Guild Wars 2

Hey guys, was doing some unrelated calculations and figured I’d go ahead and post these since I had to figure them out in the process.

Hammer
Hammer Swing [.8]
Hammer Bash [.9]
Symbol of Protection [Seems to be 1.0 for base strike + 1.5 for the symbol (divided by hits)]
Mighty Blow [1.75]
Zealot’s Embrace [.8]
Banish [1.0]

Greatsword
Strike [.8]
Vengeful Strike [.8]
Wrathful Strike [1.2]
Whirling Wrath [2.8 for primary strikes (.4 each * 7), .15 for secondary projectiles]
Leap of Faith [1.1]
Symbol of Wrath [2.75 (divided over hits)]
Binding Blade [1.0]

Staff
Wave of Wrath [.6]
Orb of Light [1.2]
Detonation [.6]

Sword
Sword of Wrath [.8]
Sword Arc [.8]
Sword Wave [1.5 (divided over hits)]
Flashing Blade [.2]
Zealot’s Defense [2.65 (divided over hits)]

Mace
True Strike [.8]
Pure Strike [1.0]
Faithful Strike [1.4 (only hits one target)]
Symbol of Faith [1.5]
Protector’s Strike [1.4]

Scepter
Orb of Wrath [.66]
Smite [4.95 (divided over hits)]

Shield
Shield of Judgement [1.0]

Focus
Ray of Judgement [.5]
Shield of Wrath [2.5]

Torch
Zealot’s Fire [2.25]
Cleansing Flame [3.3 (divided over hits)]

Smite Condition
Without Condition [.58]
With Condition [1.31]

Skill Damage = [(coefficient) * (weapon damage (which is a range)) * (power)]/armor

So with this you can calculate the damage of any of the above abilities for any given power.

NOTE: Symbol of Protection hits three times, not four as the tooltip states.

Nice. I would love to see this done for sceptre. If you can you explain how you determined these, we can do them ourselves as well.

Well, I basically already told you – Skill damage = [(coefficient) * (weapon damage (which is a range)) * (power)]/armor

So you can solve for coefficient algebraically for each ability, if you know your power and tooltip damage and weapon damage. The only missing part is that the tooltip uses 2600 as the armor value. It also uses the average weapon damage instead of a range or the top or low ends.

Scepter
Orb of Wrath [.66]
Smite [4.95 (divided over hits)]

Added the last weapons. Should be more or less complete now for most uses.

Strong work foofad

What’s the staff coefficient?

>implying staff does damage

Kidding

Wave of Wrath [.6]
Orb of Light [1.2]
Detonation [.6]

nice work!

As I suspected, Shield of Wrath is one of our hardest single-hit skills. Can crit well over 6k with full beserker.

OH YES, thank you. +1’d and bookmarked.

This is great stuff

Here are some preliminary calculations for each weapon for an “at a glance” comparison. (It assumes you’re hitting 1 target, and that all things like the different weapons all have the same stats) so if you needed to choose between comparable weapons, you can.

Keep in mind that 2 handed weapons should not be directly compared to 1 handed weapons since the damage is significantly different, and would depend on what you were using in your off hand.

Hammer

Auto Attack Cumulative = 4.7
Total Average = 1.375

Greatsword

Auto Attack Cumulative = 2.8
Total Average = Unknown because of Whirling Wrath.
Without WW = 1.275

Comparing the means of Hammer and Greatsword (1 tailed @ .05 ) yields a p-value of p = 0.4174. This is not a significant difference. What that means is there is no real statistically significant difference in choosing Hammer over Greatsword based on these numbers, though your mileage may vary! However please keep in mind that we do not have all the data for GS, and so this is an incomplete analysis, and should be treated as such!

Staff

Auto Attack Cumulative = .6
Total Average = 0.8

Sword

Auto Attack Cumulative = 3.26
Total Average = 1.246

Mace

Auto Attack Cumulative = 3.2
Total Average = 1.22

Comparing the means of Sword and Mace (1 tailed @ .05 ) yields a p-value of p = 0.17603. This is not a significant difference. What that means is there is no real statistically significant difference in choosing Mace over Sword based on these numbers, though your mileage may vary!

Scepter

Total Average =2.805

Shield

Total Average =1

Focus

Total Average =1.5

Torch

Total Average =2.775

Smite Condition

Total Average =0.945

Questions? Comments?

Thank you foofad for the data!

What do you mean by this:

Balerathon.2184:

Hammer

Auto Attack Cumulative = 4.7
Total Average = 1.375

Kaptain O.1348:

What do you mean by this:

Balerathon.2184:

Hammer

Auto Attack Cumulative = 4.7
Total Average = 1.375

Well, the first 3 attacks are really just the chain of auto attacks, so you hit once, then it’s a different attack, you hit the second time and it’s yet another attack. Three hits to complete a cycle. The cumulative for all 3 attacks is 4.7.

If you calculate the average coefficient for all attacks per weapon, and divide by the number of attacks, you get an average coefficient per weapon.

Then a simple t-test of significance and Bob’s your uncle!

That’s it really

Nice. I thank everyone …

now if someone is ambitious enough, you can start theorycrafting rotations for weapons and compare them. For example, an basic hammer rotation 2,1,1 to start with. Would that work something like this, keeping in mind that we have to normalize for execution time?

1. Average = 1.375 × 2 = 2.75 (in 4.5 seconds)
2. Average = 1.75 x 1 = 1.75 (in 0.75 seconds)

2,1,1 Rotation Average = 4.5 (in 5.25 seconds) = .857 per second

Now with GS #1 rotation only:

1. Average = 1.275 (in 1.5 seconds) = 0.85 per second

P.S. I went through the calculation myself with the numbers I had just for hammer and got a different set of co-efficients than the OP. Without boring details, I discovered that they change based on what zone you are in … I was able to reproduce the same values as the OP in Lion’s Arch. Clearly, it’s the re-scaling based on level but the results are interesting.

As example, In Malchor’s Leap near Waste Hollow’s Point, I have 568 for Hammer Swing Skill damage and 1599 Power. That gives 0.88 for a co-efficient. In Lion’s Arch I have 562 for Hammer Swing Skill damage and 1740 Power, giving the 0.8 the OP got.

I later went to Brisbane Wildlands, was rescaled to level 17 and I had a coefficient of 5.96 for Hammer Swing. That’s 7.5 times better performance than the same setup at level 80. I was surprised by that.

Anyways, bottom line is that you need to do the calculation based on a common level, 80 is obviously the most applicable.

FYI: The actual animations are longer than the tooltip-listed cast times for the various attacks. This should help, thanks to GuanglaiKangyi on the Guru forums. In other words, it takes longer to execute an autoattack chain than if you just add the tooltip times. Your effective DPS is lower than you would be led to believe. Here are the rough animation times:

Hammer:
Auto chain: 3.6s total
Mighty Blow: 1s

Greatsword:
Auto chain: .83s per swing, 2.5s total
Whirling Wrath: 2.5s (startup .5s, spins for 2s)
Leap of Faith: 1s
Symbol of Wrath: .83s
Binding Blade: 1s

Sword:
Auto chain: .83s per swing, 2.5s total
Zealot’s Defense: 2.5s (same as Whirling Wrath, see above)

Scepter:
Auto: .83s per swing
Smite: .83s

Staff:
Auto: 1s
Orb of Light: 1s
Symbol of Faith: 1s
Empower: 4s

Mace:
Auto: .83s for first two swings, 1.33s for last, 3.33s total
Symbol of Faith: 2s
Protector’s Strike: .83s upon triggering

I believe it’s a known fact that animation times exceed the actual required time to execute the skill. In fact, there are many videos that show just how and when you can maximize damage by interrupting yourself using other skills while still getting full effect.

It’s always sad when these things don’t align perfectly because it then turns out that you need to game the system a bit to be more competitive, especially in PvP.

Obtena.7952:

P.S. I went through the calculation myself with the numbers I had just for hammer and got a different set of co-efficients than the OP. Without boring details, I discovered that they change based on what zone you are in … I was able to reproduce the same values as the OP in Lion’s Arch. Clearly, it’s the re-scaling based on level but the results are interesting.

As example, In Malchor’s Leap near Waste Hollow’s Point, I have 568 for Hammer Swing Skill damage and 1599 Power. That gives 0.88 for a co-efficient. In Lion’s Arch I have 562 for Hammer Swing Skill damage and 1740 Power, giving the 0.8 the OP got.

I later went to Brisbane Wildlands, was rescaled to level 17 and I had a coefficient of 5.96 for Hammer Swing. That’s 7.5 times better performance than the same setup at level 80. I was surprised by that.

Anyways, bottom line is that you need to do the calculation based on a common level, 80 is obviously the most applicable.

What’s likely throwing you is the change in average weapon damage for the lower-leveled weapons when you get scaled down. Coefficients should be static, but it’s not clear what the scaling does to your weapons. If you’re so inclined, you can test this by comparing them to a low-level character of the same class not being scaled.

In any event, level 80 is all that really matters.

^^ I was also under the assumption that the co-efficient should be static as well. I don’t think it’s worth a lot of investigation. Simply a point of interest.

I guess rotation calculations can be done with the rough animation times. I’m going to make a crack at it when I have some time. I’m pretty excited about it. If you take it to sophisticated limits, you can determine very closely how swapping gear impacts your damage for trading off between crits and power for instance.

Some issues with your data analysis.

First of all, the total coefficient of Hammer is 4.2 assuming the target stands in your symbol for the full 3 ticks, it’s only 4.7 if you take Writ of Persistence trait.

Secondly, you quote the total as 4.7 divided between 3 attacks, to get an average per swing. That gives 1.5667, not 1.375.

Thirdly, I don’t think the average coefficient per swing is terribly useful, it would be much more useful to take the coefficient of the chain and divide by the time taken to complete the chain so 4.2 (untraited, assuming a relatively stationary boss) divided by 3.7 (time to complete the chain) so 1.1351/second, Greatsword auto gives us 2.8 coefficient divided by 2.4 seconds so 1.1667

Lastly, I’m not familiar with the “t-test for significance” but it seems to be being applied incorrectly here. This is not a set of statistics that you can run a test for significance on to determine if one data point falls sufficiently far outside the expected range to question the validity of the set. This is just a number, 1.1667 is 2.75% larger than 1.1351 – so over time you will do 2.75% more damage – whether a 2.75% damage increase is significant is determined purely by the player, not by a formula.

Not trying to be a jerk, but saying that you ran a formula and it told you that the dps difference between two weapons is insignificant is wholly inaccurate.

Balerathon.2184:

Kaptain O.1348:

What do you mean by this:

Balerathon.2184:

Hammer

Auto Attack Cumulative = 4.7
Total Average = 1.375

Well, the first 3 attacks are really just the chain of auto attacks, so you hit once, then it’s a different attack, you hit the second time and it’s yet another attack. Three hits to complete a cycle. The cumulative for all 3 attacks is 4.7.

If you calculate the average coefficient for all attacks per weapon, and divide by the number of attacks, you get an average coefficient per weapon.

Then a simple t-test of significance and Bob’s your uncle!

That’s it really

I appreciate your comments. A few clarifications on that.

If we are theorycrafting, then yes, we’re going to control for everything aside from the weapon. That is to say, the mob doesn’t move, and you manage to land every hit perfectly. Otherwise, the comparison is pointless.

Secondly, nowhere did I say I was giving an Average per swing. That was all you. The point of my cumulative total was to show the coefficient for all 3 swings, since a lot of your damage comes from auto attack. I see no issues with that. Giving an average per swing is not as useful IMO because not all 3 swings always land, and so it is incorrect to say that even if I landed just 1 hit, it would be 1.5667.

The Total average counts All coefficients, not just auto attack, and so it does come to 1.375. Check it again.

On your third point, you may disagree with the usefulness of my calculations, and that’s totally fine. That is why we have many different options It says nothing about the validity of the calculations. Take it or leave it, makes no difference to me. Though I think you’re confused as to what Auto Attack Cumulative, and Total Average mean in my post.

On your last point, I’m sorry, but I have to disagree with you. We’re dealing with numbers, and when numbers are involved, they can be subjected to statistical testing. No one is questioning the validity of the set. You are misunderstanding the point of the test. The point is to say whether or not the difference in damage between 2 weapons is likely to deviate from one another significantly by chance alone.

Now, an important caveat here, convention says we use 5% (one tail) as a cut off, but that is arbitrary (and Maybe that’s what you were referring to, I’m not sure) but in any case, 5% is pretty good.

Your conclusion is your own, but you’re making a statement that is based on your feeling, and if that works for you, great I guess you could say the same about the 5%, but the methodology behind it is completely different. Consider my analysis to be only intended for those who want a bit of conventional statistics behind their decision.

You could argue that even 0.0009% increase in DPS is totally worth swapping weapons. Is that wrong? Absolutely not. But the info should be out there, and I see no flaw in the logic of my calculations. Take from it what you will.

p.s. I take all your comments constructively

Even when theorycrafting I think it’s important that you clarify the assumptions – in this case you are assuming the target is relatively stationary, in a lot of fights this will not be the case and the numbers will be very different.

Even if you are going to assume the target is relatively stationary, you only get 4.7 if traited with “Writ of Persistence” otherwise the number is 4.2. While it’s a valid point to say “Hammer should take Writ of Persistence so the numbers should include this” you should also take into consideration the traits Greatsword should take – otherwise your numbers are an unfair comparison.

Looks like I may have misunderstood what your “Total Average” was and that’s why I asked you what they were! You are saying you took the coefficient for all abilities that do damage and averaged them? You seem to agree that the average coefficient per swing is not very useful, how is an average coefficient of all your abilties useful? Have you weighted the average to take into consideration activation or cooldown time? How can you use the average coefficient of all abilities, without taking into account the activation or cooldown times of skills, to determine which weapon does more damage?

On to your “statistical” analysis of the coefficients, you say that:

“The point is to say whether or not the difference in damage between 2 weapons is likely to deviate from one another significantly by chance alone.”

I’m not sure what you mean here, how can the “difference in damage deviate from one another”. The damage of GS and Hammer may deviate from one another (that amount would be the “difference in damage”). Also, why would I base my choice on if my damage will be significantly more based on “chance alone”? Wouldn’t I want to pick my weapon so that my damage is more based on weapon choice?

I’m not saying a test of significance isn’t a useful tool but I think you are applyingit incorrectly. In your example (and I disagree with the numbers used but we’ll use your example) you say that:

“Comparing the means of Hammer and Greatsword (1 tailed @ .05 ) yields a p-value of p = 0.4174. This is not a significant difference. What that means is there is no real statistically significant difference in choosing Hammer over Greatsword based on these numbers”

You are comparing 1.375 to 1.275, that’s an increase of 7.8%

As you say

“You could argue that even 0.0009% increase in DPS is totally worth swapping weapons. Is that wrong? Absolutely not. But the info should be out there”

The info should be out there, you should report the dps increase as 7.8% and let the reader decide if that’s a significant difference, not that “there is no statistical difference in damage done”.

Ok, I guess if I’m going to criticise your math I should do the courtesy of showing you how I feel it should be done right?

Hammer:

1. 0.8, 0.9, 1.0 (symbol for 1.5) – 3.7s activation, no cooldown.
2. 1.75 – 1.75s activation, 5s cooldown.
3. 0.8 – 2s activation, 15s cooldown
4. 1.0 – 2s activation, 25s cooldown

Assuming all other factors are constant (Power, Target Armor, Weapon) Dps can be compared by dividing the coefficient by the time taken to perform the skill. I’ll present numbers for both 1 tick and the full 3 ticks of the symbol.

1. 0.8649 (1 tick) 1.1351 (3 ticks)
2. 1.0
3. 0.4
4. 0.5

As you can see #3 and #4 are abysmal for DPS and should only be used if you need the utility. #2 does worse than just auto attacking if you are getting all 3 ticks on the target but it will blast combo fields so it’s usually worth doing for that reason!

For Greatsword we’ll assume single target dps with both a relatively stationary boss so you can get all ticks of your #4 and get inside the boss to hit all 14 hits of WW and a moving boss that gets 2 ticks from #4 and only the 7 main hits from your WW.

Greatsword:

1. 0.8, 0.8, 1.2 – 2.4s activation, no cooldown.
2. 3.5 – 2.75s activation, 10s cooldown.
3. 1.1 – 1s activation, 15s cooldown
4. 2.5 – 1.75s activation, 20s cooldown
5. 2.0 (it will hit twice vs single target) – 2.25s, 25s cooldown (also puts a 10s dot on the target that ticks for 160+0.2 of your condition damage each second for 10 seconds, this is unfortunately very difficult for us to model)

DPS is

1. 1.1667
2. 1.0309 (7 melee hits) 1.2727 (7 melee + 7 projectile hits)
3. 1.1
4. 0.5714 (2 ticks) 1.4286 (full 5 ticks)
5. 0.8889 (plus the 10 second dot)

For the purpose of evaluating damage (rather than utility) I’ll assume Hammer uses a (1,1,1),(1,1,1),2 rotation and that GS uses Auto-attack and #2/#4 on cooldown vs a stationary boss.

Moving Boss:

Hammer
8.15/9.15 = 0.8907dps

Greatsword
1.1667

Greatsword pulls out ~31% more dps than Hammer, granted the Hammer is also blasting combo fields and if they are fire fields could be adding a bunch of might to the party or healing if they’re water fields. Hammer is also putting down a protection symbol which supports the party.

Vs Stationary Boss

Hammer
10.15/9.15 = 1.1093dps

Greatsword

1. provides 1.167dps
2. provides (1.2727-1.167)*2.75/12.75 = +0.0228
3. provides (1.4286-1.167)*1.75/21.75 = +0.0210
   Total DPS = 1.2108

Greatsword only enjoys a 9% lead in dps here, Hammer making up a ton of damage by getting the boss to sit in it’s symbol consistently. Hammer is still blasting combo fields every 9 seconds buffing and supporting it’s party and is still dropping protection around the boss so it and other melee are benefitting from -33% damage taken.

Remember math and theory can only take you so far, with so many other factors in GW2 combat not considered here you cant use this to definitively decide on a weapon. Hammer’s symbol damages 5 targets so it’s good vs large numbers of targets, GS#5 was disregarded due to difficulty modelling the DoT damage, but also it has great utility pulling targets together to allow not only the Guardian but the other party members to AoE more efficiently.

I think different encounters may just call for different weapons, and when in doubt as to whether to bring a Greatsword Guardian or a Hammer Guardian with you into the Fractals of the Mists, I say you can’t go wrong with bringing both!

To his credit Kaptain, you can’t really criticize him … he made no attempt to characterize damage over time comparisons nor did he make attempts to assess rotations. He’s simply comparing the auto attack of the various weapons using a statistical tool. It’s probably over alot of people’s heads but it’s not wrong to do so, especially if you can properly interpret the result.

The attempt here isn’t to model encounters by introducing nuisance factors you can’t control like mobs moving, etc… That mob is going to move regardless of weapon so the bottom line is that damage comparisons that factor it out can be done without affecting the relative damage between the weapons. Yes, there are cases where it will affect your damage output. I don’t find that a particularly interesting factor in the assessment. You can miss hits with any weapon. You can face the wrong way too, get crippled, hit a blocker, etc…. Those are nuisance factors and aren’t suitably quantifiable for these theorycrafting exercises.

Kaptain O, I want to start off by reiterating that I welcome discussions like these because in the end, it is the community that will benefit. For example, you may have never done that analysis if it was not in the face of mine. I’m not saying I’m trying to be some helpful troll, not at all. Just that this is being taken in the spirit of cooperation and to advance our knowledge of the game

So, to your points.

I believe you and I are coming at this from two different places. If I’m interpreting you correctly, you are interested in Which weapon is better to use under various circumstances. Since you point to various scenarios like boss moving, landing all tics of symbol etc.

I’m not coming from, or heading to, the same place at all. My interest is purely academic, and not applied. I took the numbers given by foofad and ran with them. My assumptions were: 1) they are correct. 2) attacking a dummy 3) everything else is equal.

It’s the same as asking: what is the DPS of this item vs what is the effective DPS of this item? One takes into account mob movement, miss chance, blocks, parries, bad human targeting, system lag. The other just looks at it in a bubble. If everything were ideal, what could this item pump out?

It would be like saying, well, GS has a wider swing arch than sword or mace, so you’re more likely to catch another mob at the very edge, therefore GS is superior. Whether that’s true or not has no bearing on sword DPS or GS DPS. In an ideal situation, the mob gets hit with both weapons equally.

In statistical testing, you are comparing means. The average of all coefficients between hammer and sword. You’re saying you get 7.8%. Well, what does 7.8% mean? Is it big? Is it small? Is it just noise? That’s what the test purposes to answer. When the test is run, it says that there is a 95% chance that 7.8% is not statistically significant (or rather, falls within 1.96 standard deviations) . And furthermore, with a p value as high as that, it’s nowhere near.

If I reported simply something like 7.8% increase, someone might look at that, and say Holy crap! 7.8% That’s a ton! (or That’s nothing!) It is only when you interpret that number can you see the forest and not the trees. You need context, and you need to know if that 7.8% is just noise, or if it is statistically meaningful. Anyways, I don’t think the merits of statistical analyses should be in this topic

On to your own analysis. I want to mention a few things.

You’re citing activation times and CDs when earlier in this very thread, people are reporting that animation times do not correspond to activation times, so the average player, and even a skilled player may not be able to take advantage of the skill’s activation time, since his toon will still be executing the move for longer than the move takes due to ArenaNet animation fumbles.

Also, you are reporting vs a moving boss. How are you accounting for how many hits you land etc? Not criticizing, just wondering. It’s gotta be reproducible, and really, no two fights are exactly alike (as you say) so I wonder if the whole moving target is moot.

A quick point, you write DPS, but we’re talking about coefficients, did you actually work out the numbers from Skill Damage = [(coefficient) * (weapon damage (which is a range)) * (power)]/armor or was that supposed to be Coefficient and not DPS? If so, what weapon are you using in both situations (Hammer / Greatsword)?

Finally, I just have to point out that Theorycrafting is all about math and theory, and not about “in game applications” it is a tool to discover if one way is mathematically better than another way. Then players go out into the game and try, and report back that there are other factors to consider. But even then, it’s reduced to numbers and math and theory once again.

We aren’t discussing Strategy, that’s a different topic. This is about numbers and math.

Thoughts?

Sweet post, thanks for this.

Couple things. Was this done with no armor and no jewelry and no sigils on weps? And what was the target? Weapon config type, or were they all averaged together?

My calculations were wildly off as much as 1.2 to .5 with many inbetween. I used my bare guardian, no jewelry, no food, no sigils and three wep configues, cleric, beserker and condition base wep types. I did not get close to the same numbers, though a few were close if averaged out up or down.

The beauty of this approach is that how your geared does not affect the coefficient calculation. Perhaps if you post what numbers you used and how you put them in the equation, we could help you. I will also provide you a very detailed example that may also help you determine where you are making a mistake.

Eg 1. Hammer swing – First thing to do is make sure you are in a zone where you are not downscaled from level 80. The co-efficient calculation will not give you the same number as the OP if you are downscaled.

I use an exotic hammer that has a weapon damage range of 985-1111. That means my average hit is 1048. My hammer swing tool tip damage is 562. My power is 1740. The calculation uses 2600 armor (Not completely certain where that number comes from).

Therefore, the calculation is:

562 = X * 1048 * 1740/2600
X = 0.8

Testing for significance in this case is totally pointless. You test for significance when you have a data set from which you are gathering statistics, and you are attempting to ascertain whether or not the data reflect a statistically significant change. We aren’t working with a data set here. Increasing power by 100 has an absolute effect on your damage. That damage is a % increase for a given critical chance and damage, and that’s absolutely true. There is nothing to test. You will do x% more damage with 100 more power. It’s a given. There’s no chance in a sterile environment like this of it being any different.

Where you would use a test for significance, is if you smacked a monster 100 times and then had someone else smack a monster 100 times, compared your data sets, and then tested to see if the fact that your numbers are seemingly x% higher than his is in fact statistically significant given the sample size or whether that x% is just noise from your sample. That’s an appropriate test for significance.

Edited to add: I don’t even know how you would do a t-test on something like this. You need a standard deviation and a sample size.

Oh, also – I forgot to mention, utilities like Smite Condition have no relationship to weapon damage, but they still follow the same formula. Instead, some sort of weapon damage is substituted in. I assumed 1000 and when I did, I was able to reproduce my results in game, but I didn’t test it rigorously. So those coefficients may be off.

Obtena: I can criticize him because he’s mis-using a statistical tool on things are are not statistics! It’s a fine tool but it’s being completely misapplied.

Balerathon: I don’t think you a troll and I hope you don’t think I am! Yes we are approaching this differently but I’m trying to get you to see that a) Your use of a test of significance is not appropriate. b) Some of the other numbers you are getting kind of have no relevance on anything – if I’m missing how the “Total Average” coefficient you give for each weapon has ANY bearing on how much damage you do please explain it to me.

So, some of the numbers are correct, others aren’t – I think they’ve been corrected in the original post now. I gave both numbers for a stationary boss – which is the theoretical max you are interested in, as well as an arbitrary situation where a boss is moving. Just because you are not interested in the additional data I provided for those who are doesn’t invalidate the “Stationary Boss” figures.

Re: Activation/Cooldown times.

Yes, the reported activation times are not correct, I have recording the animations and timed them frame by frame to find out the actual animation times.

If you want your analysis to have any bearing on the relative damage done by two weapons you absolutely need to take into consideration the activation and cooldown times. Imagine these 3 theoretical weapon sets.

Feather:

1. 0.8 coefficient, 0.5s attack speed, no cooldown
2. 1.0 coefficient, 0.5s attack speed, 5 second cooldown
   Total Average = 0.9

Car:

1. 3.0 coefficient, 5s attack speed, no cooldown
2. 8.0 coefficient, 10s attack speed, 20 second cooldown
   Total Average = 5.5

Wet Noodle:

1. 1.0 coefficient, 1s attack speed, no cooldown
2. 10.0 coefficient, 1s attack speed, 120s cooldown.
   Total Average = 5.5

Clearly the Wet Noodle and the Car are better than the Feather right?

Wrong.

Feather will in 5.5 seconds perform 10 #1 attacks and 1 #2, giving a total coefficient of 8.2 over 5 seconds, or an average of 1.6364 coefficient per second.

Car will in 30 seconds perform 4 #1 attacks and 1 #2 attack, giving a total coefficient of 20.0 over 30 seconds, or an average of 0.6667 coefficient per second.

Wet Noodle will in 121 seconds perform 120 #1 attacks and 1 #2 attack, giving a total coefficient of 130 over 121 seconds, or an average of 1.0744 coefficient per second.

DPS

Ok regarding your quick point about DPS and asking if I calculated numbers, lets look at the formula

[Damage] = [Power]/[Armour] * [Average Weapon Damage] * [Coefficient]

Point number 3 of your assumptions is “everything else is equal”.

So I assume my Power will be equal regardless of the weapon choice I use (innacurate since GS gives a might stack from it’s Auto Attack Chain, but we can disregard that), I assume the target will have the same armour regardless of my weapon choice and that both weapons I’m choosing between are the same tier and therefore have the same Average Damage (If we’re comparing an Exotic Hammer to a Fine Greatsword it’s not really a reasonable comparison).

So I’ll say Power, Armour and Weapon damage are constant for any given situation and I’ll define a constant “k” to be = [Average Weapon Damage] * [Power]/[Armour]

Our formula is now

[Damage] = k*[coefficient]
DPS = k*[coefficient]/[time]

I can compare the dps of two skills or rotations as follows:

dps ratio = (k*[coefficient a]/[time a]) / (k*[coefficient b]/[time b])

k appears in both the numerator and denominator of this so we are left with:

ratio = ([coefficient a]/[time a]) / ([coefficient b]/[time b])

So “relative dps” can be determined by comparing the coefficient/s of the two abilities.

Moving Target:

Again, if you aren’t interested in the moving target numbers just scroll on by that section. Some people may be interested in whether a moving target affects both weapons equally, if you’re not one of those people just look at my stationary boss numbers for a potential damage comparison.

Theorycrafting is about using math to determine relevant information on how your choices affect the game. Adding up the number of letters in all the abilities in a weapon set and dividing by the number of abilities may be a legitimate way of determining the average number of letters in the names of a weapons abilities but it has no relevance on which weapon does more damage just as averaging the damage done by abilities without considering how long that ability takes to use or how often you can use it has no relevance on which weapon does more damage. It’s the theorycrafting version of looking at your screen and saying “I see big numbers, big numbers = good”.

Tests of Significance

This has no place being used to compare damage, Foofad has it 100% correct when he says:

Testing for significance in this case is totally pointless. You test for significance when you have a data set from which you are gathering statistics, and you are attempting to ascertain whether or not the data reflect a statistically significant change. We aren’t working with a data set here. Increasing power by 100 has an absolute effect on your damage. That damage is a % increase for a given critical chance and damage, and that’s absolutely true. There is nothing to test. You will do x% more damage with 100 more power. It’s a given. There’s no chance in a sterile environment like this of it being any different.

Where you would use a test for significance, is if you smacked a monster 100 times and then had someone else smack a monster 100 times, compared your data sets, and then tested to see if the fact that your numbers are seemingly x% higher than his is in fact statistically significant given the sample size or whether that x% is just noise from your sample. That’s an appropriate test for significance.

Exactly as he said, if you were collecting data and had recorded the damage done by each weapon you could use a test for significance then, if you only took 4 swings and one weapon had 10% more done that may not be a significant enough difference – perhaps it just got good RNG. After 100 swings with each weapon that same 10% difference might be more significant, after 1000 swings even more so. In essence as you record more data points (swings) your data becomes more accurate because the RNG factor should even out over larger sets of data. The more data points for each set the more likely any difference between the sets is a significant actual difference in sets and the less likely it’s due to random “noise”.

Here is an example, I have 2 six sided dice with nonstandard numbering. Which dice is “better” (i.e. going to roll higher on average)? We have 2 approaches to this.

a) Add up the values on all 6 sides and divide by 6, this gives us the EV of the Dice, if it is higher than the other dice it is better – no test for significance needed.

b) Roll each dice a number of times, record the values, average them and compare – in this case we need to perform a test of significance to see if we got enough data points in the set to justify the difference as being related to the value of the die or if it’s just because you rolled better with one die than you did with another.

Do you see the difference? Do you see how a test of significance is appropriate in situation b but not in a?

If it helps put the thread back on track, I say you’re right.

Now, I’m interested in seeing some discussion about how the coefficients can be used to assess the game. I’m going to look at some hammer and GS rotations tonight and at some point, see how crit and might stacking can be worked into this approach.

After a few days of being annoyed at the seemingly odd Sword coefficients I reexamined them and determined that I made a clerical error. The error’s been corrected, the coefficients are now accurate.

I think that for Hammer on a stationary boss the “best dps” in theory land is to just repeat 1 but Mighty Blow adds more than just raw DPS.

Mighty Blow in a Light Field (always available due to swing 3 of your Auto Attack) grants retaliation to some number of people which will trigger Altruistic Healing (assuming you are one of the 98% of guardians who use that trait). It also adds a small amount of damage when the target is hitting someone with Retaliation (looks like about 350 damage everytime the target attacks someone affected)

Where Mighty Blow really shines is if there is a Fire Field down, granting 3 stacks of Might to nearby allies. This not only heals you via Altruistic Healing (I haven’t had a chance to test if it heals you for the # of targets or the number of boons applied) but it also increases Power by 105 for 20 seconds (plus boon duration bonii). Assuming the group isn’t capped on might stacks and the average group member has between 2,000 and 2,500 Power buffed you increase each affected person’s dps by 4-5% for 20 seconds.

Old damage = power/armour*weapon*coefficient
New damage = (power+105)/armour*weapon*coefficient

since the players weapons, the coefficients of their skills and the bosses armour remain constant the ratio of new to old damage is:

(power+105)/(power)

If you hit 3 people (including yourself) with this at least once every 20 seconds you are effectively adding 12-15% of a person’s damage. If you have +boon duration, can coordinate with other team members regarding the placement/timing of fire fields and if the whole group is within range of the AE Might given out by the Blast Finisher you could be granting 3 stacks of 34 second might every 9 seconds (an average of ~11 stacks of might or +385 Power) to 5 people. Again assuming Power of 2,000 to 2,500 you are increasing their damage by between 15.4% and 19.25% each – multiplied by 5 players is another 77% or 96.25% of the average of the 5 players. I don’t think you’ll realistically get to that point but it’s good to know the potential, and I know some of the people in the thread had expressed that they wanted the figures in a “best case scenario”.

Bumping this so people see it, I’ve gotten some PMs from people who can’t find it.

Thanks for this I’ve been looking to find a way to calculate this. Can you give me a run down on how you went about finding these values?

Yeah, sure. It’s just basic algebra.

Damage = Weapon Damage * Power * Coefficient / Armor

The skill tooltips use 2600 Armor in their damage calculation. In order to find out the coefficient, we plug in the things we know: If you look at your current stats in your hero panel you can fill out your power, average weapon damage (aka the bottom value and top value listed in the weapon’s tooltip added together, then divided by two), then for Damage on the left side of the equals you use the tooltip’s listed damage for that skill.

Pulling these numbers out of my kitten, but here’s how it works: If a skill lists 800 damage, we have 1800 Power, and an average weapon damage of 952.5 (which is the damage of an exotic 1 handed weapon) we say:

800 = 1800 * 952.5 * Coefficient / 2600

Algebra-foo dictates we multiply both sides by 2600 and simplify:

2080000 = 1714500 * Coefficient

Algebra-foo dictates we divide both sides by 1714500:

Result is 1.213 = Coefficient, so for simplicity we round to 1.2. In other words, the totally fictional skill, the tooltip of which listed 800 damage for our given stats, has a skill power coefficient of 1.2 and you can use that to then calculate how much more damage you would do if you added a certain amount of power or precision or critical damage or what have you.

Hope that helps.

Why wasn’t this stickied?

Dunno! PM a moderator, if you like.

Bumping this again, for the people who are still looking for it.

whirling wrath tooltip factors in all 7 whirl hits + 2 projectile hits, so the actual damage is inconsistent depending on how many projectiles hit (with a total hit possibility of 14).

Edited (after all this time!) with an accurate Whirling Wrath coefficient.

What build (trait/gear) do you run now

Awesome work foofad, and I keep a softcopy myself of what you did

…..you guys must play asurans in game

I don’t even like math!

Added these numbers to the wiki.

Nice and useful thread! But i think there is something wrong with the time needed to execute one mace auto attack chain. It says 0.83s for first 2 hits then 1.33s for last hit so total should be 2.99s~3s not 3.33s which will make it a bad attack

I need to recheck this because I haven’t looked at it in a long time now, but as I recall the extra third of a second comes in the wind-down animation between the third hit and the cycle starting again with the first hit.

Ok thanks! I definitely appreciate this piece of work u do!

I need this for checking how much damage my bursts can do for trolls <3, I’m too lazy to paste it into a txt file and you deserve the credit for writing it up!

edit: the co-eff for Judge’s is ~.329