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On January 26 2011 22:13 Markwerf wrote:
Carapace is also better then attack against marines imo because as banelings & lings are melee units they tend to receive more damage then deal it. Armor is better then attack on melee units because it helps them receive less damage while they are closing in. All those lings and banelings that die before getting damage in did benefit from their armor upgrade, they don't benefit at all from an attack upgrade.
This is right and wrong at the same time.
So let's break it down to blings and lings.
blings hands down benefit from carapace more than they do melee attack. +4 damage on a 1-shot deal doesn't affect much in the game, especially when talking ZvT. About the only situation +1 blings are going to benefit from is attacking stimmed marines with +1 armor and no combat shield. Any other situation, the upgrade is going to be less-than-awesome, so go with +1 carapace np.
But for the lings... You're forgetting limited surface area. If I am attacking into 10 marines with 20 zerglings, my biggest concern isn't making it to them, eventually my lings will make it there, they're fast enough. The much bigger problem is surface area to attack on. I can only fit maybe 10-12 lings on that front-side of the marine ball. No amount of carapace upgrades or extra lings is going to give me higher DPS vs the marines. Melee upgrades on the other hand, will make those 10-12 lings 20% more effective. I have effectively added 2 more attacking lings to the fight. It's hard to see the difference because marines destroy things SOOO fast regardless of armor, hp, or whatever, but melee upgrades are better than carapace upgrades in the zergling vs marine situation. The major benefit of carapace is you're also upgrading EVERY OTHER ground unit at the same time.
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On January 26 2011 22:44 kazansky wrote:Show nested quote +On January 26 2011 22:33 nalgene wrote:
Shouldn't the toss units have 0/0/0 ? Including shields for their units...?
Zerglings with 0/2 needs 5 hits from 0/0/0 stalkers
Stalkers with 1/0/0 only needs 4 hits on 0/2 Zerglings
Stalkers with 1/0/0 needs 5 hits on a 0/3 Zergling
Your TvZ chart doesn't list Mutalisks as enemy units for Bio Attack( Only zerglings/hydras/roaches ) I decided not to list too many higher upgrades yet before the game is figured out more, unless there is popular demand? And for TvZ, wow, jeez, yeah, I somehow missed that, thanks. Will add it when I'm at home again.
An analysis of Viking vs Mutalisk would be awesome too  I read in a post above that +1 armor makes Vikings very cost effective against Mutas, and I would love to incorporate that into my play against Zerg if it were true. I know it would be a lot of trouble to ask to have the splash damage get calculated in too.....but if it's possible I'd love to see that numbers. Thanks!
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This analysis is great, thx for posting it. Definitely going to apply this data into my game.
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Protoss armor doesn't cancel out +1 attack because protoss units have shields and hitpoints.
+1 zergling attack effects every hit for the zerg unit whereas +1 P armor only affects the hits on the hitpoints.
The example I gave is one where this is most crucial:
A roach with +1 attack takes 10 shots to kill a stalker with no armor upgrades. (your data is wrong on that, the roach first does 4 * 18 = 72 damage to the stalker, then needs (180 - 72) / (18-1) = 6,3 => 7 shots for the rest). A roach with +2 attack however does take 9 shots to kill a stalker with +1 armor. Ie. while the difference is only 1 upgrade in each case it differs 1 shot.
Protoss critical upgrades are most annoying to calculate and put in a readable form because armor upgrades don't cancel attack upgrades.
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Thanks a lot for this post! its really interesting.
To improve it, I would suggest that
1. you indicate the upgrades one shall NOT do. (in red for instance). For instance I discovered that +1 carapace in z v p is quite useless in the beginning. I think it's worth mentioning, cause then we have a clearer idea of what to do with our upgrades (here everything seems more or less to be green or blue, which doesn't help that much to make our choice concerning upgrades)
2. maybe indicate good timings to develop upgrades: for instance +1 melee is interesting from the beginning for a zerg; whereas carapace maybe interesting only later (for instance, as you indicate, when immortals come, in the case of roaches).
thanks again!
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Aotearoa39261 Posts
Useful overview, although I've always been curious about incorporating Shield upgrades in Stalker heavy play (with the idea that your stalkers should never receive HP damage since they will always be relying on shield regeneration)
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On January 26 2011 23:12 Markwerf wrote:
Protoss armor doesn't cancel out +1 attack because protoss units have shields and hitpoints.
+1 zergling attack effects every hit for the zerg unit whereas +1 P armor only affects the hits on the hitpoints.
The example I gave is one where this is most crucial:
A roach with +1 attack takes 10 shots to kill a stalker with no armor upgrades. (your data is wrong on that, the roach first does 4 * 18 = 72 damage to the stalker, then needs (180 - 72) / (18-1) = 6,3 => 7 shots for the rest). A roach with +2 attack however does take 9 shots to kill a stalker with +1 armor. Ie. while the difference is only 1 upgrade in each case it differs 1 shot.
Protoss critical upgrades are most annoying to calculate and put in a readable form because armor upgrades don't cancel attack upgrades.
First of all, Stalkers have 80 Hitpoints and 80 Shields, so its 5,2 read 6 shots, but as you missed one shot on shields, it doesnt matter
Seems like a typo, i need to correct that. I agree, it's 10 hits for +1 Roaches.
I calculated Shields and Armor seperately, of course, but it's good to line this fact out nevertheless.
But as I stated, what I mean with armor advantage wording is +0 vs +1 upgrades. Period. Otherwise mentioned.
Because, as stated in the general analysis, damage improvement is always at least as high as armor improvement, so there are multiple cases where +2 vs +1 and even more +3 vs +2 has drastic effects.
The problem is, it isnt sure that what upgrades rather than +0 your enemy has, as it depends on build. So its harder to get applyable situations for higher upgrades, as long as the game is not figured out the way broodwar is.
Of course the upgrade math still works, and I believe you can find critical advantage for every singly upgrade in the game, the higher the upgrade, the more likely.
But it gets away from viable theory crafting in my eyes. Unless some real mainstream upgrade strategy establishes.
Although I am open minded to a discussion whether and which higher upgrades should be mentioned.
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As above poster has stated, each upgrade is "critical" at some given point whether it be visible or not. Perhaps we could look deeper into specific timings and likelihoods of certain enemy upgrades, and take advantage of timings when they lack theirs. Many people shy away from getting 2-2 upgrades at a quick pace, which could provide similar timing power to 1-1 against an opponent who has also gotten his 1-1 upgrade.
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On January 26 2011 23:39 Plexa wrote:
Useful overview, although I've always been curious about incorporating Shield upgrades in Stalker heavy play (with the idea that your stalkers should never receive HP damage since they will always be relying on shield regeneration)
I can dig into it. When we presume Stalkers dont get HP damage, I guess we can only take a look on if Shields can sustain an additional hit.
So its basically 80 with 0 and 80 with 1 armor.
Regarding the investment, you should save 2 stalkers to justify it. So its 160 damage to doge, boiled down to avoided hits, I guess.
PvP
Stalkers can take 5 hits from Stalkers with 10 shields left normally and 6 with 2 shields left when upgraded.
It takes 6 hits for Stalkers to take down Stalker shields on 0 Armor, 7 hits with 1 Armor.
Against Zealots, it takes the Zealot 6 hits (with 4 overload damage) instead of 5 hits (sharp) to get rid of the shields.
Robo units dont get affected.
Conclusion: Guess it depends on gamestage.
PvZ
It takes Zerglings 20 hits instead of 16 to take down Stalker Shields with Shield armor, Roaches 6 instead of 5 (with 10 overload damage).
For Hydras, after 7 shots they deal 4 HP Armor as shields are gone, while 3 shield remain after 7 shots.
Mutalisks do 1 damage on HP after 9 shots, while when you have +1 Shield Armor, you get 10 shots without taking damage.
Conclusion: Taking in regard that you might transition into Archons later which profit hugely from +damage and +shield armor, this might really have deep impact.
PvT
Doesnt make any difference on Tanks, against Marauder you have a buffer of 4 shields after 4 shots compared to no shields after 4 shots, so doesnt make that huge difference either.
Against Marines, you get 3 additional hits on your shields (13*6 = 78 compared to 16*5 = 80)
Conclusion: Guess it depends on if you play against MarineKing
Worth adding it?
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On January 26 2011 22:48 Synystyr wrote:Show nested quote +On January 26 2011 22:44 kazansky wrote:On January 26 2011 22:33 nalgene wrote:
Shouldn't the toss units have 0/0/0 ? Including shields for their units...?
Zerglings with 0/2 needs 5 hits from 0/0/0 stalkers
Stalkers with 1/0/0 only needs 4 hits on 0/2 Zerglings
Stalkers with 1/0/0 needs 5 hits on a 0/3 Zergling
Your TvZ chart doesn't list Mutalisks as enemy units for Bio Attack( Only zerglings/hydras/roaches ) I decided not to list too many higher upgrades yet before the game is figured out more, unless there is popular demand? And for TvZ, wow, jeez, yeah, I somehow missed that, thanks. Will add it when I'm at home again. An analysis of Viking vs Mutalisk would be awesome too I read in a post above that +1 armor makes Vikings very cost effective against Mutas, and I would love to incorporate that into my play against Zerg if it were true. I know it would be a lot of trouble to ask to have the splash damage get calculated in too.....but if it's possible I'd love to see that numbers. Thanks!
I will dodge bounce because if your enemy plays correct, he focus fires one Viking so the Bounce does only hit other Vikings, and I guess due to movement chaos it wont hit the same Viking over and over:
125 / 9 = 13,8 => 14 shots against unupgraded vikings, 125 / 8 = 15,6 => 16 shots against upgraded Vikings.
Although you should have in mind that you need 7 shots for a Mutalisk to kill it with massive overload damage (7 * (2*10) = 140 - 121 = 19), so the +1 damage would be as important I guess.
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TvT Tanks with mech +1 kill stimmed mauarders in 2 shots instead of 3.
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One variable that may screw with these numbers a bit is zerg health regeneration. A roach may be taken out by focus fire from several units at once and get zero health regen, or it may take 10 seconds to die, in which case it heals a few hit points. This could give that roach one extra shot to die depending on what unit is attacking it. The same goes for all zerg units and how long they are taking damage.
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infinity21
Canada6683 Posts
Any chance you can look at Hellions & Thor in tvp?
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Stopped reading after I read this
On January 26 2011 03:16 kazansky wrote:
For Immortals, the Upgrades don't change anything
User was temp banned for this post.
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amazing effort.
thanks very much kazansky
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Can you change the colors in the first post? I'm red-green color blind=[
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+1 Air Damage:
vs Bio: does not affect Muta vs Marines or Muta vs SCVs
disagree here. When you are raiding units, picking off running marines. The ricochets doing more damage matters a lot. but I guess you are just referring to upgrades making things die in less hits from the multiples math standpoint.
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Wouldn't it be better to take the analysis based on the number of seconds each unit survives, or how much longer it takes to kill a specific unit in a unit vs. unit matchup? That way, everything is more standardized (just like how we express unit damage output in terms of DPS).
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Wow, this is just great. I was thinking about doing it, but it just seemed to take too much effort from a busy schedule that is already stretched thin.
Really appreciate it, man. Props & thanks & cred
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On January 27 2011 01:56 infinity21 wrote:
Any chance you can look at Hellions & Thor in tvp?
Sure. I guess you refer to Mech builds in TvP, so I presume that Hellions are supposed to shoot Zealots and Stalkers (per splash) and be damage sponge, and Thors are supposed to take out Stalkers, Zealots, Colossi, Void Ray and Phoenix, and I disregard EMP for this (which would have crazy impact). Immortal damage can be looked at aswell, but if you want to kill Immortals effectively, I guess 250mm cannons beats everything else.
I will also take a look at +3 vs +3/+3, as it makes sense to see how metal performs endgame.
Basically: +attack on Blue Flames is awesome, on Thors nice against Air. +3 on Mech is sick. Plating on Thors and Hellions is nice.
Math inside.
+ Show Spoiler +
Blue Flame Hellions
Standard Hits on Zealots are 7. This turns down to 6 if you have +1 vs +0 Armor. +0 vs +1 its 7 aswell. In +1vs+1 its again 7, but once you have +3 Attack, its again 6 even with Zealots on +3 Armor and +3 Shields.
Standard Hits on Stalkers are 22. With +1 vs +0 it drops to 20 hits, with +0 vs +1armor its 24 hits. One +1vs+1 its 21 hits (so 1 better than in standard), if you have +3 Attack and the Stalkers have only full armor or shield, its 18 hits for Stalkers. But it goes up to Standard 22 once Protoss has full upgrades.
Thor
vs Zealots and Stalkers, Thors need 3 shots. Period. Regardless of Upgrades. Unless you have +3 Thors against Zealots that have not +3 on both armor and shield, then it drops to 2.
Zealots need 29 hits on a Thor with similar armor to his damage upgrade because of singular increasement on both wields, one Armor Upgrade on the thor neglects 5 hits, while one upgrade advantage on the zealots grants 4 hits.
For Stalkers, its same Armor vs Damage effect, with 31 hits in standard, 34 when Thor upgrade is higher, and 27 when Stalker Upgrades are higher.
Vs Colossi, Thors need 6 Shots unless they have +3 Weapons, then its 5 regardless of Armor.
In taking Shots, its 15 normally and 16 on +1 plating vs +0 attack. If you dont have plating and he has +1 attack, the amount drops to 13. Colossi get overiterative damage bonus, so the +1vs+1 results in 14 hits, and on +3vs+3 its only 12 hits.
Vs Voidrays, you normally need 6 hits. But in case you have +1 Attack against no upgrades or reach +2 (regardless of upgrades), Voidrays go down in 5 shots.
Taking damage was a bit rough because of the 20% damage bonus vs massive, so I took the 10/11/12/13 and made 12/13/14/15 out of it, dont know if that applies.
The damage increase it always +1 on upgrades, so armor negates attack.
Its 37 shots on even upgrades (without charge), 40 with advantage, 34 with disadvantage. Although I must admit, it's hard to justify these numbers as they ignore charge.
When shooting Phoenixes, again damage and armor negate themselves, and then its 8 shots on even upgrades for a Phoenix, 7 on advantage and 9 on disadvantage.
Fighting against Immortals, Armor is irrelevant. Only the Immortal attack counts, and once he has +1 Attack, Immortals always kill Thors in 8 shots instead of 9.
On January 27 2011 02:06 onbaton wrote:Stopped reading after I read this Show nested quote +On January 26 2011 03:16 kazansky wrote:
For Immortals, the Upgrades don't change anything
Great contribution, sir! 
On January 27 2011 10:15 CROSSENuUP wrote:
Can you change the colors in the first post? I'm red-green color blind=[
Ouch. Not really because it would turn around the standard of the OP, but i can rephrase it for you to
# for a critical upgrade, !! for huge and :: for uncritical, inside spoiler
+ Show Spoiler +ZvP- # +1 Melee Upgrade: 15% less hits for Zerglings in every setup
- # +1 Range Upgrade: Hydras kill Zealots in 2 and Colossi in 1 less hit, Roaches need less hits for every Unit.
- !!+1 Carapace Upgrade: Roaches and Hydras take more hits to kill, especially Roaches surviving another Immortal shot (4 instead of 3)
- !!+1 Flyer Damage: Mutalisks need 2 less shots on Stalkers, 1 less on Sentries, and Corrupters 2 less shots on Colossi
- #+1 Flyer Carapace: Mutalisks sustain 2 more shots from Stalkers and 4 from Sentries, Corrupters 2 more shots from Stalkers
PvZ- Attack Upgrade:
!!vs Zerglings: Hits for Zealot against Zergling drop from 3 to 2 (sidenote +2vs+1 and +3 on Colossis make Zerglings oneshots)
!!vs Roach: 1 less hit for Zealots, 4 less for Sentries, 1 less for Stalkers
!!vs Hydra: Hydras die in 1 less hit against Gateway units (Thanks to TheHumanSensation)
!!vs Muta 1 less hit for Stalkers, 2 for Sentries
- Armor Upgrade:
vs Zerlings:
#vs Roach: Zealots take one more hit
#vs Hydra: Zealots take one more hit
#vs Muta: 2 more shots for Stalkers, 1 more for Sentries
TvP- #+1 Bio Armor: Marines and Marauders take more hits from Gateway Units
- !!+1 Bio Attack: Marines kill Zealots in 4 and Stalkers in 9 less shots, Marauders kill Zealots in 1, Stalker in 1 and Colossi in 2 less shots
- !!+1 Mech Attack: Tanks take 1 less shot on Zealots, Stalkers and Collosi
PvT- !!+1 Attack: Marauders die in 1 less shot against Zealots, Stalkers and Collosi (sidenote: Marines dont get affected)
- #+1 Armor: : Zealots take 1 more hit from Marauders, Marine take 5, 4 and 10 more hits against Zealot, Stalker and Collossi
- !!+1 Air Weapons: Marines die in 1 less hit to VoidRays, Tanks take 4 less shots from Phoenixes
- #+1 Air Armor: Marines need 5 more shots to kill a VoidRay
ZvT: - +1 Armor:
!!vs Bio: Marines take 1 more hit on Ling, Bling, 8 more on Roaches, Marauders take 1 more hit on Roaches.
!!vs Mech: Zerglings survive sieged tank shot, Roaches survive 1 additional tank shot
- +1 Melee:
#vs Bio: Zerglings need 1 less hit against Marines.
!!vs Mech: Zerglings take need less hits on Tanks, Thors and Hellions (18 to 15)
- +1 Range:
#vs Bio: Roach hits on stimmed marines without shields fall from 3 to 2 (thanks to MorroW)
#vs Mech: Roaches kill Tanks in 10 shots instead of 11, and Thors in 22 instead of 25
- +1 Air Damage:
:: vs Bio: does not affect Muta vs Marines or Muta vs SCVs
!! vs Mech: Amount of shots for a Thor drop from 50 to 45
- +1 Air Carapace:
# vs Bio: Mutas take 25 instead of 21 hits from Marines
:: vs Mech: no effects on Thor hits (Sidenote: +2 Carapace against +0 Damage lets Mutas survive one more volley)
TvZ: - !!+1 Bio Armor: Zerglings need 2 more hits on Marines and 10 more on Marauders
- !!+1 Bio Attack: Marines kill Zerglings and Roaches in less hits, Marauder kill Roaches and Hydras in less hits, Marines need 3 less hits on Mutalisks (thanks to nalgene)
- !!+1 Mech Armor: Thors take 5 more hits from Mutas, 2 more from Roaches, 34 from Lings. Tanks take one more shot from Roaches, 13 from Zerglings, 3 from Mutalisks. Hellion take 7 more hits from Lings
- ::+1 Mech Attack: no effects on kill efficiency. On a Sidenote, with +2 Attack lets Mutalists die in 2 Shots instead of 3(thanks to Saechiis)
PvP: - !!+1 Ground Weapons: Colossi kill every Unit in less shots, Immortals kill everything but Zealots in less shots.
- #+1 Ground Armor: Robo Units take more shots from gateway Units, Robo vs Robo remains untouched
- #+1 Air Weapons: Voids need 1 less shot on Stalkers
- #+1 Air Armor: Voids take 2 more shots from Stalkers
TvT: - +1 Bio Armor:
#vs Bio: Shots for Marines to kill Marines increases by 1, to kill Marauders increases by 7
::vs Mech: no effects
- +1 Bio Attack:
!!vs Bio: Hits for Marines to kill Marines decrease by 1, to kill Marauders decrease by 4, for Marauders to kill Marauders decrease by 1
!!vs Mech: Hits for Marauder to kill Tanks decrease by 1, Hits for Marines to kill Tanks decrease by 8
- +1 Mech Armor:
!!vs Bio: Marauder take 1 more hit to kill Thors, Marines take 8 more for Tanks, 20 more for Thors, 3 more for Hellions
::vs Mech: no effects
- +1 Mech Attack:
#vs Bio: Thor kill Marauder in 1 less shot, Tanks need 2 shots instead of 3 for stimmed Marauder (thanks to statikg)
!!vs Mech: Tanks kill Tanks in 3 shots instead of 4 (sidenote: on +2, armor upgrades get irrelevant)
- #+1 Air Armor: battlecruisers take 3 more shots from Vikings
- ::+1 Air Attack: no effects in Viking battles.
ZvZ: - !!+1 Melee: For Zerglings 1 less hit on Zerglings, 8 less on Roaches
- !!+1 Range: Zerglings die in 2 instead of 3 shots, Roaches take 1 less hit
- !!+1 Carapace: Zerglings survive Banelings, Zerglings take 1 more hit from Zerglings, Roaches 1 more from Roaches and 13 more from Zerglings
- #+1 Flyer Damage: Mutas need 13 instead of 14 shots to kill Mutas
- #+1 Flyer Carapace: Mutas take 16 instead of 14 shots from Mutas
On January 27 2011 10:36 SpoR wrote:disagree here. When you are raiding units, picking off running marines. The ricochets doing more damage matters a lot. but I guess you are just referring to upgrades making things die in less hits from the multiples math standpoint.
I agree, the summary ricochet damage does grow by 2 per upgrade, which can have great influence. But this covers the idealized world of perfect focus fire et cetera, so although bounce is huge, it doesnt matter in this article.
On January 27 2011 11:30 celedorph wrote:
Wouldn't it be better to take the analysis based on the number of seconds each unit survives, or how much longer it takes to kill a specific unit in a unit vs. unit matchup? That way, everything is more standardized (just like how we express unit damage output in terms of DPS).
Well, the math is additional hits times hit delay, so not that hard to gather in case you are interested in. But as mentioned above, main purpose is critical upgrades as itself as in the original article of day[9] regarding broodwar.
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EPT
