|
Have you ever rolled a pack of Banelings into an army 'ball' and wondered really how cost efficient that trade off was? Or perhaps piloted your Vikings near a Protoss force in order to take out a single colossus, yet suffered a few casualties and wondered if the endeavor was worth it? Theorycrafting and analyzing the cost, potential cost, and cost efficiency of your units is a popular strategy to improve decision making in your matches. It is a common topic of many posts and even casters like Day[9], Artosis, and Chill.
In this thread, I want to introduce you to a new way of looking at unit cost and unit worth; specifically the relation of Minerals and Vespene Gas. Separated, the two are ambiguous, while combined they become far more simplistic. I will not go into supply, build time, upgrades, pre-requisites, etc; remember, were talking straight resources here.
Single Base Maximum Saturation Returns: (for your reference)
+ Show Spoiler +-1160 Minerals per Minute (real time)
---840 Minerals per Minute (Starcraft II Faster time)
-328 Vespene per Minute (real time)
---230 Vespene per Minute (Starcraft II Faster time)
EXAMPLE ONE:
+ Show Spoiler +Let me explain with an example: 2 Marauders and 6 Marines are overwhelmed with a force of 16 Roaches, 24 Zerglings, and 2 Infestors. Before falling, the Terran force is able to kill a single Infestor, 3 Zerglings, and a Roach.
Almost every player would analyze this situation in a specific way. Anyone who knows anything about Starcraft understands that Vespene Gas is a more valued resource. We see an Infestor was killed and signify the event as a victory, with the Roach and Zerglings as mere frosting on the cake. Marines and Marauders are relatively inexpensive, and are considered replaceable by all means.
Lets add up that skirmish:
Terran losses: 500 Minerals, 50 Gas (Marine:50m)(Marauder:100m 25g)
Zerg losses: 250 Minerals, 175 Gas (Infestor:100m 150g)(Zergling:25m)(Roach: 75m 25g)
Close. I’d bet most players would agree that the Zerg did indeed lose more resources in that encounter; but why? If you do straight addition, Zerg lost 125 resources less than the Terran player. Well, because of the fact that Vespene Gas is valued more than Minerals and is harder to obtain is why we can refute that claim.
Let’s see exactly what happened using some math:
(Personally, I can’t STAND Starcraft II’s ‘faster’ time – I find it incredibly annoying to constantly convert, but I will use it for the sake of the TL community)
Step 1: We need to relate Vespene Gas to Minerals. In that regard, we need a universal unit. It could be literally anything you want, dollars, bunnies, pride, but I will just called it a ‘unit of worth’. We harvest Vespene Gas at 230 per minute. Therefore (230/m) = 1 unit of worth.
Now we need to put Minerals into that same unit. So divide the Mineral collection rate, 840 Minerals per minute, into the rate of harvesting Vespene Gas (230 per minute). Therefore (840/m) = 0.2738095 units of worth.
Step 2: Use these values to combine Minerals and Vespene Gas together.
Terran lost 500 Minerals and 50 Gas. So now we convert.
500(0.2738095) + 50(1). This equates to: 186.90475 units of worth.
Zerg lost 250 Minerals and 175 Gas. Convert once again.
250(0.2738095) + 175(1). This equals: 243.452375 units of worth.
Looks like our predictions were right! Terran did get the better end of the deal in that encounter.
EXAMPLE TWO:
+ Show Spoiler +Another example:
In my gameplay (Zerg) vs Terran, I love to actively use my Mutalisks to snipe Siege Tanks. However sometimes (like most players), I overstep my boundaries and lose Mutalisks carelessly; though sometimes it’s worth it. Let’s take a look.
Say I notice his army moving out, so I swing around to his production facilities and pick off a newly spawned Siege Tank and a stationary tank which was in Siege Mode. In my haste though, a pack of stimmed marines and a volley barrage from a Thor picks off three of my Mutalisks as I fled.
Terran losses: 300 Minerals, 250 Gas (Siege Tank:150m 125g)
Zerg losses: 300 Minerals, 300 Gas (Mutalisk:100m 100g)
It’s obvious I got the shorter end of the stick on that encounter, but by how much exactly?
We can use the same values because Mineral and Gas collection rates are our constant. Plug in once more!
Terran: 300(0.2738095) + 250 = 332.14285 units of worth.
Zerg: 300(0.2738095) + 300 = 382.14285 units of worth.
EXAMPLE THREE:
+ Show Spoiler +Let’s do one final example (best for last), but change it up a bit. This time, let’s take a snapshot of a certain resource collect rate during a game. Let’s say we have a Protoss on 3 bases and a Zerg on 2 bases because his expansion was sniped.
Protoss (rough estimate) would probably have an income of 1512 minerals per minute and 552 Vespene Gas per minute. Zerg would be at around 1150 minerals per minute and maybe 414 Vespene Gas per minute.
3 Colossi, 15 Stalkers, 12 Zealots, and 4 Sentries steamroll through a Zerg’s army of 14 Roaches, 21 Hydralisks, and 3 Infestors. The Protoss has left a small garrison of 2 Colossi, 7 Stalkers, and a Sentry. It’s obvious that the Zerg lost, but by how much?
Protoss total resources lost: 2650 Minerals and 900 Vespene Gas.
Zerg total resources lost: 3450 Minerals and 1850 Vespene Gas.
Ouch, certainly a one sided battle there.
Protoss losses:
First do 552 Vespene Gas per minute divided by 1512 Minerals per minute = 0.365079365079
Now solve: 2650(0.365079365079) + 900 = 1867.46031745935 units of worth.
Zerg losses.
First do 414 Vespene Gas per minute divided by 1150 Minerals per Minute = 0.36
Now solve: 3450(0.36) + 1850 = 3092 units of worth.
If you have any questions or comments, please post below. If you are able to master this technique, it really helps you analyze your games from an economic standpoint. Some equations can even be done on the spot in your head if you have a penchant for math. (Remember, you don’t always have to put it in terms of gas, which is just what I did).
|
First of all: I just LOVE those kind of theoretic approaches.
These are things people should actually learn about, once they know how to open a game with!
I just wrote a few sentences about things you are not taking into account with your methode, but deleted them, as I really don't want to critizise you for not "solving the game" 
Yet one small thing I want to point out: statistically you are not only mining more minerals, but you need more minerals too (even a lot of the most gashungry units cost more minerals than gas), so I think if you norm it via gas ||1gas|| = 1 uow, you would actually have to use the 0.2738095 uow from minerals and multiply it with some kind of average "mineral/gas-factor". Yet Im not sure how to do it exactly, and I think your methode gives one a useful, quick calculation!
|
I want to thank you for taking the time to put this analysis together, but I'm afraid you are failing to evaluate a key piece of information. Relative Worth. Allow me to explain:
The Terran Race is limited much more by mineral count then gas count past the early game, especially when compared to Zerg. This means mineral heavy losses are much more significant to the terran player then to the zerg, who usually is extremely gas starved.
Desired Unit Composition also plays a factor in cost efficiency. For example, if I am going for a composition with Sentries and Colossus, my gas is going to be much more valuable then normal, and the weight of losing a sentry will be greater then what your math suggests.
|
This is interesting. Is there a way you could combine it with the other ways of calculating value and not lose anything?
|
I appreciate the amount of work you put into the thread, but I have a pet peeve against people who don't follow strategy forum guidelines.
Please refer to http://www.teamliquid.net/forum/viewmessage.php?topic_id=113479 and http://www.teamliquid.net/forum/viewmessage.php?topic_id=210370.
At any rate, while knowing this can probably help your play, I think it's always to do theorycrafting within context. There are times in which it is worth it to do a somewhat unfair tradeoff in order to create a certain situation. I think the easiest example is using ling/baneling to kill off marines in Marine/Tank/Medivac, since even if you have an unfair tradeoff, the mutas can reign supreme and it is important to gather a critical number of mutalisks (eventually they just rip through turrets and everything ;] )
I always take these kinds of posts with a grain of salt, because while I love number-crunching, I don't want to get caught up in the efficiency of trading units during the game. From my standpoint, there are so many factors that contribute to whether or not an engagement was wise, and I think most players know it by feel, not by specific numbers.
|
The relative worth of gas compared to minerals depends on other factors besides the mining rate of each. Most notably, how it factors into your unit composition. Extreme example: Someone going mass marine, only using gas to make 3-4 medivacs (and get upgrades), will value minerals far more than someone going tank-heavy. For the tank-player, marines or hellions are just a means to dump excess minerals and their loss is irrelevant.
Another thing to note is that one major resources was not addressed yet: Time. There's a reason that casters focus (for example) on Protoss players losing their Colossi, because even later in the game, few Protoss players use more than 2 Robos (plenty will still run on just 1). Replenishing losses of Robo units is much more costly in terms of time than replenishing a Gateway army, as late-game players tend to mass Warpgates.
For Zerg, larvae introduce yet another resource. One that is highly dependent on the desired unit-composition. All together, this means that purely looking at the gas/mineral cost of an exchange may be too simple of an approach.
|
Love the math.
A great way to equate gas and minerals.
Unfortunately they cannot be equated and everything is situational.
But this does help people choose priority targets etc.
|
I don't think this gives anybody a new way of looking at resources. All it does is attempt to quantify the general consensus that is "gas > minerals"
It's kind of just taking a conversion factor and writing it on its relative machine/system so that people have a concrete and universal basis. The problem is that there's a lot of guesswork involved and i don't think it really amounts to much concreteness at all. There are so many more variables that go into the 'real worth' of gas vs minerals and i don't think this addresses almost any of them.
That being said, as a general guide I'm sure this could be helpful for players who don't really have a feel for the game yet, but it will always come down to a case by case basis and it's more "do i want to lose 4 colossus and 16 stalkers and 21 zealots but kill 30 hydras 20 roaches and 10 corruptors and his only mining base? can he remax? can I? Would my remaxed army beat his?" than hard number vs hard number.
|
Interesting idea, however, you cannot purchase vespene gas with minerals, as you could in reality with say gold and whatever currency you may be using. Using 'Unit Worth' to determine the value of vespene in relation to minerals could be correct, but could also be wrong. When looking at a real-life scenario, the price of gold fluctuates depending on many variables. One of these is surely how scarce the resource has become.
Looking at this under your terms. It should be noted that, as the game progresses, the value of vespene gas and minerals respectively, should rely on the total amount of resource remaining in the particular game.
For the most part, it seems as your calculation will do a decent job of giving players an idea of whether or not they "won" a specific battle, but again, this is situational as well. A player with a booming economy may very well want to trade his Infestor Roaches and Lings to kill 2 Marauders and 6 Marines of a player who is not doing so well economically.
|
On June 11 2011 00:54 Ecliptium wrote:
For the most part, it seems as your calculation will do a decent job of giving players an idea of whether or not they "won" a specific battle, but again, this is situational as well. A player with a booming economy may very well want to trade his Infestor Roaches and Lings to kill 2 Marauders and 6 Marines of a player who is not doing so well economically.
Yeah if you are going to end up with a substantial army and your opponent isn't, then no matter how inefficient the damage it is still more "win-efficient" for lack of a better term to kill it.
|
If you're going to do this, then do it properly. No zerg is going to get 21 hydras vs colossus nor is a Protoss going to get 12 zealots.
|
On June 11 2011 00:58 trNimitz wrote:
If you're going to do this, then do it properly. No zerg is going to get 21 hydras vs colossus nor is a Protoss going to get 12 zealots.
It is literally completely irrelevant.
|
I am not a fan of trying to simplify things into numbers. This measurement isn't really useful unless both players are just trying to throw equal tech units at each other until one of them mines out and ggs. If you invest into higher tech units you would also expect your army to trade more efficiently resource wise than someone who sticks to low tech. Theres also things like energy and time you would need to take into consideration. But more importantly, you won't be able to quantify the complex interactions between each unit on the field and the map itself.
If you see someone trade their queen for a bishop you can't immediately call it a bad move. It could be a necessary loss for a checkmate 5 moves later. Maybe I really needed to kill that banshee even if I lose 5 stalkers to the supporting tanks. Everything depends on the context of the specific game you're playing in.
|
|
|
I hate the entire logic that a unit's monetary value is somehow equivalent to it's military vaule. If I'm using a dark templar based build as protoss, I'm not going to quibble about how many stalkers it takes me to take out all of his overseers. The important thing is that they are all dead, so my DTs can attack unimpeeded. I guess if you wanted to give a monetary value to units killed, it should be in terms of the amount of units the dead enemy unit would have killed in the next engagment.
Allow me to give an example. Lets assume a terran player is using a MMM+V build against a protos with a stalker+sentry+colossus ball. Each colossus shot is 1/5th of a marauder, and the colossi will get an average of 3 shots off in the next fight hitting 5 units each before the vikings kill them. So each colossus is equal to 3 marauders for the terran, or 300/150. So the question arises, when both sides have a good sized army, is it worth losing 2 vikings to kill a colossus? Surprisingly it is exactly equivalent to kill the colossus or to leave it until the next fight and keep the two vikings. Personally, I would say to lose the vikings, since I feel having 3 more marauders at the end of the next fight instead of 2 more vikings is a deal, but resource wise, it is the same.
Now allow me to switch the example from MMM+V to marine, tank, viking play against the same protoss. Each colossus shot is equal to 1/2 of a marine and we will assume the colossi still get off 3 shots each with 5 targets each. That means that each colossus is equal to 7.5 marines or 375 minerals. In this case, it is NOT a good deal to lose 2 vikings to take out a colossus because the group of units that the colossus would kill in the next engagement is worth significantly less than the vikings that would be lost.
Of course there are many other considerations to take into account. Trading two ghosts for a high templar that just spawned is a terrible trade, because he can only use max 1 storm in the next fight. However, 3 ghosts for 2 full energy high templar is a great trade because 3 ghosts are less useful than the units that would be killed by 4 storms.
|
Equating minerals and gas to a universal unit seems pointless. In certain builds, minerals will actually be as valuable or more valuable than gas (MMM for example, even with ghosts and vikings is mineral starved, not gas starved). In other builds, gas is several times more valuable than minerals. There isn't a set ratio in terms of value.
Also, you didn't factor in how things generally cost much more minerals than they do gas.
|
this thread is pretty pointless... you can't measure gas / minerals value, sine unless you have fully saturated bases your calucations are wrong, and you almost never have them fully saturated,
|
I am not following why you put the minerals as gas ITO minerals? (230/870 = 0.27) Shouldnt it be the other way around? Minerals ITO gas so that if gas is 1 unit, minerals are 870/230 = 3.7ish?)
Also, I use a rather simpler method whereby i use scv trips (1 mineral trip is 5 1 gas trip is 4)
Like for example, the ghost change that blizzard said kept the cost the same, didnt. You can get the ghost 2.5 scv trips faster. (40 mineral trips + 25 gas trips vs 30 mineral trips + 37.5 gas trips)
also, for a fully saturated mining base, 40 minerals are collected same time as 8 gas, once again, for blizzard to keep the ghost at the same cost, it would have been needed to be
150 + (50/8 * 40) minerals and 100 gas = 400m 100g
:D.
This is assuming a fully saturated non-muled mining base ofc.
Also, if u want a fun comparison
scouting is best.
Terran is supposed to use a 270 mineral scan right? But wait, coz of the time value of money, the scan only costs about (very rough guess) 200 minerals.
An overlord costs about 100 minerals and 8 pop (to scout, assuming it dies),
and an overseer costs 50 100 (no pop, as it probably won't die if done right. + changelings etc).
A SINGLE observer costs 250 175 (if the robo fac is not used for anything else), where obv that cost drops as the robo fac used for more and more.
And hallucinate costs 150 200 from the single sentry created just for this purpose, + the time it takes to regen 50 energy (coz sentries start on 50). (so obv that cost is also distorted as a sentry can FF and cast hallucinate again and stuff)
Some are more useful than others, but they all cost round about the same, in theory. Esp if you assume that the robo fac will be used for other things (as if it wasn't. you wouldn't build it really...)
|
I'm posting simply to support your hatred of 'faster' time in SC2. Why in the hell did they make the game speed that 99.99% of EVERYONE plays at different from 'real' time?
|
What the OP has done is an interesting exercise in comparison ... but it partially feels like a thickly veiled, 'marines ar OP' bnet thread, lawl.
While some of these mathematics concepts are somewhat intellectually interesting, it really does not offer any value to the player, or the player aspiring to become better. If I were coaching, I'd much rather teach my student to deduce the game state based on advantage-type and vulnerabilities.
I would not want my student doing math during a game, or in between games. Maybe if you're perfecting a build, but never to determine the outcome of a battle. Understanding your advantage type, or disadvantage type and the various vulnerabilities you and your opponent have should be second nature.
|
|
|
|
|
|
EPT
