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Optimal Creep Spread in Theory
Creep spread by AcerScarlett @MLG Fall Championship 2012
Introduction
Zerg OP, right? Recently,”infestor OP” is the name of the game. However, half a year ago, what all the cool kids said back then was “queen OP.” Creep spread had become so out of control post-patch in May 2012 that in August, Blizzard once tried to nerf creep tumor radius in an attempt to slow Zerg creep spread, which they scrapped the idea of later on in order to “give players more opportunities to fully explore the slowly-shifting meta-game.” As a noob, I have no idea how creep spread should be balanced, nor do I care. As a research guy, all I care is concrete numbers behind creep spread, where no subjective opinion comes into play unlike balance whine. This thread is not another “use overlord to creep spread faster” or “multiple tumors spread creep faster.” Terrain factor, spread direction etc. are ignored here, too. Rather, it’s all about math. This thread attempts to mathematically prove/calculate what the optimal creep spread is. Here is the short conclusion:
When perfectly played, the total number of creep tumors increase quadratically, not exponentially, with a dedicated creeper queen, and the total number = “y” = f(x) at “x” seconds after the moment the very first creep tumor is laid down is
![[image loading]](http://i.imgur.com/dVW56.png)
High school level math knowledge is required to fully understand the content. I believe that there are many math nerds like Day[9] in Starcraft community, but if you are not one of them, you might find it boring. Welcome to Creep Tumor Mathematics 101 class!
Prerequisite
+ Show Spoiler +Basic math/SC2 knowledge is obviously expected, but there are some things worth mentioning here. State of Creep TumorCreep tumor has 4 different states: building, cooldown, spawnable, inactive 1. Building state is the state where a creep tumor is still visible to opponent without detectors. It is the first 15 seconds after its birth. (0~15 seconds) 2. Cooldown state is the state where a creep tumor is invisible to opponent without detectors yet still unable to spawn another creep tumor. It is the second 15 seconds after its birth. (15~30 seconds) 3. Spawnable state is the state where a creep tumor is able to spawn another creep tumor after cooldown ended. (30 seconds~) 4. Inactive state is the state where a creep tumor can no longer spawn another creep tumor because it already did once. Queen’s EnergyQueen’s Spawn Creep Tumor ability costs 25 energy. All units/structures in game regenerate energy at 0.5625 [energy/second]. Therefore, it takes 25/0.5625 = 44.44…[sec] for a queen to regenerate 25 energy for the next creep tumor. For the sake of much easier calculation, duration between 2 Spawn Creep Tumor ability usages is 45[sec] in this thread. It’s possible to calculate everything with 44.44…[sec], but this is one compromise I made to keep it simple. All the creep tumors that are directly originated from a queen, not from another creep tumor, are called “original creep tumor” in this thread. Greatest Integer Function (Floor Function)Greatest Integer Function [p] is the largest integer not greater than p. For example, [3.9]=3 [4.0]=4 [4.1]=4 For reference: Wikipedia on floor and ceiling functions
Proof of the Equation
+ Show Spoiler +As you read in the introduction, with a dedicated creeper queen, the total number of creep tumors defined as y = f(x) at x seconds after the moment the very first creep tumor is laid down is This can be achieved only by a perfect play that even the best player in the world can’t perform. Regardless, it helps to know what the ultimate goal is in trying to constantly improve your play. Proof (long and possibly difficult to understand) The very first original creep tumor is spawned by a queen at x=0 by definition. After building state and cooldown state for 30 seconds in total, it spawns another creep tumor. Perfect play assumed in this proof means that spawnable state of a creep tumor lasts for 0 second, and the next creep tumor is spawned immediately. This reproductive cycle continues every 30 seconds. Therefore, the total number of creep tumors that stem from the first original creep tumor is ![[image loading]](http://i.imgur.com/upP02.png) Greatest integer function is used because the number of creep tumors can only be an integer. (at least for now) The second original creep tumor is spawned by the queen at x=45 because of the energy regeneration period. As a parent creep tumor, it spawns a child creep tumor after 30sec. Generation after generation, this cycle continues just like the first original creep tumor family did. With one child policy and 1 generation = 30sec, the total number of creep tumors that stem from the second original creep tumor is ![[image loading]](http://i.imgur.com/VwmRo.png) Domain is 45=<x. Another 45 seconds later at x=90, 3rd original creep tumor is spawned by the queen. Similarly, the total number of creep tumors that stem from the third original creep tumor is ![[image loading]](http://i.imgur.com/tn95F.png) 45*2=90 seconds. Domain is 90=<x. Generally, the total number of creep tumors that stem from the “n”th original creep tumor is ![[image loading]](http://i.imgur.com/rKhsD.png) y_1~y_3 are merely specific examples. Are you all still with me? What necessitates the greatest integer functions above is the concept that a creep tumor either counts as 1 when it exists, or counts as 0 when it doesn’t. This concept is narrow and not useful in calculating further. Therefore, by extending the concept, decimal numbers of creep tumors are allowed from here on. For example, a creep tumor that is just spawned counts as 1 creep tumor, a creep tumor that has spent 15 seconds in building state counts as 1+15/30=1.5 creep tumors, a creep tumor that has spent 15 seconds in building state and 7.5 seconds in cooldown state counts as 1+(15+7.5)/30=1.75 creep tumors, and so on. Upon reaching 1+30/30=2 creep tumors, it immediately spawns another creep tumor so that the parent one becomes inactive state that is worth 1 creep tumor again. It might help to think of a pregnant woman having a baby that becomes bigger over time in her womb until she gives birth to the baby. ![[image loading]](http://i.imgur.com/AYjWF.png) This broader concept doesn’t contradict with narrower concept, yet so much more useful. Basically, it just eliminates the greatest integer function and makes y_n continuous. One important thing to remember is that with this broader concept, y=13 could mean that there are 10 creep tumors that are worth 1, and 2 creep tumors that are worth 1.5 so that there are only 12 you can count on a map instead of 13. Using this broader concept, the total number of creep tumors that stem from the “n”th original creep tumor is ![[image loading]](http://i.imgur.com/QPBBi.png) It’s a big deal that [ ] doesn’t exist in this version. Now, what we want to know is not the total number of creep tumors that stem from a particular original creep tumor but rather the grand total of them from all original creep tumors. When “r” is defined as the total number of o”r”iginal creep tumors, the grand total “y” is ![[image loading]](http://i.imgur.com/Wd3jq.png) By calculating this, (get your math textbook if it doesn’t make sense) ![[image loading]](http://i.imgur.com/yAA2J.png) So far so good? Because r=1 at x=0 by definition and the number of original creep tumors increase every 45 seconds because of the energy regeneration period, ![[image loading]](http://i.imgur.com/Jz45j.png) Greatest integer function appears again when less than 25 energy of a queen is not taken into account. By allowing the number of original creep tumors to be a decimal according to queen’s energy up to 25, ![[image loading]](http://i.imgur.com/3Gn2B.png) Whether an equation has [ ] or not might look like a minor thing, but [ ] makes it impossible to calculate the equation in any meaningful way. Now that we have 2 equations with 3 variables, “y”, “x” , and “r”, the total number of creep tumors “y” can be shown as a function of time “x”. ![[image loading]](http://i.imgur.com/V5hl7.jpg) Hence, optimal creep spread should have Q.E.D. ![[image loading]](http://i.imgur.com/ik5q9.png) Does it make sense? Maybe I could have worded differently to make my proof easier to understand, but I guess the logic is coherent enough as it is. One intuitive way to check the equation is to substitute a random number for “x” and calculate “y”. f(0)=1, f(135)=13 etc. This table might help for reference. ![[image loading]](http://i.imgur.com/4VZbf.png)
Applying In-game Timings (ZvT)
+ Show Spoiler +At 0:00, there is no queen available. Players have to mine minerals and make them. While people make queens in ZvZ and ZvP as well, ZvT has the most standardized queen timings. Of course, bad worker pairing, drone scout, sloppy execution etc. can delay these timing, but this is the standard I use in this thread: 15 hatchery at 2:10 +100sec = done at 3:50 16 pool at 2:45 + 65sec = done at 3:50 1st/2nd queen production at 3:50 +50sec = done at 4:40 1st/2nd queen injects at 4:40 + 45sec = next 25 energy for creep tumors ready at 5:253rd/4th queen production at 4:40 + 50sec = done at 5:30 3rd/4th queen inject at 5:30 +45sec = next 25 energy for creep tumors ready at 6:155th/6th queen production at 5:30 +50sec = done at 6:20 5th/6th queen inject at 6:20. They keep injecting. (6 queen build is the maximum assumed here) Most importantly, 5:25, and 6:15 are the timings when 1st/2nd and 3rd/4th queens can use energy for creep tumors, respectively. These timing are so tight that sub-optimal play can easily delay them by 10sec or so. Note that prioritizing creep spread this way delays injects by 5 seconds every time new queens are made. In-game time = “t” in seconds. 5:25 = 325sec 6:15 = 375sec Therefore, for 1st/2nd queens, x=0 is at t=325. Similarly, x=0 at t=375 for 3rd/4th. Namely, the total number of creep tumors from 1st/2nd queens is f(t-325), and f(t-375) for 3rd/4th. ![[image loading]](http://i.imgur.com/kbnqL.png) ![[image loading]](http://i.imgur.com/hq8M4.png) The total number of creep tumors as a function of in-game time = “z”. 3 queen build = only 1st queen is used as the dedicated creeper = z_3q StarTaleLife almost always take this path with early gas. ![[image loading]](http://i.imgur.com/MOV6O.png) 4 queen build = 1st and 2nd queens are used as the dedicated creepers = z_4q ![[image loading]](http://i.imgur.com/VgN52.png) Until 5th/6th queens become available for creep tumors at t=375, there is no difference among 4/5/6 queen builds. ![[image loading]](http://i.imgur.com/YjAM9.png) 5 queen build = 1st, 2nd and 3rd queens are used as the dedicated creepers = z_5q ![[image loading]](http://i.imgur.com/3Cbn1.png) 6 queen build =1st, 2nd, 3rd and 4th queens are used as the dedicated creepers = z_6q ![[image loading]](http://i.imgur.com/4aXQd.png) Graph based on these equations: ![[image loading]](http://i.imgur.com/2Xw5Y.png) Table: ![[image loading]](http://i.imgur.com/FPvrQ.png)
Efficiency
+ Show Spoiler +Easier calculated than done. No one in the world plays as good as the theory. Then, how efficiently are we playing compared to the optimal play in terms of creep spread? To find out, I took Scarlett’s creep spread on Cloud Kingdom as an example. ![[image loading]](http://i.imgur.com/RPfIL.png) This game is a perfect example because her opponent StarTaleBomber applied almost no pressure for 14min, and Scarlett used 4 queen build with 2 queens exclusively for creep tumors after 5:25. +22 05:25~08:00 22 in total +15 08:00~09:00 37 in total +15 09:00~10:00 52 in total +17 10:00~11:00 69 in total +16 11:00~12:00 85 in total +9 12:00~13:00 94 in total By taking these numbers as numerators and using z_4q from the table above as denominators, it is possible to calculate the efficiency. ![[image loading]](http://i.imgur.com/QR0H4.png) One of the best creep spread I have ever seen among pro games still seems to have some room for improvement. 50-70% with 4 queen build is impressive nonetheless. In ZvT, Terran player’s job is to keep this efficiency as low as possible with hellion/banshee etc. For 4 queen build, my wild guess is that 50%+ would lead into out-of-control creep spread that covers the entire map. 20%- or so would be considered relatively bad creep spread and where Terran wants Zerg to be. 20% with 4 queen build at 13min mark would look like this: ![[image loading]](http://i.imgur.com/P7fRh.png) +2 queen range patch must have dramatically increased this efficiency. It would be interesting if someone made a program for calculating the efficiency from replays. With y= (x+45)(x+60)/2700 equation, efficiency for any build order in ZvX with any number of queens can be calculated. Knowing projected creep spread at arbitrary time might help some build order theorycrafting. This efficiency measurement is not without its own problem, though. Counting creep tumors in VODs/replays causes the numerators to use the greatest integer functions while such factor is eliminated for the denominators. Because of this, efficiency can never be 100% even in theory. Measuring efficiency for the first 2min or so is somewhat pointless due to high fluctuation. Also, having 90%+ efficiency is nearly impossible without some luck in picking the right moment to count. Lower than 100% theoretical ceiling makes Scarlett’s 70% look even more impressive. Despite this problem, it’s still a useful measurement in comparing the degree of creep spread.
Final Thoughts
+ Show Spoiler +
When creep spread was a popular topic right after the patch in May, I did some math on it. Slowly, the topic died down, so I decided not to post my work. Then at MLG several days ago, Scarlett showed us an amazing creep spread that convinced me to find my old work and follow through with it. Most of you probably skipped reading boring proof part, but I hope at least a few guys read the entire thread and maybe point out possible mistakes I made. If anyone has a VOD/replay that looks worth analyzing, please link. From what I’ve seen, LiquidTLO’s emphasis on creep spread gives him very high efficiency. On the other hand, Life’s emphasis on early gas and ling/muta micro tends to result in very low efficiency. Ultimately, it comes down to how much a player prioritizes creep spread with limited APM/attention. Did you enjoy reading despite tons of equations? Thank you for reading to the end. Any feedback is much appreciated. Ask me anything.
Orek's Articles/Guides
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Put a lot of work into this, very interesting
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OK that's not bad, but now calculate the area covered by creep as a function of time with different methods of creep spread.
ie - fanning them out evenly or advancing in groups of 4 (fanning out the groups, but keeping 4 tumours together for fastest directional spread).
That's very cool to have a target # of tumours to aim towards. that's crazy how far the creep gets even at 50% efficiency. Is there an AI out there somewhere that can do perfect creep spread? it doesn't need to do anything else.
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Interesting theory. How quickly do you reach the cap on effective creep tumors for spreading?
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You are awesome, the sheer amount of work you put into these threads is remarkable! Would love to see a "perfect" creep spread in-game!
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Don't forget that the more tumors you have, the better, even if you don't cover more area (because it's not possible), it will make the opponent kill your tumors slower (more scans needed, etc.).
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I feel like Day9 would be ecstatic reading this.
Math and Starcraft.
Nice work.
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more tumors, more scans to waste! yeah!!
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How long would it take a Terran to actually clear that and cross the map with an army? Luckily very few Zergs even in the pro ranks have the skills required to have creep spread that good, but in a perfect world they would have those skills. At what point would a Terran be able to actually attack/what would be the economic cost in terms of scans to cross it?
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and this is the reason we should have a full functional LaTeX embedding for tl 
next step: find out how many creep tumors you need on every map to reach the enemy base with perfect timing
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Very nice thread indeed! I scanned through most of it and agree conceptually.
I do have a remark, however. Maybe i missed some important part; in that case you can ignore this.
In this thread you describe the number of creep tumors in total. But there are active and non-active creep tumors. The number of active creep tumors is easy to describe at a point in time (every 45 seconds 1 extra active creep tumor per queen), but it might be interesting to look at the added value of each active creep tumor. I think (and of course, i did no research whatsoever) it may be possible to formulate some kind of law of diminishing returns in that regard. Of course, this is map depended as well as dependent on other factors (like opponent's intervention). Do you have any ambition of going further in that direction? Or maybe something similar to what Oboeman suggested?
@hryul: haha, agreed about latex.
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I cringe when i hear people call this 'a lot of math' or 'lot's or work' when it's just some elementary algebra.
Besides that, this is almost a completely futile exercise as nothing useful is derived from it. The premise of non-stop making tumors is not even desireable given you want some transfuses anyway... weirder though that there is absolutely no linkage between number of tumors and actual creep spread in the topic..
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reading from the tables, I assume that this equation is for spreading creep from 1 queen only? if player uses 2 queens ( I guess Scarlett uses more than 1 queen to spread from what I saw, then the efficiency must be lower in half.). Am I wrong?
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On November 10 2012 11:36 Markwerf wrote:
I cringe when i hear people call this 'a lot of math' or 'lot's or work' when it's just some elementary algebra.
Besides that, this is almost a completely futile exercise as nothing useful is derived from it. The premise of non-stop making tumors is not even desireable given you want some transfuses anyway... weirder though that there is absolutely no linkage between number of tumors and actual creep spread in the topic..
This. If the thread was truly about the fastest possible creep spread, then continuous production of queens from n hatches would be included, and statistics about how much of the map should be covered as a function of time would be included.It's creep and not creep tumours that are desirable.
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Very interesting theoretical work, but much less applicable to real games than most of Orek's previous work. There are a multitude of factors that would influence efficiency in an actual game, making this work basically meaningless from a practical standpoint.
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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.
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As a practice tool this would be a nice addition to a custom map. Show a player how well they are constantly dropping tumors and using the active tumors. You would need a way to designate how many queens are on poop duty a reserve for emergency transfuses. But showing a player a concrete number help them to see if and how much improvement to practice for.
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I def expected a comparison of spreading tumors max distance as soon as theyre on cooldown vs spreading them at the same time you spread new tumor with creep queens (the latter is much more manageable). As you get more creep spread per action.
Or some kind of # of tumors to go specific directions
TBH i didnt learn anything here thats useful in game... was there anything useful other than a rough idea of what potential creep spread # of tumors is?
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This thread is not another “use overlord to creep spread faster” or “multiple tumors spread creep faster.”
I have the solution to everyone's creep needs: Nydus Worms
But seriously, great read = )
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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. Show nested quote +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.
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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!):
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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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Hi. OP here. Thank you for the feedback.
Honestly, I’m surprised that there are this many dissatisfied readers. I guess I should have explained my intention better. This thread is not meant to provide people a method to improve their creep spread by itself. Instead, this is an attempt to derive a model that explains the degree of creep spread that players perform. In a sense, I am trying to provide a thermometer when people are boiling water because no one before me had one, but some people don’t care much about current temperature and instead demand better fuel to boil water faster. I’m afraid a thermometer vendor can’t satisfy those who want to buy fuel. Expectation is wrong there. Also, this thermometer is not meant to work in every situation, at least not yet. It’s still a crude one. Only a state-of-art thermometer would be able to measure with multiple factors such as distance, direction, speed etc. incorporated. No one can provide a sophisticated thermometer at this point despite many people’s very high expectation. I guess these mismatches between my intention and people’s expectation pretty much sum up the feedback. I wish I knew a better way to get across my ideas.
Thank you Cirqueenflex and radscorpion9 for the correction. Domains should have been 45=<x and 90=<x. Editing now. I’m the one who was just stupid and tired :D
On November 10 2012 10:42 TheRabidDeer wrote:
Interesting theory. How quickly do you reach the cap on effective creep tumors for spreading? Player's APM cap comes much earlier, and the cap on effective creep tumors depends on maps. I'm afraid it's not considered in my model.
On November 10 2012 11:23 Filter wrote:
How long would it take a Terran to actually clear that and cross the map with an army? Luckily very few Zergs even in the pro ranks have the skills required to have creep spread that good, but in a perfect world they would have those skills. At what point would a Terran be able to actually attack/what would be the economic cost in terms of scans to cross it? Once the model with distance is figured out, it's a very interesting question. At certain point, I feel having a raven is more economic than spending, say, 5 scans.
On November 10 2012 11:37 chuminh wrote:
reading from the tables, I assume that this equation is for spreading creep from 1 queen only? if player uses 2 queens ( I guess Scarlett uses more than 1 queen to spread from what I saw, then the efficiency must be lower in half.). Am I wrong? Efficiency is within the same build. 60% with 4 queen build has a better creep spread than 60% with 3 queen build. If one wants to compare between 2 different builds, using the number of creep tumors itself is more useful than comparing %.
On November 10 2012 12:18 TheGreenMachine wrote:
TBH i didnt learn anything here thats useful in game... was there anything useful other than a rough idea of what potential creep spread # of tumors is? Not meant to improve anyone's play in game with this information alone.
On November 10 2012 15:16 radscorpion9 wrote:+ Show Spoiler +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. Thank you very much for your supplement and suggestions. Your ideas as to what this research should lead to is spot-on. I hope this introductory work can help for those deeper analyses.
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I honestly really enjoy reading these threads and theories.
Thank you.
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Oh......... I thought it was going to be math on getting the best actual spreading of creep rather than a calculation of the max possible number of tumours at a given time. You did do good work on this though, and it is nice to know the upper limit (despite impracticality of achieving or applying it within a game, as you put it a "thermometer"), but it's not what I was expecting from the title.
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Your work is much appreciated, but I think you left some important things open; namely including distance into the equation. How is "effectiveness" and the number of creeptumors relevant when its all about the actual spread (the distance)? I really hoped you would cover this, since it would be really cool to know how fast you can creep up the whole map for example.
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On November 10 2012 12:27 D_K_night wrote:
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.
I really don't want to make OT, but what are they teaching you in school then? :p How to give a change?:p I don't want to be mean, but it's interesting for me what math level is in schools in other countries.
To OP, I read hole post math seems ok, maybe a bit too many transformations (especially in hand made part) which made it a bit too long, but it's fine.
If you'd like to get some criticism of your work, then I have 3 things to say:
- you said It would be interesting if someone made a program for calculating the efficiency from replays. With y= (x+45)(x+60)/2700 equation But computer program won't have any problems to handle that [ ] function so algorithm would look different way.
- If you make "science" article, treat your readers as equally smart. Other way it's a bit annoying to read it (when you're asking 100 times if we're lost just because you summed up two fractions).
- every time "x" appears as time parameter cute panda dies somewhere.
Other then that it's nice, and good job Now you can work on creep range model
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I still did not finished reading this, but I think you should use Ceiling function instead? That's because the normal practice (or should I say the most common practice, at least in engineering) is to always consider the worst case scenario and I think that Ceiling function is better suited in this case (i.e. if y_1 = 3.2 seconds, you should consider 4 seconds, merely for not throwing away that .2 second).
Thanks for your time spent in this, I enjoy reading this type of more analytical of work.
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This is so awesome. I love seeing things like this.... it not only provides food for thought, but it shows how far from perfect the current pros still are.
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Awesome work, I have always pondered about this as well, what DOES perfect creep spread look like.
If someone could make a custom map where once you drop a CT, your draw a line out from it on the minimap, and it will auto spawn new creep tumors along that spline... would be cool too test the out come, unfortunately i have no skills to do that lol
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I loved this math reminder. I'm wondering if in another two years efficiency of best players will be closer to maximum.
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On November 12 2012 05:37 F u r u y a wrote:
I still did not finished reading this, but I think you should use Ceiling function instead? That's because the normal practice (or should I say the most common practice, at least in engineering) is to always consider the worst case scenario and I think that Ceiling function is better suited in this case (i.e. if y_1 = 3.2 seconds, you should consider 4 seconds, merely for not throwing away that .2 second).
Thanks for your time spent in this, I enjoy reading this type of more analytical of work.
The floor function is correct; y is the number of creep tumors (perhaps as a function of time x, i.e. y = f(x)). To be conservative, you round whole creep tumors y at time x down.
P.S. Interesting article. I liked it! I feel inspired to analyze maximum area covered as a function of time by the optimal strategy. Alas, if I only had the time. 
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EPT
