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Jett.Jack.Alvir
Canada2250 Posts
On January 06 2015 02:25 Yurie wrote: 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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Cascade
Australia5405 Posts
 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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Ej_
47656 Posts
On January 06 2015 11:48 Jett.Jack.Alvir wrote: 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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Gowerly
United Kingdom916 Posts
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:
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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Cascade
Australia5405 Posts
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:
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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d3_crescentia
United States4054 Posts
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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Gowerly
United Kingdom916 Posts
On January 16 2015 15:25 Cascade wrote: 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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Cascade
Australia5405 Posts
On January 16 2015 19:11 Gowerly wrote: 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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Dingodile
4139 Posts
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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Sholip
Hungary422 Posts
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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