Tree of Savior Forum

[Guide] Damage formula

Re-posting my work from reddit:
yesterday i spent about 8 hours punching things without a weapon then
attacking them with a weapon, recording my highest and lowest values and
comparing them to my stats and damage via other means i did this on 5
different monsters with different levels from 1-30 this is what i got:

Actual damage = (atk+skill atk+ atk bonuses - def)
if crit multiply by 1.5 and add crit attack value from character sheet
then multiply by element/type mod (slash/stab/hit)
then add “additional damage” things like concentrate or from " bonus attack damage" stats.

the difference between attack and “bonus attack damage” is atk
appears on your sheet and goes in the beginning and gets multiplied,
bonus attack damage just adds onto the final number and is never
multiplied, but i think it also never decreases… i dont have
concentrate to fully test ill get one rank in it i guess and test out
for sure…

this formula works from 1-30 punching if i equip a +2 2handsword and
hit things weak vs slashing though it seems to be off by +/- 1-5% so im
thinking the way i do def isn’t correct, it’s probably not a entirely
flat value maybe? or maybe theres weapon damage modifiers for size? iirc
in RO 2 hand swords did more damage to small? idk that could explain
the variance. either that or weapon attack can range out of its
displayed range… idk its hard to say without knowing exactly how
defense works.


So with some testing Catar Stroke deviates from the normal formula
similar to how energy bolt does. Do all the math then multiply by 1.1.

Also the attribute for catar stroke that deals 50% of your physical
on pushed enemies is EXACTLY that, you do your atk/2 BUT, and here’s the
most interesting part, this damage IGNORES DEFENSE. I hit a level 108
enemy at 36 with 97 attack with catar did 1 damage, knocked it back, and
it took 48 damage. The implications of this def ignoring value are
fairly intrigueing

Concentrate adds FLAT damage on the end that never gets multiplied,
so if you have +5 additional damage do the whole calculation (including
crits) then slap on +5 at the end. Seems fairly pathetic… and if the
monsters def is over your attack it reduces concentrate’s damage as
well. So if your formula adds up to -5 you do “0” damage but in the case
of 0 you always round up to 1 for damage

Thrust’s attribute to add additional hits 5% of the time adds (+12.5% final damage) two hits so essentially 25% damage

End Edit

magic seems to work the same, magic amplfication being similar to
crit atk bonus but random. ranging from 15%~100% the mamp value
so something like:

(matk+skillmatk)-mdef + 15%~100% mamp

this was tested much less so it could potentally be 0%-100%… also
mdef could be at the end and amp could be inside. don’t have a magic
class so i cant be entirely sure, just had someone do about 20 minutes
of data gathering for me and thats what the results appear to show…

there are small margins of error with equipment on the formulas but
they seem to work consistently without weapons. I dunno if def has more
variables or if weapons do.

Edit: new formula 8/8/2015 8:38 pm

Extensively tested wizard’s energy bolt. figured out energy bolt is:

(matk+skillatk-mdef)*1.5 if you add up both hits.

it only APPEARS random cause the damage splits randomly into two
hits. it looks like the first hit is always bigger than the second
unless you lag. out of like 200 casts only 2 appeared in reverse order.
so its probably like 85%(matk+skillatk-def) then 35% for the second hit
with something like 30% randomly split between the two?

There appears to be 0% error in this formula if you make sure to remove all rounding errors at the proper places.

End Edit

If you find these inaccuracies please submit the following:

first step, take off all gear that gives anything other than
defense/evasion. so anything with dex/str/int, physical/magical attack,
physical/magical damage, aoe ratio, crit atk, block penetration, magic
amplification, and maybe even accuracy for good measure. make sure to
check all your armor and accessories.

level and name of monster
attack power without a weapon
crit atk/magic amp with your weapon off
how much damage you deal without a weapon (punch or cast something)
crit damage without a weapon
damage without a weapon with a buff (include buff’s description)
crit damage without a weapon with buff
skill damage without a weapon
same as above but when crit
skill damage without a weapon with a buff (include buff’s description)
same as above but when crit
skill’s damage type (hit/slash/stab/element)
ALL the above info WITH a weapon and include weapon description (attack value, upgrade, bonus stats)
Make sure with a weapon to record damage values for like 30 minutes and submit them formatted like this:

low = 50
high = 100
low crit = 75
high crit = 150

then if you want include all the raw data below that so if you did
1000 attacks just give me all 1000 results, maybe for brevity write down
each value that happens and just the number it happened so above
example again

50 x 2
61 x 4
73 x 10
80 x 20
90 x 10
100 x 7

something like this would allow me to narrow down


I just knew it was a linear damage formula. The damage bonuses from the static +damage buffs were way high, so it had to be simply minus defense rather than defence turning into a percentage reduction. Thanks for doing all the the research for us!

I also had a hunch that Concentrate was flat damage, which is why I maxed it. It works wonders with Stabbing from Hoplite. You say it’s pathetic but it’s actually awesome since it works no matter how much def the enemy has or what type of damage they’re strong against. When you’re hitting rapidly like with Stabbing or Subweapon cancel, it really adds up. I had my Concentrate and 5/5 and +1 Attribute (or was it two?) for 15 damage on each hit. For me, on bosses that is something like 5% to 10% increased damage on Stabbing. Of course the damage increase on Peirce is a bit less since that hits super hard. But anything hitting fast is amazing with Concentrate.

I tested between leather and plate armor, with a difference of 24 physical defence. The hit was 25 max slash dmg on leather and 4 max on plate armor. Additionally I also tested with stab attacks which get 50% bonus vs leather. Attacks from this type did 45 damage while versus plate they still did 1~5 damage.

same goes for magic defence

Also concentrate’s added damage also gets reduced by enemy type of armor additionally it might be increased by critical but I did not check if concentrate adds to the status window’s atk. (damage went from 3 to 9 with lvl 5 conc)

on a side note: if u say things like energy bolt is similar to normal hits but u multiply by 1.1 then I’m doubting if you actually tested yourself. Anyone with mathematical experience knows that they can’t just multiply by 1.1 without a reason.
The edit u later did again relies on the linear nature of defence.or in that case magic defence. My objection is that we do not know enemy magic defence values, thus we can’t make those 0% error speculations.
PS. The nature of your test is too small, you need to extend to multiple enemies both high and low level and of all 4 types (Fluid, Cloth, Leather, Plate).
PPS. organize your post so that u have the currently thought out formula’s on the top and the debunked versions at the bottom, not in between everything.

or you could switch weapons against different enemies when you not using skills and do tripple the damage you are doing now, you are basically gimping yourself using the wrong type with concentrate instead of just using the right type… concentrate also fails cause its a limited number of hits. it really is a waste of skill points. EVEN if you use your spear if you used bash instead you would convert to slash type and do WAY more than concentrate.

Neat stuff.
I also tested around a lot like this and I came to similar results.
However, something I need to add is this:

As magic-user you are much different from a physical attacker in that you do not have a damage range.
Physical damage is set within a min-max due to your weapon, whereas magic-users always hit for a fixed amount based on their Matk+Int.

And each skill has a base value.
The value displayed on your skill description is NOT your skill’s base value.
The damage displayed in your skill is actually: skillbase+INT for magic skills and skillbase+STR for physical skills.

For the use of skills this means that every 1 point in a stat like INT/STR, you deal exactly 2 more damage with skills.
As the formula goes as you say:
((skill base+INT/STR)+Matk/Patk + atk bonuses - def)
So 1 point in Int get’s applied to your skill’s base damage and another point get’s added through having your Matk raised by 1.

Also magic Amplification seems like a weird stat that I don’t quite grasp yet.
When I used spells with 12 Magic Amp. on, my Cure spell which always did 42 damage suddenly varied between 42-54, so I assume that Magic Amp is actually the same as Max.atk. Weird thing is just that you can also increase your Max.atk with the Max.atk stat, even as magic user. I already tested this. So I don’t get what the difference is between the two stats.

sorry you dont seem to understand, not only did I test and test to find this math but then i applied it and correctly predicted other peoples damage 100% accurately

energy bolt has a 1.5X damage modifier slapped on the end you take the damage you would predict using the formula then add 50% more, its that simple. 10 different people tested it and got the EXACT number every time they tested

please READ what i wrote instead of assuming that you know more than me without any evidence.

For def it is VERY easy you punch something, put on a buff punch it again youll notice the buff that adds 20 ATTACK will increase your final damage by 20 and a skill that has a 100 attack power will hit for 100 more than your punch, a skill that hits for 545atk will hit for punch+545 so from gathering this data with 4 different characters on different classes then cross referencing with 10+ other people we can say with ABSOLUTE certainty that 1 defense removes 1 point of damage. Before you get ahead of yourself if you have no weapon on your attack has no low~high range and you always do the same damage. now you can also put on your weapon and attack and youll get punch+weapon low~high then you hit with a skill and youll get punch+weapon low~high + skill atk

this wasnt a guess or an assumption. I TESTED IT! for like 8 hours straight one night and several more over the week. i can direct you to the reddit thread if you wanna see other people posting their values and me breaking it down and being RIGHT! EVERY. SINGLE. TIME.


Uh yes… I know. I carry all damage types. But that isn’t the point. There are times with mixed mobs where you’ll always have a strong enemy or at least a neutral. Making switching for perfect damage impossible.

Furthermore it’s simply extra damage you can apply to anything! Even your spear bash! At 5 it lasts for quite a lot of hits and in my testing, the entire stabbing process only seems to count as 1 hit for Concentrate.

Think of it this way. Concentrate gives Damage Bonus * number of hits extra damage for a little SP and a short cast time. It’s an extremely effeicient skill. It costs little, adds a lot of damage over time, and is the perfect skill to use during a boss fight while avoiding a 360 AoE. It’s simply too good to not use.

Mine was +15 with 11 hits (hits seemed extended by Stabbing) so maybe 20 hits all up. Even with 11 that +150 damage for a tiny amount of SP and, as long as you use it when you can’t attack the boss anyway, no downtime. With 20 or so hits from stabbing’s hits counting as 1 hit, it’s 300 damage. Each attribute upgrade just gives you more and more and more. If you max it out, it has something like 26 possible hits, with a huge bonus to each of them. Perfect for subweapon cancel which is probably the only way to get those 26 hits out. At attribute 0, 2626 = 676 extra damage that you can just layer on top of whatever you’re currently doing, essentially for free. And if for, whatever reason, you have to hit something that is strong against your weapon it helps even more than usual. Add in a ■■■■ ton of attributes, say, 15 (I got Bash to 15 Attributes. So Concentrate should at least go to level 15 attribute) and it’s doing 5626 = 1456 for any class that can get the 26 hits in. What if it can go higher than that? What is the max attribute? If you have 100 attribute then it’s 226*26 = 5876 damage for essentially nothing.

a lot of attributes only go to 5 but i still dont get where you are pulling the number 56 from. also consider that by level 100 you should be hitting for about 2-3k each hit and that additional 15 on a hit wont feel like its worth even casting for.

also consider it never crits, it never gets boosted by anything, it will always be exactly 15 per hit

Sure, it’ll be exactly however much you’ve attributed it upto per hit. But that is why it’s brilliant. Also no def reduction.

Plus even with bash/slash/stab I didn’t have any magic damage (no magic swordsman yet…) and so magic weak mobs were difficult to damage without something like concentrate.

I really think all static +damage skills are being severely overlooked by the community here. They’re great once attributed into.

The 56 number comes from +2 damage per attribute and +26 damage at 15/15. It does +26 damage for 26 hits at 15/15. 15 attributes ads 30 more damage. At attribute 100 it’ll hit for 226 for 26 hits.

but you just said the attribute increased the number of hits not the damage per hit. also its easy to overlook the effect of attributes cause we dont know ■■■■ about them. a lot of them are vague as ■■■■ and even the ones that aren’t are out of date on most sites.

Level increases damage and hits. Attribute gives 2 damage per. At level 5 it’s 11/11 base. At 15 it is 26/26.

I have it at level 5 + 2 attribute = 15/11.

Level 15 with 15 attribute = 56/26

oh but one thing i have to look into next beta is what you said about multi hits. from my damage calculations multi hits count as a single hit. this may be different for “hold to continue” attacks and that intrigues me…

Yeah so Cartar Stroke gives 1 hit from Concentrate. But Stabbing gives 1 hit of concentrate for each stab. But here is the thing. I only have level 5 concentrate so I have 11 hits, yet I found it hard to finish 11 hits quick enough even with stabbing and then hitting a bunch more. That is why I think stabbing only counts as 1 hit despite being so many hits. Still not 100% sure though.

also i dont get what your first paragraph is about? your comparing my outgoing damage on monster to damage taken from monsters? your also not considering that plate takes less from slashing? lemme find that chart…

left to right is cloth leather metal ghost
top to bottom is slash pierce hit ghost
the ghost things have different names but im pretty sure one means ghost and the other is like spirit, just called ghost in translations cause it was an element in RO. anyway disreguarding that you see slash does reduced damage on plate these are the old modifiers of 25% which were boosted to 50% in the newer betas.

catar stroke is only one hit, each of those small hits adds up to the total, the total only adds concentrate once. sorry i got confused there, stabbing is the only one that matters in this case. also i understand what you meant by its max potental but you also have to consider that going swordsman circle 3 to get level 15 is a HUGE investment. every class you are skipping out on is more skills and attributes you are throwing away. so far other than cleric or some wizard builds, i have not seen compelling evidence to ever pick the same class more than maybe once, and even then only cause there is no better choice.

I agree. But I think it might be worth it for a subweapon cancel build.

At 15/15 you get 26 hits of Concentrate and 45 seconds buff duration. You can rebuff after 20 seconds. If you can get 26 hits out in 20 seconds (Subweapon cancel + Aspd buff from Chronomancer?) then you can constantly rebuff Concentrate over and over and use it up just before the CD runs out. Even if you don’t do it that quick, as long as you get 26 attacks in 45 seconds you can use all of the Concentrate up and immediately buff it again.

For subweapon cancel, it can benefit even more because, afaik you need a dagger for subweapon cancel and thus your subweapon attack always does a particular style of damage.

Something like this might work out well:

You only get +19+2*X damage for 19 attacks but you pick up barbarian buffs and then try to subweapon cancel as much as you can for maximum damage. Savagery will buff the dagger attack due to it being stab damage too for extra hits.

maybe if you are relying entirely on double attack, the videos ive seen on builds focusing on it were less than impressive though. everyone else around those levels was doing like 3-4k hits and he was doing like 400-500, granted fast but idk if it was fast enough… well we will see when those classes are reachable, hopefully next beta

also I thought of another counterpoint. we tested this with other skills, bash, thrust, wagon wheel, heal, cure, zaibas, fireball, firewall, earth quake, umbal blow, energy bolt and catar stroke. Energy bolt was the only spell that was off and it was EXACTLY 1.5 off EVERY single time. same with catar and 1.1. These skills are special edge cases from what I can tell. THOUGH there might be more I did not test every skill. Either case the math still is exact every single time. The multipliers don’t make it wrong.

Thing about concentrate and blessing is that it only takes one charge per attack, but still procs off all hits you do.

At first it seems like a pittance, a measly +11 damage for a rank 5 ability? What’s the deal here? But then you get the full cafrisun set and get an extra hit. Suddenly every attack does +11 twice, for one charge per attack. Then you team up with a pyromancer and get the flame enchant, and suddenly you get +11 thrice per attack. Team up with a priest too for the holy enchant and you get four +11 procs per attack. Add blessing on top of that, which then also procs four times… All of a sudden it adds up. And as the guy says, stabbing attack from hoplite, which is like what, 10 hits on a single attack? Proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc proc.