Tree of Savior Forum

Damage Formula - Simplified

Continuing the discussion from [Damage Guide] The big formula, modifier types, and how they interact!:

The big damage formula thread has this nice big formula, but with so many brackets it took me a while to understand what was multiplying with what. Since I already put work into it, I might as well re-post a more readable formula.

Damage =
((Aggregate Attack - Aggregate Defense) * Crit factor + Critical Attack + Bonus Elemental Attack + Racial Specific Damage) * T1 * T2 * T3 * Attribute factor + Bonus Damage

Aggregate Attack =
(Skill Attack + Attack + Attack Modifier + Magic Amplification) * T0

Aggregate Defense =
(Defense + Defense Modifier) * Level penalty factor) + Elemental Resistance

Magic amplification works as a random % roll multiplied by the magic amp stat. i.e 0~1.0 * magic amp stat

Crit factor is 1.5 if critical hit occurs.

Critical attack is on your character sheet

Bonus elemental Attack is like Arde dagger

Racial Bonus attack vs. beast, plant, mutant etc.

T0 is Base damage modifier.

T1, T2, T3 are damage multipliers that are usually percentage based. e.g. quick cast 50% bonus damage

Attribute factor is your trained attribute level. lvl 50 = 1.50

Bonus damage is like concentrate / blessing


i tried running this formula against lvl 106 cockatrice as a lvl 199 fletcher.

   -crossfire lvl 10 skill dmg 1480, T0 modifier 125%.
   -atk 667-806
   -attribute lvl 27 
   -crit damage and bonuses all negligible and ignored.
   -cockatrice has def of 119
   -cockatrice is an M size target. Damage reduction T3 = 0.75 
   -crossfire is not a pierce skill. T2=1 ignoring leather armor variable.

assuming upgrades dont do anything to mitigate T3 (my bows +6)
and that im only using the first target damage of the arrow, not the xplosion,
and that its a not a critical hit.

    Aggregate Attack   =  1480+(667~806) = 2147~2286
    Aggregate Defense =  119 x 1.0 = 119
    Damage = 2028~2167 * (T1=1) * (T2=1) * (T3=0.75) * (Attribute=1.27)
                 ≈ 1937~2064

Experimental results were more along the lines of 2600~2700.
Needless to say, with crits the difference between theoretical damage is even further from experimental results. There seems to be a defensive modifier that I have not accounted, whether or not its my own oversight or the formula’s veracity is the question.

Keep in mind that, as its a non-crit and buffs were not used, there is no crit dmg, no bonus elemental atk, no racial specific damage, no bonus damage involved in the calculations to keep things simple.

I remember bow and xbow have a special hidden penalty 20% for medium and 40% for large, reduced by 0.2%/0.4% per upgrade level.

So your +6 bow should do only 92% damage on medium targets:
2898~3096 * 0.92 = 2666~2848
Should be nearer your experimental results.

And I believe the formula has been tested a lot and seems pretty much exact.

I read somewhere that they reduced the penalty to 15% for L and 10% for M.

Im not very sure if the damage should be taken as pierce or just missile.

Ah, i’m not up to date then…
Is upgrade level still reducing the penalty?

No idea. That’s why I stated

 -assuming upgrades dont do anything to mitigate T3 (my bows +6)

If you try assuming that T2=1 by taking damage as missile only, and that the penalty truly has been reduced to x0.9, the damage is lower than experimental results.

I think pierce bonus should be displayed when you hit the monster (Pierce +50%), so you may know if you need to use 1 or 1.5 for T2 (maybe)

And I don’t know maybe level penalty factor can add a defense divider if you’re over the level of the monster?

Negative. No pierce appeared. Good point. T2=1 then. Editing now.

Well going to sleep, but if you assume a monster defense 0
and a lowered penalty due to your weapon upgrades -60% of 10% penalty (only 4% penalty)
I think it’s getting closer to the experimental tests you ran.

Playing around with T3 values to match experimental values result in T3=1

      Damage = 2028~2167 * (T1=1) * (T2=1) * (T3=1) * (Attribute=1.27)
             ≈ 2575~2752

Much closer to experimental values. +6 seems to have completely mitigated T3.

Good night. As a last note, with my current bow, either the T3 value is being mitigated from 0.75 to 1.0, or the multiplier was just 0.9 to start with, dropping to approx 1.0.

Just want to ask whether the formula applies to the damage players will take.
So what if a skill like wizard’s “Lethargy” comes into play?
At max lvl 15, Lethargy reduces attack by 48.
Does that mean the aggregate attack is reduced by T0 x 48?
This also translate to reduction of damage by (T0 x 48) x (aggregated multiplier)?

Lethargy damage reduction is likely part of attack modifier:

(Skill Attack + Attack + (Attack Modifier: Lethargy - 48 damage) + Magic Amp) * T0

I haven’t tested this but I believe that’s where it goes.