These numbers are important. Extremely important. I will let you ponder why for a day or two before I tell you why. Mostly because I'm too tired to launch into an essay about it.

### Damage against Lost Souls at D24

Wow, you've really done your homework here. When I get the time, I'll try to confirm your results.

By the way, the gun puppy in T3 Lockdown takes 203 damage from expanded Polaris shots.

Great. I've never tested Lost Souls. I had no idea that they exhibited their own phenomenon of..."ultra vulnerable" --- which actually means "no protection at all"? I'll try to check some of this later. In particular, I'm curious about shard bombs. Meanwhile, thanks for all of your hard work. This is a big deal.

This is very interesting. Lost souls... hmm. They are the key to everything, it seems.

So we'll be able to calculate a lot of interesting things.

a) Damage guides to defeating bosses

b) Best weapon to use against elements

c) Best performance by a weapon OVERALL

And countless other things...

Lockdown, of course, is focused on weapons you have. Blast Network doesn't/can't be calculated, as it's 1 hit K/Os, etc.

This is a HUGE deal for the SK community. I've done some work here and there, updating numbers on the Lancer wiki and an old wiki page called Damage Data that was put to rest, after I decided that compiling into one page would be easier.

Thanks for your hard work, Zeddy and Bopp! We've accomplished what many never even thought about.

Anyone who's thanking me for the Lancer Knightz data should thank Donkeyhaute more. I believe that he has single-handedly collected at least 75% of those data, without an elevator pass. I started helping only because I was using them so heavily.

Upon closer inspection, I'm not sure that we've made as much progress as I initially thought. I just composed a big response, but now I'm deleting it an asking a question.

Zeddy, when you say "effective damage", do you mean e.g. Final Flourish on beasts? Do you also mean Divine Avenger on constructs? In particular, I don't actually understand this statement:

*The formula for damage bonus on an attack whose effective damage exceeds 131 at D24 is the following: (effective damage + 66) * damage bonus level * 4%*

Zeddy, you haven't told us how resistant damage (e.g. elemental against beasts) works, have you? Cursory calculations with the more powerful Combuster and DA strokes indicate that resistance is not just another multiple-of-65.5 effect. It really seems that resistant damage is a fraction of neutral damage, around 16%?

When I say "effective damage" I mean Final Flourish on beasts. This is not the same as Divine Avenger on constructs because Divine Avenger is half normal. For Divine Avenger on constructs, add 65.5*3. 65.5 for the elemental and 65.5*2 for the normal bit.

I'm still figuring out resistant damage. In theory, it works exactly the same as neutral and weak, with the minor exception that ALL resistant damage fall under the 131 damage treshold where defence diminishes in a manner I haven't quite yet figured out. Some kind of quadratic formula is possibly involved. Due to this, I have no earthly idea how much defence resistant defence is, but I can tell you that it's a lot more than 655.

Keep in mind that a split damage weapon that does 200 damage actually does two pieces of 100, which falls under the 131 damage treshold. This leads to shenanigans.

Thanks for clarifying on "effective damage".

Regarding the 131 threshhold: I assume that you've seen User:Exasperation. He fit a rather complicated curve to the data. To me, his fit has always seemed kind of an over-fit. I can't imagine why the damage calculation would be designed like that. I don't know what to do with the information, other than write a computer program to churn out damage numbers. In short, I can't extract much insight from it.

Regarding the shenanigans, I was looking at the DA resistant numbers above 262 --- for example, the DA charge stroke against beasts and gremlins, at damage bonus +0, +2, +4, +6. Whereas the vulnerable damage is always 65 or 66 more than the neutral damage, the resistant damage is 191, 217, 241, and 267 less than the neutral damage. So it seems to me (as it has, for at least a year) that resistant damage and vulnerable damage are being calculated by different systems. That's why I was delighted but surprised to hear that you thought you could fit resistant damage and vulnerable damage into a single framework.

Look closer.

Hail Driver damage:

Vs lost soul: 231

Vs construct: 166

Vs slime: 95

231 - 166 = 65

166 - 95 = **71** <- The flying shenanigans is this?

And a more outstanding example is, for example, Dark Retribution:

Vs lost soul: 142

Vs slime: 77

Vs construct: 46

142 - 77 = 65

77-46 = 31

Or the initial detonation of Graviton Vortex:

Vs lost soul: 19

Vs anything else: 5

19 - 5 = 14

My impression is that defence grows a bit stronger just under the treshold and beyond that starts to diminish. The reason why it does this might have something to do with poison, which, when it reduces enemy defence, also reduces this treshold. It is for this reason that Volcanic Pepperbox and max damage Deadly Shard Bomb gain a lot more damage from poison than, say, Sudaruska does. (at GTH, it's 24 damage per hit vs 18).

It's obvious why defence starts diminishing at a certain point. That's to keep weapons from dealing 0 damage. If you bring proto gun to Stratum 6, you'll find that it deals more than 0 damage. To Lost Souls they deal 24, to most other things it deal 8.

You haven't pointed out any inconsistency with Divine Avenger, by the way. Let me break it down for you.

Max damage Divine Avenger charge:

vs Lost soul: 1000

vs Undead: 804

vs Slime: 739

vs Beast: 440

What you have to remember is that Divine Avenger is a split damage weapon, and it works the most intuitive way possible: exactly like one normal and one elemental sword. Let's look at it in that light.

Max damage half a Divine Avenger charge:

vs Lost soul: 500

vs Undead: 500 - 65.5 = 434.5

vs Slime: 500 - 65.5 * 2 = 369

One half of Divine Avenger always is neutral damage, that is to say, 369. Since I haven't yet figured out the exact formula for damage below 131, let's extract the vs beast part like o:

vs Beast: 440 - 369 = 71

Combined DA charge:

vs Lost Soul: 500 + 500 = 1000

vs Undead: 369 + 434.5 = 803.5, or 804

vs Slime: 369 + 369 = 738. Actual number is 739, so we're clearly dealing with a non-integer here.

vs Beast: 369 + 71 = 440

71 is far less than 131, so there is shenanigans.

Yes, thanks for clarifying. I'm still processing some of this information...

I am too. I'm in the process of merging the lancer knightz and lost soul data into one text document made easily parsable by a program I'm going to write. Upon doing this, I can output this data in any other format I would wish it, and as such be able to make comparisons in a flash.

My first step will be to feed coordinates of soul/neutral data into wolphram alpha and have it spit back a formula at me. I'm hoping this formula will involve 65.5 in some manner.

I don't have an exact formula for you guys yet, but I can offer some speculation. Let's look at Dark Retribution again. It's two posts up, but I'll just repaste it:

Vs lost soul: 142

Vs slime: 77

Vs construct: 46

142 - 77 = 65

77-46 = 31

Neutral defence gets horribly mangled, but weak defence is untouched. Why is this? 77 is far below 131, and as such you'd expect shenanigans to happen. There are two options:

- It is a coincidence. Since defence first gets amplified after the treshold and it then declines, we just happen to be looking at the exact point where the weak defence passes through its regular value.
- The treshold is not, strictly speaking, 131.

By that I mean that, for the weak defence, the treshold is probably around 65.5. In other words, *the treshold for an amount of defence is the defence itself.* If we realise that, then we can cleanly apply this defence formula easily over to knights as well as enemies with arbitrary amounts of defence. I've discovered a law! Let's phrase it like a scientist!

*An amount of defence will act linearly upon a source of damage until the damage has been brought below the defence itself.* Then things get funky.

The exact manner in which it gets funky has yet to be determined, but it looks like a curve-thing acting upon the amount of defence that has been brought under the treshold. That is to say (2 * total defence - damage) for amount of damage that exceeds the defence. Where the defence exceeds the damage, I expect the amount of damage scaled is just the defence itself. It does, however, continue to scale as the amount of damage shrinks.

So tell me this.

Defense works similarly to attack, right? Certain monsters have more effective defenses to certain elements. Certain swords are more effective on certain monsters.

I'm curious as to how OOO coded the game.

Was damage meant to be linear? Or is it exponential? I'm trying to figure out a connection for the number 71, which seems to be recurring in your data.

Every time I look at the data, I feel like there's something strange about defense. There's just this worm of doubt in the back of my mind. You say that defense is different between every type of monster. What if... every monster had the same amount of normal defense? That would be the core of all data.

Let me see...

Also, while randomly calculating numbers through the Lancer data, I found this. KEEP IN MIND, THIS IS DEPTH 24. Depth 19 seems to not have the same similarities...

First strokes only.

Final Flourish- Damage (vulnerable) - Damage (neutral) = 65

Barbarous Thorn Blade- Damage (vuln) - Damage (neut) = 65

This is quite obvious, as they are both similar weapons.

And then, while trying to find similar data, I found a surprising one. First strokes only.

Warmaster Rocket Hammer- D (vuln) - D (neut) = 66

Fang of Vog data may be off a little...

I calculated

D (vuln) - D (neut) = 69

A little too close to our 65-66 mark, eh?

More testing coming soon.

Mahatma-Gandhi, you're on the right track, but Zeddy has already pointed out that stuff in post #1 above. In other words, these facts that you're noticing are pretty much the point of this thread.

Yes, of course.

I'm a little slow here, it seems.

Sorry :P

Anyway, I'm going to work on a graph, and link it to you guys soon.

7.5^(-5) * x^2 + x/10 + 1.8

That's the formula Wolfram Alpha spat out at me when I fed it my data. You apply that to a weapon's "true" damage at depth 24 and round it up, and you'll get resistant damage. Don't add the 1.8 at higher depths. Remove it altogether for depth 13, really.

This is not what I was looking for. I will not stop until I find out what the resistant defence for a monster is and what the exact process for applying it is.

@Mahatma-Ghandi

Fang of Vog exists at what I like to call "the treshold". At this amount, defence is a little bit stronger, which is why you get 69 instead of 65.

Oatmonster just found that Howlitzer heads also have zero defence. This means we can gather true damage values at arbitrary depths, provided we can find howlitzers in them.

I don't know if you guys want to find damages at different depths, or where I would post, but I was just at LoA and I got a +0 Voltedge slash and charge on a flying howlitzer.

D25 Voltedge+0 regular slash: 491

D25 Voltedge+0 regular charge slash: 771

comparatively...

D24 Voltedge+1 regular slash: 492

D24 Voltedge+1 regular charge slash: 773

Interesting, Zeddy's projected low damage increase of D24 damage = D25 unboosted damage

EDIT: [(p) stands for projected]

D25 WRH+0: 385

D24(p) WRH+1: 387

mmmmk, so I'm wrong. Learning is wonderful.

EDIT:

just saving some numbers in this thread.

D19 Valiance+0: 175

D24 Valiance+0: 245

D21 Spike Shower: 289

EDIT:

D26 Voltedge+0: 507

D24(p) Voltedge+2: 511

hmmm... that's off by 4 damage.

I just went into HoI to check if the real numbers were closer. Low damage for Glacius was 492 and 773. They're not exactly the same so it's more of a coincidence than anything else I think.

This thread is actually amazing.

Just found it on google while trying to understand my poison numbers.

Edit: Zeddy did you ever finish resistant defences? And can I have the data table you fed into wolfram?

Poison being doubly effective on split dmg weapons seems silly. After reading this thread I can see how the math causes that, but it seems like an oversight...

At depth 24 VV applies a 15 point overall debuff to enemy resists. This goes up to 22 for my industrial cata which is under the threshold as you said. So if I'm getting this correct, any base dmg under 131 gets fed into a different formula. This formula would be new resist= f (true damage). I assume for coding simplicity they put the base defense in as a variable so they can easily change everything at once. Which would explain why the 15 point debuff transforms into a 22 point debuff.

Pity we can't just ask the devs...

Edit: Okay I'm half asleep and obviously screwed up something because I have two lines on one graph, but doesn't resistant defense scale linearly with true damage? Either y=1.019x+16.39 y=2.286x-124.1 but obviously something is wrong because I have two distinct, very linear lines on one graph. Maybe I'll try again with some sleep...

Edit Again: I got mixed up in excel and fixed it. From all the sword data I went through resistant defense increases linearly with dmgvsLostSouls. This would then cause the quadratic effect you saw in resistant DMG...but resistant defense is definitely linear.

Here's the data I fed Wolfram. I only did pure and neutral damage as there wasn't weak/resist values for everything.

I haven't done much more attempting to figure the formula below the treshold out yet. It could be something like (defence / (defence + constant)), which is a thought I had after looking at Warframe's defence formulas. Will test later.

Thanks. What I did was I calculated values from the split dmg weapons as well using your methods. Assuming a 50% split in the pure dmg, you then end up with a table of pure dmg vs actual resistant dmg (not including the neutral). Using this to get resistant defense and throwing this into graphical analysis creates a perfectly linear line.

I should probably redo that actually because I used pureDMG+6 data on the x-axis which is wrong.

I've learnt some programming and I'd guess that there's most likely two stages to defense determination-a comparison to apply one of the three formulas based on enemy/weapon type-and then some funky stuff to keep weapons from dealing zero dmg.

I think I could probably generate enough data to find the second relationship by buying a bunch of 2 star weapons and testing in tier 3.

So the first point explains DA vs beast. No clue about DR or hail driver.

I think I might have gotten it. Give me a second to work out a few more details in the graphing process, rounding, etc. Zeddy, when you fed the data into Wolfram-Alpha did you ask for an exponential function? I used Graphmatica and did all kinds of functions, but what struck me was the power function for the relation between resist damage and pure damage. I received the equation y = 0.0379 x^1.2115 which fit well, though it seems a bit odd. I'd expect the developers to use some nice numbers and not these ridiculous things we're coming up with. I have a feeling the odd numbers are the result of the numbers we're using being rounded.

Ok so I've done a bit more research and the rounding truly is messing us up here somewhere. I went to the Impervious GTH and whacked some T1 punching bags with my Blizzbrand and the numbers I got were: 32 (neutral resist), 37 (weak resist), and 20 (strong resist). Here are your shenanigans. This has caused me to think that it's possible, slightly possible, that each tier or stratum has a partially different calculation. S5, or D24 where you whacked the Lost Souls had approximately 65 normal defense as a standard, correct? Now, wherever the T1 GTH is, the difference between a resisted hit and a normal hit is 5. Let's check.

T1 GTH Data (in the order of neutral resist/weak resist/strong resist) (note: I am only counting the first swing of swords)

Shadowtech Alchemer Mk II: 19/24/4 where 24-19=5

Blizzbrand: 32/37/20 where 37-32=5

Nightblade: 34/39/21 where 39-34=5

Swift Flourish:33/38/6 where 38-33=5

Now the problem here is that the Blizzbrand and Nightblade both have mixed normal/elemental damage *yet they both stuck to the weak-neutral relation*. Another thing. The Nightblade, being 3*, overpowered the Blizzbrand in every aspect. Ok, so T1 is just weird, or Impervious hacked their GTH (I actually suspect the level scaling thing where higher star weapons lose power in higher tiers and lower star weapons gain power in lower tiers). Let's move on to T2

T2 GTH Data

Shadowtech Alchemer Mk II: 48/76/13 where 76-48= 28

Blizzbrand: 85/112/55 where 112-85= 27 there goes the rounding again

Nightblade: 79/103/51 where 103-79=24 and you have your shenanigans

Swift Flourish: 84/113/18 where 113-84=29 huh?

So we have 24, 27, 28, and 29 for possible choices out of these four. T2 is even weirder. I don't even know what to do with this stuff so let's go to T3.

T3 GTH Data

Shadowtech Alchemer Mk II: 40/64/15 where 64-40=24 umm...? What happened to the 65? Oh, right, the threshold. Let's keep going.

Blizzbrand: 185/252/120: where 252-185=67 Ok, that's better.

Nightblade: 69/85/48 where 85-69=16 total shenaniganifiedly odd. Whatever.

Swift Flourish: 58/104/29 where 104-58= 46 ok let's skip T3. This is just messed up

The only error that you can glean from this data is that I was using inappropriate star-leveled weaponry for all of the tiers. It's a mixture of 3-4* stuff. However, this also raises the question of whether this star-level issue applies to each stratum (0* for S1, 4* for S5, etc.) or only each tier (0-1* for T1, 2-3* for T2, etc.) because you used 5* weaponry in S5 (correct?). But then again, all of my weapons stuck perfectly to the weak-neutral relation in T1. Either the result of rounding (likely) or there are more shenanigans than we expected. Why is rounding likely? Because we were dealing with 1-2 digits so that rounding occurs to an extreme, whereas in T3 we deal with mostly 3 digit damage numbers so rounding is less extreme, and as a result, shenanigans.

The base defence at the depth of T2 GTH appears to be about 29. Here is what happens with nightblade:

- Nightblade is a split shadow/normal weapon. The total power is, according to my calculations, 185, or 92.5 shadow, 92.5 normal.
- When you attack a target, the normal part is resisted by 2 x base defence, 58. 92.5 - 58 = 34.5
- 34.5 is less than 58. Ergo, shenanigans.

If you want to make accurate tests for base defence, use charge attacks and/or high amounts of damage bonus to make sure your attacks are reduced to amounts above the enemy's defence.

Whoa, sorry. I see why you said there's nothing new. I'm slow. So there are two problems as of now: the resistance formula and the below-the-base-defence shenanigans. They could possibly affect each other as many resists seem to fall below the threshold.

Anyways, I'm going to take a shot at this once I gather more data. I have a feeling that an increase in neutral damage proportionally increases resisted damage, though much rounding is involved. Somethig about rounding multiples of seven and the difference between two weapons' damage.

Kick me if I'm wrong. I woke up too early today.

I believe I have the resistance formula. Take the pure unresisted damage of any weapon and divide it by 7.777 and you should have the resisted damage within one damage accuracy. Which isn't too bad considering that Zeddy's defense theory for d25(?) is that the standard is either 65 or 66.

Confused? Sorry. Here we go. Here's my example. Zeddy's GTH data in T3 stated that standard defense was 61. A Nova Driver's regular shot at +3 damage does 221 damage. 221+61=282 which is the pure, unresisted damage. 282/7.777=36.2607... which rounds to 36, the damage of a Nova Driver when resisted at +3 damage. I am not sure whether 7.777 is the magic number for all depths or not. Charge shot damage works differently too.

There are holes, yes. This whole think could be a fluke, coincidence, stroke of bad luck, but there is proof. It could be that I don't even have the right formula and 7.777 just happened to work. Test it. Prove it. Disprove it. I want bullet holes in my postulate because there is bound to be some mistake here.

*Which isn't too bad considering that Zeddy's defense theory for d25(?) is that the standard is either 65 or 66.*

It's not either of those, it's a number between them. When doubled, the result is somewhere around 131. I doubt we are dealing with integers.

I tried your formula out, and it's close, but not close enough. For the WRH charge, for instance, it's off by 10 damage points. I still think the defence is a flat number that is affected in some manner as it reduces an amount of damage below itself. However, this is pretty close, and we may be dealing with *a formula that approaches 7x/9, where x is the undefended damage, as defence goes to infinity.*

I'm going to have to brush up on some advanced maths for this.

Like I said, this doesn't work with charges. Hey, I'm even surprised it got that close. I tried it with some others and I was about 30-40 points off. I don't think we're dealing with integers much at all.

Also, your second paragraph started talking about the problem I tackled, the resisted damage formula, then you continued on and talked about damage below the threshold. These seem to be two completely separate problems. They appear affected by different variables, one by unresisted damage and the defensive standard and the other by the defense itself.

(D24) *Blackened Crest* shield bash: 188 damage

(D26) *Blackened Crest* shield bash: 198 damage

(D24) *Ancient Plate Shield* shield bash: 196 damage

(D26) *Ancient Plate Shield* shield bash: 206 damage

Uh huh.... +5 damage per floor? I need another testpoint.

ps. you can't hit ghosties with shield bash, I tried .-.

I noticed while getting elite marks on all my missions that lost souls spawn in mission 3.2, Blades of the Fallen (depth 4). Also, the new recon item gives deathmark on activation, which may be useful if revisiting this for more datapoints.

Aye, I'm aware of those.

Howlitzer heads also have 0 defence, and I've been using howlitzers on a lot of depths for research that involves damage. (Poison's damage reduction, for instance.)

Some day, Zeddy and Bopp, you're going to be world famous for unlocking the secrets of this game.

To give credit where credit is due, this lost souls insight is all Zeddy's (and his crew's?), not mine. Cheers.

Remaining attack = rAtt = attack / 2

Remaing defence = rDef = defence - rAtt

Final damage = f(attack, defence) = rAtt - log( attack / rDef) x rDef

Or if you prefer a big 'ol jumble:

Final damage = attack/2 - log(attack / ( defence - attack/2 )) x ( defence - attack/2 )

when defence < attack < 2 x defence

Accurate to within 3 damage points for D24, but it's far too specific in range and I don't think it's accurate enough to be the true formula. The log is base 10.

It doesn't work when attack < defence because the logarithm of numbers below 1 are negative. It also doesn't work when attack > 2 x defence because then you're dealing with the logarithm of negative numbers, and I'd rather not get complex numbers involved in this.

I cracked up when I saw log. It's a fair attempt, but I think my 7.777 concept was closer, not counting charge attacks. Still, I never considered log. Mind showing your work in figuring out that formula?

I mapped out a graph of the damage numbers, and the drop is clearly not linear.

The formula definitely involves logarithms or exponents in some manner.

Using a nonlinear regression calculator, I get the formula:

defence below treshold = total defence - attack / 2

final damage = attack / 2 + defence * 0.5924241903 * ln(defence below treshold)

Accurate to within 2 damage points, still not what I'm looking for.

Your chart says that DA/GF does 511 on the first stroke (lost souls, depth 24, damage+0)? But Lancer Knightz have only 311 against vulnerable enemies. So there is a difference of 200? I would expect the difference to be about 130. Can you help me understand?

A good method for checking if an overarching equation contains a log (or power) is to plot the data on a non-linear set of axis, such as semilog. Interestingly, you can also plot on unconventional axis to find even more strange equations. If log doesn't exactly fit, its likely close to base 10. (Interestingly you can either transform the data or the axis - but the dangerous part is when you start doing both and forget what you're doing to begin with.)

The plot that Zeddy made definitely looks like a power function. My initial guess would be its more likely to be a power of 2 (say 8) than 10. Or even more interestingly a non-integer, as Zeddy has eluded to before.

The individual parts of DA are below the treshold, where funny things happen. Your estimate is also a bit on the low side. 131-ish normal defence + 65-ish elemental defence = 196. Defence below the treshold is not actually strictly diminished. It starts off being stronger than its true value.

Ah yes, I forgot to give the normal part of DA two 65-point kicks instead of one. Thanks.

I'm fully awake and ready to launch into an essay about this.

For starters, I will say that this is the most ground-breaking discovery about damage numbers that has ever been done. It explains

everything.Or at least, when I'm done with it, I will use it to explain everything.All in due time.

Examine the document linked above. Feel free to compare it to, say, the Lancer Knightz data on swords. Let's look at, ehhhh, Final Flourish. At no bonus:

Damage vs Lost Soul: 324

Damage vs Beast: 258

Damage vs Gremlin: 193

Let's ignore damage vs Slime for now. Damage values below 131 are very tricky to deal with. Why 131? All in due time. At maximum damage bonus:

Damage vs Lost Soul: 402

Damage vs Beast: 336

Damage vs Gremlin: 271

Examine these six numbers for a while. Compare. Calculate. These numbers are all you need to understand everything.

Don't get it yet?

Max damage vs Lost soul / No bonus damage vs Lost Soul = almost 1.24070707... For the time being, I'm assuming damage to be rounded

up.Go ahead and try it with any value on the chart. You'll get 24% extra every time. Multiply any value by 124% and you'll end up with the max value.Damage vs Lost Soul - Damage vs Beast = 66.

Damage vs Beast - Damage vs Gremlin = 65.

Max damage vs Lost Soul - Max Damage vs Beast = 66.

Max damage vs Beast - Max Damage vs Gremlin = 65.

Damage vs Lost Soul - Damage vs Gremlin =

131.All in due time.

A wolver has about 65.5 defence against piercing damage. This defence is doubled against shadow damage for 65.5 x 2 = 131. Because defence is linear, this makes the matter very simple to calculate. The formula for damage bonus on an attack whose effective damage exceeds 131 at D24 is the following:

(effective damage + 66) * damage bonus level * 4%More generally:

(effective damage + enemy base defence) * damage bonus level * 4%How do you find enemy defence? Well:

enemy neutral defence = enemy base defence * 2and

neutral damage = effective damage - enemy base defenceshuffle that around and

enemy base defence = effective damage - neutral damage.You can try that out with any value in the Lancer Knightz data where the end-result exceeds 131. This value is 262 for split-damage weapons because that's two different parts of 131.

What this all means