I need scissors! 61!

Today I did some science with Fehzor. Krakob and Msaad joined in for sciency fun as well. In the end, with the help of those people, Soral, Dutch-Oven, Zheninja and some other guys I can't remember but I appreciate the help of I swear, we gathered the damage numbers of every single weapon at every single level of damage bonus.
All in a day's work.
The result: three sheets full of damage numbers for different weapons on different targets in Guild Training Hall.
-Sword chart
-Gun chart
-Bomb chart
Edit: I also made wiki pages if you don't like Google Docs for some reason:
-Swords
-Guns
-Bombs
A lot of the bomb values were just copied from my bomb DPS sheet, but I still had to gather damage for resistant targets. The purpose of that other test was to compare DPS between weapons, but this time we're attempting to figure out how defence works by checking out enemy defence. We found one very notable point of interest.
Let's have a look at Dark Briar Barrage.
Neutral: 214, 227, 241, 254, 268, 281, 295
Effective: 275, 289, 302, 316, 329, 342, 356
The mathematical amongst you may already see what the interesting point here is. Let me spell it out:
Difference between neutral and effective: 61, 62, 61, 62, 61, 61, 61
I'm assuming that one 62 there due to a rounding error. Are you getting what's interesting about this? No matter how much you increase your damage, the difference between neutral and effective is a linear amount, meaning neutral damage proportionally benefits more from damage bonuses than effective damage does. It also means that multi-hit weapons stand to lose a whole lot more from neutral damage than other weapons do (or that they stand to gain a whole lot more from weaknesses, if you're a half-full glass kind of guy.)
That's not even all. Not only do weapons get defended by a linear amount between weak and neutral, it's the same linear amount. For attack doing more than 160-ish damage, the drop from weak to neutral is 61 damage. For some reason, the defence goes entirely silly below that level. Sometimes it's lower, which is kind of what you expect, but then other times it's higher. This is pretty much the reason guns and shard bombs need specialised damage more than anything else, but it's also the reason normal damage weapons become much more competetive at max damage.
At resistant targets, defense just goes wacky and gets absurdly different everywhere. Defence, presumably, works linearly up until a point where it suddenly gets exponential. If it works this way for knights, then well; Those two extra bars of defence you see on defensive armour may be worth a whole lot more than you think.
Other than that, I guess enjoy all the damage numbers at every damage increase level for all the weapons. I know Bopp will be eager to have a look-see over them. Sincere thanks to everyone who helped me gather these.

LARRRY
We finally get a decent thread in these forums, and you want to delete it?
Kids, this is why we don't want to you to "live like larry"

Found out that approximately 0.16*weak = resistant on pure damage type.
and damage bonus gives approximately 0.05 each for weak damages.

You seem to be entirely correct.
I'm using this to extrapolate some values of weapons that only exist in normal damage varieties and the results are very interesting. Add 61 for weak damage, then multply by 16% to find resisted damage. Adding 61 creates a very consistent increase in damage value, too, which definitely increases linearly.
Sorry, Bopp. I have to call shenanigans on your exponential increase theory.

I applaud you all for doing this. It shall be quite useful on the wiki.

Done some more work on the sheets. They are now split into
-Sword chart
-Gun chart
-Bomb chart
So you don't have to scroll past all those bombs and swords to find the damage values of your alchemer, say.
We've done lots of science on the numbers gathered, and we have found some more interesting points of note.
-Resisted damage seems to have base damage reduced to 16% (50% for split-damage weapons), but then damage increase works linearly with a lowered value. Each step of damage increase appears to be lowered by this same amount, so resisted damage behaves the same way as undefended damage, but with smaller numbers.
There are A LOT of weapons with identical damage values:
--Everyone knows that BTB = Final Flourish. But did you know both of those are also identical to Leviathan? Right down to the charge damage.
--Cold Iron has a bit more damage than Flamberge and Rigadoon, but their charges are identical again.
--Sudaruska, Triglav and Warmaster Rocket Hammer all share damage values. So stop comparing WMH to Divine Avenger, already.
--Valiance shots have the same damage as Wild Hunting Blade and Dread Venom Striker's non-ghost hits.
And that's just swords. There are basically only four distinct guns, in terms of damage values.
--Iron Slug and Callahan's charge share damage with Biohazard. Neutralizer is stronger, and unique.
--Expanded Polaris share damage with Nova and Umbra Driver. We already knew this. Expandid Supernova, however, shares damage with Iron Slug.
--Unexpanded Polaris/Supernova share damage with status alchemers. We already knew that too, but did you know Catalyzer falls into that category, too? Poor Catalyzer.
--Polaris charge shares damage with Nova and Umbra.
--Blitz Needle, Sentetza and Argent Peacemaker share all damage. Regular shots are alike, and each shot from the Blitz charge is as strong as one hit from the Antigua birdies. The shots preceding the bird is just regular shot damage. Don't Antiguas root you in place longer than Blitz?
--Volcanic Pepperbox and Plague Needle share damage with Dark Retribution.
--Electron Vortex share damage with Haze Bombs.
For the heck of it, I also calculated what each gun and bomb would've done before the universal buff. I'm not sure I did it the correct way.
Go science!

The bomb and handgun chart link is broken.

Ah, yes. They were swapped.
Thanks for notifying me, it's been fixed.

For Nitronome, you have a row for "weak" damage. Is there something actually weak to normal damage, or did you just do some sciencey wizardry?

It's Nitro and Dark Briar Barrage. They have identical damage values for neutral.
But yes, actually! For any weapon that only comes in normal damage type, you can simply add 61 to get damage value you'd theoretically get if that weapons was specialised.

Original post updated with wiki pages that are less cluttered with analysis.

Assumin' this is on a Stratum 6 depth or the Tier 3 Guild Training Hall.
Good work, Zeddy. Hmm, if WHB became split Piercing as people suggested, the total combo damage at Max would be 5(169+61)+5(86+61)=1150+735=1885. Interesting.
Now if we applied it to the old Shards...
...dang, defense in this game is weird.

Sorry, it took me a while to bother to open this thread, because I assumed that it was about Scissor Blades. So, anyway...
Thanks for collecting and collating all of these data. I agree that the vulnerability bonus does not seem to be affected by damage bonus. In retrospect, we should have seen this coming. In one of my favorite studies ever, User:Exasperation showed that the vulnerability bonus (at damage bonus+0) seems to be a flat 80 points or so, regardless of how big the hit is. So perhaps the damage algorithm is like this:
(A) Based on the particular attack that's happening (e.g. first stroke of Final Flourish), look up the neutral damage+0 damage number from a hand-tuned table.
(B) Multiply that number by (1.07)^B, where B is the level of damage bonus, from 0 to 6.
(C) If the target resists the damage type, then multiply the damage number by about 0.16. On the other hand, if the target is vulnerable to the damage type, then add about 80 to the damage number.
The result is the final damage number that you see. Disclaimer: The numbers 1.07, 0.16, and 80 are rough numbers, not meant to be taken exactly. Indeed, the fact that we don't have these numbers nailed down is evidence that we still don't perfectly understand the damage algorithm. Step (B) might not be exponential? But I feel that we're getting closer to the algorithm, which is great.

You're bit off. Your problem is you assume neutral damage to be base damage, but I think the truth is in damage against weak targets being base damage. Let's examine DBB again:
Effective: 275, 289, 302, 316, 329, 342, 356
Check the jump between each damage bonus:
356 - 342 = 24
289 - 275 = 24
See that? Damage scales linearly, but not at a neutral level. At neutral damage, the damage scaling seems more logarithmic due to the the defense working linearly. This means that damage bonus makes a bigger difference for neutral damage than weak damage. Here's how I figure the algorithm goes.
(A) An attack has a certain amount of "base damage". I believe this number to be somewhere in the low end. If this was my game, I'd put it somewhere between 0-32. The reason I believe this is because of all the attacks that share damage values. This point is merely speculation though.
(B) Some magic space formula is applied to increase damage with each depth. This scaling is completely linear within each stratum, and even within tiers. The only exception is that the increase is considerably lower for stratum 6 than stratum 5. For proof of this, see the bottom of the google spreadsheet for bombs, where I recorded damage for BAB at every floor.
(C) For each level of damage bonus, add about 5%. Again, this is completely linear. However, for some weapons the proportional bonus is higher. The bonus seems to be relatively higher for weapons with less damage, and this works in favour of split-damage weapons as well as multihit weapons.
(D) If the targets is "neutral" towards the attack, subtract the set amount of defence the monster has towards the damage's type. At level 23, this is 61. Of note against is that this is a bit sketchy at low amounts of damage again. There is variance amongst weapons with low base damage such as Brandish (where each damage segment is low individually), shard bombs and handguns. Sometimes the defence is less but other times, curiously, it's higher. I have yet to make sense of it. Since this defence is mostly linear, however, it works in favour of weapons that hit heavily per attack, as they will suffer much less of a penalty against neutral targets. Split damage weapons, curiously, suffer no ill from it and will only get their defence subtracted once. Hopefully this is not how it works in Lockdown.
If the target is resistant towards the attack, multiply the base damage and the damage bonus by about 16%. The base damage and the damage bonus seems to be rounded up individually. That's more of a gut-feeling than a very close study of it. Grain of salt and all that.
The result is the final damage you see. To find a normal damage weapons "true" damage, you'll need to add neutral defense to it and can find the proportion for damage increase bonus from there.

Donkeyhaute and I have updated the Lancer Knightz sword damage pages with a plot of the damage bonus effect:
* http://wiki.spiralknights.com/Lancer_Knightz_(Guild)/Sword_Damage_(Depth_19)
* http://wiki.spiralknights.com/Lancer_Knightz_(Guild)/Sword_Damage_(Depth_24)
Scroll to the bottom of each page to see a scatterplot with a best-fit line. The fit isn't perfect, but it's pretty good. Some swords deviate from the trend, especially in the middle damage range. With these caveats, the fit suggests that each level of damage bonus increases damage by 5%.
When we get some time, we'll repeat the analysis for guns and bombs. Based on previous discussions, there may be more deviation from the central trend.

Try plotting with weakness damage rather than neutral. I realise this isn't possible for hunting blade, but I guess try adding weakness "bonus" to it.

Those plots include all of the +0, +2, +4, and +6 damage numbers --- vulnerable, neutral, and resistant --- combined. I knew that you'd want those three components teased out, so I plotted them separately ahead of time, but forgot to mention them. Each one plots linearly; here are the slopes at depth 24:
* vulnerable: 1.09706
* neutral: 1.11006
* resistant: 1.11332
* combined: 1.10455
So you can see that vulnerable damage is a little out of synch with neutral and resistant damage, but not by much. And it certainly matches the idea of about 5% increase per damage level. Now we've made plots of handguns and bombs at depths 19 and 24 too (although we don't have all of them, whereas we have all of the swords):
* http://wiki.spiralknights.com/Lancer_Knightz_(Guild)/Handgun_Damage_(Depth_19)
* http://wiki.spiralknights.com/Lancer_Knightz_(Guild)/Handgun_Damage_(Depth_24)
* http://wiki.spiralknights.com/Lancer_Knightz_(Guild)/Bomb_Damage_(Depth_19)
* http://wiki.spiralknights.com/Lancer_Knightz_(Guild)/Bomb_Damage_(Depth_24)
In all six cases, the plots are roughly linear, with slopes between 1.09455 and 1.10455, suggesting somewhere between 4.621% and 5.097% damage increase per level of damage bonus. But we'll keep looking at the data, in case a different view brings out a different pattern.
Edit: After re-reading post #15 more closely, I know see that you are not arguing with the rough idea of 5% per level of damage bonus. I'll run some more tests based on the idea that vulnerable damage is actually the base damage.

you really did all this? there is a huge amount of work. thanks and gz.
P.S.: (silly mode on) in the guns, sentenza is spelled wrong.

I think you guys forgot to add the Winmillion to that list.

Per request, I have added Winmillion to the google docs, along with Heavy Deconstructor. I compared to some other 4* weapons and the results were very interesting.
-The values for the combo are identical to those of Hunting Blade and Vile Striker. Regular hits match, ghost strikes match the projectile and the finisher hits match.
-As you already know, the regular attack of Vile Striker (and therefore Winmillion) match those of Master Blaster.
-The ghost strikes (and winmillion projectile), I've recently found, match those of Blackhawk, Silversix and Strike Needle.
-The finisher strike match up with expanded Radiant Pulsar and Mega Magnus.
-I haven't been able to confirm this quite yet, but I suspect the charge attack of winmillion to have the neutral damage of Virulent Catalyzer and Mega Magnus.
-What I have been able to confirm is that the damage of the charge projectile matches those of status alchemers.
Many thanks to Lizzi for supplying me with 4* damage numbers.
So that's what you've been doing all this time. That's some dedication right there.