EPTAt least because you have to build a refinary and you only get 4 gas per trip while you get 5 minerals. Also you can push the minerals income with more workers pretty much all the time, with gas you are limited by base number. Gas is at least 25% more valuable by mere numbers. The real difference is probably around 50% as far as my experience tells.
Starcraft 2 units: a cost-effectiveness analysis. - Page 7
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Cheerio
Ukraine3178 Posts
At least because you have to build a refinary and you only get 4 gas per trip while you get 5 minerals. Also you can push the minerals income with more workers pretty much all the time, with gas you are limited by base number. Gas is at least 25% more valuable by mere numbers. The real difference is probably around 50% as far as my experience tells. | ||
oldahe
Austria534 Posts
lets say you compare a thor´s anti air vs the mineral/gas equivalent in marines. while the marines are more cost effective in the beginning of a battle, their damage output decreases over time when single marines die. the thor meanwhile keeps his entire firepower until his very last hitpoint. | ||
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Yoshi
Netherlands9 Posts
http://www.broodlings.com/cost-effectiveness.php Based on the follow formula: HEALTH*(ARMOR*1,05)/(MINERALS+(GAS*1,5))  PS/(MINERALS+(GAS*1,5))*1000 So gas is 50% more valuable than minerals and armor is taken into account, but only with a simple calculation. Each armor point is 5% more HP. For Protoss this isn't exactly right but I can live with that. | ||
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Hydrian
France12 Posts
I just want to share a updated XLSX version of this spreadsheet, because I thought the original idea was so brillant and usefull : https://docs.google.com/leaf?id=0BySa2ukZTvlpMGVjOGQ3YzAtNjRiMy00NTgzLTlmM2YtMWNkMWMzMjYzYjA2&sort=name&layout=list&num=50 sadly I think you need the last version of Excel to open it  Anyway, I've added some missing unit (Pre Igniter Hellion, Infested Terran, Baneling etc...), some number relative to upgrade (dps augmentation with each +1upgrade in %), a attempt for measuring the negative effect of armor on DPS : ([Damage] -1*[Attack number]) / [Cooldown] in % 1 is 1point of armor updated numbers with the 1.1 patch (for Ultra, Siege Tank en Battlecruiser) and some colors ^^ I think I may make another version with 1 gas = 1,2 minerals, as harvesters gather only 4 gas per trip... Voilà ! I hope it can be usefull :D Please forgive me for my terrible english (I'm french xD), and my maths may be a bit awkward : I didnt do any maths since I finished HighScool ^^, so, please, feel free to correct me if some of my numbers are totally wrong x) @Yoshi : I didn't ignore your work at all, your numbers relative to upgrades inspire me, but I thought the old presentation with, for instance [marauder vs light] and [marauder vs armor] on 2 separated lines, was more handy for comparaison  | ||
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kcdc
United States2311 Posts
Here's why health*damage/cost is a more relevant statistic than health*damage/cost^2: A unit costs a certain amount and will deal damage as long as it's alive. We'd like a measure of the total amount of damage a unit will produce before it dies per resource invested in that unit. This value will be directly proportional to the unit's health (doubling health doubles time before the unit dies, thereby doubling total damage the unit deals). It will also be directly proportional to the unit's DPS (double DPS doubles total damage the unit deals in a set time before it dies). The value is inversely proportional to the cost of the unit (doubling the cost of the unit means it deals half the 'total damage per resource invested' before it dies). The argument in favor of squaring cost in the denominator was that using health*damage/cost as your measure of unit effectiveness has the seemingly odd result that if you plug in values for 2 units, you get double the cost effectiveness of one. For example, DPS of 2 zealots * health of 2 zealots / cost of 2 zealots == 2 * zealot DPS * zealot health / zealot cost. This looks funny at first because doubling the number of units shouldn't increase the efficiency of each unit. The forumula doesn't work this way tho. It looks at a single unit. If you plug in the values of 2 zealots, the formula will spit out the cost effectiveness of a single super-zealot that has double health and double damage, but costs twice as much. Unsuprisingly, the formula tells us that super-zealots are twice as cost-effective as regular zealots because they'll survive twice as long while dealing damage twice as quickly, meaning they'll do FOUR times as much 'total damage' at a bargain price of only twice the cost. Imagine the hypothetical super-zealot with double health and double DPS against 2 regular zealots (equal cost). The super-zealot would have half its health left after killing the first zealot and would have a quarter of its health left when it finished the second zealot. There's a reason it's harder to get more expensive units with higher health and damage--they're more effective. If you want to test the chart, try matching equal effectiveness armies against eachother. For example, according to the chart, zerglings are roughly twice as cost-effective as zealots, so if I pit 50 resources in zerglings against 100 resources in zealots, it should be a roughly even fight. Of course, 1 zealot kills 2 zerglings without breaking a sweat. If you multiply the chart values by cost (translating them to health * DPS/cost instead of health * DPS/cost^2) you get results indicating that zealots are approximately equal in cost-effectiveness with zerglings. If you try matching 100 minerals in zerglings (4) against 100 minerals in zealots (1), you'll see that it's an even fight. | ||
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dizzy101
Netherlands2066 Posts
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lololol
5198 Posts
Your zealot vs zerglings comparison is flawed, because quantity does not increase effectiveness linearly. 2 zealots together are not twice as effective as a single zealot, they are actually 3 times as effective(since they are equal in strength to 3 zealots one at a time). Additionally, armor effectiveness depends on the attack of the opposing units, and can be calculated only on a case by case basis, for example the 1 base armor of the zealot is very effective vs the 5 base damage of the zergling, so that's going to have a big effect on their matchup, while it won't matter much against the 47 damage attack of an upgraded archon. Similarly, this does not take into account overkill, range, size, speed and other factors. Zealots fighting zergings in a choke are obviously going to fare better than in an open field, e.t.c. | ||
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Treehead
999 Posts
On December 10 2010 07:43 lololol wrote: HP * DPS/Cost doesn't really show anything and is very biased against cheap units. For example: stimmed marines place very low in that, yet they are obviously very cost effective units and will beat a lot of the units with better HP * DPS/Cost. Your zealot vs zerglings comparison is flawed, because quantity does not increase effectiveness linearly. 2 zealots together are not twice as effective as a single zealot, they are actually 3 times as effective(since they are equal in strength to 3 zealots one at a time). Additionally, armor effectiveness depends on the attack of the opposing units, and can be calculated only on a case by case basis, for example the 1 base armor of the zealot is very effective vs the 5 base damage of the zergling, so that's going to have a big effect on their matchup, while it won't matter much against the 47 damage attack of an upgraded archon. Similarly, this does not take into account overkill, range, size, speed and other factors. Zealots fighting zergings in a choke are obviously going to fare better than in an open field, e.t.c. The fact that it doesn't tell you the units to play with if you want to win the game regardless of positioning and micro doesn't mean it's not a good metric - it just means you have to make an additional assumption: "Assume that units are microed such that they can be as effective as if they were on top of each other in an open battlefield situation." Sometimes this isn't possible, but that doesn't mean it's not worth examining - it just means you have to take what the numbers tell you in context. Edit: Also, etc. stands for "et cetera", so e.t.c. is only a proper abbreviation if you meant one of the other phrases found at: http://en.wikipedia.org/wiki/ETC Not that it matters at all for the content of your post, but just FYI. | ||
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lololol
5198 Posts
The latter parts were all about his zealot vs zergling comparison and why actual ingame cost effectivness changes depending on multiple factors, which can't be considered in such a table and have to be looked at on a case by case basis to determine what would be the ingame end result. | ||
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clickrush
Switzerland3257 Posts
(dps/cost)*(hp/cost) ?? It should be: dps*hp/cost ! I give you an example why this is better: If you compare Zealots and Zerglings then the used formula suggests that Zerglings are more cost effective, which is completely wrong. The only szenario when Zerglings are better is when they get a nice surround and are on equal upgrades. The Zealots then need 3 shots to kill a Zergling because they overshoot with 13! damage that means 33% of his dps, that means he loses a shitton of dps in practice, despite the fact that he is more costeffective, so dont let that fool you! The Zealot being more costeffective on paper shows when you get the +1 attack because he completely dominates Zerglings then with only a slight dps increase of 14% (not counting in that he overshoots with 1 damage/kill). This chart however suggests that Zerglings are almost twice as costeffective than Zealots which should not be overcome by a 14%increase dont you think? a more theoretical/simple example: smurf: 10dps 100hp gargamel: 100dps 100hp in this example you need 10smurfs to kill a gargamel. That means a gargamel is 10* better. So letz assume the game is balanced and a gargamel costs 10minerals while a smurf costs 1 mineral. with the (wrong) formula in the OP you get the following: smurf: (10dps/1)*(100hp/1) = 1000 gargamel: (100/10)*(100/10)= 100 the smurf suddenly seems to be 10* more costeffective despite the fact that we perfectly balanced the game... I hope this shows that the used formula is completely wrong. edit: also 1gas is roughly 1.5 minerals and not 1 mineral. you need to invest 75+50*3= 225mins for 1 assi/etc to mine 114gas/min if you invest the same amount of minerals into mineral mining then you get about 150mins/min | ||
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Deleted User 132135
702 Posts
1. The max mineral gathering output at each expansion is approximately 4 times as high as on gas per timeunit. Following the system of supply and demand: 2. Gas is needed approximately half as much as minerals by the end of the game of all units/upgrades/buildings at an average --> ~4/~2=~2 | ||
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Deleted User 101379
4849 Posts
On December 10 2010 21:36 clickrush wrote: a more theoretical/simple example: smurf: 10dps 100hp gargamel: 100dps 100hp in this example you need 10smurfs to kill a gargamel. That means a gargamel is 10* better. So letz assume the game is balanced and a gargamel costs 10minerals while a smurf costs 1 mineral. This is wrong, you would actually need 4 smurfs. 1st Second: 4 Smurfs dealing a total of 40 damage => Gargamel down to 60hp 1 Gargamel dealing 100 damage => 1 Smurf dead 2nd Second 3 Smurfs dealing a total of 30 damage => Gargamel down to 30hp 1 Gargamel dealing 100 damage => 1 Smurf dead 3rd Second 2 Smurfs dealing a total of 20 damage => Gargamel down to 10hp 1 Gargamel dealing 100 damage => 1 Smurf dead 4th Second 1 Smurf dealing 10 damage => Gargamel dead 1 Gargamel at the same time dealing 100 damage => Smurf dead You should rethink your theory. EDIT - Addition: In your example the Smurfs ARE 10 times more effective since they have 10 times as many HP for the same cost with the same DPS. | ||
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clickrush
Switzerland3257 Posts
On December 10 2010 22:47 Morfildur wrote: This is wrong, you would actually need 4 smurfs. 1st Second: 4 Smurfs dealing a total of 40 damage => Gargamel down to 60hp 1 Gargamel dealing 100 damage => 1 Smurf dead 2nd Second 3 Smurfs dealing a total of 30 damage => Gargamel down to 30hp 1 Gargamel dealing 100 damage => 1 Smurf dead 3rd Second 2 Smurfs dealing a total of 20 damage => Gargamel down to 10hp 1 Gargamel dealing 100 damage => 1 Smurf dead 4th Second 1 Smurf dealing 10 damage => Gargamel dead 1 Gargamel at the same time dealing 100 damage => Smurf dead You should rethink your theory. EDIT - Addition: In your example the Smurfs ARE 10 times more effective since they have 10 times as many HP for the same cost with the same DPS. oh lol ok I can only agree. thx for educating me -.-but then I do not understand how the lings are double as cost effective as zealots. can you also clear my zealot vs ling example up? the main argument was that zealots tear up lings even with perfect surrounds when zealots have +1 attack which is only about 14% increase in dps. | ||
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Steel
Japan2283 Posts
If you take a quick look at the list though, it's easy to see why this doesn't really work. First unit is the zerglings, which is true if you are fighting...other zerglings? Any sort of splash or armored units will greatly lower their efficiency since they die really easily, but this consideres health. However, if the lings can't get any shots off (ie vs collosi or tanks) they are not very cost effective. Also, you had to get the tech for adrenal gland, much like all units need tech that cost different. Same issue with the marine and Zealot. These units need to be more cost-effective or else we wouldn't see them past the extremely early game. Then there's stim, the issue of micro...and so on. All units have their particularities that make them more cost effective than other. What's interesting though, is that the Spine Crawler is only as cost effective as photon cannons when fighting armored...doesn't this seem to be an issue? It's okay if they want to make it better against armored, but maybe make the damage against armored a bit stronger than the photon cannon, and the damage against non-armored a little lower, so its balanced. | ||
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Ruthless
United States492 Posts
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DoubleReed
United States4130 Posts
((H/R)*(D/R))*1000 = ((H * D)/R^2)*1000?? This is obviously a bad metric simply because as it has a inverse quadratic relationship to cost. And cost effectiveness should be based on Bang/Buck, not Bang/Buck^2. | ||
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kcdc
United States2311 Posts
I like the Smurf (100 health, 10 DPS) vs Gargamel (100 health, 100 DPS) example clickrush gave, so we'll stick to that for examples. We'll assume that a Smurf costs 10 coins and a Gargamel costs 50 coins. (H * D)/R approximates unit efficiency assuming each unit individually marches into battle in a line. Using this formula, you get that a Gargamel is 2 times as cost efficient as a Smurf. This would mean that in order to match 50 coins of Gargamels (1 Gargamel), we would need to have 100 coins worth of Smurfs (10 Smurfs). This is true in a sense--if the Smurfs line up and fight Gargamel one at a time, it will take 10 Smurfs to match Gargamel--but it does not reflect typical game scenarios. In a real game, the cheaper units will all fight at once, allowing the 10 Smurfs to easily beat one Gargamel. At best, this formula roughly reflect conditions where melee units fight one-another in a narrow choke. (H * D)/R^2 has a different problem. Using this formula, you find the Smurf efficiency to be 10, while Gargamel's efficiency is 4, meaning that a Smurf is 2.5 times as efficient as a Gargamel. This would mean that in order to match a 50 coin Gargamel, we would only need 2 Smurfs valued at 20 coins. In fact, Gargamel would be left with 70/100 HP after dispatching the two Smurfs. In an open field scenario where all units get to attack at once, Gargamel is equally matched against 4 Smurfs. Since 50 coins of Gargamel is equal in combat value to 40 coins of Smurfs, we'd like a formula that shows that a Gargamel is 80% as efficient as a Smurf. With a little algebra, I came up with a quadratic that reflects the scenario we want: Efficiency(Gargamel) = X * Efficiency(Smurf) * Cost(Smurf) / Cost(Gargamel) where: 0 = x^2 + x - 2 * (H(Gargamel) * (D(Gargamel)) / (H(Smurf) * D(Smurf)) Using the quadratic equation with these numbers, you can solve for X, finding that X=4, and Efficiency(Gargamel) = 0.8 Efficiency(Smurf). This could pretty quickly be applied for all the units in SC2. Just set the zergling's efficiency equal to 1 and find the efficiency of every other unit relative to the zergling. | ||
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kcdc
United States2311 Posts
Outside of static defenses, adrenal zerglings are the most efficient units in the game. Zealots are by far P's most efficient unit followed by collosi (assuming 3 hits) and immortals (vs armored). Stimmed marauders (vs armored), stimmed marines, blue flame hellions (hitting 3 light targets) and sieged tanks hitting multiple targets are T's most efficient units. This might surprise some, but hellions hitting 3 lights targets per shot came in at #1 for T. Having played zealot + HT a lot against T, this doesn't surprise me. | ||
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Bajoli
Netherlands3 Posts
-assumption 1: 100% service area of the weaker unit either when ranged or when in melee. -assumption 2: `n` is the amount of smurfs and `h` is the amount of seconds to kill 1 smurf, which is 1 in this case (1 killing hit in 1 second) In case many units fight vs one: ( sigma from 0 to n of { h* n} ) * {cost effectiveness of each individual unit} = cost effectiveness of 1 army. For people who know nothing about mathematics. "Sigma" means "count up all the values of the function" in this case from 0 to n of the function 1*n. So in the "4 smurfs win example": {sigma 1 to 4 of 1*n} = 1+2+3+4=10 so yes 4 smurfs have 10 times as much potential as 1 individual smurf when fighting against 1 gargamel. The easier formula to find this instead of adding everything together is: h*[(n^2+n)/2] To give the same example: 1* [(4^2+4)/2]= 10 I have been thinking for hours what will happen if two groups of smurfs fight against eachother with their 10 dps and 100hp.. For instance: Team blue :10 smurfs =>> (10^2+10)/2=55 times as effective vs gargamel then 1 smurf Team red: 9 smurfs=>> (9^2+9)/2=45 times as effective vs gargamel then 1 smurf But what happens mathematically when team blue fights team red? I don't know how to mathematically proof this, but i do know for a fact that team blue should win here with a wider margin then 10 - 9 = 1 smurf. The problem is though, that if both groups would oneshot eachother you would have exactly 1 smurf left for team blue. But 10 smurfs would kill 1 smurf in the first second while 9 smurfs wouldn't kill one smurf during the first second. That 10hp smurf difference will keep adding up during the fight (because basically you have 10vs 8 dps-wise for a short time after the first second) and i wouldn't be surprised if team blue wins with 3, maybe even 4 or 5 smurfs left instead of 1. Ofcourse it all depends on the AI or micro of the units, but with perfect focusfire the dps of team red will diminish faster then that of team blue, especially if that 10 health smurf would keep doing dps during the rest of the fight for instance. How on earth could you proof that theory mathematically? No matter how you proof it, it will show how important the supply lead is during the game. Another idea: we should add an "micro potential parameter" for instance if there are perfect forcefields the micro potential of zerglings is 0, but if you have a perfect surround it might be close to 1 depending on the amount of zerglings you have and how many of them can do dps. What happens to cost effectiveness if only 50% of your zerglings can do dps in a chokepoint? etc. | ||
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brickrd
United States4894 Posts
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