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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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On January 03 2015 05:54 playa wrote:
Does anyone know the phoenix vs phoenix breakdown?
You go for the +1 Weapons. This is the best choice against 0/0/0 Phoenixes, but even if the opponent upgrades any of the upgrades, the weapon upgrade is still the best.
Now if the opponent knows this, they will choose +1 Weapons as well. Against 1/0/0 Phoenixes, your best upgrade is +2 Weapons. If opponent already has +2 attack, then +2 attack and +1 armor are equally good. If they already have 1/1/0, the situation is the same. So best is to go +2 Weapons I think, as this is always the best choice. (Note: if opponent went for +1 Armor first, for some reason, then you may consider +1 Armor after +1 Weapons. This is better against 0/1/0 than +2 Weapons, later will be equally good as +2 attack against 1/1/0, but will be inferior to it against 0/2/0.)
Let's just suppose both players have +2 Attack. Then +1 Armor is the best against 2/0/0, later +1 Armor or +3 Weapons equally good against 2/1/0 and against 3/0/0, but +3 Weapons is the best against 2/0/1.
Here there are already a lot of possibilities, so you can choose whichever you wish. Keep in mind, though, that lower upgrade tiers are always cheaper and shorter, so that can always be a deciding factor.
In short, I think the best sequence is +1 Weapons -> +2 Weapons -> whatever you feel like upgrading, but +1 Armor is the cheapest.
It just makes things more complicated that Shield upgrades can be researched concurrently with Air upgrades, so I guess if the great phoenix wars ensue, just chrono the Forge for those as well.
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On January 03 2015 06:30 Sholip wrote:Show nested quote +On January 03 2015 05:54 playa wrote:
Does anyone know the phoenix vs phoenix breakdown? You go for the +1 Weapons. This is the best choice against 0/0/0 Phoenixes, but even if the opponent upgrades any of the upgrades, the weapon upgrade is still the best. Now if the opponent knows this, they will choose +1 Weapons as well. Against 1/0/0 Phoenixes, your best upgrade is +2 Weapons. If opponent already has +2 attack, then +2 attack and +1 armor are equally good. If they already have 1/1/0, the situation is the same. So best is to go +2 Weapons I think, as this is always the best choice. (Note: if opponent went for +1 Armor first, for some reason, then you may consider +1 Armor after +1 Weapons. This is better against 0/1/0 than +2 Weapons, later will be equally good as +2 attack against 1/1/0, but will be inferior to it against 0/2/0.) Let's just suppose both players have +2 Attack. Then +1 Armor is the best against 2/0/0, later +1 Armor or +3 Weapons equally good against 2/1/0 and against 3/0/0, but +3 Weapons is the best against 2/0/1. Here there are already a lot of possibilities, so you can choose whichever you wish. Keep in mind, though, that lower upgrade tiers are always cheaper and shorter, so that can always be a deciding factor. In short, I think the best sequence is +1 Weapons -> +2 Weapons -> whatever you feel like upgrading, but +1 Armor is the cheapest. It just makes things more complicated that Shield upgrades can be researched concurrently with Air upgrades, so I guess if the great phoenix wars ensue, just chrono the Forge for those as well.
Wow, thanks a lot.
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Actually I would like to add, that for muta vs muta getting 1/1 after the first carapace upgrade is better than 0/2 even though it's less effective, because the one extra Muta does make a bigger difference.
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excellent as usual!
+1 attack offers more opportunity even if other upgrades seems/are more useful. Killing base/building or overloards faster etc.
In other thread from you, about stim, the mobility is the biggest reason/strength, not the fight with it.
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Awesome work! Just a quick question: is the attack range of the units taken into account? For example when a marine fights a zergling, the marine will already have gotten a few shots off before the zergling can start attacking, meaning the unit with more range might benefit more from attack upgrades (so it gets as much damage done as possible before the other gets close enough to fight back) while the unit with less range might benefit more from armor upgrades (so it survives long enough to get close enough to fight back).
Is this already included in the equations or is this a factor I have to consider on top of these results myself?
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United Kingdom20286 Posts
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)
A big part of the value of shield upgrades is that they are the only upgrade to apply to buildings, so they are extremely effective particularly for use on cannons against ling/muta (shield upgrades on a small blob of cannons has the same effect as armor upgrades in muta vs muta; very powerful - and vs lings, lings do very little damage so reducing the damage done by 2 or 3 is a huge percentage of their total damage per hit)
Is this already included in the equations or is this a factor I have to consider on top of these results myself?
I think this just assumes that both units are in range and attacking, which would artificially lower the value of attack upgrades on units that have a range advantage
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I wonder why don't toss go for the shield upgrades? Even the pros usually leave it till the mid-late game...then only they upgrade shields..hmm..
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Canada28396 Posts
On January 03 2015 17:49 skylinefan wrote:
I wonder why don't toss go for the shield upgrades? Even the pros usually leave it till the mid-late game...then only they upgrade shields..hmm..
I think it's just more expensive, and earlier into the game that's very hard to afford.
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Upon trying to read the PDF:
Google Drive
We're sorry. You can't access this item because it is in violation of our Terms of Service.
 Care to reupload somewhere else?
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On January 03 2015 09:54 Koektrommel wrote:
Awesome work! Just a quick question: is the attack range of the units taken into account? For example when a marine fights a zergling, the marine will already have gotten a few shots off before the zergling can start attacking, meaning the unit with more range might benefit more from attack upgrades (so it gets as much damage done as possible before the other gets close enough to fight back) while the unit with less range might benefit more from armor upgrades (so it survives long enough to get close enough to fight back).
Is this already included in the equations or is this a factor I have to consider on top of these results myself?
This factor is not included, so the attack upgrade may be a bit better in the early game for ranged units like Marines then it seems here. Once Charge/Zergling speed + Creep comes into play, though, this effect becomes marginal I think.
On January 03 2015 18:34 Perfi wrote:Upon trying to read the PDF: Show nested quote +Google Drive
We're sorry. You can't access this item because it is in violation of our Terms of Service. Care to reupload somewhere else?
I reuploaded it to Drive, but it acts weird so there still may be some error, I don't know why . What's in the pdf is exactly what is in the spoiler tags, though, so you don't miss out on anything.
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Really awesome work. I skimmed over it at first but I forced myself to go back and actually try to understand it a bit. Really cool way to round things out into comparable numbers! I was actually suprised that the formula suggests +1 armor over weapons for marines versus zealots.
Quick question, did marines have combat shields in the examples you provided? I also wonder if you could simulate constant medivac healing by seeing how many ticks of healing it will accomplish before the unit dies and add that(times amount healed) to the total health. Or I guess in the terms of your formula, just see how many attacks it takes to kill a unit being healed by a full energy medivac.
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On January 04 2015 03:33 feardragon wrote:
Really awesome work. I skimmed over it at first but I forced myself to go back and actually try to understand it a bit. Really cool way to round things out into comparable numbers! I was actually suprised that the formula suggests +1 armor over weapons for marines versus zealots.
Quick question, did marines have combat shields in the examples you provided? I also wonder if you could simulate constant medivac healing by seeing how many ticks of healing it will accomplish before the unit dies and add that(times amount healed) to the total health. Or I guess in the terms of your formula, just see how many attacks it takes to kill a unit being healed by a full energy medivac.
In case of Marines vs. Zealots, it might change things that Marines can fire one or two shots before Zealots can attack, so +1 Weapons might be more effective than what the formula suggests.
As for Combat Shields, no, Zealots in the example had no upgrades. However, the formula will say +1 Armor still with Combat Shields against Zealots.
With Medivacs, the problem is that one unit will have its health modified from two sources, the enemy attacks and the healing. You can't say how many attacks it takes to kill a unit healed by a Medivac, because it depends on how many units attack it, as the Medivac's healing is time-based. If one unit attacks a Marine, the Medivac may heal it constantly, so the Marine does not die to any number of attacks. If 20 units attack the Marine, the unit kills in one shot, and poor Medivac suddenly has no unit to heal.
The advantage of my formula is that you can express how many units one unit kills over a period of time, and it can work with critical upgrades very well. If there are two or more sources of health modifications, the only way to go, in my opinion, is to work with DPS (and healing per second) values, as you can't exactly tell how many attacks a unit takes to kill another.
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Great to still see some community content inkling out, despite the consistently dwindling population. Cool stuff, Great job!
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For the case of mutalisks vs. mutalisks, I seem to remember someone calculating that when zerglings are added to the battle, the second upgrade is more efficient as an attack upgrade, even though this is less efficient for the straight air battle...
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Another great post Sholip.
I always wondered why terran prefer attack and protoss armor in tvp.
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On January 04 2015 07:27 Hollandrock wrote:
For the case of mutalisks vs. mutalisks, I seem to remember someone calculating that when zerglings are added to the battle, the second upgrade is more efficient as an attack upgrade, even though this is less efficient for the straight air battle...
semi relevant but can anyone reputable confirm the popular notion that lings under mutas actually affect glaive splash? recently i saw a muta vs muta in an online korean cup i think and i noticed that health bars were on "damaged only" and lings were directly underneath yet i didnt see them take any damage. i would have thought that glaive bounce has attack priority like any other attack and would tend to bounce only onto mutas if enough are present. but i'm not arguing with anyone, just going off what i've seen. anyone tested this directly?
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On January 03 2015 19:55 Sholip wrote:Show nested quote +On January 03 2015 09:54 Koektrommel wrote:
Awesome work! Just a quick question: is the attack range of the units taken into account? For example when a marine fights a zergling, the marine will already have gotten a few shots off before the zergling can start attacking, meaning the unit with more range might benefit more from attack upgrades (so it gets as much damage done as possible before the other gets close enough to fight back) while the unit with less range might benefit more from armor upgrades (so it survives long enough to get close enough to fight back).
Is this already included in the equations or is this a factor I have to consider on top of these results myself? This factor is not included, so the attack upgrade may be a bit better in the early game for ranged units like Marines then it seems here. Once Charge/Zergling speed + Creep comes into play, though, this effect becomes marginal I think.
I think the best argument in favor of marine +1 Attack has nothing to do with zerglings or mutas, it's banelings. Lings and mutas can't really damage massed marines, only banelings can. Armor has little effect on Banes as their damage is so high, so you'll mitigate far more damage by shooting banelings before they arrive.
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On January 03 2015 17:49 skylinefan wrote:
I wonder why don't toss go for the shield upgrades? Even the pros usually leave it till the mid-late game...then only they upgrade shields..hmm..
Toss generally doesnt go for shield upgrades as
a) it can be destroyed by EMP; but more importantly;
b) units normally has more HP than shield, so the armour 'buffer' can occur more times in a fight than a 'shield' buffer will (eg with made-up numbers, a zealot's with no shield can take 4 hits before shield disappears vs 5 hits with +1 shield, a zealot with 0 armour can take 8 hits, but with +1 armour can take 10 hits - so the armour upgrades allows an extra hit before death that the shield doesnt).
i am curious when a shield upgrade is actually the preferred one (im guessing it'd be in situations where +3 armour is already upgraded)
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On January 05 2015 14:24 worosei wrote:Show nested quote +On January 03 2015 17:49 skylinefan wrote:
I wonder why don't toss go for the shield upgrades? Even the pros usually leave it till the mid-late game...then only they upgrade shields..hmm.. Toss generally doesnt go for shield upgrades as a) it can be destroyed by EMP; but more importantly; b) units normally has more HP than shield, so the armour 'buffer' can occur more times in a fight than a 'shield' buffer will (eg with made-up numbers, a zealot's with no shield can take 4 hits before shield disappears vs 5 hits with +1 shield, a zealot with 0 armour can take 8 hits, but with +1 armour can take 10 hits - so the armour upgrades allows an extra hit before death that the shield doesnt). i am curious when a shield upgrade is actually the preferred one (im guessing it'd be in situations where +3 armour is already upgraded)
I have seen many pros go +shields with blink stalkers into archon/zealots. It wrecks unprepared terrans, but this hardly happens because pros are so good at reading tech and scouting.
I can't think of any other scenario for protoss to go for shields.
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On January 05 2015 14:46 Jett.Jack.Alvir wrote:Show nested quote +On January 05 2015 14:24 worosei wrote:On January 03 2015 17:49 skylinefan wrote:
I wonder why don't toss go for the shield upgrades? Even the pros usually leave it till the mid-late game...then only they upgrade shields..hmm.. Toss generally doesnt go for shield upgrades as a) it can be destroyed by EMP; but more importantly; b) units normally has more HP than shield, so the armour 'buffer' can occur more times in a fight than a 'shield' buffer will (eg with made-up numbers, a zealot's with no shield can take 4 hits before shield disappears vs 5 hits with +1 shield, a zealot with 0 armour can take 8 hits, but with +1 armour can take 10 hits - so the armour upgrades allows an extra hit before death that the shield doesnt). i am curious when a shield upgrade is actually the preferred one (im guessing it'd be in situations where +3 armour is already upgraded) I have seen many pros go +shields with blink stalkers into archon/zealots. It wrecks unprepared terrans, but this hardly happens because pros are so good at reading tech and scouting. I can't think of any other scenario for protoss to go for shields.
Wouldn't a planned ground into air transition use shield over armour?
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On January 06 2015 02:25 Yurie wrote:Show nested quote +On January 05 2015 14:46 Jett.Jack.Alvir wrote:On January 05 2015 14:24 worosei wrote:On January 03 2015 17:49 skylinefan wrote:
I wonder why don't toss go for the shield upgrades? Even the pros usually leave it till the mid-late game...then only they upgrade shields..hmm.. Toss generally doesnt go for shield upgrades as a) it can be destroyed by EMP; but more importantly; b) units normally has more HP than shield, so the armour 'buffer' can occur more times in a fight than a 'shield' buffer will (eg with made-up numbers, a zealot's with no shield can take 4 hits before shield disappears vs 5 hits with +1 shield, a zealot with 0 armour can take 8 hits, but with +1 armour can take 10 hits - so the armour upgrades allows an extra hit before death that the shield doesnt). i am curious when a shield upgrade is actually the preferred one (im guessing it'd be in situations where +3 armour is already upgraded) I have seen many pros go +shields with blink stalkers into archon/zealots. It wrecks unprepared terrans, but this hardly happens because pros are so good at reading tech and scouting. I can't think of any other scenario for protoss to go for shields. Wouldn't a planned ground into air transition use shield over armour?
Perhaps, but that leaves a lot of protoss vulnerable. A ground to air tech switch costs loads of gas, and goes into the very late game.
By this time, air upgrades are the only thing left anyways.
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A bit uninspired Sholip. 
You just do some very basic division and round. I know you can do more! In the end you leave out so many effects that the results are rarely useful or reliable in practice. Even misleading for the ling vs lots. I expected you to at least try to take a few more things into account to be able to get more useful results.
How about game theory on the choice of upgrades of lings and zealots? Upgrades with common unit compositions. Runtime for ranged vs melee. Splash damage.
I say this mainly tongue in cheek (thanks for op), but not only.
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On January 06 2015 11:48 Jett.Jack.Alvir wrote:Show nested quote +On January 06 2015 02:25 Yurie wrote:On January 05 2015 14:46 Jett.Jack.Alvir wrote:On January 05 2015 14:24 worosei wrote:On January 03 2015 17:49 skylinefan wrote:
I wonder why don't toss go for the shield upgrades? Even the pros usually leave it till the mid-late game...then only they upgrade shields..hmm.. Toss generally doesnt go for shield upgrades as a) it can be destroyed by EMP; but more importantly; b) units normally has more HP than shield, so the armour 'buffer' can occur more times in a fight than a 'shield' buffer will (eg with made-up numbers, a zealot's with no shield can take 4 hits before shield disappears vs 5 hits with +1 shield, a zealot with 0 armour can take 8 hits, but with +1 armour can take 10 hits - so the armour upgrades allows an extra hit before death that the shield doesnt). i am curious when a shield upgrade is actually the preferred one (im guessing it'd be in situations where +3 armour is already upgraded) I have seen many pros go +shields with blink stalkers into archon/zealots. It wrecks unprepared terrans, but this hardly happens because pros are so good at reading tech and scouting. I can't think of any other scenario for protoss to go for shields. Wouldn't a planned ground into air transition use shield over armour? Perhaps, but that leaves a lot of protoss vulnerable. A ground to air tech switch costs loads of gas, and goes into the very late game. By this time, air upgrades are the only thing left anyways.
I've seen people start upgrading shields over armor in PvZ when doing air transitions
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Something to discuss with upgrades in general is cost.
Yesterday in the GSL there was the Roach vs Roach fighting that went on. Here is a rough breakdown of upgrades as they affect roach vs roach:
Roach: 145 HP - 16 (+2) Attack Damage - 1 (+1) Armour
Values here are Attack upgrade (left) vs armour upgrade (right)
Upgrade Level | Damage | Shots to Kill
0 - 0 | 16 - 1 | 10
1 - 0 | 18 - 1 | 9
2 - 0 | 20 - 1 | 8
3 - 0 | 22 - 1 | 7
0 - 1 | 16 - 2 | 11
1 - 1 | 18 - 2 | 10
2 - 1 | 20 - 2 | 9
3 - 1 | 22 - 2 | 8
0 - 2 | 16 - 3 | 12
1 - 2 | 18 - 3 | 10
2 - 2 | 20 - 3 | 9
3 - 2 | 22 - 3 | 8
0 - 3 | 16 - 4 | 13
1 - 3 | 18 - 4 | 11
2 - 3 | 20 - 4 | 10
3 - 3 | 22 - 4 | 9
This doesn't take into account regen, but base zerg regen is 0.27 hp/game second.
The only thing this would affect is anything that equates to values barely above 145. This only seems to concern values where the final number (attack - armour) is 21. This is because 7 * 21 = 147, so after 8 seconds from the first attack, the roach will heal enough to be on more than 0.0 HP after the next attack.
There was an attack where it was 2-2 vs 1-1.
This would equate to one set of roaches being on the 2-1 row and the others being on the 1-2 row.
Effectively this means that one set of roaches would take 9 shots to kill and the others would take 10.
This would mean that one player would need 11% more roaches to kill off the more upgraded roaches.
getting to 2-2 from 1-1 (excluding the cost of lair as you want that anyway for roach speed) is 375/375.
Mineral-wise this is 5 roaches, gas-wise it's 15.
So, depending on what's starving you, if your opponent has 45 or fewer roaches, the upgrade isn't worth it.
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On January 16 2015 00:49 Gowerly wrote:Something to discuss with upgrades in general is cost. Yesterday in the GSL there was the Roach vs Roach fighting that went on. Here is a rough breakdown of upgrades as they affect roach vs roach:
Roach: 145 HP - 16 (+2) Attack Damage - 1 (+1) Armour
Values here are Attack upgrade (left) vs armour upgrade (right)
Upgrade Level | Damage | Shots to Kill
0 - 0 | 16 - 1 | 10
1 - 0 | 18 - 1 | 9
2 - 0 | 20 - 1 | 8
3 - 0 | 22 - 1 | 7
0 - 1 | 16 - 2 | 11
1 - 1 | 18 - 2 | 10
2 - 1 | 20 - 2 | 9
3 - 1 | 22 - 2 | 8
0 - 2 | 16 - 3 | 12
1 - 2 | 18 - 3 | 10
2 - 2 | 20 - 3 | 9
3 - 2 | 22 - 3 | 8
0 - 3 | 16 - 4 | 13
1 - 3 | 18 - 4 | 11
2 - 3 | 20 - 4 | 10
3 - 3 | 22 - 4 | 9
This doesn't take into account regen, but base zerg regen is 0.27 hp/game second. The only thing this would affect is anything that equates to values barely above 145. This only seems to concern values where the final number (attack - armour) is 21. This is because 7 * 21 = 147, so after 8 seconds from the first attack, the roach will heal enough to be on more than 0.0 HP after the next attack. There was an attack where it was 2-2 vs 1-1. This would equate to one set of roaches being on the 2-1 row and the others being on the 1-2 row. Effectively this means that one set of roaches would take 9 shots to kill and the others would take 10. This would mean that one player would need 11% more roaches to kill off the more upgraded roaches. getting to 2-2 from 1-1 (excluding the cost of lair as you want that anyway for roach speed) is 375/375. Mineral-wise this is 5 roaches, gas-wise it's 15. So, depending on what's starving you, if your opponent has 45 or fewer roaches, the upgrade isn't worth it.
I think you missed a few things here:
1) 11% more roaches would have the same effective dps (in roach kills per second), but would have more total hit points due to more roaches.
2) In large roach-roach, not all roaches can fire, which is why concaves and positioning is so important. This makes the upgrades more valuable, as you have more concentrated firepower.
3) If you max out at 200/200, you can't spend spare money on upgrades.
It is an important point you bring up, and a very relevant question: "should I build roaches or do the upgrade?", but I think you need to take more factors into account to be able to give a confident answer. It is an interesting observation that a 2-2 upgrade costs you at least 5 roaches, but I don't think your analysis is thorough enough to claim that it is a bad choice if the opponent has less than 45 roaches.
Also, I think the time factor is a huge deterrent against upgrades: you spend the money, but they'll give you nothing until they are done, no matter how good the upgrade is, essentially making you 5 (or up to 15) roaches short compared to not doing upgrades. Preferable you'd include that as well.
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Cool! I've done some work on Starcraft and Lanchester's laws before, but my math has gotten pretty rusty since then. Still, it's nice to see that my work (mostly) matches yours.
Here's what I'm wondering - are you planning on creating something (a map, perhaps) that will test the theory through experimental evidence at any point in time? I'm aware you've done some preliminary testing, but it'd be cool to get a probability distribution or something like that.
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On January 16 2015 15:25 Cascade wrote:Show nested quote +On January 16 2015 00:49 Gowerly wrote:Something to discuss with upgrades in general is cost. Yesterday in the GSL there was the Roach vs Roach fighting that went on. Here is a rough breakdown of upgrades as they affect roach vs roach:
Roach: 145 HP - 16 (+2) Attack Damage - 1 (+1) Armour
Values here are Attack upgrade (left) vs armour upgrade (right)
Upgrade Level | Damage | Shots to Kill
0 - 0 | 16 - 1 | 10
1 - 0 | 18 - 1 | 9
2 - 0 | 20 - 1 | 8
3 - 0 | 22 - 1 | 7
0 - 1 | 16 - 2 | 11
1 - 1 | 18 - 2 | 10
2 - 1 | 20 - 2 | 9
3 - 1 | 22 - 2 | 8
0 - 2 | 16 - 3 | 12
1 - 2 | 18 - 3 | 10
2 - 2 | 20 - 3 | 9
3 - 2 | 22 - 3 | 8
0 - 3 | 16 - 4 | 13
1 - 3 | 18 - 4 | 11
2 - 3 | 20 - 4 | 10
3 - 3 | 22 - 4 | 9
This doesn't take into account regen, but base zerg regen is 0.27 hp/game second. The only thing this would affect is anything that equates to values barely above 145. This only seems to concern values where the final number (attack - armour) is 21. This is because 7 * 21 = 147, so after 8 seconds from the first attack, the roach will heal enough to be on more than 0.0 HP after the next attack. There was an attack where it was 2-2 vs 1-1. This would equate to one set of roaches being on the 2-1 row and the others being on the 1-2 row. Effectively this means that one set of roaches would take 9 shots to kill and the others would take 10. This would mean that one player would need 11% more roaches to kill off the more upgraded roaches. getting to 2-2 from 1-1 (excluding the cost of lair as you want that anyway for roach speed) is 375/375. Mineral-wise this is 5 roaches, gas-wise it's 15. So, depending on what's starving you, if your opponent has 45 or fewer roaches, the upgrade isn't worth it. I think you missed a few things here: 1) 11% more roaches would have the same effective dps (in roach kills per second), but would have more total hit points due to more roaches. 2) In large roach-roach, not all roaches can fire, which is why concaves and positioning is so important. This makes the upgrades more valuable, as you have more concentrated firepower. 3) If you max out at 200/200, you can't spend spare money on upgrades. It is an important point you bring up, and a very relevant question: "should I build roaches or do the upgrade?", but I think you need to take more factors into account to be able to give a confident answer. It is an interesting observation that a 2-2 upgrade costs you at least 5 roaches, but I don't think your analysis is thorough enough to claim that it is a bad choice if the opponent has less than 45 roaches. Also, I think the time factor is a huge deterrent against upgrades: you spend the money, but they'll give you nothing until they are done, no matter how good the upgrade is, essentially making you 5 (or up to 15) roaches short compared to not doing upgrades. Preferable you'd include that as well.
Your first point is not quite correct. Yes, the more roaches will have more HP, but we're not just straight up talking about HP, we're talking more about Effective Hitpoints (EHP), which will be the same.
In roach vs roach, it is possible to ignore the actual 145HP of the roaches themselves and just have them as "number of hits to be killed".
If you are 2-2 vs the opponents 1-1, then your roaches have 10 EHP and theirs have 9. Both your roaches do 1 damage each. Thinking of it this way it's easier to show that once they have 11% more roaches than you they effectively then have the same number of hitpoints.
The second point is valid in that there's more to think about than simply numbers. Some roaches do not fire in RvR engagements. I will be looking at this with Stargraphed as and when I get the code in to see if there's a way of quantitatively measuring engagement efficiency. For the time being I just have to take it as read that all will fire.
If you're maxed you have two options: Bank up for re-maxing or spend them on upgrades. Each has plus and minus points there.
You make a very good point about the timing of the upgrades. This is something that should be taken into consideration when playing. If you see 1-1 roaches and the evo chambers going, you know you could just build roaches and attack before 2-2 is done because you'll have the numbers advantage.
Another thing I had missed from the first post was the act of killing off roaches.
When you have fewer, more powerful units, killing one of them off will hurt your overall DPS more than losing one of the more, less powerful units. However, you'll be losing more of the more units and fewer of the fewer units. I am unsure how this works out in larger battles.
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On January 16 2015 19:11 Gowerly wrote:Show nested quote +On January 16 2015 15:25 Cascade wrote:On January 16 2015 00:49 Gowerly wrote:Something to discuss with upgrades in general is cost. Yesterday in the GSL there was the Roach vs Roach fighting that went on. Here is a rough breakdown of upgrades as they affect roach vs roach:
Roach: 145 HP - 16 (+2) Attack Damage - 1 (+1) Armour
Values here are Attack upgrade (left) vs armour upgrade (right)
Upgrade Level | Damage | Shots to Kill
0 - 0 | 16 - 1 | 10
1 - 0 | 18 - 1 | 9
2 - 0 | 20 - 1 | 8
3 - 0 | 22 - 1 | 7
0 - 1 | 16 - 2 | 11
1 - 1 | 18 - 2 | 10
2 - 1 | 20 - 2 | 9
3 - 1 | 22 - 2 | 8
0 - 2 | 16 - 3 | 12
1 - 2 | 18 - 3 | 10
2 - 2 | 20 - 3 | 9
3 - 2 | 22 - 3 | 8
0 - 3 | 16 - 4 | 13
1 - 3 | 18 - 4 | 11
2 - 3 | 20 - 4 | 10
3 - 3 | 22 - 4 | 9
This doesn't take into account regen, but base zerg regen is 0.27 hp/game second. The only thing this would affect is anything that equates to values barely above 145. This only seems to concern values where the final number (attack - armour) is 21. This is because 7 * 21 = 147, so after 8 seconds from the first attack, the roach will heal enough to be on more than 0.0 HP after the next attack. There was an attack where it was 2-2 vs 1-1. This would equate to one set of roaches being on the 2-1 row and the others being on the 1-2 row. Effectively this means that one set of roaches would take 9 shots to kill and the others would take 10. This would mean that one player would need 11% more roaches to kill off the more upgraded roaches. getting to 2-2 from 1-1 (excluding the cost of lair as you want that anyway for roach speed) is 375/375. Mineral-wise this is 5 roaches, gas-wise it's 15. So, depending on what's starving you, if your opponent has 45 or fewer roaches, the upgrade isn't worth it. I think you missed a few things here: 1) 11% more roaches would have the same effective dps (in roach kills per second), but would have more total hit points due to more roaches. 2) In large roach-roach, not all roaches can fire, which is why concaves and positioning is so important. This makes the upgrades more valuable, as you have more concentrated firepower. 3) If you max out at 200/200, you can't spend spare money on upgrades. It is an important point you bring up, and a very relevant question: "should I build roaches or do the upgrade?", but I think you need to take more factors into account to be able to give a confident answer. It is an interesting observation that a 2-2 upgrade costs you at least 5 roaches, but I don't think your analysis is thorough enough to claim that it is a bad choice if the opponent has less than 45 roaches. Also, I think the time factor is a huge deterrent against upgrades: you spend the money, but they'll give you nothing until they are done, no matter how good the upgrade is, essentially making you 5 (or up to 15) roaches short compared to not doing upgrades. Preferable you'd include that as well. Your first point is not quite correct. Yes, the more roaches will have more HP, but we're not just straight up talking about HP, we're talking more about Effective Hitpoints (EHP), which will be the same. In roach vs roach, it is possible to ignore the actual 145HP of the roaches themselves and just have them as "number of hits to be killed". If you are 2-2 vs the opponents 1-1, then your roaches have 10 EHP and theirs have 9. Both your roaches do 1 damage each. Thinking of it this way it's easier to show that once they have 11% more roaches than you they effectively then have the same number of hitpoints. The second point is valid in that there's more to think about than simply numbers. Some roaches do not fire in RvR engagements. I will be looking at this with Stargraphed as and when I get the code in to see if there's a way of quantitatively measuring engagement efficiency. For the time being I just have to take it as read that all will fire. If you're maxed you have two options: Bank up for re-maxing or spend them on upgrades. Each has plus and minus points there. You make a very good point about the timing of the upgrades. This is something that should be taken into consideration when playing. If you see 1-1 roaches and the evo chambers going, you know you could just build roaches and attack before 2-2 is done because you'll have the numbers advantage. Another thing I had missed from the first post was the act of killing off roaches. When you have fewer, more powerful units, killing one of them off will hurt your overall DPS more than losing one of the more, less powerful units. However, you'll be losing more of the more units and fewer of the fewer units. I am unsure how this works out in larger battles.
Ok, let me explain the first point in detail then.
As you did in your second post, you can formulate it in terms of both doing same damage (1), but having different amounts of hitpoint (9 or 10), and the weaker side has 11% more roaches, then yes, they will have the same EHP, but the weaker side will have 11% more dps, as they are 11% as many with same dps per roach. It boils down to the fighting power of a (group of) units goes as the DPS times the EHP. You calculated that one side has 11% more DPS than the other per roach, or 11% more EHP, both increasing the fighting power by 11%. However, increasing the number of roaches by 11% will increase BOTH their DPS and EHP by 11%, thus giving them a factor 1.11^2 = 1.23 more power. So to make up for 11% more EHP per unit (unchanged DPS per unit), you need sqrt(1.11) times as many units, or about 5% more.
But that calculation is ofc assuming that every unit can attack straight away. If you fight in a tight choke, where only a fix (small) number of roaches can attack at the same time, then your calculation is accurate, as the power of a group of units will now only go linearly with the number of units, rather than quadratic as in the "everyone can attack" approximation. That shows that if you have an upgrade advantage (and thus possibly fewer roaches) it is advantageous to fight in a choke where numbers are as important, but upgrades still help you at full power. Which we already knew, but nice to reproduce known results, I guess.... Just goes to show how hard it is to find new knowledge by mathematical analsysis of sc2.
Problem with maxing out is that you wanted to have upgraded 2 minutes ago, as you would have maxed out anyway. So I think that if you think that you will reach max before a fight, you should almost always do upgrades. Actually, if you think that the upgrade will go through before you fight, it is almost always beneficial. Even if you just barely come out even in the fight against your opponent that didn't do the upgrade, you will be at an advantage as you now have the upgrade he doesn't, and you both have almost no roaches.
Does anyone ever stockpile resources at 200/200 to remax rather than doing the upgrade? I honestly don't know, but it'd surprise me if anyone does.
edit: typos
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Gowerly shows perfectly why (we see) 200/200 vs 200/200 are "2sec" fights.
1-1 takes more shots to kill than 2-2 or 3-3.
0-1 takes more shots to kill than 1-2 or 2-3.
1-0 and 2-1 take more shots than 3-2.
We should assume that 200 vs 200 have some upgrades.
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On January 16 2015 00:49 Gowerly wrote:
This doesn't take into account regen, but base zerg regen is 0.27 hp/game second.
The only thing this would affect is anything that equates to values barely above 145. This only seems to concern values where the final number (attack - armour) is 21. This is because 7 * 21 = 147, so after 8 seconds from the first attack, the roach will heal enough to be on more than 0.0 HP after the next attack.
When considering Zerg regeneration, I usually add one additional needed attack, when a number of attack would exactly kill a Zerg unit. For example, if a Zerg unit had, say, 50 HP, and another unit with 10 damage were to attack it, I would say it takes 6 hits to kill, because 50/10 = exactly 5. In any other case I usually just take hp/damage rounded upwards (I calculated in OP like this as well).
This means that for a unit with 49 HP, the number of attacks required would be 5. This may, or may not, be one more in reality, depending on how long the unit lives, which we can't really say. Because of the 0.27 HP/gs regeneration, a unit heals 1 HP in about 4 gs. So if the 49 HP unit lives longer than that, it will need one more hit to be killed. For units with 48, 47, etc. HP, this time allowance is 2*4 gs, 3*4 gs, etc.
On January 16 2015 16:03 d3_crescentia wrote:
Cool! I've done some work on Starcraft and Lanchester's laws before, but my math has gotten pretty rusty since then. Still, it's nice to see that my work (mostly) matches yours.
Here's what I'm wondering - are you planning on creating something (a map, perhaps) that will test the theory through experimental evidence at any point in time? I'm aware you've done some preliminary testing, but it'd be cool to get a probability distribution or something like that.
Well, as you said, I have done some testing already to make sure that Lanchester's Square Law works in SCII at least roughly. Testing what this upgrade analysis suggests would basically mean testing Lanchester's Square Law more thoroughly, which, honestly, I have not planned.
I am currently working on some kind of an engagement simulator, though, which is based on Lanchester's Square Law. My concern is, though, that melee units don't really obey that law, and from time to time even ranged units fail (with not all of them attacking at the same time). If you have any suggestions on a model that could be used here, it would be welcome.
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