the hellions outweighs the build order advantage of a CC first.
my point: it's complicated to turn these things into mathematical calculations.
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On August 30 2012 11:42 Cascade wrote:Ok, it is a good start, but I think the approach is a bit too simple to be really useful. - You assume that the defending player would not build workers otherwise, which is almost always not true, making your formula almost always inaccurate. If you want to get a useful formula, you kindof have to include that. - You should probably mention that your odd/even number of bases in the formula only works on 1 or 2 bases. plugging in 3 bases will handle it as if you had one base.  Maybe better to just provide one formula for 1 base, and the other for 2 bases, instead of messing around with the (-1)^b... - I think you need to take into account that a mineral at 5 minutes is worth more than a mineral at 8 minutes, so spending 400 minerals for hellions to set someone back 400 minerals 2 minutes later should be counted as a loss for the aggressor. And even if you dont include the resources to build the factory and rector (yes, you would build them later anyways), you now need to spend the resources for them earlier, which is a big deal. So the approach definitely works, but you need to think it through more for it to actually be useful imo. good luck.
You bring up some valid points although I feel like I addressed two of the main concerns.
Bored wrote: If they're already in the process of building workers than the most current worker won't be used to put them a head but rather put them behind one full cycle. This means you're already pushing them back 17 seconds of building + 386 minerals.
I did mention that I was working on getting three bases into the equation, although I didn't exactly stress the point. Yes, you're 100% correct though, putting in three bases will treat this as a one base equation. I was thinking of making them separate equations, but for the sake of easy use I tried to make it all in one equation.
When it comes to this:
I think you need to take into account that a mineral at 5 minutes is worth more than a mineral at 8 minutes, so spending 400 minerals for hellions to set someone back 400 minerals 2 minutes later should be counted as a loss for the aggressor.
There's no real way for me to give you the true value of the minerals that they lost. I'm not saying that it wall always be cost effective so long as they lose more than you spent, since I believe that's in the players eyes. This is basically just a way of telling them how much damage was done. I suppose you could consider this to be the actual cost, rather than the opportunity cost. 
Glad you took the time to respond, thanks for the advice in what needs to be fixed. 
EDIT: I'm thinking of a way to further show your first point in the calculation itself, but that eludes me at the moment. So long as they aren't over the saturation cap it should always set them back the same amount and cause them to reproduce the unit.
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On August 30 2012 11:51 pique wrote: this is nice. you seem to have put a lot of effort into it.
if i'm understanding it correctly, your equation tells how many 'potential' minerals worker harass is taking away from an opponent? the problem you'll find is that effectiveness of harassment is not only a measurement of whether the harassing units 'paid' for themselves in the form of worker disruption. there are a whole lot of other factors to consider in order to evaluate how successful harassment needs to be. for example, differences between build orders. in a TvT where both players open up CC first into a similar mid game, you can, relatively easily, weigh the benefits of any given harassment. if however, one player where to open with a blue-flame hellion drop, it wouldn't be so easy to assess whether damage from the hellions outweighs the build order advantage of a CC first.
my point: it's complicated to turn these things into mathematical calculations.
Oh I definitely agree with your point, at no point would I ever say "Oh I gained a 50 mineral lead, therefore my deviated build was worth it." because everything is SO situational that this tool is really only designed to tell you just how much of a lead you've gained.
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On August 30 2012 11:36 EggYsc2 wrote: is there an equation for how much economic dmg is done when a players is not mining?
ie situation you want to go into his mineral line and you opponent is dancing with his harvesters
Not really. The thing about this equation is that it doesn't ever factor game time into it. It's all based on the change of your economy from one point in time to another, and stopping all mining time would have to take into consideration how many workers you have and how long you stopped.
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I think you could fix it like this maybe:
To measure how much you lose (by building the hellions or losing drones) you have to compare to something. You are (in the formula you give) comparing to a player that would otherwise sit on his hands and stare at his minerals rise.
Try comparing to a more realistic behaviour. Like, the terran going for 2 base 150 supply push with marines, tanks and medivacs. How much later will that push come if he will build an earlier factory and 4 hellions at time T (and then lose them)? And comparably, take a zerg doing a 3 base roach max or something, and calculate how delayed the max will be if he loses x drones (and maybe y minerals in mining time) at time T+S?
I realise such a calculation is kindof messy, but it should be possible to estimate pretty well if you copy a build from a pro replay, and it will give a MUCH more accurate measure on if the harass was worth it. It will also give a good measure on how lost mining time compare to lost drones if you chose to include that.
Drawback is ofc that it will be build specific. But I think that this calculation IS build specific. That is, depending on what build the terran and zerg is doing, you have to kill a different number of drones. For example, if you put down a cc before hellions you will probably have to kill less compared to a one base hellion. Similarly, a low eco zerg (building up to some all in) will probably suffer more from losing 10 drones than a zerg that is powering drones like crazy. On that note, you will probably want to use a more ZvT build rather than the roach max.
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Very interesting write up. It looks good
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On August 30 2012 12:12 Cascade wrote:I think you could fix it like this maybe: To measure how much you lose (by building the hellions or losing drones) you have to compare to something. You are (in the formula you give) comparing to a player that would otherwise sit on his hands and stare at his minerals rise. Try comparing to a more realistic behaviour. Like, the terran going for 2 base 150 supply push with marines, tanks and medivacs. How much later will that push come if he will build an earlier factory and 4 hellions at time T (and then lose them)? And comparably, take a zerg doing a 3 base roach max or something, and calculate how delayed the max will be if he loses x drones (and maybe y minerals in mining time) at time T+S? I realise such a calculation is kindof messy, but it should be possible to estimate pretty well if you copy a build from a pro replay, and it will give a MUCH more accurate measure on if the harass was worth it. It will also give a good measure on how lost mining time compare to lost drones if you chose to include that. Drawback is ofc that it will be build specific. But I think that this calculation IS build specific. That is, depending on what build the terran and zerg is doing, you have to kill a different number of drones. For example, if you put down a cc before hellions you will probably have to kill less compared to a one base hellion. Similarly, a low eco zerg (building up to some all in) will probably suffer more from losing 10 drones than a zerg that is powering drones like crazy. On that note, you will probably want to use a more ZvT build rather than the roach max. 
I think that in the long run I can probably do that, it'd be nice to see how delayed your push is if you decide to go for an attack and how much it'll set him back. I'll give it a go, although I feel like this'll take a bit longer than a few hours that the current one I did. Thanks for the idea!
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Wow I love the way you included an if -> then statement into a mathematical equation. I could definitely see this equation/concept being used when refining build orders; it could help determine the viability of harass. It could also give people a solid number of workers a set build has to kill to be cost effective.
The only drawback to this, is that it only measure the quantitative data. There is no way you can include how much you may throw a player off balance into a mathematical equation.
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On August 30 2012 12:17 Bored wrote:Show nested quote +On August 30 2012 12:12 Cascade wrote:I think you could fix it like this maybe: To measure how much you lose (by building the hellions or losing drones) you have to compare to something. You are (in the formula you give) comparing to a player that would otherwise sit on his hands and stare at his minerals rise. Try comparing to a more realistic behaviour. Like, the terran going for 2 base 150 supply push with marines, tanks and medivacs. How much later will that push come if he will build an earlier factory and 4 hellions at time T (and then lose them)? And comparably, take a zerg doing a 3 base roach max or something, and calculate how delayed the max will be if he loses x drones (and maybe y minerals in mining time) at time T+S? I realise such a calculation is kindof messy, but it should be possible to estimate pretty well if you copy a build from a pro replay, and it will give a MUCH more accurate measure on if the harass was worth it. It will also give a good measure on how lost mining time compare to lost drones if you chose to include that. Drawback is ofc that it will be build specific. But I think that this calculation IS build specific. That is, depending on what build the terran and zerg is doing, you have to kill a different number of drones. For example, if you put down a cc before hellions you will probably have to kill less compared to a one base hellion. Similarly, a low eco zerg (building up to some all in) will probably suffer more from losing 10 drones than a zerg that is powering drones like crazy. On that note, you will probably want to use a more ZvT build rather than the roach max.  I think that in the long run I can probably do that, it'd be nice to see how delayed your push is if you decide to go for an attack and how much it'll set him back. I'll give it a go, although I feel like this'll take a bit longer than a few hours that the current one I did. Thanks for the idea! yeah, it's a quite big project I think, I'd be impressed if you manage to go through with it.
You could even look at a specific game, as use the builds they used in that game. Then compare to what would have happened if he had not built the earlier factory and the starport, how much earlier would his first push after that be, and how much earlier would the zerg have the units he used to defend that push. That would be really cool, if you could say that MVP needed to kill at least 9.3 drones, or take at least 94 drone-seconds of mining, or a corresponding combination, to make up for his investement.
Ofc then you will have issues like, without the hellions his creep would be much further, no safety from ling all-ins etc etc, but that will have to be another story I believe, as it is very hard to transform into economy...
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On August 30 2012 12:25 Cascade wrote: yeah, it's a quite big project I think, I'd be impressed if you manage to go through with it.
You could even look at a specific game, as use the builds they used in that game. Then compare to what would have happened if he had not built the earlier factory and the starport, how much earlier would his first push after that be, and how much earlier would the zerg have the units he used to defend that push. That would be really cool, if you could say that MVP needed to kill at least 9.3 drones, or take at least 94 drone-seconds of mining, or a corresponding combination, to make up for his investement.
Ofc then you will have issues like, without the hellions his creep would be much further, no safety from ling all-ins etc etc, but that will have to be another story I believe, as it is very hard to transform into economy...
Well I'll probably grab a friend of mine so I don't have to do it on my own haha. It'd be a fun project actually.
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On August 30 2012 10:59 Maxd11 wrote: How do you modify the equation for each race to factor in chrono boost/the facts that zerg can (theoretically) replenish all their workers at the same time using larvae? This is really important — namely for zerg. Each drone kill that an opposing player gets on a zerg isn't really worth much more than 63 minerals worth of killing anything else (spine crawlers, zerglings, etc.), while tat number would be considerably higher for other races since they can't produce workers as fast (produce workers instead of army)
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I'm just going to throw a couple of ideas out there. I like what you've done here and I think it's great that you are trying to model economic damage. It is something that I have thought about doing a couple of times but have always been too lazy. There are a couple of things that don't seem quite right to me though:
- the 50 minerals spent on the worker is a sunk cost. So whether the worker gets killed or not the player has already spent 50 minerals on it, and it should no longer be taken into consideration. It is true that the player will have to spend 50 extra minerals on an additional worker, but because most of the time the player will be constantly producing workers anyway, these 50 additional minerals do not actually come into effect until the player would have had all the SCVs they need for the game (eg. if you're terran and you stop at 65 SCVs, you will have to build a 66th SCV to replace the one you lost). That means if you lose a worker at 6 minutes you won't feel the cost of replacing it until 12-13 minutes (depending on your build), by which time minerals aren't worth nearly as much due to the time value of minerals.
- What you do feel is the lost income, and think this is a far better indicator of economic damage. A worker mines approximately 40 minerals per minute (less if the base is fully saturated). This means that if you lose a worker at time 0, you have 40 minerals less than you would have at minute 1. At 2 minutes you would have 80 minerals less, and so on. Then you should be adjusting for the time value of money. For example, losing 40 minerals in 1 minute might only be as bad as losing 30 minerals right now, and losing 40 minerals in 2 minutes time might only be as bad as losing 23 minerals right now and so on. If you add all these discounted future mineral flows, you get the true present cost of losing the SCV. There are problems with using this method of course, the most obvious being that it is practically impossible to work out the time value of minerals. Also, once you get to your full worker count, the lost SCV has essentially been replaced, so you should only discount up to the time that full workers are obtained.
tl;dr: workers are worth way more than 50 minerals. They are a stupidly good investment and that is why players get so many of them.
I hope that makes sense. What you have done is quite good, certainly better than nothing, but I feel it doesn't paint the truest picture of the economic damage done.
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I enjoy this concept alot, but thinking about the idea, conceptually, a polynomial equation will never be able to adequetly describe a constantly changing rate of information (i'm thinking about the resource collection rate tab in replay).
Aside, I do think there should be some kind of derivative which we could use to measure differences at resource collection rates at 2 points in the game, say before and after harass.
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On August 30 2012 10:58 Aild246 wrote:Show nested quote + The Equation: 50x+(0.5x)(x+1)(11.33333)((((-1)^(b))-1)/2))^2)+(1/8)(7+(-1)^x+8x+2x^2)(11.33333)(((-1)^(b)+1)/2) where x=WORKERS and b=BASES ]
Oh god I laughed until my sides hurt Me too and then again after I read this.
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Just in case I misunderstood: X and B are number of opponents workers you killed, and number of bases the opponent has? Additionally, I read through twice to check, but did you mention that you're implying you're on the same number of bases before the attacks?
On the premise that you only look at the number of bases your opponent has, I can't take your formula seriously at all. I mean, killing 8 drones with gas first hellion rush vs 3 hatch before pool Zerg has a drastically different effect. In the same vein of Cascade arguing that minerals at some point are worth more than minerals at another point, and the different effects different builds have, delaying your expansion also costs you money. When I play 1rax expo before depot vs reactor hellion, I think my orbital is done about two minutes later. So I'm putting myself 2x worker production for two minutes down in workers. Otherwise killing 10 scvs with 4gate vs 1rax expo would make it seem sick. I understand that this strays toward build specific differences but would you take into account how long you delay your expo (minute wise) also.
Anyway, different builds make this formula pretty neat but I think too shallow to use to actually develop strategies (although of course, I just steal pro builds, so maybe I'm wrong). I mean TvZ revolves around marine tank pushes to shut down the 7-8th gas of Zerg while you grab your 4th. If you do a ton of hellion harrass but have no follow to stop the Zerg from redroning, or let the Zerg reach infestor/corrupter/broodlord because you delayed you attack too much because of hellions, the huge number this formula gave me is worth nothing. And hellion harrass does delay any attack I do, the only question being how much. I mean I saw Guhmiho go CC first into 3rd cc before has into tanks and did marine pressure on the 3rd with medivacs, and still was able to hit a 2/2 1/0 180 supply tank push around 12:30. Can any formula quantify that by hitting around then, there's almost no way at all you'll have to face hive tech (I've seen 11 min hives but I don't think they'd finish in time for ultra den to be built and ultras to spawn). And by facing a lair tech army, you're going to be more cost efficient probably, just by the nature of Zerg lair tech units? If it seems like I'm asking an impossible task, it's because in my opinion it is impossible (without significant computing power to get results in decent speed or something else like a genetic algorithm), or at least very difficult.
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What do the variables have to be to equal TERRIBLE TERRIBLE DAMAGE?
On a more serious note, how do the bases for zerg differ from that of the other two '1 worker building at a time' bases such as Terran's Command Center and the nexus of Protoss?
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This equation underestimates the amount of damage done. It is only valid if the player has stopped producing workers because he is saturated.
In reality, if you lose 1 worker, you will be one worker behind on your build until the point where you reach your intended number of workers. So the number of 'cycles' lost is much larger than indicated.
However, as a counterbalancing effect: If you kill workers while the opponent has more than 16 workers per mineral line, the lost mining will be less than if there are 16 or less workers per mineral line.
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I commend you for your effort but........
The Equation: 50x+(0.5x)(x+1)(11.33333)((((-1)^(b))-1)/2))^2)+(1/8)(7+(-1)^x+8x+2x^2)(11.33333)(((-1)^(b)+1)/2) where x=WORKERS and b=BASES
Mother of god.
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I feel like this wouldn't be too useful for players, since the only way to really tune a build down in terms of opportunity cost to you and your opponent is to play it a bunch of times against a skilled opponent; that's the only thing that can take into account all of the qualitative elements of opportunity cost, like map control (you would have otherwise had those hellions out on the map killing lings and holding down watchtowers), psychological impact on their responses (may push your opponent to all-in or take a fast next expo), etcetera.
That said, I think this could be really useful in two contexts and I really commend OP on the work.
(1) in combination with an evolutionary algorithm to create build orders (remember the seven roach rush?), this could be very useful. You could give the evolutionary algorithm a parameter to maximize other than "I want more roaches". AFAIK so far most of the successful builds from evolutionary algorithms have been allins, because it's so hard to parameterize anything else to optimize.
(2) more importantly, for casters. This would be a really interesting thing for casters to show during games where some sort of worker harass takes place. It would give a sort of running update on how strong the economic harass was from either player.
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On August 30 2012 10:59 Maxd11 wrote:Show nested quote +On August 30 2012 10:55 Bored wrote:On August 30 2012 10:54 Maxd11 wrote: This is very cool but during a game I really don't care I just like to bbq drones. Admittedly it isn't very useful for when you're IN a game, but it can help you figure out how much damage you should be doing in order for you to be working effectively. But yes flaming drones are a funny sight, although it's not one I particularly enjoy since I play zerg :[ How do you modify the equation for each race to factor in chrono boost/the facts that zerg can (theoretically) replenish all their workers at the same time using larvae? For Zerg there could be an additional factor in it because you force them to spend larvae on Drones and not units, thus limiting their offensive potential. Killing enough Queens to have less than one per Hatchery would also deal a lot of economic damage.
On the other hand I dont think it is a good thing to "figure out SC2 mathematically", because that makes it less interesting as a game if people start looking at pure numbers only. Some benefits cant be counted like pulling the army of your opponent out of position. If a math solution is available people will start asking for that ... just like the idiots who ask in a brand new MMO "which is the best [=most powerful] class?" and totally ignore the fact that there are situational decisions which tip the scale to one side or the other. Relying on pure math is never a good thing!
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Italy12246 Posts
While the idea is really nice, starcraft is a really really fucking complex system and hoping to model it through one simple algebrical equation is quite optimistic. In particular, your model doesn't things like timings and other ingame situation, it just compares the resources devoted to harassment to the damage inflicted to someone's economy, which is only part of why someone would invest in harassment.
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On August 30 2012 10:58 Aild246 wrote:Show nested quote + The Equation: 50x+(0.5x)(x+1)(11.33333)((((-1)^(b))-1)/2))^2)+(1/8)(7+(-1)^x+8x+2x^2)(11.33333)(((-1)^(b)+1)/2) where x=WORKERS and b=BASES ]
Oh god I laughed until my sides hurt it doesn't look that complicated if you work a lot with programs such as maples or sites like wolframalpha
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Don't know how that would be useful, it's a nice statistic though i guess.
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nice calculator,P2 is a little hard to calculate.
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On August 30 2012 10:59 Maxd11 wrote:Show nested quote +On August 30 2012 10:55 Bored wrote:On August 30 2012 10:54 Maxd11 wrote: This is very cool but during a game I really don't care I just like to bbq drones. Admittedly it isn't very useful for when you're IN a game, but it can help you figure out how much damage you should be doing in order for you to be working effectively. But yes flaming drones are a funny sight, although it's not one I particularly enjoy since I play zerg :[ How do you modify the equation for each race to factor in chrono boost/the facts that zerg can (theoretically) replenish all their workers at the same time using larvae?
For Chrono, just divide the 11.33333 values (2 occurrences) in the equation by 1.5 (assuming constant Chrono on probes).
Zerg is more complicated, since Larvae are a resource and their value depends on the build the Z is doing and the current game-state.
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