Author Topic: Zerg Hex Science  (Read 737 times)

guguizg

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Re: Zerg Hex Science
« on: September 04, 2021, 06:46:55 pm »
When and who do you bouble?

This one is loaded with maths, but if u want, u can skip to the conclusion.

So, the "bouble" is a techlab speel that costs 2k energy and gives allied units inside +3 dmg (with the exception of firebats apparently) and reduces enemy armor to 0 inside an area for 10 seconds.

Who to bouble?

Well that is kind of a simple question. Considering -1 armor has the same effect compared to +1 damage, the only scenario in which boubling the enemy is better is when they have more than 3 armor. Consider a roach (armor 2): if you bouble it, you will reduce his armor to zero (-2 armor) while if you bouble your own marine, it would be +3 damage - a 1 damage difference. Now, brutas (armor 7) are different, bacause the bouble would cause a -7 to them or a +3 to the marines. So if all brutas are running through a path, it's better to bouble the path - making all the units that pass through it affected.

When to bouble?

Now this is a little bit more complex. Have no doubt that boubling increases damage in all cases, so if you need to kill something faster it is obviously recommended, such as:
-Big spine (armor 2): bouble marines, specially if they are normal marines (3 dmg -> reduced to 1 by the armor) or vets (6dmg -> reduced to 4 by the armor)
-Infused roach (armor 2): can be dangerous when in big numbers with other zerg units; bouble marines
-Roaches (armor 2): when in large numbers specially when you don't have shattering 2 or walls defending you; bouble marines
-Primals (armor 3): bouble marines if no bruta are out bouble primals if there are also brutas in the mix,
-Brutas (armor 7): defenitely bouble brutas if they are getting too close to your marines xD

The problem is though, when does the bouble become more energy efficient compared to no bouble? Basically when the bouble saves you more than 2k energy. I'll analize some situations to see if that happens at all.

-Early game marines shooting nest spawners: spawners have 2 armor, while small spines and nest have 1. I'll consider only spawners, because i'm assuming the zerg will build some more adding to the 4 default ones. I'll use a already explored variable: DMG/NRG, which is how much damage can be done with 1 energy.
    -No penetrating laser: Before=1DMG/NRG; After=4DMG/NRG. That is a significant increase, so let's make a function to see when it stats being worth it to bouble (x is energy and y is damage and -c is the initial cost of the bouble, but the cost of the bouble in damage depends on how much damage the unit without the bouble could do with 2k energy. So we have to substitute 2000 in the f(x)). For no bouble marines: f(x)= 1x; for bouble marines: g(x)=4x - 2000. To find the intersection the maths are f(x)=g(x); so x=4x-2000; 3x=2000; x=666.6 NRG. So what does that mean? It means that it starts being worth it after marines have shoot 666 times (1 energy consumed per shot). Marines have 0.4 attack speed, so for the duration of the bouble it can shoot 25 times. For it to be worth it then, you need at least 27 marines.
     -With penetrating laser: Before 2DMG/NRG; After=5DMG/NRG. Using the same process, f(x)=2x; g(x)=5x - 4000 -> 2x = 5x - 4000 -> x = 1333. That means you need 53 marines shooting with penetrating laser for the bouble to be worth it.
      -With overcharge: overcharge doubles the attack speed for 5 seconds, meaning that instead of shooting 25 times in the duration of a bouble, a marine will shoot 37.5 times, so bouble starts being worth it energy wise after 14 marines for no penetrating laser and 27 for with penetrating laser.

- Midgame vets with conservation 1, shattering 1 and penetrating laser against armor 2 roaches:  f(x)=5.625x; g(x)=7.5x -11.250 -> x=6000. Veterans energy consumption per shot with conservation 1 is 1.6, so 6000 energy is equal to 3,750 shots fired. With overcharge, it would need 100 veterans for the bouble to be worth it in terms of energy. Note that bouble +3 does not apply to shattering damage, only penetrating laser and armory buff.

- Endgame elites fully upgraded against armor 7 brutalisk (bouble on bruta): In this case the bouble "+7" caused by the -7 armor does apply to shattering. f(x)=12x; g(x)=26x-24,000 -> x=1,714.3. For fully upgraded elites, 1,714.3 energy means 1,142 shots fired (energy consumption of 1.5). That would mean it would need 31 elites shooting with overcharge. Without overcharge, the value would be 46 elites. That number only applies to a 100% bruta army coming non stop through a bouble, which is not very realistic, but still is a surprising result that bouble doesnt even consume that much energy if you think about it.

Conclusion: The bouble indeed can save energy in a lot of situations. When on early game if you want to push really soon, maybe get penetrating laser, overcharge and bouble your marines to get the structures faster and saving energy (if you have around 30 marines). If you dont have penetrating laser, you defenitely should bouble when you have more than 15 marines. Don't be afraid to use the bouble when you have a lot of units on you, specially if you use overcharge, it doesnt waste 2 charges, it might even save you some.

Problem: All of the values are from a perfect scenario in which all marines are shooting at the same target kind. That means it would be a pure bruta army, a pure roach army, or in the case of the spawners, no spawning units while you shoot at the spawners. Still, the results can be useful, considering the numbers should be a bit more depending on how much variaty there is on the zerg army compostion, or in the case of the spawners, if there are a lot of units around.

Notes: the DMG/NRG values can be found in one of my previous posts. There is a spreadsheet with all of the upgrades against each armor value.
« Last Edit: September 05, 2021, 05:54:12 pm by guguizg »
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