Tree of Savior Forum

Skill damage calculations (Pyromancer/Elementalist)

This post will serve as a collection of the information I have determined through testing various skills. Since my character is Pyromancer C2/Elementalist C2, it will focus primarily on magic damage and skills available to those circles, but hopefully other classes can extrapolate from this information and apply it to their own skills.

A lot of this information was originally posted in the replies to Dynemanti’s damage formula post. I obtained my results independently and for the most part they match up with his, but there are some important specifics I found that should be noted. There is going to be a lot of information here, but I want to put everything I have in one place so I can refer to it easily as well as clear up a lot of misinformation going around. I intend to keep this post updated as I do further testing.

Damage calculation

Let’s start with basic magic attack. The formula I ended up with is

MAtk - MDef + MAmpRand + [ElemAtk * ElemMod]... (for each element)

where MAtk and MDef are your Magic Attack and the target’s Magic Defense respectively, MAmpRand is a random value ranging from 0 to Magic Amplification stat, ElemAtk indicates any elemental attack damage stats you may have, and ElemMod is the damage modifier for hitting the target’s element with that attack element.

The key takeaway here is that elemental attack boosts are modified individually. The base damage is elementless magic damage.

With skills though, things get kind of interesting. At first I assumed it would use the same formula and simply add the skill base damage, but experimentation yielded something slightly different. Here’s what I got:

(SkillDmg + MAtk - MDef + MAmpRand + [ElemAtk * ElemMod]...) * SkillElemMod * AttrEnhance

SkillDmg is the skill’s base damage (usually called “Attack” in the tooltip), SkillElemMod is the elemental modifier for the skill’s element, and AttrEnhance is the multiplier from the Enhance skill attributes (the max Lv100 ones that increase damage).

If any of this is confusing, you can read a detailed explanation of how I got to these results in my original comment:

There are a few things going on here that are worth pointing out.

  1. Elemental attack stats are applied to both skills and basic attacks. Each value will have its own elemental modifier applied. For skills, this still happens, and the total damage is then converted to the skill’s element and another modifier is applied for the total.
  2. The Enhance damage attributes are effectively final damage multipliers. This means that these attributes make your Magic Attack more valuable. Since this is one of the few multiplicative scalings available in the game, this makes the Enhance attributes look a lot more attractive than they may have originally.
  3. PENDING TEST: Blessing (and Concentrate for Swordsmen) is additive final damage and applies after multipliers. So bonus attack damage you get from those skills is exactly the stated value and not multiplied by anything.

Note that I have not tested any other bonus damage attribute (such as the Wizard’s bonus damage with targets affected by Sleep or Lethargy). I have not tested where the elemental resistances fit in either.

So, practically speaking, what does all this mean?

Most importantly, damage calculation is per hit, meaning that multi-hit skills will deal this calculated value on each tick of damage. So for classes with a lot of multi-hit skills (Pyromancer!) this makes the Magic Attack stat (and consequently, INT) a lot more valuable than it may seem. For example, Earthquake only hits once, so it scales with your Magic Attack at a 1:1 ratio. However, a Lv10 Fireball deals 10 hits, meaning the total damage scales with your Magic Attack at a 10:1 ratio. Of course, this depends on how many of those ticks actually hit your target, but even if only half of them hit a 5:1 ratio is a lot better than 1:1. Keep this in mind before advertising full SPR or CON builds.

There has been a lot of discussion surrounding the Arde Dagger. If you are not aware of this item, it is a Lv75 dagger that gives Fire Attack +153. The importance of this number is that you gain this damage on basic attacks as well as each hit of each skill, not just Fire skills and not just basic attacks. (Some skills may be different due to unique damage calculations. More info on this later.) THIS IS NOT A BUG. It is, however, an extremely efficient item for its level that basically makes one-handed rods completely superior to two-handed staffs simply by virtue of allowing you to equip the dagger. The Fire Attack bonus might be nerfed (or they may change the damage formula entirely) but it is not a “bugged item”.

Skill-specific notes

Energy Bolt (Wizard C1) / Ice Bolt (Cryomancer C1)
See Dynemanti’s post linked at the top of this post. In summary, the damage is added up as one hit and then randomly divided into two hits. So, Blessing will be applied twice, but the total damage will scale as though it were one hit.

Charging appears to simply correspond to the skill levels (e.g. charging to Lv1 casts it as a Lv1 skill). See this comment chain:

I was initially surprised that Cartar Stroke could charge all the way to Lv15 since all my charge skills only go up to Lv5, but I realized that I’ve only ranked those skills to Lv5 in the first place, so it makes sense.

Additionally, these skills have a built-in 1.5 damage multiplier, so the formula looks something like

(SkillDmg + MAtk - MDef + MAmpRand + [ElemAtk * ElemMod]...) * (1.5 + SkillElemMod) * AttrEnhance

Energy Bolt has no skill element, but in the case of Ice Bolt the element multiplier stacks additively with the skill’s built-in multiplier. For more information about skill multipliers, check out the link at the bottom of the post.

Enchant Fire (Pyromancer C1) / Sacrament (Priest C2)
Enchant Fire is a very underrated Pyromancer skill. It does two different things that the skill description completely fails to explain.

The first is that it adds +X Fire Attack. This is fairly straightforward, and like any other elemental attack stat it is added to both basic attacks and skills.

The second and more interesting one is that it adds a second hit to your basic attacks. Skills do not trigger it. This hit has some unique properties. The damage is calculated as follows:

(EnchantFireValue + [ElemAtk * ElemMod]...) * FireElemMod

The extra hit procs on both physical and magical basic attacks, but the damage itself is neither physical nor magical. Consequently, enemy Defense or Magic Defense is not applied to this hit, effectively making it true damage. The flip side is that your Physical Attack, Magic Attack, and Magic Amplification are not applied either. However, elemental attack stats are applied (Arde Dagger!). Final bonus damage (Blessing, Concentrate) is applied as well. Pyromancers will be throwing out a lot of basic attacks while waiting for cooldowns, so this actually adds quite a bit to your damage output.

Sacrament works the exact same way similarly except with the Holy element. Try stacking Blessing, Sacrament, and Enchant Fire on a Swordsman with Concentrate. It’s pretty bonkers.

Update: For some reason, it seems that Sacrament does not give you +X Holy Attack. The tooltip reads exactly the same as Enchant Fire so I’m not sure if this is a bug, but it does definitely give you the extra attack that has the Holy element.

As an additional note, if you want to test the stacking of Enchant Fire and Sacrament, don’t do it on Kepas or Hanamings. For whatever reason, the third hit does not proc. I have no idea why. Also, there’s some weird number voodoo that makes the value vary by 1-2 points. Again, I have no idea why.

Electrocute (Elementalist C1)
This skill is a total headache. We’ll start with the number of hits. If you only hit one target, it will hit 4 times. Each extra target hit by the spell causes all previous targets to take one extra hit. So, hitting 3 targets would cause the first target to take 6 hits, second to take 5, and the third to take 4. With 7 targets, it’s 10, 9, 8, 7, 6, 5, 4.

The damage has a hidden 0.8 multiplier that happens before defense is subtracted. After that, the rest is calculated as normal. However, each target hit after the first suffers an additional damage penalty. I have no idea how this penalty works, but the damage dealt definitely decreases with each extra target.

Basically, the takeaway here is it is best to hit as many targets with Electrocute as possible because each extra target that it jumps to will cause extra damage to all previous targets.

Meteor (Elementalist C2)
A charge move like Energy Bolt, it only has a single hit but has a 4.0 multiplier instead of 1.5. Unlike Ice Bolt, however, this 4.0 stacks multiplicatively with the element multiplier. That means if you hit an Ice monster you get a whopping 6.0 total multiplier before attribute enhancement. See all those 22k damage values in the monster damage rankings? Probably all Elementalists.

The interaction of different multipliers for skills like Energy/Ice Bolt and Meteor is a bit convoluted. Another post does a good job of explaining how they stack, so I won’t go into it.

This post explains where other kinds of modifiers fit in, as well as lists a bunch of skills with built-in damage modifiers. Crit damage is in there too! Check it out for more information.

I will be updating my post as I test more stuff out. Feel free to test it with your own skills! Always make sure you have no Magic Amplification when testing. Easiest thing to do is to test with no equipment and turn off all attributes that you can.


The same with all other classes, archer and swordman with Str. Except Clerics, which each Spell states if they are affected by int and how exactly.

For the Cleric skills that mention INT, your INT is added to the base skill value in addition to everything else. In other words, those skills scale doubly well with INT as other skills.

Yup this is why with max int at at lvl 600, cure hits harder than any wizard/cleric spell except for druids nuke.

there was a bit of an error with your enchant fire description. it does get affected by element weakness/resistance. element weak enemies take double iirc and resistance either halves it or reduces it to 1 I think? it certainly can be mitigated but it doesnt change like other types of damage. this does not affect the other components (blessing/sacrament) applied to it

Yes, it is treated as a Fire attack, hence the * FireElemMod multiplier. I said that the defense stat was ignored, but the element is applied as normal.

Updated references and Sacrament info, and added Meteor info.

does lightning attack / poison attack in some armors works like arde dagger fire attack?

also did i get the INT right. lets say i have 153 int vs 0 int
would that add as 153 final dmg on every series of hits of our skills such as electrocute ? like 153 arde dagger fire atck?

and btw by any chance could you explain how Magic Penetration / Magic Hit rate works?

sorry im very noob at these things. thank you for explaining the elementalist skill formula i was completely bought out by the full con/spr build w/o a second thought after 9/10 threads ive read about INT

Yes, every elemental attack stat works the same.

It’s not final damage, but yes, it is added on every hit. 100 INT = 100 MAtk = 100 more damage before (most) multipliers. There are differences between Magic Attack and Fire Attack, but they’re close enough.

Magic Penetration and Magic Hit Rate are old names for Magic Amplification, which adds a random value to the base damage ranging from 0 to the Magic Amplification stat. So 100 Magic Amp means that each hit will get from 0-100 extra base damage.

I feel sorry about digging an old post. But I cannot stop myself to find out the math of dmg electrocute to frozen enemies.

According to your post, there is a hidden 0.8 multiplier. Is that caused the math like this?

[(SkillAtk + SkillAtkBonus + Matk)x0.8 - MDef]x(Modifier)x(Attribute)

There is a +1.0 Matk, while this lv2, in the Math. But I don’t know where to place in the Math!! May I have your kindly reply?? /_\

In fact, I found an old experiment result from youtube.

And the result from this experiment is 4062 dmg on those Lepusbunny. But I failed. I think I missed something. So, I come here and look for help. Please /_~~

Here the status, He/She posted
Matk = 1095,
15lv Electrocute, Attribute Enhance 20%
Electrocute Another Attribute 2/2 : Deals Additional Damage 100% On Frozen enemies
Rain : Lightning Property Additional Damage 35%
200% on Lepusbunny(Ice elements)

by these calculations:
Zaibas (Krivis lightining atack skill) at level 15 with a full int character (577 int, 279 invested) will be hitting 19 times for {[(356+int)+Matk]-Mdef}xAtribute???
for christ sake! its 57.380 points of damage without consideration for Mdef, AND EQUIPS… its just…absurd!

with full attribute, INT will be calculated 4 times per hit… its 76 times in all the hits…1 INt = 76 damage!