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Author Topic: Armor/Talent Calculator  (Read 1126 times)

bobucles

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Armor/Talent Calculator
« on: December 31, 2019, 06:01:30 AM »

I've been playing around with the combat sim a bit, trying to figure out exactly how the armor formula works. This is what I have so far, feel free to comment or copy it for your own use:
https://docs.google.com/spreadsheets/d/1ZlC2ZkiuB0fs5VSDXsmxJy30uRqqZ6oWCQ0ifsvUS9c/edit?usp=sharing

Here are the takeaways:
* +150 armor is hands down the single best talent point you will put into a hull. It is ALWAYS active and vastly increases hull durability, and is supremely effective against weapons that deal <100 damage. I.E. most weapons.
* 90% DR is more meaningful for high armor ships( duh!) but can still show potential at the armor floor against low power kinetics like needlers.
* -20% Armor damage double dips, both reducing the "weight" and direct damage of weapons.
* The overall huge gains of hull, armor and survivability from Impact mitigation make all 3 points a valuable addition for EVERY officer.
* -50% KE vs. armor is broken ayy eff. It triple dips on armor protection, giving half the "weight", half the damage, and half the damage AGAIN. Can you say 13 gauss damage? It also contributes to bare hull defense.
* Most other armor talents have no effect at 0 armor. No, not even the 5% floor will contribute.

These are the damage formulae as I best understand them:
Basic:
Damage = DMG*Type *  Weakerresist( 0.15, (DMG*Type)/(DMG*Type+armor) )
Armor = Previous armor - damage

Talents:
Damage  = (DMG*Type*AC1*IM3) * AC1 * TA3 * Weakerresist[0.15 or IM2, ((DMG*Type*AC1*IM3)*TA3)   /   ((DMG*Type*AC1*IM3)+((IM1+armor*EA3)) ]

Stripped armor:
Damage = (DMG) * Weakerresist[0.15 or IM2, (DMG * AC1) / ((DMG * AC1) + (IM1+.05*Startarmor)) ]

I don't have the attack talents figured out yet, I.E. +15% damage and +50% anti armor weight. My initial testing shows they're pretty well worth it though.

I'd like to thank all my officers for patiently sitting by as I shot the hell out of them.

References:
IM1 : +150 armor
IM2 : 90% resist cap
IM3 : -20% Armor dmg and weapon weight
AC1 : -50% KE weapon weight, damage, and damage(!)
EA3 : +50% value of existing armor
TA3 : +50% Anti armor weight. Not sure if right?


[attachment deleted by admin]
« Last Edit: December 31, 2019, 06:08:09 AM by bobucles »
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SCC

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Re: Armor/Talent Calculator
« Reply #1 on: December 31, 2019, 07:16:23 AM »

You were figuring this out in combat? Advanced Countermeasures 1 seems really broken.
I'm not sure of the armour formula (I tested it, but not extensively, certainly not for AC1), but this is what I use for my calculations. MAX() function picks the biggest value. Damage type is assumed to have already come into play before any other modifiers applied. IM2's value in this equation is considered to be 2/3.
As for stripped armour? I assume the calculation is exactly the same, just with armour value capped at 5% of the base. I recall Alex statements amounting to something like "Armour never goes below 5%".
Code
NewArmour=Armour-MAX((Damage^2*IM3*OE3*AC1*TA3/(Damage*IM3*OE3*AC1+IM1+Armour*EA3));Damage*IM3*OE3*AC1*TA3*0,15*IM2)
I wonder if the double dipping isn't the result of Alex organising things a bit like this:
Code
Damage=Base*Type*IM3*OE3*AC1*TA3
NewArmour=Armour-MAX((Damage^2/(Damage+IM1+Armour*EA3);Damage*0,15*IM2)

Plantissue

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Re: Armor/Talent Calculator
« Reply #2 on: December 31, 2019, 09:37:07 AM »

* -50% KE vs. armor is broken ayy eff. It triple dips on armor protection, giving half the "weight", half the damage, and half the damage AGAIN. Can you say 13 gauss damage? It also contributes to bare hull defense.
Are you sure about that? My observations are that the KE modifier is only applied once, not three times.

I use :

Damage on Hull = Weapon Damage *(Weapon Damage*damage type modifier)/(Weapon Damage + armour)

which correlates with KE damage on a completely depleted hull correctly.

Plugging in the numbers results out that an Mark IX Autocannon should do 426.67 damage to a bare Onslaught Hull and when I observed this in game one time, 427 damage was done so my formula seems accurate.
« Last Edit: December 31, 2019, 09:39:55 AM by Plantissue »
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bobucles

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Re: Armor/Talent Calculator
« Reply #3 on: December 31, 2019, 10:58:21 AM »

Quote
Are you sure about that? My observations are that the KE modifier is only applied once, not three times.
I pulled numbers from the sim, and tweaked the equations to match. Gauss hits for 700 kinetic. With talents it can go down to 13 against armor. That's
90% damage reduction => 700 to 70
80% armor damage => 70 to 56
50% KE damage: 56 to 28
50% KE damage (again!) : 28 to 14.

The reason is because DMG shows up 3 times in the damage equation. It's generically (DMG^2) / (DMG+armor), but after running those numbers it very clearly gets cut in half again. See if it does that on your end!

The damage number says 13, but when I ran it around 76% CR for a tiny damage boost and it went up to 14. The decimal place is pretty close and it probably truncates rather than rounds off.
Quote
KE damage on a completely depleted hull correctly.
Gauss against bare naked hull seems to not do the extra 50% step. However, having even the thinnest paper armor on hand can easily cut hundreds of damage off. I have some scratch pad numbers on the side from the sim.

Gauss against bare hull is still extremely deadly. It just gets absolutely ruined by any level of existing armor.
« Last Edit: December 31, 2019, 11:02:43 AM by bobucles »
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Thaago

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Re: Armor/Talent Calculator
« Reply #4 on: December 31, 2019, 11:37:26 AM »

Lets see, the 50% KE damage is once for the weapon damage type vs armor, and once for the skill - that makes sense to me! Hull, even when it has residual armor, gets neither of these bonuses so Gauss is going to be doing at least 4 times more damage.

Nice to see these tests, thanks for taking the time to post your findings! Evasive Action 3 for the +50% armor for damage reduction helps keep enemy small guns locked to medium damage as well, and can push what counts as 'small' up a size category. I don't know how it stacks with the +150 armor for that purpose skill, but if it works like range modifiers then its (base armor * 1.5 + 150), ie the 150 does not get multiplied.

An eye opening test when it comes to skills vs no skills light kinetics is to see what Broadswords will do to a ship. Skills are going to cut their damage down, compared to no skills, by (2/3) * .8 * .5 = 26.7% damage done to armor in the minimum damage band (which is also highly extended).
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bobucles

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Re: Armor/Talent Calculator
« Reply #5 on: December 31, 2019, 11:52:46 AM »

Lets see, the 50% KE damage is once for the weapon damage type vs armor, and once for the skill
Hey, you're not the only one stuck with doing a double take on this. The damage against armor is 50% for the kinetic type, 50% for the talent modifying weapon damage, and 50% for the talent modifying armor damage. Normally, you'd expect the kind of damage would look something like:
- Damage resist cap, then cut in half by 50%
right? That would make sense, you cap out and the talent boosts it some more. Instead, the 1/2 step is happening both on the weapon damage and on the overall damage. Believe me, I spent some time trying to make the equation fit the results!

Here are my results when spanking a fresh 750 armor Heron with 1 gauss shot:
Quote
No perks: 111
IM3 : 66
IM1, AC1: 28
EA3, AC1: 26
IM3, EA3, AC1, 13

Quote
but if it works like range modifiers then its (base armor * 1.5 + 150), ie the 150 does not get multiplied.
That matches what I saw. The +50% perk only applies to the remaining bits of armor on your ship. The 5% "superstructure" armor and +150 skill do not count. However, AC1 (-50% KE) will make the 5%+150 armor more effective, at least from what I saw.

The +150 armor perk on its own will cap your hull resistance against any KE that deals 50 or less damage, and any frag that deals less than 100 damage. It is a massive difference against light machine guns, needlers, locusts, and a massive boost in hull endurance for all ship classes in general.
« Last Edit: December 31, 2019, 12:20:20 PM by bobucles »
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Thaago

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Re: Armor/Talent Calculator
« Reply #6 on: December 31, 2019, 01:03:12 PM »

Oh, so the +150 does apply to residual armor? Awesome! That was an unresolved question I've had for a long time. That makes a HUGE difference!

(The equivalent of having 3000 armor before it being knocked out, as 5% of 3000 is 150. That is amazing.)

Lets see, the 50% KE damage is once for the weapon damage type vs armor, and once for the skill
Hey, you're not the only one stuck with doing a double take on this. The damage against armor is 50% for the kinetic type, 50% for the talent modifying weapon damage, and 50% for the talent modifying armor damage. Normally, you'd expect the kind of damage would look something like:
- Damage resist cap, then cut in half by 50%
right? That would make sense, you cap out and the talent boosts it some more. Instead, the 1/2 step is happening both on the weapon damage and on the overall damage. Believe me, I spent some time trying to make the equation fit the results!

Here are my results when spanking a fresh 750 armor Heron with 1 gauss shot:
Quote
No perks: 111
IM3 : 66
IM1, AC1: 28
EA3, AC1: 26
IM3, EA3, AC1, 13

Quote
but if it works like range modifiers then its (base armor * 1.5 + 150), ie the 150 does not get multiplied.
That matches what I saw. The +50% perk only applies to the remaining bits of armor on your ship. The 5% "superstructure" armor and +150 skill do not count. However, AC1 (-50% KE) will make the 5%+150 armor more effective, at least from what I saw.

The +150 armor perk on its own will cap your hull resistance against any KE that deals 50 or less damage, and any frag that deals less than 100 damage. It is a massive difference against light machine guns, needlers, locusts, and a massive boost in hull endurance for all ship classes in general.

I think those numbers make perfect sense without any triple dipping from the skill though. For the fully skilled one:

(.5*.8*.5*700/(.5*.8*.5*700+750*1.5+150)) = .099, so the shot is at 10% damage (capped by skills).  This is the "For Purposes of Armor Reduction" part of the calculation. And then:


.8*.5*.5*700*.1 = 14, The actual damage done to armor.

And as you noticed by ticking the damage up by like 1% with CR, the 13 may be a truncation rather than a rounding (very elegant way of checking by the way, nice!)

Thats impact mitigation 3, Advanced Countermeasures 1 , the normal KE damage type, and the Impact Mitigation 2 max damage reduction threshold - no double counting of AC 1 needed, though it does also show up in the "armor reduction" part of the calculation as well so if out of the range of minimum armor it will be helping in a non-linear way.
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Plantissue

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Re: Armor/Talent Calculator
« Reply #7 on: January 01, 2020, 08:52:36 AM »

Quote
Are you sure about that? My observations are that the KE modifier is only applied once, not three times.
I pulled numbers from the sim, and tweaked the equations to match. Gauss hits for 700 kinetic. With talents it can go down to 13 against armor. That's
90% damage reduction => 700 to 70
80% armor damage => 70 to 56
50% KE damage: 56 to 28
50% KE damage (again!) : 28 to 14.
I don't see how that is triple dipping at all. You have the normal armour reduction and then you have the two skills modifier applied once, then the KE modifier is applied once. It would helps to say which skills, so it's the Impact Mitigation level 3 (-20% armor damage taken) and Advanced Countermeasures level 1 (-50% kinetic damage taken by armor). There is no triple dipping happening at all.

It'll be akin to saying HE damage modifier to shields is triple dipped by 50% HE damage, 80% shield damage, and 75% HE damage, but what is happening is HE modifier applied once and two skills applied once each. So normal HE damage modifier applied once, then skills of Defensive Systems Level 2 (-20% damage taken by shields) and Advanced Countermeasures Level 2 (-25% high-explosive damage taken by shields). There is no triple dipping of HE there either.


As an aside, if the +150 armour is always added last and is not affect by the 5%or original value, then that's useful information and I thank you for clarifying that as I have no idea about the order in which the skills are applied.
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FooF

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Re: Armor/Talent Calculator
« Reply #8 on: January 01, 2020, 03:13:30 PM »

When I wrote the armor guide many moons ago, Advanced Countermeasures wasn't in the game. Interesting that AC1 has such a profound impact. As far as Impact Mitigation 1 (+150 for calculation), it has always been a very good first choice but even in the armor guide discussion, there was no definitive answer as to whether or not it applied to the 5% minimum for hull damage. If it does, it makes the hull extremely durable relative to an unskilled ship.

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SCC

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Re: Armor/Talent Calculator
« Reply #9 on: January 01, 2020, 03:29:12 PM »

Quote from: Alex
Armor value for damage reduction no longer goes below 5% of base armor value
From the 0.8a release patch notes. I almost got it, close enough that it took me a bit of time to find this. It's kinda funny I assumed this to be somewhat known, even though I initially missed it myself...

bobucles

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Re: Armor/Talent Calculator
« Reply #10 on: January 02, 2020, 03:37:21 PM »

Quote
I think those numbers make perfect sense without any triple dipping from the skill though. For the fully skilled one:
Yeah, that seems right. I went through many iterations of the formula and clearly locked in on the wrong one. The skill remains exceptionally powerful because it both directly reduces KE damage against armor AND it increases the overall mitigation as well. The skill definitely double dips, so you can get 75% less KE damage on your armor because of the combined bonus.  -50% KE vs. armor also provides residual armor protection for bare hull, which stacks massively with +150 armor for even stronger KE protection.

As long as you have +150 armor, feel free to bounce storm needlers, squalls and most fighter weapons off your armor and hull all day. The 90% DR talent even kicks in with some of the smaller (<75) KE weapons, and combos with AC1 to make a hard hull even harder to crack. Impact mitigation is definitely a must have for all your officers, all 3 points give a massive increase in life that's too good to pass up. AC1 is probably less useful except as a player perk, because the AI will typically soak KE damage into the shields.

I haven't looked into the benefits of the damage boosting talents or the extra bonuses/penalties of CR. I suspect they all will double dip, where both damage AND armor penetration are gained or lost in tandem. The calculator also doesn't deal with the armor tile system. Drilling into a single armor location is the most effective way to destroy it, but most damage tends to splash across the armor and will last much longer. You can also lose more armor than your armor rating in a single attack, due to how it spreads out. But that's a puzzle for another day.
« Last Edit: January 02, 2020, 03:45:46 PM by bobucles »
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Plantissue

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Re: Armor/Talent Calculator
« Reply #11 on: January 03, 2020, 09:45:31 AM »

Nobody has as of yet posted how armour really works. I cannot claim to fully understand it either. Its pretty strange all around. Damage to armour seems to be:

Damage = Weapon Damage  * Weapon Damage  / (Weapon Damage + armour)

or with damage type modifier:

Damage = Weapon Damage  * damage type modifier * (Weapon Damage  * damage type modifier) / (Weapon Damage *damage type modifier + armour)


Only when you have done enough total armour damage (yellow damage) to the same amount as the armor rating, will you start to be able to do hull damage (red).  A second layer of armour damage that seems to total half of the original armour exists after the first layer of armour. However this time the damage that would be done to armor is now done to Hull HP and damage done to this second layer of armour seems to be calculated as if full armour again and is not something I understand as it is possible it decreases progressively instead of increasing progressively.

Once both of these layers if armour are completely depleted, does the 5% effective armour value seems to act and now the only damage done is completely to Hull HP.

So there are a three layers of damage.
First band of armour, which solely armour damage is done to. This totals the total armour of the ship.
Second band of armour which both armour and hull (HP) damage is done to. The armour totals half the total armour of the ship.
Thirdly, pure hull damage.
« Last Edit: January 03, 2020, 10:46:28 AM by Plantissue »
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SCC

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Re: Armor/Talent Calculator
« Reply #12 on: January 03, 2020, 10:48:11 AM »

If you check out the "Armor and you" guide and scroll to the "Armor Cells" section, you will understand what's happening. The summary is that armour cells further away contribute only half their armour, but also take only half the damage, so the damage is split between cells that lost all armour (where you deal hull damage) and cells that still have some (where you deal armour damage).

Plantissue

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Re: Armor/Talent Calculator
« Reply #13 on: January 03, 2020, 11:19:22 AM »

As long as the shots are all hitting the same place, only the same cells are taking damage. So you can safely ignore the effect of cells. That thread has useful info but is strangely formatted, often taking a page to describe something that can be explained in a couple of sentences and stressing the wrong things.

The info in that thread implies that once armour has taken full armour damage, full hull damage occurs, but that is not the case. If you've never observed it yourself before, you can try it out yourself, always carefully hitting one spot with a beam weapon. Doesn't have to be a beam weapon if you can aim well. There is a transitional point where you are no longer doing pure armour damage or pure hull damage, but is doing both.




Lets say an Eagle with 1000 armour take a heavy blaster shot of damage 500.
Damage = 500*500/(500+1000) = 167 damage which bears out in practice.

Once 1000 damage is done to armour, that thread implies that Damage = 500*500/(500+50) = 455 damage which does not bear out in practice.

There appears to be a secondary layer of armour which has to be fully stripped again where less than 455 hull damage is done and then and only then that is fully stripped, 455 damage is done. That thread completely misses that out.

You can try it out yourself by carefully doing 1000 damage (perhaps using a beam) on the rear of an eagle, then shooting a Heavy Blaster at it.
« Last Edit: January 03, 2020, 11:39:02 AM by Plantissue »
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SCC

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Re: Armor/Talent Calculator
« Reply #14 on: January 03, 2020, 11:59:46 AM »

As long as the shots are all hitting the same place, only the same cells are taking damage. So you can safely ignore the effect of cells.
You appear to have missed the part where outermost cells contribute only half of their armour and take only half the damage. There's no second layer of armour, it's just that even if you destroy armour on the 9 inside cells, there are 12 outside cells that still have armour (because they took only half the damage). Once you destroy those 12 cells completely, then the hull will take full damage.
This is easy to notice once you add up those cells — 21! — but see that each cell has 1/15th of the armour value. If all cells contributed fully their armour, then armour value in combat would appear to be 40% higher, than the one listed as the ship's stat. What does add up, however, is that inner 9 cells contribute fully (9/15) and outer 12 cells contribute only half of their armour (12/2/15=6/15).

Link to the thread where Alex himself explains this. Which is the exact same explanation as the one used in the guide. And, well, I expect Alex to know mechanics better than you.
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