Update; the formula is very likely to be set to this after all;
log10(((Attack / (Defense+ 1)) ^ 0.9 + 1) * Attack
However, a mobs defense is being modified compared to their actual file values as seen on ToSneet; so, since we haven’t solved anything until that formula is found, discussion continues~
From our Patch Notes (May 15th) https://treeofsavior.com/page/news/view.php?n=975 :
(% factor) x attack x log10 ((attack / defense + 1)^0.x + 1) + additional damage
From Developer’s Blog (May 10th) https://treeofsavior.com/page/news/view.php?n=920
(% factor) x attack x log10 ((attack / defense + 1)^0.x + 1) + additional damage
From Combat System Changes Dossier Pt. 3 (May 2nd) https://treeofsavior.com/page/news/view.php?n=955 :
(% increase factor) x attack x min {1, log10 ((attack / (defense + 1))^0.8 + 1)} + (+ increase)
From Combat System Changes Dossier Pt. 1 (April 26th) https://treeofsavior.com/page/news/view.php?n=948 :
(% increase factor) x attack x min {1, log10 ((attack / (defense + 1))^0.8 + 1)} + (+ increase)
I don’t know about you but it doesnt seem like IMC knows what their formula is either.
Just go try it in game, plug your number in the one you posted. It’s wrong.
If you’re lazy and just want me to prove it instead like usually happens in these cases, here:
650 Attack Power
Greentoshell, 805 Defense
The formula you posted :
650 x log10(650 / (805 + 1) + 1)^0.9
= 191.244499
The one from Dossier Pt. 3 :
650 x log10 ((650 / (805 + 1))^0.8 + 1
= 172.423568
The one from patch notes and developer blog, as well as the one in this post :
650 x log10((650 / 805 + 1) ^ 0.x + 1)
= 185
What this thread is : Solve for x in above, and find out how x is determined. Because IMC doesn’t know either.
You’re a better man than me Eternal, I gave up during Ktest.
At least there’s definitely a rule to it. I listed the values from highest to lowest and so far, consistently :
If Attack / Defense ~= 8
then Exponent ~= 1
Unfortunately, it’s not quite as simple as (Attack / Defense) / 8 = 0.x, since else negative values would be impossible. 
I solved your post before you edited numbers.
650 x (log10(((650 / 758 + 1) ^ 0.x + 1))= 146
X=0.582
must be some unknown since this one is -0.629 and way out of expected bounds.
I edited them because that was a Terra Imp, ghost armor, which reduces melee damage. You weren’t going to get an accurate number there regardless. Switched to Greentoshells which are plate.
Also 650 x (log10(((650 / 758 + 1) ^ 0.582 + 1)) = 251.096929
Though because the formula is so disastrous, I do want to know how you arrived at 0.582. It’d be interesting to see other’s thought process on how they read the formula. I read it like a calculator (or google, really just copy paste it in the adress bar on chrome) would.
650 x (log10(((650 / 805 + 1) ^ 0.x + 1))
= 185
For this one x= 0.708 or about 0.71
I’m on my phone at the moment, but I can show you step by step how to solve this formula when I get to my computer and can type out a response in full.
Edit: Getting a negative here
x = (-)0.13
Are you checking for resistance?
Eg if they have hidden SLash/pierce/strike/fire/ice and what not resist.
You’re doing Attack / (Defense + 1)
Let me fill you in on why this isn’t right.
If a monster has 1 less defense than you have attack, that would become (A / (A-1) +1) = 1
In a scenario like that, the log10 would ALWAYS be log10(2).
I did this myself : Went to find a monster with exactly 1 less defense than my attack. If it was Attack / (Defense + 1), then the value would have been log10(2) * Attack.
It wasn’t. Therefore it must be (Attack / Defense) + 1
I have. I found 3 mobs with leather, plate and cloth, all with the exact same Defense value (they were different levels)
I did the same damage on each and every one of them. Therefore there is no armor modifier in play. Weaponless attacks are type-less, aside from being Melee (thus still lowered by Ghost)
Btw. If you want me to seriously double check the math, in need to know if here is a pierce/slash/strike bonus. Make sure there is 0 elemental damage added.
Nope, no bonus. And I’m wearing nothing nor have any buffs, so no elemental damage either. Literally the only damage stat I have is Attack (and Critical Attack I guess)
And it’s not like I’m mad at you for solving for x LOL. I was just wondering how you got those values, that’s all. It was just an example anyway, knowing that specific x doesn’t do much more than give more data for finding how x is created.
Also, I just used the formula you came up with and solved for x. That’s it. I didn’t do anything other than provide a service.
Edit: the fix your parenthesis you have too many on one side
I see you are 8 levels under mobs level. Can you go into the 5 range without increasing your stats and repeat the attack?
I’m curious to see if there is still some damage penalty. Thanks!
It was only a closing one I missed. No effect on the outcome. Thanks though.
Are you on Klai Eternal?
Get a thauma to swell you.
It may be of merit to consider if 0.x is calculated before or after defense reduction.
It’s important, I was assuming you added an extra to the left. Which leaves a lot of guesswork as to where to remove or add one. It’s not as small a detail as you may think.
Fedimian, unfortunately.
Seems to be after: Pommel Beat says it ignores 1% on mobs, but if I only do that and keep the 0.x calculated from a base attack prior to that, the damage doesn’t match. There could be way more at work of course. Never know for sure.
@TheAlleyCats Sure thing, here, with Green Rafflesia, level 223
644 Defense
Dossier Pt. 4
650 x log10(650 / (644 + 1) + 1)^0.9
= 221.736668
Dossier Pt. 3
650 x log10 ((650 / (644 + 1))^0.8 + 1
= 196.542791
Patch Notes / Dev Blog
650 x log10((650 / 644 + 1) ^ 0.x + 1)
= 213
I obtained this [result](https://www.wolframalpha.com/input/?i=plot+650+*+log10((650+%2F+644+%2B+1)+^+x+%2B+1)+%3D+213+x+%3D+0+to+1) with last formula.
Edit:
The first one goes in the [negative range](https://www.wolframalpha.com/input/?i=plot+650+*+log10((650+%2F+805+%2B+1)+^+x+%2B+1)+%3D+185+x+%3D±1+to+1)
Yep, it can indeed go negative. More accurately, the moment I start doing less than 195.xxxx damage (where ^0.x = 0). That’s around 700 defense somewhere if I had to guess, compared to my 650 attack.