|
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.
|
This is very cool but during a game I really don't care I just like to bbq drones.
|
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 :[
|
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
|
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?
|
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.
|
LOL
User was banned for this post.
|
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.
|
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.
|
Why is it that everyone is being so negative? Appreciate this guys work, dont just mock specific parts of what he said.
|
Once again, shows that SC2 is fucking complex..
|
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
|
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.
|
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.
|
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.
|
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.
|
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.
|
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.
|
Very interesting write up. It looks good
|
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!
|
|
|
|
|
|
EPT
