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# Damage Calculation, A Guide (Now With Crits, Too!)

By MathAvenger January 14, 2007, 11:52:30

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, 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 Raziel or 13 to 21 (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 Fake Claw of Ceangal), 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" -- The spell with this name boost the Power value for Weapon attacks only.
• 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, for example, the relevant stat for Shovel of Judgement is Chance. If, for some reason, the relevant stat is a negative number, treat it as zero for the calculation.
• Power-- Some items/spells say "Power" (e.g. Daudgee or Wheel of Fortune); such effects modify this variable. "Multiply damage by 2" doesn't truly multiply damage by 2, it adds +100% damage. "Multiply damage by 3" adds +200% damage. (Spells shouldn't say this anymore, instead listing Power directly, but older guilds may still say this, as well as Power's old name of %damage)
• ''Damage" -- Some items/spells say "+x damage" (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 + Power) / 100) ) + damage

Example

Coins Throwing, level 3. base_damage = 8-10. 230 (+242) chance, so relevant stat = 472. Power = 7%. damage = +14.

So the minimum damage is:

floor( 8 x ( 1 + (472 + 7)/100 ) ) + 14
= floor( 8 x (1 + 479/100) ) + 14
= floor (8 x 5.79) + 14 = 46 + 14 = 60

And the maximum damage is:

floor( 10 x ( 1 + (472 + 7)/100 ) ) + 14
= floor( 10 x (1 + 479/100) ) + 14
= floor (10 x 5.79) + 14 = 57 + 14 = 71

If Fortune (level 5) is cast, then Power is boosted by 200 on the following turn. If we re-calculate for that turn, we find the new minimum is 76 and the new maximum is 91.

As an aside, low base damage spells, like Leek Pie, are affected very little by your relevant stat and Power, and are affected much more by +Damage.

Healing spells use basically the same calculation, with a few differences. Mainly, +damage and Power 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.

Last updated June 2, 2014
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Damage from Weapons

They basically work exactly as spells do. Weapon Skill bonus is treated as a simple Power bonus (albeit one that applies to weapon attacks only). Critical Bonus, as mentioned above, is added directly to the base damage before any other calculations are made (e.g., getting a critical hit on a weapon that does 5-10 base damage and has a +7 Critical Bonus means the base damage is 12-17 on a critical hit). Other than that, the formula is exactly the same.

You're welcome. Go now, and share your knowledge. Use it for good.

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

Mod edit: Updated June 1st, 2014 to match changes in Weapon Skill.

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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:

QUOTE
Agility = a, your player's agility (a is always >= 0)
Basecrit = x, where 1/x is the weapon crit rate
Equipcrit = y, where y is the total +crits on a character, including your order
Finalcrit = 1/z, where z = floor( (x-y) * ( (e * 1.1) / ln(a + 12) ) )

Notes:
If 1/z is a lower (worse) crit rate than 1/x, then the final crit rate is 1/x.
If 1/z is a higher (better) crit rate than 1/2, then the final crit rate is 1/2.
e is the natural number.

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

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