Spiral Knights - Weapon Damage (Howlitzer Heads + Lost Souls)

Weapon Damage (Howlitzer Heads + Lost Souls)

30 replies [Last post]

Mon, 02/24/2014 - 07:54

Skepticraven

Early data (starting on the D9 sheet)
0*
Proto Sword
Proto Gun
Proto Bomb
Hatchet
1*
Heavy Hatchet
Bolted Blade
2*
Flourish
3*
Rigadoon
Grim Buster
4*
Barrier Cannon
5*
Lionheart Honor Blade
Iron Slug
WRH
Supernova

I've been working a bit more on figuring out armor and noticed that I can get close but often ran into rounding problems that did not make sense.
I then decided to guess that the actual damage numbers we read are rounded as the last step (after armor is applied).
I started to test this and something interesting happened...

I narrowed AP's first shot damage for depth 9 to be between 60.001 and 60.095.
Why is this significant? It does not envelop an integer. It has to be calculated off other things (including depth, tier, a general damage unit).
Also, the damage reduced from armor is calculated while this number is still not an integer. The rounding occurs after all the calculations.

This is only measuring pure damage with increments of +1 damage increase and +20% damage boost (pickup) against D9 dark souls (using an alt for D9 danger mission).
The only assumptions are that the damage increase is a 4% multiple from the base damage, and that the boost pickup is 20%.

My current working damage calculation functions as such:
D = roundup(B*(1+0.04*A)*(1+0.20*P)*(1+0.10*F))

B = Narrowed Base Damage
P = 20% Boost active (0 or 1)
A = Damage increase level (+0 to +6)
D = Resulting pure damage
F = 10% Drakon Frenzied Firestorm Boost (0 or 1)

Damage is calculated from a variety of possible operations, but the order is known.
"The Unit" → Weapon attack specific, Heat, Depth Multipliers → Equipment Reduction → Boost Multipliers → Armor → Roundup

/me needs to reread the research with "the unit" for weapon damage.

Observations
Proto sword's first swing base damage is 20
Proto bomb's blast base damage is 21.5
Hatchet first swing's base damage is 23
S1 depth multiplier is 5/24 for the three above weapons
5* heating curve is estimated with supernova in this post.

List of missions with Howlizters or Lost Souls(by depth)
D1 2-2 Angels from Antiquity
D2 2-2 Angels from Antiquity
D4 3-2 Blades of the Fallen
D9 Rank 4-6 Danger Prestige
D11 5-1 Work For Idle Hands
D14 6-2 Whipping and Mishandling
D19 Rank 7 Danger Prestige
D24 Rank 8-10 Danger Prestige
D26 9-1 Occurrence at Owlite Keep

Tue, 02/25/2014 - 22:23

Skepticraven

Hrm...

I might be onto something here.
Yes it is messy, but I highlighted where you should look (predict, predict 2)

Currently, the base damage for the WRH first swing is either 56.2-56.7 if D1 is holds the base damage...
Or 49.5-50 if D0 holds the base damage.

I can play around with the numbers a bit to try and make them fit the model (we depends on 2 things, a base damage and an increase per depth).
Interestingly enough, I should be able to isolate the increase per depth by using a second damage value.
So I got to work on using the pure damage values for WRH's dash. It seems like both models reject the D7 value (so it is probably an incorrect value or something interesting is happening).

If I narrow the ranges even more, it may be interesting to see if there is a pattern different for each stratum.
I do know from my shield HP values, T3 acts very different for S5/S6.

Edit: Since this post, the new data for D7 shows that is is near impossible to model T1 using the current guess.
The has only a base damage and a multiplier. An alternative that has not been tested yet is base, multiplier, added constant.

Tue, 02/25/2014 - 21:28

Bopp

rounding afterward

It's unsurprising that rounding happens after all of the calculations. In fact, I wouldn't be surprised if health is just floating point always, but the user interface just shows us the nearest integer.

As for the actual content of your study, I will have to wait until I have a better Internet connection to check it out. Anyway, cheers and good luck.

Wed, 02/26/2014 - 09:14

Skepticraven

@Bopp

I'm fairly sure with my D1 respawning blocks that health is not a floating point number.
Those blocks deal 1 damage no matter what you are wearing, be it lvl 1 proto gear to fully heated ancient plate (I havent tried with UVs).

I also realized this morning that I was going about this wrong (and not used info I knew from my shield HP values).
Tiers don't act number wise as we think. The best way to identify where they change is by using 0*, 1*, 2* and so on.
I just grabbed a proto gun and chilling duelist to see how their damage compares. Proto gun stops gaining damage around D2. CD around 4 or 5 (need to find more howlitzers).

Thu, 03/06/2014 - 13:05

Skepticraven

Update...

I have reason to believe...

Proto Sword deals...
D1 = 30 damage
D2 = 36.25
D3 = 42.5
0* items stop gaining damage after D3 (stratum 1).
D4 = 42.5

The only problem is that 6.25 is not a clean percentage of 30.
It is, however, 5/24. Could this be our multiplier for S1? Or is there a separate value for damage increasing?
The really interesting part is that this 5/24 matches the shield HP increase I've measured over here in this thread and the proto bomb damage (but not scaled down 5* weps, or guns).

Thu, 03/06/2014 - 13:13

Epic-Gear-Knight

if DMG > DEF:
modifier = 1/2 - (DMG - DEF)/(2*DMG)

if DEF > DMG:
modifier = 1/2 + 0.19 * log((DEF - DMG)/15 + 1)

final damage = DMG * (1 - mod)

when DMG > DEF, the expression simplifies to DMG - DEF/2.

note: DMG includes damage bonus modifiers before performing this calculation

Thu, 03/06/2014 - 13:40

Skepticraven

@Gear-Storm

Within your equations, I'm finding DMG as it changes per depth before armor is applied (howlitzer heads and lost souls).

Those equations fit a cursory look over the data that I have both pure damage (unarmored) and armored (estimating the monster armor).
Once I narrow down the equations a bit more for unarmored damage, I'll be tackling the next aspect of the equation: armor.

Tue, 03/25/2014 - 07:44

Skepticraven

↓

Ok, so since the proto gun wasn't really making sense at lvl 10 (since it was already a non-integer), I decided to get the heating curve for the proto sword (and the gun afterwards).

I've added a new link to the proto sword sheets in the first post.

Some things I would like to note are:
Drakon firestorm adds 10% damage bonus and can stack with pickup/armor bonuses [max base bonus is (1+.04*6)*1.2*1.1=1.6368 multiplier]
Item level affects damage before multipliers.

Wed, 05/07/2014 - 11:50

Skepticraven

↓

I haven't posted this information yet, because I wanted to double-check with a second point of data (along with plenty I don't know yet).

There is a raw damage cap for items being used on a lower depth than their star count. This cap is applied after raw damage is calculated (heating is calculated before).

This creates an interesting phenomena where a 5* item in stratum 4 will deal the same damage whether level 1 heated or level 10 heated.
This is likely similar to the equipment reductions seen directly with health on armor and helmets.

Sun, 06/01/2014 - 06:58

Skepticraven

↓

I have now amassed enough information to adequately conclude that normal armor on D1 is in fact 10. This will make D1 damage values above 20 raw damage significantly easier to obtain (don't need unarmored if the damage shown is greater than 11).

D2 on the other hand is somewhere between 13 and 14. Unfortunately, 10*5/24 (the current magic number that I've found) is 2.083. This means that there is likely another fractional depth multiplier for armor (and possibly other uses). Have there been any monster armor buffs in the history of SK? (similar to the gun/bomb buff).

Sun, 06/01/2014 - 07:53

#10

Bopp

you want before-and-after data?

Why do you want to know about monster armor buffs? You want before-and-after data, to determine the amount of the buff, in the hopes that it reveals something about the mechanics of defense?

Just a month or so before SK launched, many of the monster defense that we take for granted (for example, slimes are vulnerable to shadow) were finally set. But you might not be able to find data from before then.

Sun, 06/01/2014 - 12:16

#11

Skepticraven

↓

I doubt I will find that type of data. I'm more interested in how many, if any, changed with monster armor existed. [Is it as easy as shield's 2*5/24, or are there more multipliers in there?]

Knowing the history of the gun+bomb buff allowed me to identify the progression for them with less models to test from. Proto gun makes a bit more sense with the 10% buff knowledge. Not complete sense yet, but perhaps someday.

Sun, 06/01/2014 - 18:44

#12

Bopp

was hoping

I was hoping that you could get old damage numbers by scouring the histories of the wiki pages. But for example Divine Avenger didn't get a damage table until May 2011. It's not looking good.

Tue, 07/08/2014 - 06:14

#13

Skepticraven

↓

Interesting observation I just made:

When a knight is poisoned, the poison affects the raw damage number (as all other buff modifiers currently function). This was observed by seeing a deathmarked damage value then poisoning one's self (with a poison hazard) then observing the next attack (while still deathmarked).

Specifically the mission "The Rotting Metropolis" will be an excellent place to observe both poison mechanics (hazard has weak, boss has strong) as well as monsters with "buffed" armor (final zombies have it 100% of the time, D22).

Tue, 07/08/2014 - 11:54

#14

Zeddy

I could've told you about how poison works.

In fact, I thought I had. I made a spreadsheet and everything.

Actually, I'd already gathered all the numbers present in this thread. Have I not been sharing them?

Tue, 07/08/2014 - 13:48

#15

Skepticraven

↓

"Actually, I'd already gathered all the numbers present in this thread. Have I not been sharing them?"

I find that comment rather arrogant. Zeddy, please link me to your heating curve of the proto sword with a tenth of a damage worth of precision. Mine is here, the second link in the thread.

I have looked over your data before, and it is more than often extrapolations without much precision. In fact, you often use minimization of error to guess at the "correct" result. This thread is about figuring out the precise numbers - of which I have found 1 so far. 5/24 (proto sword multiplier on raw damage for depth increase in T1).

Now to the poison.
I mentioned where the poison modifier is applied. I am aware you used the same technique here, but is there a problem with having two players confirm the same thing? I was, for the most part, noting that there were multiple poisons present along with multiple armor values.

Also if you have already done everything in this thread, please explain the proto gun's damage-by-depth for level 10. I'm still fairly uncertain about how it funcitons. My current best guess is it uses the 5/24 multiplier as well and during the buff (10% for all guns), the hard cap at D3 was not raised as well. This is still off by about 0.5 for the estimate. (For reference D1 = 19, D2 = 23, D3+ = 24).

With added precision, I can address with uncertainty questions such as these.

Tue, 07/08/2014 - 15:20

#16

Skepticraven

↓

I just took data on the proto bomb. Using the D4 minimized values for a lvl 1 bomb, I was able to accurately extrapolate (down to the 3rd decimal) the damage values for lvl 10 (which were used to check). 5/24 appears to be the same multiplier for depth, and the heat curve for the difference between lvl 1 and 10 are identical.

In fact, a level 4 proto sword's first swing is identical to a level 1 proto bomb blast. If anyone wishes to check the rest of the heat curve for the proto bomb, feel free (link added in the first post).

Wed, 07/09/2014 - 09:29

#17

Zeddy

Oh, right. Links. I was looking at the numbers in the thread itself. That's certainly in-depth.

Sorry about derps.

Are you sure that 5/24 number is all that precise? It seems odd for it to only apply to a single weapon.

Thu, 07/10/2014 - 17:25

#18

Skepticraven

↓

That 5/24 is the same for both proto sword and proto bomb. Two isn't all that much better of an argument, but it appears that depth modifiers are fractions.

There is also some strange capping/reductions which is why this 5/24 value seems to only directly apply to 0* weapons in S1 (and likely, but not tested yet 1* weapons in S2).

Edit:
Hatchet (0*) uses 5/24 as well.
Heavy Hatchet's (1*) lvl 1 uses 4/23 (or some other fraction close to 0.174).

Edit2:
Thinking out loud with respect to Zeddy "precise" comment...

It really isn't as precise as I would like it to be. It is still minimizing errors and at some point we kind of just have to guess. I'm essentially plotting a couple minimized datapoints (for highest and lowest variation of values on different depths), then attempting to find an equation that fits them. With the heavy hatchet lvl 1 data, I got a linear curve through least squares to have an R^2 value of about 0.999955 (1 = identical match) saying that the base damage was 25.325 with a depth modifier of 0.1741(and a lot more decimal points). That doesn't discount that there exists a small range of values that will provide a correct estimate of the values.

I don't know that 5/24 or 4/23 are the depth multipliers, but they are pretty darn close. In fact values outside of +/- 0.5% will not work. Maybe if I search through all the weapons I could minimize this down to +/- 0.1%. I probably will have to achieve a resolution of +/- 0.01% to adequately model 5* weapons. This tolerance works well for for 0* and 1* weapons, though (because none of them exceed 100 damage through maximum boosting). [Please correct me if I'm wrong with this logic.]

Fri, 08/08/2014 - 00:11

#19

Deleted-Knight

If I may necro...

Gear-Storm's post encouraged me to do a little...code-exploring. I hope the Devs understand there was no malicious intent.

Interpreting Equipment Tooltip Bar
Each bar starts with a mini-icon (sword, shield, houglass, status symbol). The actual bar begins at the exact center of the icon. The max length is 164 pixels.
Armor: bar length = floor[value*(3/8)] + 14
Weapon: bar length = floor[value*(5/12)] + 14
Wep Speed: bar length = value*15 + 14
Status: bar length = |value| + 8

The respective "values" may very well be the base stats, or at least some codified form for the base stats. Unfortunately the floor function adds some uncertainty so the actual value will be 0-2 units above the value you get by inverting the formula. The 164 cap on the bar length also makes some 5* equipment ambiguous.
The speed bars give integer values between 1 and 10. The status values are 10, 20, 30, 40.

Buffs
Damage, CTR -> 0.08
Speed (ASI?) -> 0.04
Health -> 40 (I think that's already known)
Tag(Duration?) -> 0.1

I suspect damage buffs are applied to only half the base power. This makes it appear as if the increase is 4%.

Damage Scaling by Depths
Linear interpolation is applied as the depth increases between a minimum and maximum float value. Most likely the min/max values is some multiple of the weapon's base power. The scaling between tiers may be quadratic, with a separate min/max for each tier. I think scaling is applied before bonuses.
^This means it will be rather difficult for anyone to "guess" the depth scaling. We will need to get recon-ranger deathmark damage from the lowest and highest depth of each tier for a lot of different weapons.

Fri, 08/08/2014 - 02:45

#20

Sir-Pandabear

This is interesting.

"I suspect damage buffs are applied to only half the base power. This makes it appear as if the increase is 4%."

This might actually explain a lot. Could it be that only one part of split damage swords get buffed? There are most certainly ways to determine this.

Fri, 08/08/2014 - 18:04

#21

Skepticraven

↓

@Auto-Target

This means it will be rather difficult for anyone to "guess" the depth scaling. We will need to get recon-ranger deathmark damage from the lowest and highest depth of each tier for a lot of different weapons.
Yes, I'm gathering tons of data, but it appears the more I do it... the less data I have to take. Thus far, the depth scaling and heating curve appears the same for all weapons of the same star count.

@Zeddy

I'll hopefully have a definite answer once I get to 4/5* weps and split damage.

Fri, 08/29/2014 - 00:36

#22

Sir-Pandabear

@Gear-Storm

This is, like, way late.

But thank you.

I can finally rest.

Fri, 08/29/2014 - 04:32

#23

Bopp

does they fit the data?

I'm not sure how Gear-Storm got those equations. What is the current state of checking that the equations fit the data? Do they fit exactly (up to rounding)?

Sat, 08/30/2014 - 04:06

#24

Zeddy

I will perfom a thorough investigation.

@Skepticraven, do you know whether damage numbers ultimately round up or down?

Sat, 08/30/2014 - 05:39

#25

Skepticraven

↓

@Zeddy

My testing suggests damage gets rounded up. The rounding occurs as the last step (Raw → Heat/Depth/Boost Modifiers → Armor → Rounding).

Reasoning: Assuming the damage is not hardcoded, respawning ghost and crystal blocks deal 1 normal damage no matter what you wear (full ancient plate or dragon scale). Resapawning indestructible blocks deal 50 normal damage reduced by armor.

Sat, 08/30/2014 - 14:42

#26

Zeddy

I ran a check for every damage number for every non-split weapon on on depth 24 with raw damage below 270, and it checks out for that particular selection, at least.

Here's the code I used to check it with.

That big array there is grouped in 4s; going raw, weak, neutral, resisted; but that should be fairly evident from the code itself.

Sun, 02/01/2015 - 09:43

#27

Skepticraven

↓

Started doing heating curve for supernova S6.
Also, got a bunch of armor values for lvl 10 iron slug S6.

Fri, 02/06/2015 - 21:42

#28

Skepticraven

↓

Just finished the 5* heating curve for supernova.

You can see the estimated base multipliers on the summary sheet.

lvl2 = +0.01*base
lvl3 = +0.015
lvl4 = +0.015
lvl5 = +0.025
lvl6 = +0.035
lvl7 = +0.035
lvl8 = +0.035
lvl9 = +0.04
lvl10 = +0.04
Total of +0.25

That means that for base damage... lvl 10 5* weapons are 25% stronger than a lvl 1 5* weapon (or lvl 1 is 20% weaker than lvl 10)

Also, all damage for this supernova heating curve have been minimized to a maximum error of less than 0.083. The best datapoint was level 4 at a range of 0.0198.
With fairly good certainty, I am concluding that Supernova's expanded attack deals 210.645 raw base damage on depth 24.

Additionally, as noted with the lvl 1 and lvl 10 D4 damage values... there is no 25% damage increase. This confirms earlier data that depth damage reduction occurs independent of the heating multiplier.

Fri, 02/27/2015 - 16:23

#29

Skepticraven

↓

With my arsenal full of 10 different proto swords, I decided to try and start tackling the armor issue [using poison].

D1 range suggests that poison low reduces neutral damage 15.44 and 15.2% [Zeddy has 15.25% listed]. I'm going to assume Zeddy is correct to test even more armor values in the D13.

Earlier in this thread, equations without data were presented.

D13 was the first depth that I used that would be outside the linear range.
With proto swords, it is extremely outside the linear range [<41 damage going up against 55+ armor].

Adding on a roundup after final damage is calculated, I am currently estimating a moderate armor of 114.9807-115.0155 for D13 GH training [Interpolating from wiki chart, it should be between 106 and 121... since the equation used is 2x the wiki's values].

Currently, the two limiting datapoints are ProtoSwordLvl8+1 and ProtoSwordLvl9+3DrakPois. As of the time of this post, I have less than half the possible datapoints I can take, and may get further reduction of range or even possibly disproving the equation [Or Zeddy's poison... one of the two].

Edit:
D23 Proto sword values are up.
244.9991-245.3793 resulting neutral armor range, if we can trust Gear-Storm's equations.

TLDR:
Since I'm happy with the heating curve for 5*, I'm working on finding enemy defense values.
Lots of new datapoints, and Gear-Storm's equations are currently holding up.

Fri, 07/28/2017 - 03:32

#30

Skepticraven

↑↑↓↓←→←→ba

I know this is an odd revival of this thread, but recent tinkering has shown that the maximum boost one can get for certain weapons is not what it was previously thought.

For weapons with delayed attacks, it is possible to stack weapon damage pickup and maskeraith cloak boost.
This works primarily well for long delayed attacks, such as shard bombs, DR, and tortoguns. The strategy is as follows:
Find pickup, use charge attack, immediately activate shield, don't attack to break shield.

Alternatively, you can break the shield and find a boost pickup immediately after for an additional increase (since breaking shield removes all currently active boosts and replaces with just 2).

Although I haven't checked extensively, they do appear to be multiplicative with each other (as all other boost are).
This changes my initial equations to the following:
D = roundup(B*(1+0.04*A)*(1+0.20*P_p)*(1+0.20*P_m)*(1+0.10*F))

B = Narrowed Base Damage
P_p = 20% Pickup Boost active (0 or 1)
P_m = 20% Maskeraith Boost active (0 or 1)
A = Damage increase level (+0 to +6)
D = Resulting pure damage
F = 10% Drakon Frenzied Firestorm Boost (0 or 1)

This results in a maximum possible damage boost multiplier of 1.96416.
Previous maximum was thought to be 1.6368.
That being said, solo players can only achieve 1.7856 (because the 1.96416 requires 2 sprite skills simultaneously active).

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Weapon Damage (Howlitzer Heads + Lost Souls)