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#Post#: 2238--------------------------------------------------
Zerg Hex Science
By: guguizg Date: September 3, 2021, 3:34 pm
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I started a quest to develop Zerg Hex science. I'm currently
studying economics and i'll use zerg hex to also understand some
concepts and maybe try to apply.
I'll start sharing something that took me longer than i'd like
to admit: I reproduced the map block-to-block on Excel. That way
i can calculate distances and stuff on the map. Unit speed is in
squares/sec, therefore it also enables us to calculate time for
units to get to point A to point B.
I'll be making some updates here, if u have any ideas or
something feel free to share.
#Post#: 2239--------------------------------------------------
Re: Zerg Hex Science
By: guguizg Date: September 3, 2021, 3:36 pm
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Calculating energy efficiency
Now i'll share my maths on what impact each terran upgrade has
against each armor value from the zerg units. This allows u to
understand what upgrade is more important against each oponent
playing style. I used the variable DMG/NRG, which is how much
damage can be done with 1 energy for marines, veterans and
elites. Note that what i am analyzing is not to kill enemy units
faster, but to use less energy on doing so. The % value is how
much the DMG/NRG has changed with the upgrade.
The attatchment is the result with all the details.
Conclusion:
- Shattering1 is extremely powerful at reducing energy
consumption - even more than conservation 1 with 2
exceptions:normal marines against amor 1 while in range of
armory and normal marines against armor 0 outside armory range.
Therefore, it is very important to get it if under pressure,
because it not only increases your dps, but it also reduces
energy consumption by a lot.
-Confirmed common knowledge that Shattering 2 is very strong
against roaches and primals - more than Conservation 2.
-By the maths, i feel like Cons2 kinda sucks, Cons3 is 2.4x more
effective even though it only costs 1.6x more.
-Elite scope is a interesting upgrade: against brutalisk it can
make energy consumption 20% more efficient, which is basically
1/3 of what Cons3 does, and also increases you dps, so its cool
:)
Problems: I did not consider "overkilled" units. For exemple, if
a fully upgraded elite shoots a 10HP zergling and shattering get
2 more 10HP zerglings, ure basically wasting more then 100
damage, so its kind of complicated. Now that i think about it,
strikelings can just suck up a lot of dmg even having only 1HP.
For that reason, maybe firebats can be used to kill those tiny
units before elites get to waste their damage on that. That is a
topic to explore tho, but its not the time for that yet.
Next steps: Now that we have all the information for terran
units, we can study what zerg unit drains up the most energy
from terrans, so movement speed, spawner cap, health, armor,
will all be factors to be considered.
#Post#: 2240--------------------------------------------------
Re: Zerg Hex Science
By: guguizg Date: September 3, 2021, 5:05 pm
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How many batteries do you need to supply your marines?
Now that i spend a lot of time developing this answer, i realize
how stupid this question is :D
Metodology:
1. First i used the map in Excel and designed a standard base
with normal cyard and armory placement. Then i calculated the
distances and used the movement speed from the batteries (3.0
and 3.5 for normal and advanced) for 2 different routes,
generator>armory>cyard>generator (33.4 seconds for normal and
28.6s for advanced) and generator>armory>generator (24.6s for
normal and 21.1s for advanced).
2. Then i tested how much energy/second a battery can transfer.
For that i used a siege tank that has 4k energy to get more
precision. Turns out it is 200 energy per second for both
advanced and normal. That didnt make much sense, because marines
actually took a long time to charge up, but with this maths it
would only take 0.3s.
3. With that in mind, i emptied a bunch of marine's energy and
put a battery to charge them. It took 20 seconds to fill 20
normal marines instead of 6, so 14 seconds were wasted swiching
targets - something that happened 20 times. Therefore i assume
it takes around 0,7 seconds for a battery to swich target.
4. For a battery on a route, i created a variable called TTE:
time to empty, which is the tame it takes for it to empy its
reserves before going back to the generator. So that way i can
calculate how long it takes for a full battery to come back
empty. Now, marines can hold 60 energy, vets 120 and elites 180,
so a full normal battery takes 11.6 seconds to unload to
marines, 7.58 seconds for vets and 6.2 seconds for elites, while
a advanced battery is 41.6, 27 and 6.2. Note that the time it
takes decrases, because the battery takes longer to swich
targets than to charge a target, so the more capacity each
target has, the faster it will be.
5. Now i know how long does it takes for a battery to do a full
cycle so i can extract how much energy per second your marines
can consume. For plain marines, a full armory route including
TTE would take around 36.3s to complete and a cyard route would
take 45.1s; a advanced battery would be 62.8s and 70.3s. So for
plain marines, that would mean 19.2 nrg/s on short route,
15.5nrg/s on long route and for a advanced battery, 39.8nrg/s
and 35.5nrg/s. I'll spare u more text and just attatch a sheet.
Conclusion: A normal battery can carry around 20 energy per
second on the amory route (the most used) and a advanced battery
varies between 40 and 60nrg/s depending on what marine tier you
are on. With that you can controll how many batteries you need
with your generator upgrades: for every 7 upgrades you would
need a aditional normal battery or every 13-20 upgrades for a
advanced battery if you are using all your generator's energy to
shoot with your marines.
Problem: I didnt consider batteries goofing on the patrol
routes, sometimes they can get stuck on units, but i guess u can
fix that with a precise rally.
Next steps: When is it worth it to get power pylons?
#Post#: 2241--------------------------------------------------
Re: Zerg Hex Science
By: guguizg Date: September 4, 2021, 11:46 am
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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.
#Post#: 2242--------------------------------------------------
Re: Zerg Hex Science
By: guguizg Date: September 5, 2021, 10:49 am
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Hello and shock troopers: how good are they?
Well before doing any maths i can already tell they're pretty
good. They have a basic attack that costs 2 energy per shot and
has a area damage plus 2 speels - Ground Pulse (EMP) and Instant
discharge (needs armory research). Also, they are tier 1 units,
meaning you can get them pretty early on without even getting a
tech lab. So my first question is:
Can a shock trooper basic attack be better compared to a marine
basic attack?
- Against 0 armor units: Shock troopers basic attack does 5
damage to units, consuming 2 energy, but because they have area
damage, his total potential DMG/NRG depends on the zerg influx
of units, but it is 2.5DMG/NRG for each target hit. In that
case, compared to a plain marine (3 DMG/NRG), a shock trooper
would have to hit in avarage 1.2 unit for the attack to be worth
it in ou DMG/RNG variable. In case of upgraded tier 1 marines
(shattering, pen laser and conservation 1), the shock trooper
would have to hit 5.6 units, which is not very realistic.
- Against armor 1 units (tankling): Using the already published
DMG/NRG results for each unit armor and upgrades, a plain marine
would now have 2DMG/NRG and the shock trooper 2DMG/NRG for each
unit hit. In that case, aparently a shock trooper would only
have to hit a single unit to be more cost efficient compared to
a marine, so hitting additional targes would only be profit. How
about upgraded tier 1 marines? - you might ask: they have
8.75DMG/NRG, so a shock trooper would have to hit 4.375 targets
in average, which is maybe viable, but probably the avarege
units hit is lower than that.
- Against a structure: Shock troopers do 8 damage against a
structure. Spawners and big spines have 2 armor and other zerg
buildings have 1. In that case, for armor 1 buildings a plain
marine would have 2DMG/NRG, with pen laser 3DMG/NRG and a
trooper 3.5DMG/NRG. In case of a 2 armor structure, plain marine
would have 1DMG/NRG, pen laser marine 2DMG/NRG and the trooper
3DMG/NRG. Therefore, it can be considered that against
structures, shock trooper's basic attack is stronger than
marines, even with pen laser.
How about the spells, besides being very powerful for doing a
lot of damage in short amount of time, do they "waste" energy?
-Instant discharge: costs 50 energy and does 80 damage. Being a
spell, it ignores completely armor. In that case, it has
1,6DMG/NRG, no matter what they are targeting. The only
exception would be if it overkills a unit, but using instant
discharge on a zergling is unecessary i'd say xD. In that case,
Instant Discharge can only save energy if your other options
would be plain marines against armor 2 or more target (spawners,
big spines, roaches, primals, brutas).
-Ground Pulse (EMP): costs 50 energy too and does 20DMG in area.
That means that per target hit, the DMG/NRG increases by 0.4. A
plain marine without armory has 3DMG/NRG, so a EMP has to hit
7.5 targets for no wasting energy. Or in case of a armor 1
oponent (tankling) versus plain marines with no armory
(2DMG/NRG) would have to hit 5 targets. I'd say that it can be
realistic.
Can you use Instant Discharge to kill big spines?
We'll it does look like a tasty option ;p because they do
outrange the big spines and they do have 2 armor that getts
nullfied by the spell. So how many discharges do you need to
kill a big spine? The answer is 16.25, which is worth 812.5
energy. That makes me think: how many infestors do you need to
heal for each shock trooper added? A infestor regenerates 1
energy per second and can spend 150 energy to heal 300HP. So it
can basically heal 2HP per second, while a shock trooper has a
30 seconds cooldown on the Instant Discharge which would be 2.66
DMG/s. Meaning that you need for each Shock Trooper 1.33
infestor.
Conclusion: Shoock troopers are very strong on early game, it's
basic attack can be cost efficient if it hits more than 1.2
targets in average and the Ground Pulse (EMP) can also save
energy if it hits 7.5 amor 0 targets or 5 armor 1 targets. Shock
troopers on early game can be extremely powerful against
tanklings, as their DMG/NRG is the same as a plain marine, even
if it hits a single target, meaning that if a shock trooper hits
more than 1 tankling it is saving you energy. The problem with
shock troopers though, is how useless they get on mid to late
game, because after marines get their upgrades, they're DMG/NRG
gets way better. The only use would be Instant Pulsing big
spines, but it is a big investment and can be countered by
infestors (1.3 infestor for each shock trooper).
Problem: I'm not sure about how i can make a fair comparison
marine-shock trooper, because of the cost of the unit: Shock
trooper is 15 minerals 30 gas and a marine 16/5. I proved that
on early game shock troopers might save money on energy
depending on what the zerg is doing, but it still cots 6 times
more gas, and I'm not really sure about how I can compute that.
#Post#: 2243--------------------------------------------------
Re: Zerg Hex Science
By: guguizg Date: September 6, 2021, 1:57 pm
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Terran eco figured out (minerals only)
This post is heavily inspired by Turb007's post and i'm not
doing it because i dont trust him- he is a very experinced
player- but because i'm a nerd and i like maths so here we go. I
also want to add some new concepts I'm learning on university,
like the return on investment (mineral per minute by gas
invested) and the comment i saw from Mett on Turb007's post: how
long does it take for sheep and cows to pay for themselfs
(mineral wise) and how long does it take for cows to overcome
sheeps - that sounds confusing but i hope it will make sense
soon. I will not discuss build orders on this post.
Buildings' aggregated value:
Fruit Farms: Costs 30 gas and produces 1 fruit every 6 seconds,
when no animals eat it, it gives +1 mineral. That is equal to 10
minerals per minute. And a return on investment of 0.33 minerals
per minute by gas invested.
Sheep farms (no sheep): Costs 40 gas and produced 1 mineral
every 10 seconds, meaning 6 minerals per minute. The ROI (return
on investment) is 0.15 minerals per minute by gas invested.
-With sheep: For each fruit eaten by the sheep, the value
added compared to left decayed is +1 with no advanced farming.
The mineral per minute then increases by 3.33 and adding the
sheep farm itself, 9.33, making the ROI 0.233 minerals per
minute by gas invested. Considering that a sheep costs 5
minerals, it would also take 90 seconds for the sheep to pay for
itself.
Upgraded sheep farms (no sheep): Costs a additional 20 minerals
and 20 gas (on top of normal sheep farm), upgrades the sheep
farm to produce now 2 minerals every 10 seconds instead of 1,
which is a 6 mineral per minute increase on income. The ROI of
that operation is 0.3 mineral per minute by gas invested.
Considering the 20 mineral cost, the time it takes for it to pay
for itself is 200 seconds (3 minutes and 20 seconds). The ROI of
the upgraded sheep farm in total (not just the upgrade), is 0.2
mineral per minute by gas invested, and if you consider the
sheep too, 0.255. It is important to diferenciate those
scenarios, because in 1 gas situations, you might not have space
for all sheep to be on fruit farms.
Cow farms (no cows): Costs 30 minerals and 60 gas, providing 2
minerals every 10 seconds, a 12 mineral per minute increase. The
ROI would be 0.2 minerals per minute by gas invested and it
would take 150 seconds (2 minutes and 30 seconds) for the farm
to pay for itself.
-With cows: Costs additional 15 minerals, increases the
income by 10 minerals per minute (making it 22 in total), and
takes 90 seconds to pay for itself (1 minute and 30 seconds).
The ROI then becomes 0.366 minerals per minute by gas invested.
Considering mineral cost
Before we address advanced farming upgrades, i'd like to take a
moment to analyze a very interesting comment from Mett:
"cows generate more income compared to sheep only after about
3mins. So when you are building cow farms you need to expect the
game to last another 3mins before it ends."
Comparing cow farms with cows to unupgraded sheep farms with
sheep, lets make some basic functions to figure that out. I wont
consider gas cost for this, only minerals. s(x)=0.155x-5 and
c(x)=0.366x-45. The (-) values are the innitial mineral cost and
the constant multiplying x (time in seconds) is the minerals per
second that sheeps (s) and cows (c) provide. One starts being
better then the other when they both intersect at 187 seconds,
confirming Mett's statement. I'll make a graph to show this.
Still, note that cows are very superior on the long run, after
10 minutes, while a sheep farm with a sheep will give you 88
minerals, a cow farm with a cow will give 175 minerals, which is
basically 2 times more - and the difference will just keep
growing.
Advanced Farming upgrades
Advanced Farming 1:
This 300 gas cost upgrade increases the sheep mineral income
when it eats a fruit by +1 and cows by +1 too. So when does it
start being worth it? Well now that we calculated the ROI for
each combination (excel is attached), the ROI increase from adv.
farming times the number of farms has to be bigger than the cost
of oportunity, which is the ROI of 300 gas worth of farms.
-Unupgraded sheep farms with sheep: ROI=0.23 --> after
upgrade ROI=0.316. Therefore, the ROI increase is 0.083. With
300 gas, you can make 7,5 sheep farms, but you cant make half a
farm, so 7 farms, meaning a ROI of 0.23*7=1.633. For the upgrade
to be worth it, 0.083 * number of farms = 1.633, which is equal
to 19.6 farms (20 farms).
-Cow farms with cows: ROI=0.366 --> after upgrade
ROI=0.422. The ROI increase is 0.055 and with 300 gas you can
make 5 cow farms, which is worth a 1.83 ROI. So, for the upgrade
to be worth it, 0.055 * number of farms = 1.83. The result is 33
cow farms.
Advanced farming 2:
This upgrade costs 400 gas and increases sheep mineral income
when it eats a fruit by +1 and cows by +2. Lets repeat the same
process.
-Unupgraded sheep farms with sheep: ROI=0,316 --> after
upgrade ROI=0,4; ROI increase = 0,083. The cost of opportunity
is 3,16 (with 400 gas you can make 10 sheep farms, which is
worth 10*0,316), meaning 38 farms.
-Cow farms with cows: ROI=0.422 --> after upgrade
ROI=0.533; ROI increase = 0.111. Cost of opportunity=3.2,
meaning 29 farms (28.8 ).
What does this all mean? Does it mean that advanced farming is
crap?
Well, no. On a terran's base high ground with a standard layout
(3 fruit farms and the tech lab), you can fit 30 sheep or cow
farms, meaning that when you fill it all up it is worth it to
get adv. farming, but it is a ultra late game upgrade. Before i
read Turb007's post i used to get adv farming pretty early on,
but apparantly that is not the way to go. That doesn't mean that
getting it before 30 cow farms is not worth it. We did not
consider the mineral cost of 30 farms, which is 1,350. And also,
advanced farming reduced the time a farm takes to pay for
itself: for cows, its inicially 122 seconds, then 106 seconds,
then 84 seconds. So maybe in a scenario where you need urgently
to get more minerals and cant wait to max out on farms and wait
for the farms to pay for themselfs before giving you minerals
back, it might be worth it to get advanced farming before it's
"optimal timing".
Conclusions:
1. On ealy game
Fruit farms are evidently the best choice for eco on early game,
as gas is very limited, you want to maximize your mineral income
by gas cost. If you are under a lot of pressure, getting sheep
farms might help, their return on gas investment is 30% lower
and it costs 5 minerals, but it is a much safer option.
2. Upgrading sheep farms
The return on gas investment for upgrading sheep farms is double
the value of making a new sheep farm with no sheep and 30% more
than making a new sheep farm with a sheep. Meaning that if gas
is the limited factor, you always want to upgrade your sheep
farms for more mineral income. The problem though, is that the
upgrade takes 2 minutes and 20 seconds to pay for itself mineral
wise, so if you can't wait 200 seconds for it to start giving
you minerals, you probably shouldn't do it.
3. Cows vs Sheep
As Mett said, because of the time it takes for the cow farm to
pay for itself, cows are ment for longer games, meaning that
your push will be delayed and fewer pressure will be applied to
the zerg. It is a tradeoff, to put it in economics terms, eco X
pressure.
4. Advanced farming
The optimal time to get it considering only gas cost, would be
when you have 30 cow farms or 20 sheep farms for advanced
farming 1 and 30 cow farms or 38 sheep farms for advanced
farming 2. But as it was discussed, advanced farming doesnt cost
any minerals, meaning that you might want to get it earlier if
you are under a lot of pressure or you need to push soon.
Next steps: Might be time to go deeper into game theory and
maybe try to consolidade team strategy. For exemple, we saw that
cows after 10 minutes have already given the player double the
mineral value sheeps would have given, but because it takes a
lot of time for it to pay itself, meaning that little to no
pressure is applied. What if the team has a strategy in which 2
players apply t1 pressure while the other one ecos for a t2 doom
push to finish the game? What if 2 players eco and 1 tries to
clear the 3 nests with a super agressive terran build while the
others prepare a heavy push? What if the 3 players just t1 push?
What if the 3 players just t2 push? What other possibilities are
there? Is there a dominant strategy? How should the zerg react
to each of them?
Notes: Thank you Turbo and Mett for your
contributions/inspirations and I hope I added something to the
discussion xD. The attachment has some cool charts about each
building eco info for normal, advanced farming 1 and advanced
farming 2 values and also the comparison cow x sheep and sheep x
upped sheep.
#Post#: 2244--------------------------------------------------
Re: Zerg Hex Science
By: guguizg Date: September 7, 2021, 11:53 pm
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Can turrets save energy?
Early game
As weird as it may sound, yes. Turrets if compared to t1
unupgraded marines or shock troopers can save energy,
considering that it not only has a area attack, but also a
better DMG/NRG.
Turret stats:
Damage = 16
Energy cost = 3
DMG/NRG = 5.33
Marine stats:
Damage = 3
Energy cost = 1
DMG/NRG= 3
Shock Trooper stats:
Damage = 5
Energy cost = 2
DMG/NRG = 2.5
It's important to note though, that the more is invested into
static defense, the less ofensive power you have and less
threatening you become to the zerg, which can be bad for you and
specially for your allies. Also, because they are so expensive,
it would save even more energy if you got shattering for your
marines, that also increases offensive power. Compared to
upgraded marines, a turret's DMG/NRG falls behind pretty fast,
leaving a huge unwanted investment. The only use I can see being
helpful for turrets is denying infestors feeding: you can build
one at your construction yard and leave it off, then when a
infestor attacks it, you can turn it on. They are useful on that
case specially for beginers because they're hard to kill and
have high enough dps to actually kill infestors.
Late game
Now considering upgraded turrets against upgraded elites, the
turrets also fall very far behind. The area damage stops working
when the target is as big as a bruta, leaving a 25(-7) damage
per 4 energy, making the DMG/NRG against bruta 4.5, which is
significantly lower than a elite's 14 DMG/NRG. That means that
every time a turret shoots you waste more and more energy.
Damage wise, turrets are also not very good on late game,
considering that a fully upgraded elite has a total 52.5 DPS
potential while a upgraded turret has 36.
#Post#: 2245--------------------------------------------------
Re: Zerg Hex Science
By: guguizg Date: September 8, 2021, 5:24 pm
---------------------------------------------------------
Zerg Eco figured out
Just to be clear before I start, this post is not about winning,
it is about eco, which is basically the most important tool you
have for winning. I guess in that logic this post might help you
win.
How zerg eco works
For those who don't know, zerg hex has a very interesting
economy, that consists on this equation:
I = S * E + H
I(income in minerals per minute); S(spawners); E(extractors);
H(hive)
The spawners value is shared between the zerg allies, meaning
that building more spawners will increase your allie's economy
just as much as your own - but not in the same value.
Hive (H)
A lot of people haven't actually noticed this, but hives
actually generates 80 minerals per minute for each zerg player.
A solo zerg then would get 160 minerals per minute from hives.
That makes about 20% of a zerg's economy when the game starts.
Extractors (E)
Extractors cost 200 minerals and 15 supply. There are also the
greater mineral extractors, that do the same as 4 normal
extractors combined, and for that reason costs 660 minerals and
45 supply on top of a normal spawner. So other than saving space
and taking longer to get enough resources to get it, a greater
mineral extractor is the same as a normal one, it even has the
cost of 3 unused drones.
The game starts with 6 extractors for each zerg, meaning that
the "S" value will be multiplied by 6.
So what is the so called "ratio"? In a multiplication of S*E,
the closer both values are, the bigger the result will be. For
exemple, if you have 10 points to distribute for S or E, giving
5 and 5 is the best combination possible.
1*9=9; 2*8=16; 3*7=21; 4*6=24; 5*5=25.
In reality, that means that the closer you spawners to
extractors ratio is, more efficient you have spent your
resources eco wise. So if you are the kind of zerg who only
builds a lot of extractors, you might be actually making your
economy worse. That also applies for the kind of zerg who builds
a lot of spawners and makes no extractors - notice how 1*9 is
almost 3 times smaller than 5*5, so maybe if you made at least a
few extractors, your eco can increase by a lot and therefore
your offensive potential too.
The indicator in game that shows you "the ratio" (if you should
make more extractors or more spawners) appears when you click on
the extractors. The "extract minerals" numbers shows you the "S"
value, meaning that adding a new extractor would add that value
to your income, and the "spawner income info" shows you how many
minerals per minute would be added to your and your allie's
economy combined if a mineral container (counts as 4 spawners)
was built - that's a useful information, because a mineral
extractor is worth 15 supply, the same as a mineral container.
That means that if the "extract minerals" combined ("S" value)
number is higher than the "spawner income info", you should make
more extractors and if it's the other way around, adding more
spawners would increase your economy more than a extractor
would.
Spawners (S)
The "S" from our equation consists of a sum of 4 different
values.
1. Number of small spawners * 1
2. Number of large spawners *4
3. Number of mineral containers *4
4. A constant (30)
For exemple, in the start of the game, each zerg starts with 12
spawners, so in total there are 24 spawners. In that case, the
"S" value will be 30(the constant)+24*1+0*4+0*4=54
So if all small spawners give the same economical return, why do
people say that strikelings are so good for economy? Well, there
are 2 reasons for that.
To answer that, I'll make a comparison between strikelings and
slowlings spawners.
- Slowling: costs 50 minerals and 4 supply
- Strikelings? costs 70 minerals and 3 supply
First reason:
If you build 1 slowling or 1 strikeling, your economy will
increase by the same amount, but how much does a slowling cost
compared to a strikeling?
The spawner costs in reality is usually lower then the supply
cost of a spawner. The first 45 supply costs 600 minerals, the
second 725 and the third 850, increasing the cost 125 minerals
every time you buy it. Lets now analyse the real cost of a
spawner for each supply.
-First supply (600)
Slowling=50 + 53.3 = 103.3
Strikeling= 70 + 40 = 110
-Second supply (725)
Slowling=50 + 64.4 = 114.4
Strikeling= 70 + 48.3 = 118.3
-Third supply (850)
Slowling=50 + 75.5 = 125.5
Strikeling=70 + 56.6 = 126.6
-Fourth supply (975)
Slowling= 50 + 86.6 = 136.3
Strikeling = 70 + 65 = 135
You can see that after the fourth supply strikelings start being
cheaper compared to zerglings, becuase they cost one less supply
and that difference will only grow with time. The equation to
know the real cost of any supply is:
C=p+[(600+125n)/45]*s
C(cost); p(price of the spawner); n(supply number); s(how much
supply the spawner uses)
I'll attach a excel with all the spawners real cost for each
supply and a cool graph to make it visual :)
Second and more important reason:
With the same amount of supply (and not spawners) strikelings
increase the "S" value more. For instance, if u buy a supply
(45), with slowlings, you can afford 11 spawners, increasing the
"S" value by 11, while if you buy 45 supply of strikelings, you
can afford 15 spawners, increasing the "S" value by 15. If you
have 10 extractors, that makes a difference of 40 minerals per
minute, which and add up a lot considering that the economy of
zerg is exponential - the more it grows, the faster it will
grow.
If you look at the attachment, a lot of things start to make
sense, such as why you want to stay away from having many
tanklings or many brutas (for your eco).
Next steps: I would like to analyze how much eco damage capacity
upgrades can cause to a zerg's economy and also the tankling
maths to see how bad it really is. Also, would be interesting to
see how much positive impact eco sharing can have on the zerg's
economy.
#Post#: 2253--------------------------------------------------
Re: Zerg Hex Science
By: ZergTriumph Date: September 13, 2021, 7:20 pm
---------------------------------------------------------
[quote author=guguizg link=topic=244.msg2245#msg2245
date=1631139847]
You can see that after the fourth supply strikelings start being
cheaper compared to zerglings, becuase they cost one less supply
and that difference will only grow with time.
[/quote]
Good to know. Thank you.
#Post#: 2255--------------------------------------------------
Re: Zerg Hex Science
By: guguizg Date: September 24, 2021, 2:26 pm
---------------------------------------------------------
Is zerg eco exponencial?
To answer this question i got into some weird math to get an
answer. It's getting very technical, but I'll try my best to
explain the concepts I'm using. I'm working currently on a zerg
eco simulator on python and i can later confirm my conclusions.
Short answer is: No, it's not exponencial.
Btw I'm sorry for the low quality graphs, I dont have my full
setup atm
Concessions:
I'll make a few assumptions so i can make a working mathematical
model. This is far from a guide or a realistic situation, I'm
only investigating if the eco is exponencial or not.
1. The player is a solo zerg
2. Starting supply isnt 54, it will be zero - wont really matter
as I'm not looking for realistic numbers, just a working model
on the long run.
3. Building count is not an integer variable. Again, I know you
can't make 0.5 a spawner, but it doesn't matter if the
investigation is to find out wheter the eco is exponencial or
not.
4. Time will not be a factor. To analyze the behaviour of zerg
eco growth, I'll consider the costs and benefits from each
supply, so for this exercise it wont matter the time - I will
cover it soon when i make a simulator.
5. The only buildings available are the slowling spawners and
mineral extractors.
Metodology/The nerdy maths
1. Figuring out the ratio mathematically
When playing the game, players can follow the ratio by reading
what's written on the extractor, but when making a mathematical
that doesn't work. In a simulation it might, but we'll need to
use a different strategy.
In economy we have a concept called PPF - (Production
Possibility Frontier). It basically sets the limits of
production you have, that in your case is how many spawners and
extractors we can produce with the limited amount of 45 supply.
The PPF is then 4x + 15y <= 90n
That's a lot of letters and I'll explain each one of them:
x: Number of spawners. They cost 4 supply so the constant
multiplying it is 4.
y: Number of extractors. They cost 15 supply.
n: Number of the supply. Each supply gives you 45 supply
capacity, and when you're solo zerg the supply cost increases
only every 2 supplies, so that's why its 90n and not 45n. So for
now on, each time we see "n", we have to remember it means 2
supply worth.
This expression basically means that a combination of x spawners
and y extractors can never use more than 90 supply for each
supply you bought.
HTML https://imgur.com/vJkRjt4
Now that we have set our limitations, we have to choose the best
possible combination within our limitations. For that I'll use a
utility curve. In a utility curve, all points have the same
value, so in our case, in the utility curve all points represent
the same amount of economy. The maximum value we can get from a
supply is represented by the intersection between the utility
curve and our PPF, because that's the highest utility avalible
given the PPF restrictions.
HTML https://imgur.com/6ZlbSh1
Our utility curve (economy) is given by:
U(x,y)=(54+x)*(12+y)
Again, x represents the number of spawners and y is the number
of extractors. 54 and 12 are the starting values of spawners and
extractors.
To figure out the intersection, the derivative of both functions
must have the same value. Given that our utility curve is a
tradeoff between 2 variables, we get 2 funcions back:
Spawner count law
x=(45n-18) / 4
Extractor count law
y=3n+ 6/5
This values are the amount of extractors and spawners for each
supply to maximize the income.
To find out the proportion between spawners and extractors, all
we need to do is devide x by z, which gives us:
15/4 - 15/(5n+2)
Now this is the first cool thing we can analyse. As you can see
the "n", which represents supply is divinding numbers, meaning
that the more time goes on, more valuable spawners become,
meaning that you would need less extractors per supply as time
goes on. If the supply went to infinity, the spawners/extractors
ratio becomes stable at 15/4 = 3.75 (In each supply, for every
extractor you build 3.75 spawners)
HTML https://imgur.com/tz7Cwk1
Now that we have modeled our "ratio" depending on what supply
we're on, we can calculate our income in a "n" supply. To figure
it out, all we need to do is substitute our spawner and
extractor count laws on our x and y values from our utility
curve. That would mean that the player has followed the correct
ratio perfectly. The outocme is:
Income per minute = 27/20 * (5n +22)^2
HTML https://imgur.com/UJkM855
We just got to a second cool conclusion. The income per minute
for each supply follows a quadratic formula. Do we have our
answer then? No, it's never that simple xD. We haven't
considered our costs. Our costs for each supply varies for 2
reasons: first the ratio keeps changing (spawners get more
valuable over time) and second the supply costs will follow a
600+125n function.
2. Calculating supply cost variation
The supply cost variation is simple: 125 minerals for each
supply bought.
The extractor and minerals one though, is hard, because the
ratio keeps changing. As we know how many spawners and
extractors we have on each supply (n), what we can do is to
multiply the spawner count variation by spawner cost and the
same for the extractors and then subtract the values from the
last supply (n-1). The math looks like this:
Δc=(70∗(45n−18)/4+220*3n+6/5)−(70∗(
45(n−1)−18)/4+220∗3(n−1)+6/5)+125
Δc=1572.5
Long story short, that means that the cost variation for each
supply is costant, meaning that supply get more expensive
linearly. How about the income, how is it's variation behaviour?
3. Calculating income variation for each supply
The process for this one is similar, as we have figured out the
income per minute on each supply (n), all we have to do is
subtract it from the last supply (n-1). The maths are:
ΔU=27/20∗(5n+22)^2−27/20∗(5(n−1)+22
)^2
ΔU=27/4∗(10n+39)
Now if we pay attention to that, we will see that the variation
of income for each supply varies linearly, which makes a lot of
sense given that the income per minute on each supply is
quadratic - it's variation would be the derivative.
4. Calculating effective economy variation for each supply
We have figured out how much the cost changes with suppy and how
much income changes, to figure out the effective increase, we
just need to devide ΔU/Δc (economy variation/cost
variation). As cost variation is constant, the effective economy
variation will also be linear, as it has the same degree as the
income growth without considering cost,but it will be "slower"
(the line will be less tilted):
ΔE=ΔU/Δc
ΔE=27n/629+1053/6290
HTML https://imgur.com/9HdyK8p
Conclusion
We know that the economy effective variation with each supply is
linear. Meaning that our variable "n" is powered by 1.
If we integrate the income per minute effective variation per
supply, we will discover the income per minute per supply, and
our "n" variable will be powered by 2. That would mean a
quadratic funcition.
If we integrate that again, it would give us our minerals, which
will be a function with "n" powered by 3.
Meaning that the income grows like a quadratic function and
your accumulated mineral bank will grow cubically. That means
that eco is not exponencial - it would be if stuff was powered
by "n", not the other way around. Mathematically, exponencial
are the fastest growing curve compared to all arithimatic ("n"
powered by something) in the long run, but in short term
(meaning early game), arithmatic funcions can be faster and then
get slower than exponencial.
Problems/next steps:
As i have adressed, I haven't considered a lot of things that
needed to be consider for these numbers to be comparable to a
real game, but is only possible with a simulation I think. I'm
currently working on a python script to simulate the economy and
understand better whats going on.
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