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I wanted to share my thinking / calculation here and pls. let me know if this sounds solid to you - or if there are any gaps.
Example: Terran Marine
costs 50 mins;
dps = ~7;
upgrade costs 100/100 =~ 400 min (gas*3)* and finally....
the dps we gain is ~1,15 per marine.
*(( a full saturated Terran CC with constants mule mining and constant worker production generates 3 times more gas than mines))
Given that we calculate that the alternative of the weapon upgrade cost, is 8 marines (400/50=8) and 8 marines are 8*7dps= 56dps - it takes at least 48 marines that the upgrade gives you more dps than the according amount of marines you can produce. well that is the theory.. (if we tread gas only twice as high not factor 3 it is still 36 marines - so a bunch)
So bare numbers need to be interpreted ...
1. given if you have the mins&gas for producing marines AND the upgrade - you might be blocked production-wise and can not use your resources at the same time - so in these situations it is better to upgrade than having overmints unused. (especially if you expect a battle battle in 1min) - pro upgrade
2. 8 alternative marines might die - whereas your marines benefit from the upgrades till the end of the game even if the ebay gets crushed. (pro upgrade)
3. If you spare the upgrade and run into an even situation battle-wise - say 10 marines vs. 10 marines and you lose (bad micro) you might not have a second chance to bring out the 8 marines because the enemy raids your base and you lose the game with 100 / 100 on the bank. (pro early upgrade).
4. Other units have different dps gains from upgrades - having 2 tank and 2 thors pays already off - and it does not take 30 units for the vehicle dps upgrade. (pro upgrade)
So "my" net is:
- A) If you are in the situation - you can either upgrade or build, because you do not have enough resourced to do both - you better build units unless you have already a bunch (20+) marines.
If you are in the situation - you have resources for both and you plan to have a group of 10+ marines and relay on that unit in the future - better build both now or build another rax/fax and build more units. 
- B) If you are in the situation to face 200 supply limit you want to have already upgraded units - but if your army has been standing idle for 10 minutes to gather until 200 supply, (pro early upgrade) where you could have harassed at 140 already - you lost a lot of time/initiative or you have given your opponent a lot of time - which might cost you the win anyway upgraded or not.
So no biggy at the end - never have idle time on rax and fax.
I am only bronze ... thanks for taking this non-experience into consideration when answering...
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from a common gamer's perspective:
say if you were to upgrade Terran Infantry +1 = 100min/100gas
you would be seeing effect when you have more than 12 marines. because that 100 minerals can be used to produce 2 marines. and the combined fire power of 2 marines is 12(6+6).
if you have anything less than 12 marines, say 9 marines...after the research each of your 9 marines would get +1 for a total of +9 damage. it would be more beneficial at this time to just get 2 marines for +12 damage than +1 Infantry upgrade for a total of +9 damage.
so it's safe to say a when the benefit of the extra damage output out weights the added damage of an additional unit of that type, it's time to upgrade.
so the equation (Damage output of Minerals of the Upgrade Research > Damage of the Production of an additional unit equal of equal value)
so you can see it differs with each race and unit type...so you gotta do the math
**also i discounted the gas because in the equation minerals are the limiting factor...not gas.
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A lot of the time the is a "zone" where you take 1 less shot to kill things. The best example is +1 Zealots kill Zerglings in 2 hits instead of one.
Always good to have a +1 weapons though
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It also depends what upgrades decrease the number of attacks needed to kill specific units.
E.g. as Protoss against mass Stalkers, your own Stalkers don't gain any real benefit until +2 weapons while Immortals need one less attack with the +1 upgrade already.
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On October 20 2010 02:10 DreamSailor wrote:
A lot of the time the is a "zone" where you take 1 less shot to kill things. The best example is +1 Zealots kill Zerglings in 2 hits instead of one.
Always good to have a +1 weapons though
This hits it on the head. Upgrades only matter if they actually decrease the number of attacks required to kill a unit. There are some fairly common breakpoints that are well known (+1 Zealots against Zerglings, +1 Roaches against Zerglings, etc.) but the math is easy enough that if you want to figure out some of the more important ones, Excel is your friend.
The other situation where upgrades come in handy is to keep up with your opponent's armor upgrades, since he can create his own breakpoints with a key armor upgrade. This is a reactive approach however, and since upgrades take so damn long to finish you're better off having a good sense of the match up and being aware if armor upgrades are popular (against Zerg for instance). I've seen a lot of games get won or lost because one side didn't keep up with weapon/armor upgrades and it made the difference in the mid/late game.
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On October 20 2010 04:13 ZasZ. wrote:Show nested quote +On October 20 2010 02:10 DreamSailor wrote:
A lot of the time the is a "zone" where you take 1 less shot to kill things. The best example is +1 Zealots kill Zerglings in 2 hits instead of one.
Always good to have a +1 weapons though This hits it on the head. Upgrades only matter if they actually decrease the number of attacks required to kill a unit. There are some fairly common breakpoints that are well known (+1 Zealots against Zerglings, +1 Roaches against Zerglings, etc.) but the math is easy enough that if you want to figure out some of the more important ones, Excel is your friend. The other situation where upgrades come in handy is to keep up with your opponent's armor upgrades, since he can create his own breakpoints with a key armor upgrade. This is a reactive approach however, and since upgrades take so damn long to finish you're better off having a good sense of the match up and being aware if armor upgrades are popular (against Zerg for instance). I've seen a lot of games get won or lost because one side didn't keep up with weapon/armor upgrades and it made the difference in the mid/late game.
This is over-simplistic for starcraft.
Unless you plan to attack with ONLY one type of unit against one type of unit, then upgrades make sense even when you don't cross a magic breakpoint. Because in a more practical matchup you've got zealots, sentries and stalkers hitting lings, roaches and queens in all sorts of unpredictable combinations, making all sorts of breakpoints (This roach is being hit by a stalker and 2 zealots, but one zealot dies when the roach is at half health, etc, etc).
Upgrades on units make them more effective in choke points where you can't FIT the extra units you could have purchased by passing up the upgrades. Upgrades make drops more effective, where you're also limited in the number of units you can use. You may be able to afford more marines but you can still only put 8 into a dropship so those extra guys will have to stay at home.
Also, if you let your upgrades fall behind too far, life gets difficult. I remember this one game I played against a terran, I was zerg and neglected my upgrades. All of a sudden he's got this unstoppable ball of 3/3 marines steamrolling across the map. It was pretty ugly.
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As far as OP recommending to only upgrade when you have units to begin with, I don't this is the case with zerg.
I mean, the ideal situation is as a zerg player to never ever produce attacking units until someone is starting to move out across the map.
There's a point where you can start affording upgrades (double evo chambers are awesome by the way) and you most certainly do not need more units to make it "cost effective", simply because zerg can macro up armies a lot faster.
And remember, upgrades aren't just the statistical ones, there also the key functionality ones that must be considered too.
Like Tanks, you gonna build tanks w/o siege tech? Heck, most people probably won't build tanks until siege tank is about to finish.
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Upgrades just simply should not be neglected for all the reasons specified here. Attack and armor upgrades cause breakpoints in specific matchups (100 zerglings with no upgrades loses to 10 zealots with 1 attack and 3 armor upgrades. Add one attack upgrades to the zerglings and they win with about 50% casualties).
But as Clamps said before I could, matchups are usually dynamic, with a unit taking damage from multiple attack types. A marine, for example survives a single Stalker shot and two from a zealot with no upgrades involved. Give the Protoss an attack upgrade and the Marine dies.
You can't really measure it in DPS most of the time because it comes down to "how many hits does it take to kill X with Y?" where Y can represent several units. You also can't simply measure it that way, because all races have the ability to regenerate health if a units survive a battle (Terran can even do this effectively mid battle).
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one important note is that your front line will be a lot stronger with upgrades. For example if you have two groups of marines fighting, the marines with +1 will hold their concave better and get an advantage from their naturally superior positioning.
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There is a lot to be considered about upgrades.
As a Zerg player, I will list some of the times when I value upgrading a lot.
ZvP +1 melee for Zerglings:
Any high level Zerg or Protoss should be aware of these next 3.
Zergling vs Zealot
35 hits to kill 1 Zealot
+1
29 hits to kill 1 Zealot
Zergling vs Stalker
36 hits to kill 1 Stalker
+1
30 hits to kill 1 Stalker
That is 6 swings per Zealot or Stalker difference. Considering you will almost always get 2-4 Zerglings attacking a target, the +1 CANNOT be made up with MORE Zerglings.
Zealot vs Zergling
3 swings to kill 1 Zergling
+1
2 swings
Zealots kill Zerglings 50% faster with +1. Again, this cannot be made up with more Zealots.
+1 carapace vs Terran
Marine vs Zergling
6 shots to kill a Zergling
+1
7 shots to kill a Zergling
Adding 15% survivability to your Zerglings gives you a lot of time to get your more important (and expensive) units in position and doing damage before they are getting hit back
Marine vs Baneling
5 shots to kill a Baneling
+1
6 shots to kill a Baneling
Every Terran player knows how annoying Banelings are vs Marines, not many realize that +1 carapace makes them get 20% closer before dying.
Thor vs Mutalisk
3 shots to kill a Mutalisk
+2 Thor attacks vs <+2 carapace on the muta
2 shots to kill a Mutalisk
+2 Thor attack vs +2 carapace on the muta
3 shots to kill
+0 Thor attack vs +3 carapace on the muta
4 shots to kill
You might have known that Thors can 2-shot mutalisks if they get +2 weapons, but did you realize that if your Terran buddy ISN'T upgrading his Thors, getting +3 carapace will actually make those mutas live longer?
In the end, I'm saying the same thing everybody else is:
Get upgrades when they matter.
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I didn't know most of those numbers, thanks for the post.
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There's so many factors that influence the usefulness of an upgrade. The DPS calculation is just a part of it. Some other aspects to consider are:
12 Marines obviously have more HP than 10 Marines with +1 weapons, so they live longer in a fight, which means that the DPS they deal decreases more slowly. Even if the DPS is equal, the larger group of Marines lives longer and may do more damage in the long run (long run could be a couple of seconds in a fight).
12 Marines may have a harder time getting a nice concave, and may block each other from shooting at an enemy. 10 Marines can more easily should at the same enemy at the same time. In other words, the extra units do not contribute to the DPS if they have to sit in the second row waiting until they can reach the enemy. Good micro can help to some degree.
And in a few cases, as has already been mentioned, there is a breaking point where +1 weapons decreases the number of hits to kill something significantly, like:
Zealot kills Zergling in 3 hits, +1 Zealot kills Zergling in 2 hits,
Colossus kills Zergling in 2 hits, +1 Colossus kills Zergling in 1 hit
It's mostly in fight against low HP units that this matters, so Zergling and workers.
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On October 20 2010 05:53 Haploid wrote:
There's so many factors that influence the usefulness of an upgrade. The DPS calculation is just a part of it. Some other aspects to consider are:
12 Marines obviously have more HP than 10 Marines with +1 weapons, so they live longer in a fight, which means that the DPS they deal decreases more slowly. Even if the DPS is equal, the larger group of Marines lives longer and may do more damage in the long run (long run could be a couple of seconds in a fight).
12 Marines may have a harder time getting a nice concave, and may block each other from shooting at an enemy. 10 Marines can more easily should at the same enemy at the same time. In other words, the extra units do not contribute to the DPS if they have to sit in the second row waiting until they can reach the enemy. Good micro can help to some degree.
And in a few cases, as has already been mentioned, there is a breaking point where +1 weapons decreases the number of hits to kill something significantly, like:
Zealot kills Zergling in 3 hits, +1 Zealot kills Zergling in 2 hits,
Colossus kills Zergling in 2 hits, +1 Colossus kills Zergling in 1 hit
It's mostly in fight against low HP units that this matters, so Zergling and workers.
Colossus need +2 in order to 1-shot zerglings. If zerg got +1 carapace you need + 2 weapons, and if he got +2 carapace you need +3 weapons, and finally lings don't benefit from getting any armor if you got + 3 weapons on colossus. That is because colossus got two attacks, so ling armor will decrease the attack on both.
Also zealot obviously gets really ineffective if you upgrade the oposing forces armor without getting weaponupgrade on the lots. Imagine +3 marauder (+1 base) armor vs unupgraded zealot, he would deal a total of 8 damage for each doubleswing.
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It does matter significantly in the midgame, as well as the late game. Last I checked, Zerglings were still used as a harass unit at these stages of the game, as well as Zealots are still used as meatshields (and as a wall to prevent the opposing army from moving forward).
Also, Armor matters in the same regard. If +1 Armor is researched for Zerg, a Tank can't 1 shot a Zergling.
So to answer the question of when it pays off, it depends on the matchup, but in my eyes, upgrades will always pay off.
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On October 20 2010 06:16 Mellon wrote:
Colossus need +2 in order to 1-shot zerglings. If zerg got +1 carapace you need + 2 weapons, and if he got +2 carapace you need +3 weapons, and finally lings don't benefit from getting any armor if you got + 3 weapons on colossus. That is because colossus got two attacks, so ling armor will decrease the attack on both.
Also zealot obviously gets really ineffective if you upgrade the oposing forces armor without getting weaponupgrade on the lots. Imagine +3 marauder (+1 base) armor vs unupgraded zealot, he would deal a total of 8 damage for each doubleswing.
Yeah, lol, I copy-pasted the Zealot line and replaced the word Colossus, but forgot to say +2 weapons.
Also, since Zealots are melee units, they benefit more from upgrades than ranged units. Melee units have a much harder time attacking all at the same time. A large group of Marines can easily just take one step forward and they can all shoot at the enemy. In a large group of Zealots, only the front line can attack directly, while the rest has to run around to flank the enemy. And we all know how easily Terrans can kite Zealots; flanking isn't easy. You're better off upgrading Zealots than massing them.
Not that this is something that anyone would really do. You'll always mix Zealots with ranged units. That's another thing that makes the DPS calculation even more complex: mixed peanuts.
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I feel that in regards to upgrade, people tend to miss the long run. Because while 1/1 doesn't look that harsh, a 0/0 vs 2/2 will turn huge number battles in equal tier forces.
A 0/0 marine vs a 3/3 Marine is 3 damage dealt/9 taken vs 9 dealt/ 3 taken. We are talking about marines that are trice as strong. Sure, that 1/1 won't hurt you that much. 2/2 , you suddenly have a ratio of 8/4. His marines already double yours.
On top of that, if your units die twice as fast, there is a cascade. 10 marines vs 10 doesn't mean he'll have 5 left because his are twice as strong. It's more like 8 because you loose firepower so much faster.
Roaches with armor lvl 3 have 4 armor, basically eliminating your 0 marine firepower.
Ling vs ling turn from a 5 vs 5 to a 8 vs 2 damage race. It's sheer obliteration.
A full armor Ultra tanks awesome amounts of damage if your units are not upgraded.
Mutas suffer if you upgrade your armor because their splash gets cut down more than it grows from their own upgrades.
Of course there are those "key" upgrade points. But when your 1/0 key upgraded army suddenly faces a full 3/3, prepare for a nasty experience.
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First of all thank you for the vivid discussion.
A lot of good things I learned from your posts.
I agree that it makes sense not only to take a look at dps but also at classic counters situations: 3 marines vs 1 stalker, 1stalker vs 2 Zealots and so on.Very good post from Jermstuddog . Valid in the first 5 minutes when these classic "clean" encounters happen. Afterwards you have in most cases a mixture of different units, partly upgraded, half dead, maybe 2of10 of your units are behind a ramp/down a ledge and can not shoot yet, or are outside of reach, one is group is idle and rdy to attack while the others have to move / are moving and one starts attacking. So clean situations like in the unit tester are not that often in mid/endgame. If at all. Rarely the fight on "Steps of war" is right in the middle when both armies are simultaneously moving towards each other and start attacking at the same time. Hits works fine if both have the same range and same delay.
This hit discussion I think is misleading the answer that can be answered with this is "unit X >> unit Y" because it takes only 2 hits - but that is putting SC2 in a oversimplistic corner. Reason 1 is the delay between a hit of a banshee (2 attacks/ 1,25 delay) is different compared to a marine (one attack delay 0,8608). So hits dont work very well here - only if the pause between each attack is very long.
Yes - encounters are very dynamic and depend on map.
The example from "Clamps" is an interesting one - having 3/3 bio ball means - he invested - 2x 525 mins and 2x 525 gas (weapon AND armor - that takes 9minutes) which can be translated into either "4 additional medivacs plus 2 raven and and 2 marine". (or 2 battle cruiser and 2 raven / or ~40-60 marines) So I wonder if he would have "steamrolled" you with this army as well? Maybe - maybe not bcause he cant micro 4 different units - who knows. Maybe he could have faked a drop- or attack from 2 sides ... no one can prove ..... however I am sure this does not prove "Zerg can be crused in late game when you have a 3/3 bio ball." I think we all agree that this would be too shortsighted.
Upgrades for choke point- & drop-units are absolutely valuable - sometimes a must - I agree.
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A somewhat simplified way to look at things is to just take into consideration how much extra power a upgrade in general gives to your army.
For that you first need to define the power of a army. A simple and quite logic way to do that is:
ArmyPower = ArmyDPS * ArmyHP
Both DPS and HP have a linear effect on your army power, in general a Army or unit with higher power according to this definition will win a fight (excluding things like overkill, armor, positioning, melee getting into place etc etc.)
Now a attackupgrade will simply improve your DPS by a certain percentage depending on the units it's affecting. Usually this lies between 10 and 15%.
For example marines go from 6 to 7 attack an increase in DPS of 16.7% as a result your armypower if you army is exclusively marines will increase with 16.7% as well (if its marine/marauder it will be between 10 and 16.7%).
Now you have to compare this increase in armypower to how simply making more marines would affect your army. If you make more units, for example increase your army size by 20%, you get 20% more DPS and 20% more HP thus increasing your army by 1.2^2 = 1.44
Therefore enlarging your army by a factor x will increase the power of that army by x^2.
So to see how much of a army increase a 16.7% DPS increase is you simply have to take the square root of that. Sqrt(1.167) = 1.08
So in other words the first attack upgrade for marines is worth about the same as simply having 8% more marines. To see when which is more effective you simply have to compare when making 8% more marines would cost about the same as the first attack upgrade.
Given that marines are mineral only and the attack upgrade costs gas we will have to make some arbitrary mineral:gas ratio. I'd use 2 as I think that's a proper reflection for the comparitive value in game.
So lets call x the number of marines we are currently having. Then follows:
50 * x * 0.08 = 300 => x = 75
So as far as strict army power goes if you were to be using only marines you need 75 marines for the attack upgrade to be equally usefull for your army strength as simply getting more marines.
Offcourse this is a bit of a high number which contradicts what you would think from game experience. This is because there are so many factors at stake you virtually can't account for in a analytical view of the subject, to name a few:
- upgrades last the entire game so even if you do not have the actual x from the theory yet when you get the upgrade as long as you get that number over the course of the game it was worth it already. The x is basically a bit of a bottom line, if you ever get more then that number you should be thinking seriously about why you didnt get the upgrade
- upgrades need a building, some matchups you want that anyway as the upgrade structure enables turrets/cannons other times you only want the upgrades and thus have to pay an additional cost
- upgrades take long to be in effect. If you get attacked before the upgrade finishes or your army is gone before it finishes the upgrade doesn't do much
- Armor matters, marines get a relatively larger damage increase against units with armor then those without as going from 6 to 7 is less then from 5 to 6 for example.
- upgrades can have a huge influence on the amount of overkill your units generally make or put differently: there are some 'critical' upgrades that decrease the number of hits very effectively. The most notorious one is +1 attack for zealots vs zerglings.
- upgrades are generally a gas outlet. Some strategies are gas heavy (terran mech + viking for example) and have a harder time finding use for upgrades then mineral heavy strats such as MMM. The relative value for gas to minerals offcourse differs from strat to strat. With MMM I value minerals about as high as gas for example in the later game (when you already have stim, reactors etc in place) whereas with tank viking i'd rate gas at least 3x so useful as minerals.
- some units function as damage dealers generally while others soak damage more. Colossi generally benefit more from attack then armor for example whereas zealots benefit more from armor then attack as they run more then they do actually attack. The actual power of your army is therefore not as simple as described above but the above is a fairly decent representation.
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A somewhat simplified way to look at things is to just take into consideration how much extra power a upgrade in general gives to your army.
For that you first need to define the power of a army. A simple and quite logic way to do that is:
ArmyPower = ArmyDPS * ArmyHP
Both DPS and HP have a linear effect on your army power, in general a Army or unit with higher power according to this definition will win a fight (excluding things like overkill, armor, positioning, melee getting into place etc etc.)
Now a attackupgrade will simply improve your DPS by a certain percentage depending on the units it's affecting. Usually this lies between 10 and 15%.
For example marines go from 6 to 7 attack an increase in DPS of 16.7% as a result your armypower if you army is exclusively marines will increase with 16.7% as well (if its marine/marauder it will be between 10 and 16.7%).
Now you have to compare this increase in armypower to how simply making more marines would affect your army. If you make more units, for example increase your army size by 20%, you get 20% more DPS and 20% more HP thus increasing your army by 1.2^2 = 1.44
Therefore enlarging your army by a factor x will increase the power of that army by x^2.
So to see how much of a army increase a 16.7% DPS increase is you simply have to take the square root of that. Sqrt(1.167) = 1.08
So in other words the first attack upgrade for marines is worth about the same as simply having 8% more marines. To see when which is more effective you simply have to compare when making 8% more marines would cost about the same as the first attack upgrade.
Given that marines are mineral only and the attack upgrade costs gas we will have to make some arbitrary mineral:gas ratio. I'd use 2 as I think that's a proper reflection for the comparitive value in game.
So lets call x the number of marines we are currently having. Then follows:
50 * x * 0.08 = 300 => x = 75
So as far as strict army power goes if you were to be using only marines you need 75 marines for the attack upgrade to be equally usefull for your army strength as simply getting more marines.
Offcourse this is a bit of a high number which contradicts what you would think from game experience. This is because there are so many factors at stake you virtually can't account for in a analytical view of the subject, to name a few:
- upgrades last the entire game so even if you do not have the actual x from the theory yet when you get the upgrade as long as you get that number over the course of the game it was worth it already. The x is basically a bit of a bottom line, if you ever get more then that number you should be thinking seriously about why you didnt get the upgrade
- upgrades need a building, some matchups you want that anyway as the upgrade structure enables turrets/cannons other times you only want the upgrades and thus have to pay an additional cost
- upgrades take long to be in effect. If you get attacked before the upgrade finishes or your army is gone before it finishes the upgrade doesn't do much
- Armor matters, marines get a relatively larger damage increase against units with armor then those without as going from 6 to 7 is less then from 5 to 6 for example.
- upgrades can have a huge influence on the amount of overkill your units generally make or put differently: there are some 'critical' upgrades that decrease the number of hits very effectively. The most notorious one is +1 attack for zealots vs zerglings.
- upgrades are generally a gas outlet. Some strategies are gas heavy (terran mech + viking for example) and have a harder time finding use for upgrades then mineral heavy strats such as MMM. The relative value for gas to minerals offcourse differs from strat to strat. With MMM I value minerals about as high as gas for example in the later game (when you already have stim, reactors etc in place) whereas with tank viking i'd rate gas at least 3x so useful as minerals.
- some units function as damage dealers generally while others soak damage more. Colossi generally benefit more from attack then armor for example whereas zealots benefit more from armor then attack as they run more then they do actually attack. The actual power of your army is therefore not as simple as described above but the above is a fairly decent representation.
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From a theoretical standpoint, they pay off when the extra damage is more efficient than producing an extra unit or two with the same resources.
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EPT
