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Someone know the dmg formula of Valkyrie?
I guess its a balance thing why its doing diminishing returns but im curious what the formula actually is.
My own test:
Amount of stacked Wraiths and their leftover HP after one Valkyrie volley (8x6 dmg).
1 - 72/120 = 48 of 48 dmg (0% diminishing returns)
2 - 2x 84/120 = 72 of 96 dmg (25%)
3 - 96/120, 86/120, 84/120 = 94 of 144 dmg (35%)
3 - 102/120, 96/120, 66/120 = 96 of 144 dmg (33%)
4 - 4x 90/120 = 120 of 192 dmg (37%)
4 - 96/120, 2x 90/120, 84/120 = 120 of 192 dmg (37%)
5 - 2x 98/120, 2x 90/120, 84/120 = 140 of 240 dmg (42%)
6 - 102/120, 2x 96/120, 90/120, 2x 84/120 = 168 of 288 dmg (42%)
11 - 7x 96/120, 92/120, 3x 90/120 = 286 of 528 dmg (46%)
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 Valkyrie
Isn't the "Advanced Mechanics" section explaining what you're looking for? All the rocket placements, etc.
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Well no, there seem to be a specific formula for it. It doesnt seem to matter how many times i try, i get the same results every time.
As you can see on my test this doesnt count for one Wraith where it always is 100% no matter where the missiles land.
I even tried stacked vs non-stacked where it yielded the same result. This one i tested above is stacked.
I will post my test of the non-stacked dmg also. If they wind out to be the same as stacked, there has to be a diminishing returns formula involved as it doesnt matter where the targets are.
Look at my second 3 Wraith test. One got 66/120 HP left, which should seem impossible ye? It seems calculate how many targets are in the area and what dmg should be dished out in total, no matter to whom it gets which is why it got down to 66/120 instead of 72/120 which would be the max dmg possible from a single volley vs one single target.
If the image of the missiles landing spots are true, i would be able to place a Wraith at every those locations and have no diminishing returns. Each wraith should end up with 72/120 or even more (splash), which im pretty sure wont be the case but ill try it anyway :D
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United States1721 Posts
Just tested it myself and you are right. This is kinda crazy. It confirms my intuitive understanding that mutas seem to survive a lot longer against valks than I expect them to. The diminishing returns seem even bigger versus mutas than wraiths actually (maybe cuz of the hitbox). With more than 3 clumped together, I see the originally targetted muta taking 10, 11 damage as opposed to 24 (48/2 since explosive damage is halved versus small units), which is a loss of almost 60%.
There definitely seems to be some algorithm that governs how to spread out the damage of a valk missile for every unit in its splash radius, an algorithm different from all other kinds of splash damage. Maybe someone who knows the source code (bwapi?) can explain it.
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United States1721 Posts
Are you sure about the 66/120? I've never been able to recreate that and it does seem impossible.
My second theory is that when there's only one unit, there's a special algorithm to deal 100% of the damage.
When there's more than one, the default splash algorithm kicks in. Per liquipedia, 36% of the missiles hit the target, dealing 100%, and 64% miss, dealing between 25% and 50% (so let's say 37.5% average). So the expected damage is 100%*36% + 37.5%*64% = 60%, meaning that you would expect to lose 40% of the damage to the target. However, this only applies to the direct target; other targets slightly off center will be missed more. For example, if a unit is at the corner of the missile box then it will be missed completely by a few missiles. Therefore, you would expect to lose more than 40% of the damage, maybe 50% or more. This calculation then explains the findings you are seeing, without having to invent a new splash algorithm. This calculation also explains why mutas take even less damage (smaller hit boxes leading to less splash dealt).
EDIT: According to List of Unit and Building Sizes , mutas have larger sizes than wraiths, but this table might not refer to hit boxes.
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Would you say that cloning the valks to separate muta would increase the damage done by them?
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United States1721 Posts
No, because as long as there is more than one muta in the splash radius, I believe the standard splash algorithm applies.
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I don't think there is any explicit diminished return formula for Valks. Unfortunately you don't give any description of your testing method, which makes it hard to zero in on likely candidates for an explanation.
How did you stack the target Wraiths?
Were they holding position or moving while being hit?
Did you keep track of which one was the primary target and whether that received the full damage?
How many repeats did you run for each number?
Did you get the exact same distribution of remaining HP each time? And can you keep tests running without ever getting a differing result?
Which known factors did you already control for (if any) and how?
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On December 29 2020 02:00 StRyKeR wrote:Are you sure about the 66/120? I've never been able to recreate that and it does seem impossible. My second theory is that when there's only one unit, there's a special algorithm to deal 100% of the damage. When there's more than one, the default splash algorithm kicks in. Per liquipedia, 36% of the missiles hit the target, dealing 100%, and 64% miss, dealing between 25% and 50% (so let's say 37.5% average). So the expected damage is 100%*36% + 37.5%*64% = 60%, meaning that you would expect to lose 40% of the damage to the target. However, this only applies to the direct target; other targets slightly off center will be missed more. For example, if a unit is at the corner of the missile box then it will be missed completely by a few missiles. Therefore, you would expect to lose more than 40% of the damage, maybe 50% or more. This calculation then explains the findings you are seeing, without having to invent a new splash algorithm. This calculation also explains why mutas take even less damage (smaller hit boxes leading to less splash dealt). EDIT: According to List of Unit and Building Sizes , mutas have larger sizes than wraiths, but this table might not refer to hit boxes.
To be fair, if Valkyrie did 100% at all times they would be way way OP :D
Having a splash algo seems just fair, however it would be nice to know it just for fun 
Maybe should test where it maxes out, how many targets it can hit until it stops diminishing dmg per target. This might be at 50%
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You guys are massively overthinking this. Air unit repulsion is the simple answer to this problem: A perfect stack is just not possible, the more air units you stack, the more and faster they will drift apart, This (in conjunction with any other unit movement) means that the relative position of each stacked unit relative to the rocket explosions is slightly different and that the more target units there are, the more spread out they will be and the more the primary target will be relatively off-centre of the stack, meaning that statistically the they will be less likely to be hit by all the explosions.
If you want to estimate this effect in one single mathematical formula, you'll have to build a fairly sophisticated statistical model first, I am afraid.
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United States1721 Posts
I'm leaning towards Freakling's take as well. I think it isn't anything specific to the valkyrie (except the single target taking 100% damage, which is the only exception).
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On January 04 2021 02:53 StRyKeR wrote:
I'm leaning towards Freakling's take as well. I think it isn't anything specific to the valkyrie (except the single target taking 100% damage, which is the only exception).
It is also worth noting this seemingly rather strange fact: Due to the exact spread pattern of the missiles, a Valkyrie's primary target is consistently the one target in a stack that receives the least damage.
In fact, I'd challenge the OP on the claim that a single targeted Wraith received 100% missile damage. This is not very reproduceable, at least not with a stationary Wraith. A moving Wraith with a lucky spread pattern might work, though, but that would be a statistical outlier.
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United States1721 Posts
On January 05 2021 06:31 Freakling wrote:Show nested quote +On January 04 2021 02:53 StRyKeR wrote:
I'm leaning towards Freakling's take as well. I think it isn't anything specific to the valkyrie (except the single target taking 100% damage, which is the only exception). It is also worth noting this seemingly rather strange fact: Due to the exact spread pattern of the missiles, a Valkyrie's primary target is consistently the one target in a stack that receives the least damage. In fact, I'd challenge the OP on the claim that a single targeted Wraith received 100% missile damage. This is not very reproduceable, at least not with a stationary Wraith. A moving Wraith with a lucky spread pattern might work, though, but that would be a statistical outlier.
OP is correct on this one. This is the first thing I recreated. For single targets, the damage is 100% every single time.
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United States1721 Posts
I just checked out the replay. WOW the 3 wraith version (second one) actually DOES go down to 66 hp after one volley! That's crazy. It's not clear if the general splash algo does this or something specific to the valkyrie. Anyone from BWAPI wanna chime in here? Sonko?
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United States1721 Posts
I have an explanation for the single target case.
Given what we know about the spaghetti code, my bet is that Blizzard wanted you to be able to attack allies / your own units. But the issue is that valks (like reavers) cannot splash damage your own units. So if only the default splash algorithm is used for the valk, attacking yourself would cause 0 damage since they're splash only, even the intended target. They didn't want that, so they made every missile hit with 100% damage to the target unit regardless of miss. But if they do this with multiple units, valks would nonsensically do 100% to every unit even if miss. So once there's more than one target in the splash zone, they apply regular damage. Sloppy code imo, but consistent with their other sloppy coding.
Doesn't explain the > 100% damage though.
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United States1721 Posts
Okay guys.
So I believe the behavior versus a single target is indeed SPECIFIC to air units in general. Here are the tests.
Unit - 100% damage rate to single target
Valkyrie - YES
Reaver - NO
Lurker - NO
Firebat - NO (tested vs vulture with speed)
Siege Tank - NO
Archon - NO (tested vs vulture with speed)
Corsair - YES (tested vs interceptors and always did full damage)
Infested Terran - NO (tested vs torrasque)
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United States1721 Posts
Got some more data.
In the longer replay MeSaber attached, I isolated the moment 02:17 when things go awry.
https://imgur.com/a/tpmDA2n
There are three wraiths stacked in this image.
This is after the first two missiles of the volley. It did 9 and then 9 damage to one of the wraiths, which should be impossible.
But interestingly enough, one of the other two wraiths took 0 damage and has 120/120 hp left.
So it would seem that the unlucky wraith took additional damage intended for the lucky one, and it has to do with the fact that they're exactly overlapped.
I can't imagine what kind of terrible code would result in this.
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Stryker nice research man! Gotta hand it to ya! =)
I will give this "issue" another shot today by looking at where the missiles actually hit according to liquipedia.
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I got a treat for you Stryker! https://ufile.io/hchdrvq4
![[image loading]](https://liquipedia.net/commons/images/1/1b/ValkyrieAttackPoints.png)
If we go by this image as a reference, the top left should take one hit, bottom right 2 hits, center 5 hits at the most per each, this is however not the case as the replay shows.
The map has the test layouts copied so they should act quite the same per each 'site test' but it does not. Top left takes just as much damage as center and bottom right in most cases. Center rarely takes the most damage even though it should.
The damage imo seems to be equalized over how many targets are in the area.
https://ufile.io/n1r8b3mj
Replay of the next test of expanding the ring until only the center target takes damage.
A big conclusion from this test is that the AOE of valkyrie missiles are insanely large, and my guesses would be that wherever the missile lands it will split the damage to all units that are hit (liquipedia states 3x3 matrix). When its one unit (the target) it will always hit inside a 3x3 matrix of the unit, which means it can never miss a single volley versus its target.
This means also that it may be possible for missiles to land in the same spot many times, seems highly likely after looking at the damage from first replay. And thats why a unit who should be taking less damage (according to image above) gets more damage than the others.
Anything to add Stryker? :D
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EPT
