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Hi everyone! For the new year I am back with a new analysis! This one is about upgrades in StarCraft. In the pdf, and in the spoiler tags, you can read detailed information about the topic. There is a short introduction about critical upgrades and how to express quantitatively how "critical" an upgrade is. The main part of the analysis is about which upgrade one should choose in different situations.
This part is based on Lanchester's Square Law, about which I have already written. Without further ado, here is the thorough analysis:
+ Show Spoiler +
Unfortunately I can only include so many upgrade scenarios in one post, so I attached only the most common early game unit match-ups. But despair not! For those of you who would like to experiment around, here is a link to the program I used for the calculation of these values.
Note: the program is by no means finished at all, I just thought you would like to see the values yourselves.
If you have any feedback, criticism, etc., or ideas for me to write about, it is more than appreciated! 
Also feel free to check out my previous works:
+ Show Spoiler +
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Nice..amazing as always even though I don't understand majority of it :-P
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That's nice work.
I see that this model ends up predicting that +Armor is better for marines vs zergling and zealot. I think we pick +attack though because we hold the assumption that we'll be able to micro our marines for them to get hit the least possible, so we first boost the dps we can draw out of them.
This is definitely something to take into account. Like if you make blink stalkers, you intend for them to never drop health ideally (and only shield) so in theory you wouldn't need armor at all, so you upgrade +Attack in that sense.
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United States996 Posts
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Amazing stuff, I don't follow some of it (Due to my own limitations in the brain  )
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curiously, does getting a shield upgrade, ever turn out to be the best upgrade?
(im presuming archon... or theoretically blink stalkers)
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Nice! I've always been a fan ever since you started these even though I've only recently made an account.. :D
Seems like going for +1 attack in ZvP and ZvZ is a go-to option since Lings are already good against Stalkers. The only matchup I could see myself getting +1 armor first is in ZvT but I don't know what kind of build you would have to be doing to grab only that. I guess if you have your Evos up but not enough gas for +1/+1 yet and know that there's no aggression coming?
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All I know is that I have to rush 3-3 marines because zerg players are always complaining about it lol. That's all the math I need.
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This is amazing! Very interesting even in my limited scope of understanding.
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One question, since Zealot +1 atk vs lings is so huge, why is it recommended for the zerg to get +1 melee vs zealots and not +1 carapace?
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On January 02 2015 14:08 wptlzkwjd wrote:
All I know is that I have to rush 3-3 marines because zerg players are always complaining about it lol. That's all the math I need.
3/3 for terran is pretty devastating as it shreds through ling muta like butter, especially since usually terran will get 3/3 before zerg, and even when zerg does get 3/3 they at a disadvantage forcing the need to go for higher tech
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On January 02 2015 16:32 Cricketer12 wrote:Show nested quote +On January 02 2015 14:08 wptlzkwjd wrote:
All I know is that I have to rush 3-3 marines because zerg players are always complaining about it lol. That's all the math I need. 3/3 for terran is pretty devastating as it shreds through ling muta like butter, especially since usually terran will get 3/3 before zerg, and even when zerg does get 3/3 they at a disadvantage forcing the need to go for higher tech
3/5 ultras are pretty scary. At least I don't feel very "advantaged" when I have to deal with them.
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This is some cool stuff. I knew some of these because they reduce the amount of hits needed (+1 zealots kill lings in 2 attacks instead of 3) but nice to see some of the others.
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Cool stuff! I think for the early game that's sufficient, but u are often forced to think a little ahead. According to ur calculations Marines would have more benefit from +1 armor vs zerglings. Taking into account I wanna get early stim and push, I wonder how much the ratio between alpha and beta would alter during the process of stim. And for any other unit that gets a temporal armor/ weapon increase.
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On January 02 2015 16:30 Cricketer12 wrote:
One question, since Zealot +1 atk vs lings is so huge, why is it recommended for the zerg to get +1 melee vs zealots and not +1 carapace?
I imagine the set scenario is 0-0 zerlings fighting 0-0 zealots.
So comparing +1 carapace zerglings fighting 0-0 zealot to +1 attack zerglings fighting 0-0 zealots, the +1 attack zerglings are mathematically better.
+1 carapace zerglings will perform better than +1 attack zerglings fighting +1 attack zealot though.
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On January 02 2015 11:48 worosei wrote:
curiously, does getting a shield upgrade, ever turn out to be the best upgrade?
(im presuming archon... or theoretically blink stalkers)
Yes, Archons benefit greatly from shields, of course, and in about half the unit match-ups the shield is the best upgrade. There are some cases where shields are just as effective as armor and/or weapons, e. g. in Roach vs. Zealot. There is not really a scenario where shields would be explicitly better than anything else, though (I found DTs in certain situations are better with shields but you don't really want to upgrade it because of this). Blink Stalkers are yes, theoretically, but since this model can't deal with any kind of micro, it will not give shields to be the best upgrade as result.
On January 02 2015 18:11 Phaenoman wrote:
Cool stuff! I think for the early game that's sufficient, but u are often forced to think a little forward. According to ur calculations Marines would have more benefit from +1 armor vs zerglings. Taking into account I wanna get early stim and push, I wonder how much the ratio between alpha and beta would alter during the process of stim. And for any other unit that gets a temporal armor/ weapon increase.
Marines, theoretically, benefit from +1 Armor better than from +1 Weapons against unupgraded lings with or without Stim (a stimmed Marine counts as a unit with only 35 HP and faster attack). Once the Zerglings have +1 Armor, though, the weapon upgrade becomes more effective. If you would like to know more about the effects of stimming, check out this post. You can also plot the "stim functions" with the linked program.
On January 02 2015 18:17 papapanda wrote:Show nested quote +On January 02 2015 16:30 Cricketer12 wrote:
One question, since Zealot +1 atk vs lings is so huge, why is it recommended for the zerg to get +1 melee vs zealots and not +1 carapace? I imagine the set scenario is 0-0 zerlings fighting 0-0 zealots. So comparing +1 carapace zerglings fighting 0-0 zealot to +1 attack zerglings fighting 0-0 zealots, the +1 attack zerglings are mathematically better. +1 carapace zerglings will perform better than +1 attack zerglings fighting +1 attack zealot though.
Exactly. +1 attack Zerglings do better against unupgraded Zealots than +1 armor lings, but once +1 attack is out for the Protoss, you will be at a great disadvantage as Zerg. However, if you go for the +1 armor on your lings, Zealots no longer benefit from +1 attack, so Protoss might as well go for armor instead. In which case, the armor on the lings becomes worthless, and +1 attack instead becomes the better choice... In short, you don't know what the opponent is going for, so you can only compare to the information you already have (which upgrade they have at the moment).
You can, of course, know what the meta is and anticipate your opponent's moves. Most Protosses will opt for +1 attack, hitting a timing before Zerg has any upgrades. If the Zerg is ling heavy, though, and you don't particularly want to hit a timing, you may consider upgrading +1 armor, as both Zealots and Stalkers are better with armor upgrade than with weapon upgrade against +1/+1 lings.
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On January 02 2015 22:17 Sholip wrote:Show nested quote +On January 02 2015 11:48 worosei wrote:
curiously, does getting a shield upgrade, ever turn out to be the best upgrade?
(im presuming archon... or theoretically blink stalkers) Yes, Archons benefit greatly from shields, of course, and in about half the unit match-ups the shield is the best upgrade. There are some cases where shields are just as effective as armor and/or weapons, e. g. in Roach vs. Zealot. There is not really a scenario where shields would be explicitly better than anything else, though (I found DTs in certain situations are better with shields but you don't really want to upgrade it because of this). Blink Stalkers are yes, theoretically, but since this model can't deal with any kind of micro, it will not give shields to be the best upgrade as result. Show nested quote +On January 02 2015 18:11 Phaenoman wrote:
Cool stuff! I think for the early game that's sufficient, but u are often forced to think a little forward. According to ur calculations Marines would have more benefit from +1 armor vs zerglings. Taking into account I wanna get early stim and push, I wonder how much the ratio between alpha and beta would alter during the process of stim. And for any other unit that gets a temporal armor/ weapon increase. Marines, theoretically, benefit from +1 Armor better than from +1 Weapons against unupgraded lings with or without Stim (a stimmed Marine counts as a unit with only 35 HP and faster attack). Once the Zerglings have +1 Armor, though, the weapon upgrade becomes more effective. If you would like to know more about the effects of stimming, check out this post. You can also plot the "stim functions" with the linked program. Show nested quote +On January 02 2015 18:17 papapanda wrote:On January 02 2015 16:30 Cricketer12 wrote:
One question, since Zealot +1 atk vs lings is so huge, why is it recommended for the zerg to get +1 melee vs zealots and not +1 carapace? I imagine the set scenario is 0-0 zerlings fighting 0-0 zealots. So comparing +1 carapace zerglings fighting 0-0 zealot to +1 attack zerglings fighting 0-0 zealots, the +1 attack zerglings are mathematically better. +1 carapace zerglings will perform better than +1 attack zerglings fighting +1 attack zealot though. Exactly. +1 attack Zerglings do better against unupgraded Zealots than +1 armor lings, but once +1 attack is out for the Protoss, you will be at a great disadvantage as Zerg. However, if you go for the +1 armor on your lings, Zealots no longer benefit from +1 attack, so Protoss might as well go for armor instead. In which case, the armor on the lings becomes worthless, and +1 attack instead becomes the better choice... In short, you don't know what the opponent is going for, so you can only compare to the information you already have (which upgrade they have at the moment). You can, of course, know what the meta is and anticipate your opponent's moves. Most Protosses will opt for +1 attack, hitting a timing before Zerg has any upgrades. If the Zerg is ling heavy, though, and you don't particularly want to hit a timing, you may consider upgrading +1 armor, as both Zealots and Stalkers are better with armor upgrade than with weapon upgrade against +1/+1 lings.
good to know, I as the zerg usually just go for +1/+1 for lings at the same time, but all the same i should prob go for more +1 attack strats as I almost never kill my opponent off early
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On January 03 2015 04:37 Cricketer12 wrote:Show nested quote +On January 02 2015 22:17 Sholip wrote:On January 02 2015 11:48 worosei wrote:
curiously, does getting a shield upgrade, ever turn out to be the best upgrade?
(im presuming archon... or theoretically blink stalkers) Yes, Archons benefit greatly from shields, of course, and in about half the unit match-ups the shield is the best upgrade. There are some cases where shields are just as effective as armor and/or weapons, e. g. in Roach vs. Zealot. There is not really a scenario where shields would be explicitly better than anything else, though (I found DTs in certain situations are better with shields but you don't really want to upgrade it because of this). Blink Stalkers are yes, theoretically, but since this model can't deal with any kind of micro, it will not give shields to be the best upgrade as result. On January 02 2015 18:11 Phaenoman wrote:
Cool stuff! I think for the early game that's sufficient, but u are often forced to think a little forward. According to ur calculations Marines would have more benefit from +1 armor vs zerglings. Taking into account I wanna get early stim and push, I wonder how much the ratio between alpha and beta would alter during the process of stim. And for any other unit that gets a temporal armor/ weapon increase. Marines, theoretically, benefit from +1 Armor better than from +1 Weapons against unupgraded lings with or without Stim (a stimmed Marine counts as a unit with only 35 HP and faster attack). Once the Zerglings have +1 Armor, though, the weapon upgrade becomes more effective. If you would like to know more about the effects of stimming, check out this post. You can also plot the "stim functions" with the linked program. On January 02 2015 18:17 papapanda wrote:On January 02 2015 16:30 Cricketer12 wrote:
One question, since Zealot +1 atk vs lings is so huge, why is it recommended for the zerg to get +1 melee vs zealots and not +1 carapace? I imagine the set scenario is 0-0 zerlings fighting 0-0 zealots. So comparing +1 carapace zerglings fighting 0-0 zealot to +1 attack zerglings fighting 0-0 zealots, the +1 attack zerglings are mathematically better. +1 carapace zerglings will perform better than +1 attack zerglings fighting +1 attack zealot though. Exactly. +1 attack Zerglings do better against unupgraded Zealots than +1 armor lings, but once +1 attack is out for the Protoss, you will be at a great disadvantage as Zerg. However, if you go for the +1 armor on your lings, Zealots no longer benefit from +1 attack, so Protoss might as well go for armor instead. In which case, the armor on the lings becomes worthless, and +1 attack instead becomes the better choice... In short, you don't know what the opponent is going for, so you can only compare to the information you already have (which upgrade they have at the moment). You can, of course, know what the meta is and anticipate your opponent's moves. Most Protosses will opt for +1 attack, hitting a timing before Zerg has any upgrades. If the Zerg is ling heavy, though, and you don't particularly want to hit a timing, you may consider upgrading +1 armor, as both Zealots and Stalkers are better with armor upgrade than with weapon upgrade against +1/+1 lings. good to know, I as the zerg usually just go for +1/+1 for lings at the same time, but all the same i should prob go for more +1 attack strats as I almost never kill my opponent off early
+1 Armor for lings is the safer way against Zealots, though, especially if you don't plan to be aggressive. You may be better off with melee damage against unupgraded Zealots, but sooner or later, the Protoss upgrade will be finished (rather sooner than later, usually), and it will almost always be +1 weapons for Zealots. And you really don't want to have +1 attack Zealots against 0 armor lings. But I think Zergs often start both upgrades at the same time, don't they?
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On January 02 2015 18:17 papapanda wrote:Show nested quote +On January 02 2015 16:30 Cricketer12 wrote:
One question, since Zealot +1 atk vs lings is so huge, why is it recommended for the zerg to get +1 melee vs zealots and not +1 carapace? I imagine the set scenario is 0-0 zerlings fighting 0-0 zealots. So comparing +1 carapace zerglings fighting 0-0 zealot to +1 attack zerglings fighting 0-0 zealots, the +1 attack zerglings are mathematically better. +1 carapace zerglings will perform better than +1 attack zerglings fighting +1 attack zealot though.
Yeah, but a lot of early game timings revolve around a quick +1 from Protoss for that reason.
So while mathematically +1 attack might be better, it's probably a bette practical choice to get +1 armor
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Does anyone know the phoenix vs phoenix breakdown?
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EPT![[image loading]](http://i.imgur.com/1KHGaCs.jpg)
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