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[Guide] Calculating Damage

warrior math

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#1 Cowmonaut

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Posted 17 October 2012 - 08:35 PM

Introduction

Damage is central to what we Warriors do.  As such, it is important to know how to calculate damage when creating a new build.  Knowing how damage works means you will know how durable or powerful a build is, just from a few numbers.

In this guide I will walk you through how damage is calculated and how to work out the math for yourselves.

Base 80 Stats
Before we get too far, lets take a look at what a naked Level 80 Warrior looks like:

Power: 916

Precision: 916

Toughness: 916

Vitality: 916

Crit Chance: 4%

Armor: 2127

Health: 18372


This information will be important later.


Damage

Generally speaking, there are two types of damage in this came: Direct Damage and Condition Damage.  The differences are pretty straight forward.  Direct Damage is damage done by a Skill or Trait while Condition Damage is damage dealt over time by a Condition.

Direct Damage
This type of damage is the most common source of damage.  It can benefit from any effect that give you a percent bonus, such as Critical Hits or a Sigil of Force.  Lets take a look at the damage formula itself:
Damage Done = (Weapon Strength) * (Power) * (Skill Coefficient) / (Target's Armor)
As you can see, we have a few variables we will have to identify before we can calculate Direct Damage per Hit.

Weapon Strength: All weapons have a Weapon Strength, which is the range of damage they can inflict.  The weapons with the highest Weapon Strength have a rarity type of Exotic or above.  When calculating damage, you will want to average the damage your equipped weapon can deal.

Interestingly enough, the average weapon damage is the same for aquatic weapons and one handed weapons that aren't off-hand only.  For my personal convenience I've calculated all the averages.

Spoiler


Power: Before you can calculate how much damage you do, you need to know your total Power.  If you are using a build calculator be careful!  I have yet to find one that actually takes all attribute sources into consideration, even just from Items.

Also remember that each stack of Might gives you 35 Power and Condition Damage at level 80.  With "For Great Justice!" you should always have a minimum of 3 stacks of Might on you, or +105 Power and Condition Damage.  There may be other Boons that you are 'always' under the affect of.  Make sure to take those into consideration where appropriate.

Skill Coefficient: Skill Coefficients are unique to each Skill.  They are not published. Luckily, we know enough we can calculate what they are.  For my personal convenience I had done so already.

Spoiler


To calculate these values yourself the process is simple thanks to the GW2Wiki.  The Wiki entry for each Skill will list the damage shown on the tooltip when you mouse over a Skill.  This is calculated using the damage formula and using your average equipped Weapon Strength, current Power, and an assumed target armor of 2600.

Luckily for us, this info was all captured by looking at the tool tip with a naked level 80 character with a max Weapon Strength weapon equipped.

So how do we determine the Skill Coefficient?  Simply by performing some basic Algebra.  We have values for everything but the Skill Coefficient thanks to the GW2Wiki, so just solve for X:  

Skill Coefficient = ( Tooltip Damage * Target Armor) / ( Average Weapon Strength * Power )
The Target Armor would equal 2600, our Power would equal 916, and then we just need the right Average Weapon Strength for the Skill in question.

Keep in mind some skills give you multiple hits per Activation.  Damage is calculated on a per Hit basis, so take that into consideration if you decide to calculate the coefficient yourself.

Target Armor Value: For tooltips it has already been mentioned this is assumed to be 2600. This also happens to be the Armor rating of the "heavy armor" dummy that was used during the BWE in the PvP Training Area.

You can also see from the damage equation that Armor directly affects the amount of damage you can take.  Keep that in mind when you are designing a build.


Condition Damage
Several conditions do damage over time.  This damage is calculated differently than Direct Damage.  Most notably it ignores Armor and does not benefit from effects that gives you a percent bonus to damage (so things like Protection or Vulnerability have no affect on it).

Condition Damage is more complicated because each Condition has its own equation:

Burning
8 + (4 * Level) + (0.25 * Condition Damage)
Bleeding
2.5 + (0.5 * Level) + (0.05 * Condition Damage)
Poison
4 + Level + (0.1 * Condition Damage)
Confusion
10 + (1.5 * Level) + (0.15 * Condition Damage)
Condition Damage is easy to calculate up to a point.  Simply using the equations above will give you the damage per stack.  At that point you would need to know the duration of the Condition and its trigger.  For example, Bleeding deals damage every full second but Confusion does it per enemy Skill activation.


Damage Over Time

Damage Per Second (DPS) is the common measure of how effective a given build is at dishing out damage.  Calculating the your DPS is relatively straight forward, as it is literally your damage over (divided by) time.  Where it gets sticky is in the details we have to take into consideration with Guild Wars 2.

When we calculate the Direct Damage over time we have to take into consideration how long it takes to perform the attack as well as how often we can perform the attack.  Then we have to consider how many Critical Hits we landed, and any abilities that deal damage that could have triggered from such events.  Once we have that information, we also have to factor in the Condition Damage dealt over that same period of time.

Skill Activation Times
When you press the button to use a Skill it goes through an animation.  Damage is dealt when the animation completes.  Our life is made much easier because of the guys and gals at the GW2 Wiki, yet again.  They've already sorted out the Activation Time for these skills for us.

Spoiler


Some Skills did not have a listed Activation time.  These Skills appear to work instantly or have another factor you have to take into consideration, such as the range to target.

As far as I can tell, the animation for a Skill lasts only as long as the Skill's activation time.  


If anyone else cares to confirm or disprove this, then by all means do so.  My testing could be suspect.  I tested several times using a stopwatch and a few times simply counting outloud "one one thousand".  I did this in game, and did not appear to be having any latency issues.

TeamTempestGaming has a wonderful YouTube video detailing the attack animations for all the Warrior Skills:



I've gone through and done the same here and it seems to be the same case.  I'd be very interested if someone can prove otherwise, but for now I'm convinced that the Activation Time is equal to the Animation Time.  Given GW2 developers have gone on the record as stating that the animations are meshed with the Skill mechanics this isn't surprising.


Recharge Times
Once a Skill has Activated it typically has a recharge time before you can use the Skill again.  Generally speaking, the more powerful a Skill the longer the cool down period.

Spoiler


Some Skills have no Recharge period.  Most Skills  with no Recharge are part of a Chain, in which case the Skill is unavailable until you complete the Chain.  In all cases, you still have the Activation Time acting as a buffer between actions, so Direct Damage is dealt as fast as the Activation Time allows.

Note that this is why Quickness is a powerful buff, as it allows you to perform actions twice as fast.  With short activation times (usually half a second), the short duration of most sources of Quickness tends to be effective for quite a lot of attacks.

Skill Rotation
Your Skill rotation is the next piece of information we need.  This is simply the Skills you are going to work through when you are in a fight.  Obviously this is a very fluid thing in GW2 compared to other MMOs, so this won't be what you necessarily actually use every time.  But in an ideal situation (you and your target are stationary and you aren't getting hit back) you will have a rotation that will give you the most amount of damage.

The easiest way to figure your rotation out is to have computed the Direct Damage you can inflict with each available Skill.  Generally speaking, you won't want to use a Skill that deals a lower amount of Direct Damage than your Chain attack.  The exception is if the Skill has an effect you need to take advantage of, such as Fierce Blow causing Weakness, or the buffs from Signet of Rage.

Once you know which Skills you want to use in your rotation, take a look at their Recharge times.  The largest Recharge time is roughly how long your rotation will last.  Usually for the Warrior this is around 30 seconds.

Note that the time frame you are measuring your damage output in is completely arbitrary.  I prefer to break it down to my Skill rotation when I'm estimating my build's damage output.  Feel free to use a different number if you prefer.

Now that we have a time frame, we can start cramming Skills into it.  Compare the Recharge time of each Skill to your time frame and figure out how many times you can use that Skill within the time allotted.  Refrain from counting up your Chain Skills until after you have dealt with all the other options.

Let's use the Hammer as a very basic example:
Earthshaker: 10 Seconds
Hammer Swing: Chain 1
Hammer Bash: Chain 2
Hammer Smash: Chain 3
Fierce Blow: 12 Seconds
Hammer Shock: 12 Seconds
Staggering Blow: 20 Seconds
Backbreaker: 30 Seconds
Here we have a Skill that is fairly circumstantial: Hammer Shock and Earthshaker.  Both do less direct damage than any of the other Skills, but Hammer Shock does sent out a wave that Cripples enemies and Earthshaker has a Stun effect.  Neither of these are Skills you want to just spam, particularly in PvE.  They have their uses, but from a damage perspective you are better off with your Chain attack.  For Skills like this, I typically ignore them unless they have an effect central to the Build.

Backbreaker deals the most damage out of all our Hammer Skills, and with its knockdown effect gives us a potential damage boost from Defense Trait Line.  We can fit in Staggering Blow once and Fierce Blow twice.  So how many Chain Attacks?

Well, now we need to factor in that Activation time.  Backbreaker, Staggering Blow, and Fierce Blow have a total Activation time of 3.25 seconds.  I have counted Fierce Blow twice, though its important to remember I can't use it until at least 12 seconds after the first time.  With the total activation time subtracted from our total available time, we have 26.75 seconds remaining

A full Chain with the Hammer takes 0.75 seconds.  We can fit in 34 full Chains into the remaining 26.75 seconds.  We even have 1.25 seconds left over, in which we can fit another hit from one of the Chain skills, though we could not complete the chain.


Direct Damage Per Second
So how do we figure out the total damage done in that 30 second period?  Start adding and multiplying.  Let's use the numbers from the GW2Wiki as a basis:
Hammer Swing: 333
Hammer Bash: 333
Hammer Smash: 444
Fierce Blow: 518
Staggering Blow: 481
Backbreaker: 554
For each full Chain we have to add the damage.  Using the numbers above we end up with 1110 damage per Chain.  Now we just need to add up everything:
 ( 34 * 1110 ) + 333 + ( 2 * 518 ) + 481 + 554 = 40144
Seems like quite a lot of damage.  But that's the total damage for the 30 second period, which is an eternity in a fight.  To get the damage per second simply divide this total by the total available time:
40144 / 30 = 1338.13 damage per second
Doesn't seem so unreasonable now, does it?



Conditions




--- Work in Progress ---

Will be adding more on how to calculate DPS, but this should get most of you started!

Edited by Cowmonaut, 19 October 2012 - 09:17 PM.


#2 Sithicus Dias

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Posted 17 October 2012 - 09:26 PM

Great idea starting this thread, i've been theory-crafting for Warrior Healing, I was hoping somebody would begin one for damage too. Looking forward to reading the rest!

#3 Anam Itheoir

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Posted 17 October 2012 - 11:20 PM

Haha, I was just about to email you, Cow.  I wanted to see if you had any calculations on Mace Auto Attack 1 x3 because i keep seeing broad numbers that don't make a lot of sense to me.  I love the mace, and find it's damage much better even if sluggish at times.

The calculations I would like is how quickness affects weapons in terms of their damage coefficients.  It should be easy but i am at work ;p.  Also does Quickness stack, say time warp and frenzy.

I was never a math major, but I do work with math all day.  I am a pump tech and industrial tank sales/tech so numbers are a part of my life.  However, pulling quick calculations out of my hat or studying the mathematical formulas has never been my forte.  What I am good at is taking the math and explaining it in terms that the layperson is able to understand clearly.  

I am a bit baffled that Rifle is the highest avg damage, but some of the worst coefficients.  Hammer and Mace have the best coefficient's across the board, but Axe and Rifle have the best burst skill coefficients which makes sense.

Edited by Anam Itheoir, 17 October 2012 - 11:22 PM.


#4 Cowmonaut

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Posted 18 October 2012 - 03:32 PM

View PostSithicus Dias, on 17 October 2012 - 09:26 PM, said:

Great idea starting this thread, i've been theory-crafting for Warrior Healing, I was hoping somebody would begin one for damage too. Looking forward to reading the rest!
Thank you!  I hope to update the OP in the next few days.  I'd be very interested to see what you have regarding Healing, since I haven't really looked at that side of things at all.  I don't like not knowing how things work!

View PostAnam Itheoir, on 17 October 2012 - 11:20 PM, said:

Haha, I was just about to email you, Cow.  I wanted to see if you had any calculations on Mace Auto Attack 1 x3 because i keep seeing broad numbers that don't make a lot of sense to me.  I love the mace, and find it's damage much better even if sluggish at times.

The calculations I would like is how quickness affects weapons in terms of their damage coefficients.  It should be easy but i am at work ;p.  Also does Quickness stack, say time warp and frenzy.

I was never a math major, but I do work with math all day.  I am a pump tech and industrial tank sales/tech so numbers are a part of my life.  However, pulling quick calculations out of my hat or studying the mathematical formulas has never been my forte.  What I am good at is taking the math and explaining it in terms that the layperson is able to understand clearly.  

I am a bit baffled that Rifle is the highest avg damage, but some of the worst coefficients.  Hammer and Mace have the best coefficient's across the board, but Axe and Rifle have the best burst skill coefficients which makes sense.
I noticed pretty quickly in the few threads I was participating in that people were asking the same questions, so I figured we could all benefit from getting a thread down on how to figure this stuff out.  Plus this way if I've been doing it wrong someone smarter than me can point it out!

I'm writing up the piece about factoring in activation/cooldown times and will include it in the original post.  I expect to see most of these weapons land closer than most of us think in some ways.  The time between attacks for the Rifle for example may help offset its higher average damage.

Or it might not.  The numbers won't lie.

#5 Cowmonaut

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Posted 18 October 2012 - 08:35 PM

Oops, missed this bit:

View PostAnam Itheoir, on 17 October 2012 - 11:20 PM, said:

The calculations I would like is how quickness affects weapons in terms of their damage coefficients.  It should be easy but i am at work ;p.  Also does Quickness stack, say time warp and frenzy.

As far as I'm aware, Quickness stacks in duration, just like Fury, and not Intensity.    In fact only Might stacks in Intensity.  Every other Boon seems to stack in duration only.

Also, it wouldn't affect the coefficient at all.  Its affect pertains to the Activation time (and possibly Recharge time?).  So it definitely increases your damage output, but only because it allows you to do more in the same time frame.  It doesn't affect your per-hit damage.

#6 Sithicus Dias

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Posted 18 October 2012 - 09:12 PM

View PostCowmonaut, on 18 October 2012 - 03:32 PM, said:

Thank you!  I hope to update the OP in the next few days.  I'd be very interested to see what you have regarding Healing, since I haven't really looked at that side of things at all.  I don't like not knowing how things work!
Or it might not.  The numbers won't lie.

Fantastic, the threads I made are here. First one is a descriptive comparison, second one is where the mathsy stuff is :)

http://www.guildwars...lds-think-tank/

http://www.guildwars...rical-analysis/

Keep up the good work! Threads like this are great to work on over time, since I find there's so much to say you can never think of it all in one sitting :)

#7 Anam Itheoir

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Posted 18 October 2012 - 09:54 PM

View PostCowmonaut, on 18 October 2012 - 08:35 PM, said:

Oops, missed this bit:



As far as I'm aware, Quickness stacks in duration, just like Fury, and not Intensity. In fact only Might stacks in Intensity.  Every other Boon seems to stack in duration only.

Also, it wouldn't affect the coefficient at all.  Its affect pertains to the Activation time (and possibly Recharge time?).  So it definitely increases your damage output, but only because it allows you to do more in the same time frame.  It doesn't affect your per-hit damage.

I don't think quickness stacks at all.  From my experience any personal quickness overrides elite skill Timewarp.  Wiki doesn't say anything about it.  You are correct, I was confusing damage per hit with damage per second.  Sometimes I get so far ahead I don't slow down.

#8 Cowmonaut

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Posted 18 October 2012 - 10:30 PM

Looks like Quickness is not technically a Boon so you are likely right and it doesn't stack period.  Just means that some builds could see 'wasted' procs of Quickness if its already going, but it seems unlikely to be a problem really.

#9 Anam Itheoir

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Posted 18 October 2012 - 10:47 PM

It's a bit odd that Axes while easily the fastest activation time in our one handed weapon department also has the highest coefficients.  While the Mace, has decent coefficients put it's offset by the extended timer.

It would be interesting to see the coefficients calculated by swing timer.

#10 paradiselight

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Posted 18 October 2012 - 10:49 PM

Two things
1) Each stack of might adds 35 power and condition damage, not 105.

2) There is much more to the casting of a skill than just skill activation. Skill activation time is incredibly inaccurate in figuring out the actual time taken to finish a skill. I know that from my experiment with Guardian that GS autoattack (with a listed 1/2 second activation time for all 3 strikes) has almost the same rate as scepter's autoattack (with a listed 1/4 second activation time).

More testing and info are needed before one could figure out the actual skill completion time.

#11 Sithicus Dias

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Posted 19 October 2012 - 08:12 AM

One of the reasons i'm so interested in this thread is to see how different weapon combos emerge. Since by all appearances I think most people would attest to Main Hand (MH) Mace being a lot weaker than Axe for example. I build very defensively and use a shield, but depending on the situation I switch between Mace and Axe. Mace is of course nice because of the Weakness you apply to enemies, and also for an extra block, and a Daze. But then when they aren't required I just switch out to an Axe for more damage. Since my goal with my build is to build defensively in order to survive overwhelming pressure effectively, the other side to that is the aim to try and do as much damage as possible without sacrificing that.

#12 Cowmonaut

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Posted 19 October 2012 - 02:55 PM

View Postparadiselight, on 18 October 2012 - 10:49 PM, said:

Two things
1) Each stack of might adds 35 power and condition damage, not 105.

Correct.  3 x 35 = 105.  All Warrior builds can pretty much Guarantee 105 bonus Power and Condition Damage at all times thanks to "For Great Justice!".  I apparently said things backwards.  Correcting that!

View Postparadiselight, on 18 October 2012 - 10:49 PM, said:

2) There is much more to the casting of a skill than just skill activation. Skill activation time is incredibly inaccurate in figuring out the actual time taken to finish a skill. I know that from my experiment with Guardian that GS autoattack (with a listed 1/2 second activation time for all 3 strikes) has almost the same rate as scepter's autoattack (with a listed 1/4 second activation time).

More testing and info are needed before one could figure out the actual skill completion time.
That section is not finished.  For the most part though, the 'activation time' listed is the time it takes to go through the animation.  It seems some things may have changed in the updates since launch and the GW2Wiki is just out of date.  I'll be doing a more thorough test this weekend.

#13 Anam Itheoir

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Posted 19 October 2012 - 03:10 PM

View PostSithicus Dias, on 19 October 2012 - 08:12 AM, said:

One of the reasons i'm so interested in this thread is to see how different weapon combos emerge. Since by all appearances I think most people would attest to Main Hand (MH) Mace being a lot weaker than Axe for example. I build very defensively and use a shield, but depending on the situation I switch between Mace and Axe. Mace is of course nice because of the Weakness you apply to enemies, and also for an extra block, and a Daze. But then when they aren't required I just switch out to an Axe for more damage. Since my goal with my build is to build defensively in order to survive overwhelming pressure effectively, the other side to that is the aim to try and do as much damage as possible without sacrificing that.

I am firm believer in using Offensive weapons with defensive gear and defensive weapons with offensive gear.  Even though the mace looks like a defensive weapon, you can gear it to be a complete offensive weapon.  The mace with offensive gear = a great damage support weapon.  Remember support is not just healing it's controlling or eliminating another targets defense.  Plus Maces and Hammers will allow you to push your stats a bit more offensively because you will have to spec at least 20 points into your defensive tree.





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