Damage Calculation, A Guide (Now With Crits, Too!) I'm confused! How do I compute my damage? HeLP mE PL0X!11:
Easy there, young adventurer. Have a seat and I will tell you the tale of damage and how to calculate it.

First, if you just want a quick and easy way to plug in numbers, check out some calculators others have made.

Second, beware that I will be invoking the Goddess Math. She is kindly to those who respect her, but not all enjoy visiting her temple.


You're boring me! Just tell me how to do it!:
Patience, young one. First we need to define our variables and terms:

Variables

• Base Damage -- This is the damage a weapon or spell gives in its description (e.g. 26 to 40 (neutral) for Razielle or 10 to 18 (water) for Shovel of Judgement at level 5).
• Critical Hit Bonus -- On a critical hit, weapons gain a bonus(e.g. +10 for Fishing Bow or +15 for Fake Ceangal Claw), which boosts the base damage. On a critical hit, the bonus is added to the base damage, making a new base damage. Spells often do more damage on a critical hit, too, but for spells there isn't always a universal additive bonus -- sometimes a different value is added to the high end from the low end. So for spells it's usually easier to just use the listed damage range on a critical hit rather than trying to add a bonus to the regular base damage.
• ''Weapon Skill" -- Each weapon has an associated weapon skill; depending on the level it can boost from 10% to 65% -- only close combat weapons are affected by weapon skills.
• Relevant Stat -- There are 5 elements that are boosted by the 4 main stats: strength boosts neutral and earth damage; intelligence boosts fire; agility boosts air; and chance boosts water. The relevant stat is the one that boosts the damage of a spell or weapon, so the relevant stat for Shovel of Judgement is chance.
• Class Bonus -- All classes have a bonus (though it can be negative or zero) with each type of weapon. Note that this only applies to close combat with weapons, not spells.
• %Damage -- Some items/spells say "Damage increased by x%" or "Multiply damages by x" (e.g. Daudgee or Wheel of Fortune); such effects modify this variable. "Multiply damages by 2" doesn't truly multiply damage by 2, it adds +100% damage. "Multiply damages by 3" adds +200% damage.
• ''Damage" -- Some items/spells say "+ x to damages" (e.g. Ringtree or Bravery Guide); such effects modify this variable.

Terms

• Rounding -- This mathematical term refers to truncating (or cutting off at a digit) somewhere. For our purposes, we'll always round to the nearest integer (e.g. -1, 0, 1, 2, etc.). So if the rounding digit (i.e. the one after the decimal place here) is 5 or higher, the preceding digit is rounded up; if the rounding digit is below 5, the preceding digit is rounded down. E.g. 5.7 rounds to 6, 5.4 rounds to 5, and 5.5 rounds to 6.
• Flooring -- This mathematical term is like rounding, except that you always round down. E.g. 5.7 floors to 5, 5.4 floors to 5, and 5.5 floors to 5. So if you see Floor(x), that just means that whatever value x has

Argh! I get it! I already know this. What's my damage!:
You're cleverer than I thought, not everyone knows these terms. Now that we're all on the same page, we can look at how damage is calculated. As damage from weapons is calculated slightly differently than damage from spells, we'll treat them as two different calculations. First we'll do the easier one: spells.

Damage from Spells

Total_Damage = Floor( base_damage x (1 + (relevant_stat + %damage) / 100) ) + damage

Example

Coins Throwing, level 3. base_damage = 1-4. 230 (+242) chance, so relevant stat = 472. %damage = 7. damage = 14.

So the minimum damage is:

floor( 1 x ( 1 + (472 + 7)/100 ) ) + 14
= floor( 1 + 479/100) + 14
= floor (5.79) + 14 = 5 + 14 = 19

And the maximum damage is:

floor( 4 x ( 1 + (472 + 7)/100 ) ) + 14
= floor( 4 x (1 + 479/100) ) + 14
= floor (4 x5.79) + 14 = 23 + 14 = 37

If Fortune (level 5) is cast and a 60 is rolled, then relevant stat is boosted by 60 (as Fortune boosts chance). If we re-calculate, we find the new minimum is 20 and the new maximum is 39.

As an aside, this is an example of how low base damage spells, like Coins Throwing, are affected very little by your relevant stat and %damage -- a 12.5% boost in relevant_stat/%damage created a 7% increase in total average damage; and a mere +14 +damage accounts for ~50% of the total damage.

Healing spells use the same calculation, with a few differences. Mainly, +damage and damage% are not included in the calculations, but +heals are. Otherwise, the steps are the same, leading to the equation:

Total_Healing = Floor( base_healing x (1 + (relevant_stat) / 100) ) + heals

In this case, the relevant_stat is always Intelligence.

Damage from Weapons

Total_Damage = Floor (Floor( Floor( base_damage x (1 + weapon_skill / 100) ) x (1 + (relevant_stat + %damage) / 100) ) x (1 + class_penalty) ) + damage

Note that base damage is modified by the weapon skill before anything else enters the calculation, and class penalty is applied to the damage as a whole, before the final +damage step.

Example

Fake Ceangal Claw. base_damage = 21-40 (neutral). Sword Skill, level 6. weapon_skill = 35. 300 (+300) strength. relevant_stat = 600. +damage = 40. %damage = 50. class_penalty = -5.

So the minimum damage is:

floor (floor (floor ( 21 x (1 + 35/100) ) x ( 1 + ( 600 + 50 ) / 100 ) x ( 1 - 0.05) ) + 40
= floor (floor (floor ( 21 x 1.35) x 7.5 ) x .95 ) + 40
= floor (floor ( 28 x 7.5 ) x .95 ) + 40
= floor ( 210 x .95 ) + 40
= 199 + 40
= 239

And the maximum damage is:

floor (floor (floor ( 40 x 1.35) x 7.5 ) x .95 ) + 40
= floor (floor ( 54 x 7.5 ) x .95 ) + 40
= floor ( 405 x .95 ) + 40
= 384 + 40
= 424

On a critical hit, the base damage is boosted by 15 from the critical hit bonus. So the minimum on a critical hit is:

floor (floor (floor ( 36 x 1.35) x 7.5 ) x .95 ) + 40
= 382

The maximum damage on a critical hit is:

floor (floor (floor ( 55 x 1.35) x 7.5 ) x .95 ) + 40
= 567

Without Sword Skill, the damage on a regular hit is 189 to 325 and on a critical hit is 296 to 432. This shows the utility of a weapon skill. The higher the base damage, the greater the effect of weapon skill will be.


Thanks, now I can do it myself!:
You're welcome. Go now, and share your knowledge. Use it for good. And return to me, if you have questions. Comments or questions can be addressed here.

Edit: Updated for Version 1.20 changes to Weapon Skills and class weapon bonuses/penalties.

In the interest of keeping the damage-related calculations together, I'm adding this in here.

So how exactly do I calculate the odds of a critical hit? I hear Agility has something to do with it...

Well, you'll have to break out the Scientific Calculator for this one, because it uses more than just percentages and basic arithmetic, and delves into logarithms and trancendental irrational numbers.

The exact equation was finally hashed out here, in the Math with Math topic, which I just copy wholesale for your convenience:

(And, additionally, "ln" is the natural logarithm function)

This post has been edited by [MOD]Raiu: 3 Oct 2009, 10:40

Frist things first; thanks for taking the time to put all this down for everyone to use.

Calculating damage is not as hard as it seems. Just remember that the spell or weapon you use gets a +%damage increase from its corresponding element and add in the +%damage from your gear and buffs, then when that is calculated just add +damage from gear and buffs.

Take a lvl 5 ghostly claw casted by an osa with these stats/buffs:
9-12 damage
100 intellegence
+50% damage pet
+10 damage
Thats comes out to 32-40 with out even having to write everything down, but I will for the sake of the people who cannot do it in their heads.
min = 32 = (9+150%)+10
or
min = 32 = (9*2.5)+10
or
min-dmg = (9*(1+((100int+50)/100))+10 = 32

The wikia's damage calculation is much more versatile because it includes the resistances of the target and can be used for either weapons or spells with out changing anything. If you do not want to go through so much just put the calculation in a spreadsheet or something. Then when ever you need it you can just fill in the characters stats, buffs, and the weapon/spell's min and max dmg.

In my opinion, it is nice to know what your critical hit dmg will be. However I find it silly to rely on critical hits so I do not bother with them UNLESS you have a really high chance of getting them such as 1/2.

This post has been edited by ChaplainAdrian: 18 Dec 2008, 05:02