Logwheel Testing: Mystery Solved?

[Juli]

Hmm, it seems that the Physical Defense stat also applies to arcane damage (and I'm guessing all other forms of damage). So it is actually a mislabeled "All Defenses" stat. The approximation I use for the effect of Defense is AR * 0.9 - DEF * 0.5. It gets a little more complicated when AR drops below DEF, but while AR > DEF, this has always been accurate for me within a few points of damage. 273 * 0.9 - 224 * 0.5 = 133. Pretty close to the 130 you got.

It's hard to say how much Arcane damage you're dealing in the UTF mode when a 7% damage reduction reduces damage by 1, because there's a lot of room for rounding errors, but assuming no rounding problems, 796P+51A = 617 damage should be a final damage split of ~603 physical, ~14 arcane. To check it against my damage estimation, 796 * 0.9 - 224 * 0.5 = 604.4, while 51 arcane AR goes through a slightly more complicated equation and comes out to ~12.27 estimated damage.

[Magicisoverrated]

So it is actually a mislabeled "All Defenses" stat. The approximation I use for the effect of Defense is AR * 0.9 - DEF * 0.5. It gets a little more complicated when AR drops below DEF, but while AR > DEF, this has always been accurate for me within a few points of damage. 273 * 0.9 - 224 * 0.5 = 133. Pretty close to the 130 you got.

Very good math so far juli, i'm rather impressed as a student as for what i've seen in this thread. But can you clarify the point i put in bold for me? i've been running over the math in this thread for fun just lurking.

[Juli]

Defense reduces damage by 0.5 per point as long as it is equal to or less than the AR of the incoming attack. As defense rises above the AR of an attack, it experiences diminishing returns. So e.g. 200 defense will reduce the damage of an incoming 200 AR attack by 100. However, 300 defense will not reduce damage of an incoming 200 AR attack by 150, since it experiences diminishing returns. Here's an image I made of the formulas I use:



I'm not positive I got the notation for the sigma correct. The elongated form of the lower formula would be:

m = 0.4ax - (0.5^(1 + 1d/(ax)^2) + 0.5^(1 + 2d/(ax)^2) ... + 0.5^(1 + kd/(ax)^2)) where k = d - ax.

[Magicisoverrated]

Defense reduces damage by 0.5 per point as long as it is equal to or less than the AR of the incoming attack. As defense rises above the AR of an attack, it experiences diminishing returns. So e.g. 200 defense will reduce the damage of an incoming 200 AR attack by 100. However, 300 defense will not reduce damage of an incoming 200 AR attack by 150, since it experiences diminishing returns. Here's an image I made of the formulas I use:



I'm not positive I got the notation for the sigma correct. The elongated form of the lower formula would be:

m = 0.4ax - (0.5^(1 + 1d/(ax)^2) + 0.5^(1 + 2d/(ax)^2) ... + 0.5^(1 + kd/(ax)^2)) where k = d - ax.

Woo hoo! i get to use Calculus skills!

okay so in your theoretical situation where 200 AR vs 200 defense i think i'm missing something, so i set it up like this

0
∫ .5^(1+(1*200/200^2)) dx => ..... comes out to x/(2*2^(1/200)) ≈ .4ax - x/2.006
1

could use some help here see if im on the right track or not?

[Juli]

200 AR vs. 200 Defense would use the top formula. You only use the bottom one if AR < DEF. 200 AR vs. 201 Defense would use the bottom one like so:

0.4*200 - 0.5^(1 + 1*201/200^2)
80 - 0.5^(1 + 201/40,000)
80 - 0.5^1.005025
80 - ~0.49826 = ~79.50174

For 200 AR vs. 202 Defense, it would be

0.4*200 - (0.5^(1 + 1*202/200^2) + 0.5^(1 + 2*202/200^2))
80 - (0.5^(1 + 202/40,000) + 0.5^(1 + 404/40,000))
80 - (0.5^(1 + 0.00505) + 0.5^(1 + 0.0101))
80 - (0.5^1.00505 + 0.5^1.0101)
80 - (~0.49825 + ~0.49651) = ~79.00524

etc., assuming x = 1. It is for most R1 attacks, so I'll assume it is unless stated otherwise.

tbh the last time I took a math class was when I was 13, so I know exactly nothing about calculus. I cannot even parse what you wrote because I have no idea what ∫ means.

[Magicisoverrated]

200 AR vs. 200 Defense would use the top formula. You only use the bottom one if AR < DEF. 200 AR vs. 201 Defense would use the bottom one like so:

0.4*200 - 0.5^(1 + 1*201/200^2)
80 - 0.5^(1 + 201/40,000)
80 - 0.5^1.005025
80 - ~0.49826 = ~79.50174

For 200 AR vs. 202 Defense, it would be

0.4*200 - (0.5^(1 + 1*202/200^2) + 0.5^(1 + 2*202/200^2))
80 - (0.5^(1 + 202/40,000) + 0.5^(1 + 404/40,000))
80 - (0.5^(1 + 0.00505) + 0.5^(1 + 0.0101))
80 - (0.5^1.00505 + 0.5^1.0101)
80 - (~0.49825 + ~0.49651) = ~79.00524

etc., assuming x = 1. It is for most R1 attacks, so I'll assume it is unless stated otherwise.

tbh the last time I took a math class was when I was 13, so I know exactly nothing about calculus. I cannot even parse what you wrote because I have no idea what ∫ means.

Top one was exactly what i got in my calculaions

the ∫ is integration which i feel is a lot less work than summation for the exact same result.

[Tsmp]

Defense reduces damage by 0.5 per point as long as it is equal to or less than the AR of the incoming attack. As defense rises above the AR of an attack, it experiences diminishing returns. So e.g. 200 defense will reduce the damage of an incoming 200 AR attack by 100. However, 300 defense will not reduce damage of an incoming 200 AR attack by 150, since it experiences diminishing returns. Here's an image I made of the formulas I use:



I'm not positive I got the notation for the sigma correct. The elongated form of the lower formula would be:

m = 0.4ax - (0.5^(1 + 1d/(ax)^2) + 0.5^(1 + 2d/(ax)^2) ... + 0.5^(1 + kd/(ax)^2)) where k = d - ax.

So in other words... the stat labeled "Physical DEF" is actually just the "fuck split damage weapons" stat.

[Astrichthyes]

Very nice work, gentlemen. It should be noted that any possible difference in calculation, assuming these formulas are correct, is likely due to multiple truncations throughout the calculations (which you don't seem to be doing, but that they may be guilty of) or they have some sort of constant or small adjustment on the end like -3 damage or -0.015def. Given what we see here, I would say that arcane is an all or nothing thing and only becomes worth it when you have it high enough to fight that mitigation. The only way I see a hybrid working on the Logwheel is 50/25+ with 3 nourishing gems at 23.6% and it still may not be enough since the returns from the physical side are so great.

[Juli]

So in other words... the stat labeled "Physical DEF" is actually just the "fuck split damage weapons" stat.

Seems like it. It'd be nice to see some more data in order to be sure that Physical DEF is actually affecting non-physical damage.

@Astrichthyes: the formulas are almost certainly not what the game uses, but they are useful approximations.

[Astrichthyes]

So in other words... the stat labeled "Physical DEF" is actually just the "fuck split damage weapons" stat.

Seems like it. It'd be nice to see some more data in order to be sure that Physical DEF is actually affecting non-physical damage.

@Astrichthyes: the formulas are almost certainly not what the game uses, but they are useful approximations.

I didn't think they were absolutely perfect, but I do think we can make your formulas a little more accurate if we can find a final constant or additional formula at the end of the equation.

So, with 3 top-tier Nourishing gems and 50s/25a, the Logwheel will have 730PhysAR and 120ArcAR in the UTF state. If my original calculations are correct on the TF state, the AR's should be 468P+498A. Multiply that ArcAR by 1.4 for 4 revs and you have your approximate max AR at 468P+697A. The approximate damage in the TF state with all 4 revs against a no-rune naked SL 110 player would be approximately 309 on the physical side and 515 from the arcane side for a 1.0 multiplier attack.

Edit: I think I've figured out why scaling gems have higher damage efficiency than percent gems. Base AR may not be proportionally as powerful as scaling AR, so multiplying it still gives you that same proportional efficiency. Raw AR is currently better than pure scaling AR only due to the sheer amount you gain from multiplying it. If gems were additive, scaling gems could be potentially better than percent, but I believe this would mess with pve balance since you'd essentially be reducing damage output by 20-30% in order to make these gems worth using.

[Astrichthyes]

Just to update, I am making a 20/50 wheel build and I'll be testing how well it fares compared to the pure strength version. I don't expect it to perform as well as the pure physical except with flat arcane gems or multiple revs, but who knows. More testing soon to come!

[Astrichthyes]

In a spur of the moment bout of testing, NPC_invader and i have come up with some rather interesting data regarding the Logarius wheel. The original goal of the testing was to see how much potential Beasthood had for the weapon and to use the data to calculate the AR multiplier in going to the TF state. We also managed to play around with Lead Elixirs a bit and, unfortunately, the only attack the Wheel does that has no recoil against LE is the 1h r2. We also disproved the idea of Vilebloods taking extra damage from church weapons. It simply has no effect. Without further ado, here is the data:

50/10 Logwheel+10 vs NPC_invader SL120, 234 natural def, no armor

W/ 3x 27.2% phys gems
AR: 796P+51A
DMG:
UTF r1: 609
TF r1: 445

W/ 2x 31.5% blunt + 32.6% blunt
AR: 887P+51A
DMG:
UTF r1: 698
TF r1: 500

W/ 2x 31.5% blunt +32.6% blunt, 400+ beasthood
AR: 1508P+51A
DMG:
UTF r1: 1338
TF r1: 934
UTF QS r1: 1025
TF QS r1: 906

First of all, neither of us expected that UTF r1 to almost OHKO NPC_invader. The charged r2 would have outright killed him, possibly despite any armor he put on. More importantly, I got AR to go high enough that mitigation was almost completely negated. Using my AR efficiency formula, I now have the means to calculate the AR multiplier for the physical side of the TF state, though i won't neglect the UTF state:

(Dmg2 - Dmg1)/(AR2 - AR1)
UTF = (1338 - 698)/(1508 - 887) = 1.03
TF = (934 - 500)/(1508 - 887)
= 0.6989803/0.97 = 0.7206/1.03 = 0.699

There you have it! The physical multiplier for the TF state is 0.7 or 70% of the UTF state. Updating the OP for the physical side of things. More to come when i get my hands on good arcane gems for my 50arc Logwheel.

[DidoRumbus]

Hey astri, quick question -- are you saying that wheel damage scales with beasthood? Or is that 1338 R1 after using a pellet and maxing the beast meter?

I swear I'm going to read this whole thread at some point...

[Astrichthyes]

.

Hey astri, quick question -- are you saying that wheel damage scales with beasthood? Or is that 1338 R1 after using a pellet and maxing the beast meter?

I swear I'm going to read this whole thread at some point...

I used a pellet and maxed beasthood for the full 1.7 multiplier on my physAR. The beasthood stat determines how high your beasthood damage multiplier can go and how long it will last. With the full ashen set and 0 insight, you break that max breakpoint by a huge margin and can maintain it with consistent attacks. Getting it that high in PvP is another matter entirely.

[Astrichthyes]

I did some new testing with strength scaling gems on the wheel compared to percent gems. With the exact same AR for both setups, the damage was exactly the same, so scaling gems actually DON'T have higher damage efficiency than percent. They are utterly useless and should either be removed from the game or modified to become useful, the latter of which would require changing the nature of these gems to multiplicative instead of additive OR their values are adjusted to be high enough to compare to the percent gems. I haven't tested the damage in pvp, but i don't expect there to be any change.

On another note, arcane gems are proving to be much more difficult to obtain than is even reasonable, but hopefully the pre-expansion patch that they'll almost certainly release fixes that. I may have to resort to farming Ebrietas and hope for a secondary effect like reduced stamina cost or increased durability so that it does not interfere with my testing. Shouldn't be too hard since she's so weak to bolt, and i happen to have a good setup for with my kirk. I'll begin work on this tonight.

[Astrichthyes]

Alright, i got another round of testing done. This time, i investigated the arcane side of the TF state. The theory here is that i should be able to find a relatively close AR multiplier by using my damage efficiency formula. Tests vs CY axeman NG++ with 20/50 LW+10

Trial with 2x 19.3% nourishing gems
AR: 394P+107A
DMG: 573 TF r1

Trial with 2x 19.3% nourishing + 27.2%ARC
AR: 394P+136A
DMG: 692 TF r1

Calculating the damage efficiency, i get 4.1. Now, if it had been less than 4.0, i would have assumed it was a flat 4. Since it exceeds 4.0, however, it's possible that the AR multiplier is anywhere between 4.1 and 5.

Using Juli's damage formula, for the physical side, my damage is:

0.9(0.7)(PhysAR) - 0.5(70) = 248

That means damage on the arcane side is 692-248 for trial 2, or 443.

0.9(x)(136) - 0.5(67) = 443
x = (443+0.5(67))/(0.9*136)
= 3.9

The values don't line up, but what we do know is that while Juli's formula is close, the damage efficiency formula is closer because it relies on real data values to produce the resulting AR modifier. I don't have perfect arcane gems just yet for further testing, but i should have them soon.

[Astrichthyes]

I have a lot of new info that will be released soon regarding the wheel. Finding the arcane gems for my wheel has been terrible, so I probably won't be doing that round of testing, but i've done much more. Stay tuned!

[Astrichthyes]

The guide is out and it explains everything you ever wanted to know about the wheel! Gems, builds, moveset analysis, recalculated moveset modifiers, the works.

http://fextralife.com/forums/t47964/log ... eel-guide/