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maybe i'm just stupid or too tired, but "Domain is x=<45." and "45*2=90 seconds. Domain is x=<90" does not make any sense to me. Shouldn't it be the other way around? As in "Domain is x>=45"? Or do i owe the game two creep tumors at x=0 (when i start creeping) and get even after 60 seconds when i plan on planting a third creep tumor down?
Other than that, a quadratic function was to be expected, given the fact that each creep tumor would spawn one child, plus the queen pitching in a new one from time to time, which resulted in a formula similar to 1+2+3+...+n (not as pretty, but the same kind).
Also you gotta be darn good to keep up that creep spread at 50% efficiency for 7:35 minutes. Given the fact that not putting them down perfectly (aka waiting for example for energy for two new ones to be placed down in the same cycle as all active ones being used) and the complication of not being able to creep up ramps and the huge distance you have to scroll to put all down in one go, i am even more impressed.
And to conclude, if i wasn't a math geek i would have been really disappointed, as i read the title "Optimal Creep Spread in Theory", then watched the picture below, and noticed that the bottom right base and the left-handed way are not creeped up, leaving both paths vulnerable for drop ships, attacks, or even a base on the bottom right. This ain't optimal at all! Good thing i like math and continued to read =)
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As a fellow math guy, this makes me proud to read  Really thorough job, and nice explanations! Using Scarlett's game as a model for efficiency (or really non-efficiency, but realistic creep spread and behavior) was a really good idea!
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i think zerg got buffed very wrong reasons, they tried so long with banes and zerlings. lets say that zerg with perfect meganics uses perceft creep spread, in this situatin terran has to go early raven or use ton of scans with leads ultimatly allways lost. zerg got buffed even tough they didnt use race strength (creepspread/queens/early roach press) and cried op 2rax or something. Today we have seen so much creative play that makes me think why didnt they tried this before. i really hope that no zerg get this kind of creepsread overtime, crazy
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Put a lot of work into basically nothing. Always kind of interesting to see all the varied forms hubris can take, and in the OP its faith in math. Optimal creep spread? Optimal to what, winning the game? That has nothing to do with math, it has to do with the interplay of the meta game, units, map, potential resources, psychology, limited attention span, multitasking and APM. The timing and methods of getting creep out faster simply isnt really worth noting. This is a game with people, and a thousand incalculable variables....
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Put a lot of work into basically nothing. Always kind of interesting to see all the varied forms hubris can take, and in the OP its faith in math. Optimal creep spread? Optimal to what, winning the game? That has nothing to do with math, it has to do with the interplay of the meta game, units, map, potential resources, psychology, limited attention span, multitasking and APM. The timing and methods of getting creep out faster simply isnt really worth noting. This is a game with people, and a thousand incalculable variables....
Boy, you should hope that no one building your software or engineering your buildings and factories has the same opinion as you on optimal models.
Great work OP. Really cool work that can increase our understanding.
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put 2 tumors right next to each other, the creep spreads _FASTER_ in range of the tumors. Use this at first to give your creep spread a boost, then spread it out. adding in 1 tumor with a creep can accelerate creep spread
edit: Hydra -- i'm growin up 4real
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This is a cool post, however it does deal with just creep spreading everywhere, what's more interesting is how to get the quickest creep spread to particularly useful areas of the map to have it on the quickest (i.e more straight line extension than circular expansion).
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Thing is, this creep spread is only seen in TvZ. In ZvZ or ZvP, rarely do you see such creep spread. It's like no one cares about creep in other match ups but TvZ, which is probably why Blizzard won't nerf this map hack..
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On November 10 2012 14:38 geokilla wrote:
Thing is, this creep spread is only seen in TvZ. In ZvZ or ZvP, rarely do you see such creep spread. It's like no one cares about creep in other match ups but TvZ, which is probably why Blizzard won't nerf this map hack..
Thats because ZvZ creep spread can be detrimental and ZvP protoss always has observers. Most decent terrans deny creep spread because they know how dangerous it is, while zergs try their damnedest to spread it in ZvT because without it, it is ridiculously hard to engage a terran army in a cost efficient manner.
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O_o eventually terran will get 1 raven and fake push with group of units... With that creep spread i assume she was way ahead.
That creep spread is not more overpowered than a terran late game with 5 pfs , tanks ant turrets, for defenses on the map, with like 7-10 orbitals for mass money, working on like 30 scvs for a bigger army.
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I liked reading your proof, I think you did make an error though like Cirqueenflex noted. I'm pretty sure that the domain for those example functions you listed should have had x => 45,90,etc., since those functions only begin to exist at x = 45,90.
And even if they did somehow exist before 45,90 (etc.) then you would have negative creep tumors (tons of negative creep tumors for a large n!), which doesn't make sense.
I think that's the only confusing part. The only other aspect is when you give a closed form expression for the sum of n positive integers.
But that should be easy to reproduce so that people can clearly see how its derived. You could use Gauss' proof for the some of n integers. Just add the series going forwards with the series going backwards, and you get (1/2)(n)(n+1). I learned it in university by the way  .
In case anyone's interested, for the sum of the first n positive integers (its really small!):
+ Show Spoiler +
Sn = 1 + 2 + 3 + ... + n
Sn = n + (n-1) + (n-2) + ... + 1
So if you add the sums, you get: 2Sn = (1 + n) + (1 + n) + (1 + n) + ... + (1 + n)
But clearly since there are n terms, then there are n (1+n) terms. Then 2Sn = n(1 + n) and Sn = (1/2)(n)(1 + n)
Gauss supposedly discovered this as a child, when a teacher told him to add the numbers from 1 to 100 as a form of punishment in grade school. Gauss rules!
On November 10 2012 12:27 D_K_night wrote:
...You're missing the entire point of this. What is the theoretical, fastest possible way to creep up the entire map, backed up by solid math and evidence? This post is it. Please don't be so condescending, especially when, in your words, "there is nothing concrete" that you could even come up with any of this.
I have to agree with other people in the thread, this analysis actually doesn't answer the core question: How fast can you cover the map with creep? All it does is talk about the number of creep tumors that you can make using one queen + the older ones.
Ultimately the rate of creep spread needs to be included for this analysis to be meaningful, and also production of secondary or tertiary queens at hatcheries to spread extra creep as well. Aren't creep tumors limited (in terms of placement) by how fast the creep extends? Also don't multiple creep tumors increase the rate of creep spread? So what is the optimal balance? None of this was really covered, it was just a formula that shows you how the *number* of creep tumors increases. It would be better to discover what the ideal scenario for generation of creep would be to cover the map as fast as possible using the least number of queens (possibly also taking into account terrain changes).
Perhaps it would also be worthwhile to investigate how fast the map could be covered with the aid of overlords generating creep, so that creep tumors can be placed to their furthest extent without having to wait for the creep to extend normally?
I know its a lot to ask, but these are the kinds of questions that would need to be answered. I commend the OP on his work, it certainly does help in some simpler ways from his examples, but it needs to be improved upon for people to extract something more meaningful out of it.
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On November 10 2012 14:02 whatevername wrote:
Put a lot of work into basically nothing. Always kind of interesting to see all the varied forms hubris can take, and in the OP its faith in math. Optimal creep spread? Optimal to what, winning the game? That has nothing to do with math, it has to do with the interplay of the meta game, units, map, potential resources, psychology, limited attention span, multitasking and APM. The timing and methods of getting creep out faster simply isnt really worth noting. This is a game with people, and a thousand incalculable variables....
No need to disrespect the nice math / explanations / visuals put forth by the OP - his motive is none of your business and you're an asshole for assuming anything.
In fact, I quite enjoyed the read for the topic's seeming mundaneness.
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I just wanted to simply say your threads never cease to amaze me in regards to the amount of effort you put into them; master's thesis / dissertation level of attention to such mundane things in a game is both creepy and interesting
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Yeah, I just want to chime in and say very well done. Things like this keep the game going Love analysis, thanks! Also, impressive Scarlett play
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Orek: Another great post. Some of your functions would be prettier if you factored out some common factors like 15.
Awesome.
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On November 10 2012 12:27 D_K_night wrote:Show nested quote +On November 10 2012 12:01 Ballistixz wrote:no offense but there is nothing concrete when u theory craft with numbers alone. if u want real concrete answers then play the game, cute equations wont get u very far because there are to many unknown factors. High school level math knowledge is required to fully understand the content. this is more middle school level math knowledge tho. No it isn't. Are you seriously stating that some high school kid would be able to figure all the equations out, on his own? Middle school you're just learning whatever the teacher is instructing from the blackboard, and doing assigned exercises. No chance in hell that suddenly a high school kid has an epiphany and suddenly just comes up with all these formulas out of thin air. You're missing the entire point of this. What is the theoretical, fastest possible way to creep up the entire map, backed up by solid math and evidence? This post is it. Please don't be so condescending, especially when, in your words, "there is nothing concrete" that you could even come up with any of this.
i think you are missing the point. there are to many unknowns that can happen in a game to easily prevent the "fastest possible way to creep up the entire map". thats is why it is pointless information. get in a game and there will be a bunch of factors that determine how fast or how slow u spread creep. knowing the maximum speed of creep spread based on non interruptions is very useless information.
long story short, OP is talking about a PERFECT game. there is no such thing as a perfect game unless u are playing against someone that is shit tier bad or against someone that is to lazy to deal with creep spreading.
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On November 10 2012 12:27 D_K_night wrote:Show nested quote +On November 10 2012 12:01 Ballistixz wrote:no offense but there is nothing concrete when u theory craft with numbers alone. if u want real concrete answers then play the game, cute equations wont get u very far because there are to many unknown factors. High school level math knowledge is required to fully understand the content. this is more middle school level math knowledge tho. No it isn't. Are you seriously stating that some high school kid would be able to figure all the equations out, on his own? Middle school you're just learning whatever the teacher is instructing from the blackboard, and doing assigned exercises. No chance in hell that suddenly a high school kid has an epiphany and suddenly just comes up with all these formulas out of thin air. You're missing the entire point of this. What is the theoretical, fastest possible way to creep up the entire map, backed up by solid math and evidence? This post is it. Please don't be so condescending, especially when, in your words, "there is nothing concrete" that you could even come up with any of this.
They won't figure out, but the OP was talking about solving that equation. And tbh I learned that since I was 5th grade.
//May be I'm Asian, but still anyone can solve that equation with highschool algebra.
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You have calculated optimal quantity of creep tumors, not optimal creep spread. Unless each queen is expanding creep in exactly one perfectly straight line without coming close to any other creep spreading queen (or edge of map, or cliff, or other creep), then this method does not provide very accurate information. Optimal creep spread in theory would vary greatly map to map.
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On November 10 2012 16:51 tuho12345 wrote:Show nested quote +On November 10 2012 12:27 D_K_night wrote:On November 10 2012 12:01 Ballistixz wrote:no offense but there is nothing concrete when u theory craft with numbers alone. if u want real concrete answers then play the game, cute equations wont get u very far because there are to many unknown factors. High school level math knowledge is required to fully understand the content. this is more middle school level math knowledge tho. No it isn't. Are you seriously stating that some high school kid would be able to figure all the equations out, on his own? Middle school you're just learning whatever the teacher is instructing from the blackboard, and doing assigned exercises. No chance in hell that suddenly a high school kid has an epiphany and suddenly just comes up with all these formulas out of thin air. You're missing the entire point of this. What is the theoretical, fastest possible way to creep up the entire map, backed up by solid math and evidence? This post is it. Please don't be so condescending, especially when, in your words, "there is nothing concrete" that you could even come up with any of this. They won't figure out, but the OP was talking about solving that equation. And tbh I learned that since I was 5th grade. //May be I'm Asian, but still anyone can solve that equation with highschool algebra.
Pretty much, and in year 10 maths at our school we were figuring out problems of about the same difficulty.
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EPT
