Table of Contents
- The Basics
- Aspects of WoW Math
last updated: 3/11/11
When many people look at wow math they either try and skip over it as fast as possible because they have no idea what it means, or they simply try and avoid it completely. I believe that this is a problem and this guide is going to attempt to help people not be so afraid of math in WoW.
Yes, my puns are awful, and yes, prolonged exposure to them can cause serious injury and/or death.
Common misconceptions about WoW math:
1. It's very complicated.If you can add, subtract, multiply, and divide you can do ~98% of the math that occurs in WoW. Just because an equation is long does not mean it is complicated, most long equations are broken down in to what I call “aspects,” which I will be explaining in this guide.
2. You don't need to know math to be good at WoW, so what's the point? While you may not directly need to know the math in order to be good at playing the game, you do need to know the math in order to truly UNDERSTAND the game, which in turn can make you better at the game.
3. Math is hard.It's easy if you know it.
Percentages:In math all percentages are expressed as decimals. for example 47% is written as 0.47 in the equation
If a tooltip says that it increases something by some percent, when you multiply it, you must multiply by the math by 1 plus (+) the percent. For example, if something increases damage by 30%, it would look like 1.3(damage).
If a tooltip says that it decreases something by a percent, when you multiply (*) it, you must multiply (*) the math by 1 minus (-) the percent change. for example if something decreases damage by 30%, it would look like 0.7(damage).
If increasing add(+) to 1 then multiply(*), if decreasing subtract(-) from 1 then multiply(*).
Remember order of operations:
Parenthesis:Always do the math in the inner most parenthesis first, then start working your way out.
Do this fourth(Do this third(Do this second(Do this first)))
for each set of parenthesis, remember to do the math in this order:
Exponents (^) > multiplication (*)/Division (/) > Addition (+) / Subtraction (-)work left to right within each set of parenthesis.
Symbols:Multiplication: x , * , n(math). In the 3rd case multiply the number n by everything inside the parenthesis: ( )
Division: / , ÷
When Dividing (÷):
top(aka numerator) / bottom(aka denominator)
This site helped me out the most when I was learning to understand math in WoW. There are pages that explain pretty much every mechanic in the game.
The tooltips of abilities on wowhead make it really easy to figure out the ability math, just plug the proper numbers in to the variables on your calculator.
Aspects of Math in WoW:
- Rates (_____ per ______)
- Weapon damage
- Spell Power Coefficients
- DIM (damage increase modifiers)
Rates (____ per ____):
What this aspect is:
whenever you compare something over something else, you have a rate. Damage per second, damage taken per second, healing per second, damage per GCD, etc. these are all rates.
What it looks like:
z is a rate, with units of x per y (or xpy, if you make an acronym out of it)
While you won't necessarily find rates (z) inside of equations, the goal of most wow math is to determine some sort of a rate. They are the easiest aspect to start out with, but can become more complex once other aspects are introduced in to finding a given rate.
Time is fat, and checks it's weight on a timescale:
And because time is fat, it's on the bottom of the equation in most cases because it doesn't like to crush its friends.
Most rates involve time in some way shape or form. How you express time is VERY important to the result of your calculations.
Note: When ever I say "on an infinite time scale", that means as time approaches infinity, the DPS of the ability average out to be what ever the answer happens to be.The hardest part of dealing with time that most people have is figuring out how much time to use in your equation.
for all of these examples I will be using DPS equations, though you can apply this to any form of a rate equation.
The Basic Idea:
Damage/ usage= DPSLet's say you have an instant ability that does 1500 damage with no cooldown. If you were to hit that ability every GCD it would do:
Divide how much damage an ability does by how often you use it. (this can be longer than the cooldown if it is not your highest priority ability, so make sure your usage is accurate)
1500/1.5=1000 DPSNow lets say you have an ability with a 4 second cooldown, that does 5000 damage. If you were to hit that ability on cooldown you it would do:
5000/1.5 = 3333.33 DPS FOR THAT GCDNow let's say you have a DoT, that does 1500 damage when applied, and every 1.5 seconds for 9 seconds, for a total of 15000 damage.
5000/4 = 1250 DPS over an infinite time scale
1500/1.5 = 1000 DPS for that GCDnow here's the crazy part. Because that DoT does 15000 damage, you could also say that it does 150000 DPGCD (damage per GCD), which makes it more valuable than the 5000 damage ability with the 4 second cooldown.
15000/9 = 1666.66 DPS on an infinite time scale.
In general ability priority systems are concerned with damage per GCD, and rotations are concerned with DPS on an infinite time scale.
Understanding the weapon damage aspect of wow math is probably the most “complicated” part to understand initially because of the division, but don't worry, that's what I am here for.
What pattern to look for:
((Max wep damage + Min weapon damage)/2)+(attack power/14)x wep speed
The big thing to look for is the /14, this calculation is only done for weapon damage type calculations (barring anomalous equations)
(Average weapon base damage) + (Damage gained from attack power)
What does this aspect mean?
Essentially the goal is to find out how much damage an average hit will do.
In a step by step format:
- find the average weapon base damage → ((Max wep damage + Min weapon damage)/2)
- Find how much DPS is gained from attack power → (attack power/14)
- Multiply (*) DPS gained from attack power by the speed of the weapon → x wep speed
- Add (+) the damage gained from attack power to the average base damage → average weapon base damage + Damage gained from attack power
Some instant attacks will use "normalized" weapon speeds to calculate their damage instead of your weapons actual speed.
Daggers have a normalized speed of 1.7
Other 1 handed weapons have a normalized speed of 2.4
2 handed weapons have a normalized speed of 3.3
Ranged weapons have a normalized speed of 2.8
What does this mean?
this means that when ever you wish to wish to calculate the damage of an ability that uses normalized weapon damage, use the proper normalized speed instead of your weapons actual speed.
How do I know if an attack is normalized?
either you can do a ton of testing, or you can go to Wowwiki.com/Normalization and look at the list of normalized attacks.
Spell Power Coefficients:
When ever you cast a spell, you gain damage or healing from your spell power. Because not all spells have the same cast time, Spell power coefficients make the damage/healing gained from your spell power proportional to the cast time.
How to determine the Coefficient of a Direct cast spell (ex. Shadow Bolt, or Healing Wave)
Coefficient = Base cast time / 3.5For healing spells you need to multiply the equation by 1.88, making it look like this:
Coefficient = (Base cast time / 3.5)*1.88
For instant cast spells, and any spell with a base cast time under 1, the cast time is treated as being 1.5s when calculating the coefficient.
What does the above coefficient mean?
it means that you need to multiply the coefficient you just found by how much spell power, which will give you the amount of damage/healing gained from your spell power.
Coefficient * Spell power= damage/healing gained from spell power.
From there just add that to the base damage/ healing of the spell, and you will have the answer of exactly how much damage/healing that direct cast spell will do.
DoT's & HoT's
The the process is pretty similar, just with a few different numbers.
Damage Coefficient = Base Duration/15
Healing Coefficient = (Base Duration/15)*1.88
Unlike Direct cast spells, there isn't a minimum duration for the calculation, use what ever the base duration is when calculating the coefficient.
If you wish to find the coefficient for each individual tick of a HoT/DoT, then divide the coefficient equation by the total number of ticks.
For example, if a HoT ticked 7 times, the equation would look like this:
Healing Tick Coefficient = ((Base Duration/15)*1.88)/7Channeled Spells
It looks exactly like the Direct Cast spell equation, but instead of cast time, it's the Duration of the channel:
Damage Coefficient = Base Duration / 3.5To determine the Coefficient for each tick, just divide the equation by the number of ticks of the spell.
Healing Coefficient = (Base Duration / 3.5)*1.88
For example, if it's a damage spell that ticks 5 times it would look like this:
Tick Damage Coefficient = (Base Duration / 3.5)/5AoE Spells
the only thing that changes is that you double the amount that you divide the base cast time/duration by.
instead of it being Damage Coefficient = Base Duration / 3.5, it would be
Damage Coefficient = Base Duration or cast time / 7Hybrid Spells
Healing Coefficient = (Base Duration or cast time / 7)*1.88
Hybrid spells deal direct damage, and have a DoT/HoT component as well.
Currently no one has figured out a coefficient equation that works for hybrid healing spells, so just make something up and assume you are wrong, because that's the best that you are going to get.
Someone has however figured out the coefficient equation for Hybrid damage spells. It also happens to fit in the category of the 2% of WoW math that isn't simply add/subtract/multiply/divide. Because I'm a little sadistic, I'm going to include the formula, but I will be nice and white it out so you only have to see it if you want to.
x = Duration / 15
y = Cast Time / 3.5
CDoT = x2 / (x + y)
CDD = y2 / (x + y)
CTotal = CDoT + CD D
Don't freak out at me unless you intend to also purchase my comforting services (info at the end of this guide), I warned you.
If you would like to know more about how spell power works in relation to your spells, I highly suggest you read the page on WoWwiki about it: wowwiki.com/Spell_power
DIM's (damage increase modifier):
These are everywhere. Talents that increase damage by percent values are a great example of DIM's.
What pattern to look for:
x, y, and z in the above example are the DIM's.
What does this aspect mean?
DIM's are things that modify damage by a percentage. These percentages are expressed in decimal form and are multiplied (*) to the base damage of an ability/attack.
In most cases each individual DIM will be between 2 and 0, but if there are more than one DIM, and the person who is posting the math simplified all of the DIM's to be a single number, it could be greater. DIM's will never ever ever be negative, if you see a negative coefficient (a number that is being multiplied by a bunch of things inside parenthesis) something is very wrong.
A DIM that is between 0 and 1 means that it is decreasing the damage of something, and a DIM that is greater than 1 means it is increasing the damage of something, with that something being what ever it is you are trying to calculate.
Offhand damage always has a base DIM of 0.5 (meaning it's damage is reduced by 50%).
DIM's in your DIM's so you can DIM while you DIM:
In general you can just multiply(*) all the DIM's together to simplify the equation, but there are a few DIM's that need to be added (+) together and not multiplied.
A notable occurrence of this is with Shield block value when the talent Shield Mastery, and the ability Shield block are are introduced.
Talent gives +30%
Shield Block gives +100%
Additive = 230% total (not 260% = 130% * 200%)
(Blatantly copy/pasted from Wartotem's post in this thread)
What is it?
If you have something that isn't up all the time such as a proc (I'll get to those, don't worry); when you do the math to account for that thing, you need to know what it's 'up time' is, because this will tell you how big on an effect the thing you are trying to account for has on the rest of your math.
What to look for:
Note that the above equation only works for procs that do not have an ICD (internal cooldown)
a is the chance to proc
b is the number of chances to proc per duration of the buff.
Fury warriors are generally interested in how often flurry is up, so you will commonly see equations floating around fury warrior discussions that look like 1-(1-c)^x where c is your chance to crit, and x is the number of attacks that occur during 3 weapon swings.
Why this is important:
Using flurry up time as an example again; people regularly will think that because flurry lasts for 3 swings, that if you have 33% chance to crit you will have 100% flurry up time, which is completely false. As you get more and more crit, your flurry uptime will approach 100%, but will never actually reach 100% until you have 100% chance to crit.
This aspect is what makes equations look really scary because they can add a lot of length to it, but that doesn't mean it's that complicated.
What Procs do:
Procs are buffs/effects that are not always active.
Because proc's are not active 100% of the time, when someone is doing math that deals with procs, they need to factor in uptimes, which is to calculate the effect of the proc when it is up multiplied(*) by it's % uptime, plus (+) the effect of not having the proc active, multiplied (*) by the % of time it is not up.
What to look for:
These look a lot like DIM's, but look for the 1-y, and repetition of calculations. If you don't see a 1-y but there is repetition, chances are the person posting the math simplified the equation, and if you were to do 1-y it should be the coefficient of the repeated math.
Procs are DIM's that aren't always there.
Crit's work under the same principles as Procs:
%crit(ability crit damage)+((1-%crit)(ability hit damage))
When Procs congregate, they take up a lot of space:
lets say that a proc (a) has an uptime of (c)%, and another proc (b) has an uptime of (d)%. This means there are 4 possible combination's of those two procs: a and b; a; b; not a or b. this means that there will be four repetitions of what ever these things are modifying.
For the sake of not adding any extra length, both a and b will be simple DIM's
Step by step
1) figure out what percent of the time both a and b will be up: multiply (*) the uptime of a,(c) and the uptime of b, (d) together:
c*d2) calculate for both a and b being up with the found uptime
(c*d)(a*b(ability math))3) figure out the uptime that only a will be up take it's base uptime, subtracted (-) by the uptime of both a and b
c-(c*d)4) calculate for only a being up
(c-(c*d))(a(ability math))5) figure out the uptime that only b will be up take it's base uptime, subtracted (-) by the uptime of both a and b
d-(c*d)6) Calculate for only b being up
(d-(c*d))(b(ability math)7) figure out the percentage of time that neither a or b will be up using a similar method to how you found the uptime of both and b together.
(1-c)*(1-d)8) multiply(*) the normal ability damage math by that amount
((1-c)*(1-d))(ability math)9) combine all of the parts with addition (+) signs:
(c*d)(a*b(ability math))+(c-(c*d))(a(ability math))+(d-(c*d))(b(ability math)+((1-c)*(1-d))(ability math)
As you can see procs create a ton of extra length, but that's mostly because it repeats the same things over and over.
I am scared PLZ HALP:
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I understand it! Does this mean I am a WoW math expert?
No. These are just common pieces of many of the equations that you will find when people post WoW math. There are tons of specific formulas for certain abilities or stats. It isn't that scary, and if you are having troubles understanding it go ahead and post the equation in this thread, and describe what about the equation doesn't make sense, and I will do my best to help you understand it.
If you think there is some aspect of wow math I missed, please let me know and I will add it to the guide.