Attack speed 2.0

[Kaylon]

Wanted to verify how durgan's enchantment stacks with different attack speed buffs and I found pretty surprising results. Here are my findings:

 

1. There are different categories of bonuses affecting the attack speed even if they share the same name in game:

- armor recovery - durgan reinforced, Pilferer's Grip, Armored Grace - all stack additively with armor's recovery penalty

- melee speed - Vulnerable Attack

- ranged speed - Penetrating Shot (include spells)

- two weapons speed - Two Weapon Style 

- fire rate - Vicious Aim, Sure-Handed Ila Nocked Her Arrows with Speed (only ranged weapons)

- reload speed - Gunner, Swift Aim, Sure-Handed Ila Nocked Her Arrows with Speed

- attack speed - Cautious Attack, Swift Aim, attack speed enchantments on weapons/items, all attack speed buffs from spells/potions

- action speed - dexterity

 

2. Reload speed buffs from ranger and chanter don't stack anymore

- reload speed reduction from Swift Aim will suppress the one from Sure-Handed Ila Nocked Her Arrows with Speed - thus a ranger with Swift Aim and Gunner is the best you can get.

 

3. Attack speed buffs stack multiplicatively:

- the best you could have is a weapon with attack speed enchantment (20%), durgan refined (15%), Gauntlets of Quickness (15%), Deleterious Alacrity of Motion (50%) which will give 1.2x1.15x1.15x1.5=2.38 bonus speed. That means it will remove up to 138% recovery from your weapon. 

 

4. Attack speed enhancements from different categories stack additively:

- chanter using Sure-Handed Ila Nocked Her Arrows with Speed, Deleterious Alacrity of Motion, The Rain of Godagh Field durgan refined, Gauntlets of Swiftness, durgan reinforced plate and Penetrating Shot would have 100%-20%-138%+35%+20%=-3% ie no recovery with the bow

- a dual wielder could also wear plate and use Vulnerable Attack with no penalty if he's stacking speeds

Edited January 15, 2016 by Kaylon

[Boeroer]

Nice!

 

Pilferer's Grip doesn't stack with Durgan Reinforcement (or Armored Grace, not sure which one) though. It gets suppressed if you have a fighter with Armored Grace and durgan reinforced armor (as I used to have). I was really sad.

 

Speed from abilities (Frenzy, Swift Aim, Swift Strikes) doesn't stack with each other nor with +speed from potions or spells (Potion of Power, Alacrity and so on). E.g. Frenzy suppresses Potion of Power, Alacrity suppresses Frenzy. Outlander's Frenzy suppresses Swift Aim and Swift Strikes.

 

I never tried if Alacrity suppresses Swift Aim - but it should.

Edited January 15, 2016 by Boeroer

[Kaylon]

Nice!

 

Pilferer's Grip doesn't stack with Durgan Reinforcement (or Armored Grace, not sure which one) though. It gets suppressed if you have a fighter with Armored Grace and durgan reinforced armor (as I used to have).

With durgan reinforced armor because same enchantments on armor/clothes/accessories don't stack. Passive talents stack with everything.

[Boeroer]

Thanks for the quick answer. I also thought it was Durgan Reinforcement but was not 100% sure. I saw that they didn't stack... and never used them again.

[AndreaColombo]

3. Attack speed buffs stack multiplicatively:

- the best you could have is a weapon with attack speed enchantment (20%), durgan refined (15%), Gauntlets of Quickness (15%), Deleterious Alacrity of Motion (50%) which will give 1.2x1.15x1.15x1.5=2.38 bonus speed. That means it will remove up to 138% recovery from your weapon. 

 

What makes you think that?

 

IME counting frames, these stack additively. In your example, they'd get you 20+15+15+50 = 100% shorter recovery (not that it matters, since the difference between -100% and -138% recovery is zero.)

 

Dexterity applies multiplicatively after every other modifier has been accounted for.

 

 

That said, I've just confirmed that I can get my LoP build to attack with no recovery using the Gauntlets of Swift Action. Not sure why I had never tried that—guess I was too attached to the Gauntlets of Accuracy to consider any alternative, for some reason. I will mention this next time I update my build (when TWM pt. II comes out.)

[Boeroer]

I also thought it stacks additively - but I only had the impression - I never did any real tests. I read somewhere that the reloading buffs (Gunner + Swift Aim) stack multiplicatively. Don't know if that's right.

Edited January 15, 2016 by Boeroer

[Kaylon]

I also thought it stacks additively - but I only had the impression - I never did any real tests. I read somewhere that the reloading buffs (Gunner + Swift Aim) stack multiplicatively. Don't know if that's right.

Yes, it was me who tested that too...  Back then they stacked with the chant.

 

 

3. Attack speed buffs stack multiplicatively:

- the best you could have is a weapon with attack speed enchantment (20%), durgan refined (15%), Gauntlets of Quickness (15%), Deleterious Alacrity of Motion (50%) which will give 1.2x1.15x1.15x1.5=2.38 bonus speed. That means it will remove up to 138% recovery from your weapon. 

 

What makes you think that?

Because I have tested...  Also it's very easy to verify they're not additive - if they were additive you would have just 100% recovery reduction and you wouldn't be able to wear also a durgan reinforced plate and attack without recovery time.

Edited January 15, 2016 by Kaylon

[AndreaColombo]

 Also it's very easy to verify they're not additive - if they were additive you would have just 100% recovery reduction and you wouldn't be able to wear also a durgan reinforced plate and attack without recovery time.

 

If you have a recovery time of, say, 50 frames and you reduce it by 100% (i.e. you reduce it by 50 frames), by definition you attack without recovery.

 

If you reduce it by 138% (i.e. you reduce it by 69 frames) you still attack with no recovery because negative recovery makes no sense and I don't think the engine contemplates it If you wear a durgan-reinforced plate with Armored Grace, you're left with a 15% recovery (7.5 frames using my example), which gets further reduced by your DEX score. Playing at 60 FPS, 7.5 frames equal 0.13333333333 seconds, so probably no bar would appear over your character's head.

 

How were your tests conducted? Mine were mere frame counting; the latest can be found here.

 

I could never get the math to be 100% accurate (mostly because DEX doesn't really apply a full 3% action speed bonus for some reason) but it was fairly close.

 

EDIT:

 

I've just run another frame-by-frame analysis and I could indeed attack with no recovery (just the 4-frame delay) using a character with 10 DEX that packs the bonuses Kaylon listed. This supports his claim that bonuses are multiplicative, otherwise I would have encountered the 7.5 frames I expected based on the above. A character with higher DEX would have a faster attack animation, but still only recover for the 4-frame delay like the 10-DEX one (I tested that too.)

 

Not sure how to reconcile this with my previous tests, however

Edited January 15, 2016 by AndreaColombo

[Boeroer]

So what about adding dual wielding (+20%) to the mix? If you had two speedy weapons which are both durgan refined? Would you end up with  1.2x1.15x1.15x1.5x1.2 = 286 (186%)?

 

And what about the durgan reinforcement for shields? Does this omnious -15% attack speed penalty also improve your attack speed (1.2x1.15x1.15x1.5x1.15 = 274 = 174%)? Because then it would be somewhat stupid to take Two Weapon Style. Nearly as fast as dual wielding while having lots of deflection and reflex? Deal!

 

Only exception would be all the special attacks that work with "Full Attacks". 

Edited January 15, 2016 by Boeroer

[AndreaColombo]

And what about the durgan reinforcement for shields? Does this omnious -15% attack speed penalty also improve your attack speed (1.2x1.15x1.15x1.5x1.15 = 274 = 174%)? Because then it would be somewhat stupid to take Two Weapon Style. Nearly as fast as dual wielding while having lots of deflection and reflex? Deal!

 

You'd still get a penalty to Accuracy from the shield, though—and dual-wielding weapons with on-hit and on-crit effects would still make sense from a CC perspective.

 

I'm pretty sure the durgan-enhancement on shields says +15% attack speed with a single weapon, though (shields incur in no recovery penalty themselves.)

[Boeroer]

Small shields don't cause a penatly to ACC. 

 

Yeah, that's why I said "omnious". It says "-15% attack speed penalty". Since shields don't cause such a thing I'm really wondering what it truly does. Who wants to do some tests? Hm? Hmmm?

Edited January 15, 2016 by Boeroer

[AndreaColombo]

I'll get around to it over the weekend

[Boeroer]

I like! 

[Kaylon]

 

 Also it's very easy to verify they're not additive - if they were additive you would have just 100% recovery reduction and you wouldn't be able to wear also a durgan reinforced plate and attack without recovery time.

 

If you have a recovery time of, say, 50 frames and you reduce it by 100% (i.e. you reduce it by 50 frames), by definition you attack without recovery.

 

If you reduce it by 138% (i.e. you reduce it by 69 frames) you still attack with no recovery because negative recovery makes no sense and I don't think the engine contemplates it If you wear a durgan-reinforced plate with Armored Grace, you're left with a 15% recovery (7.5 frames using my example), which gets further reduced by your DEX score. Playing at 60 FPS, 7.5 frames equal 0.13333333333 seconds, so probably no bar would appear over your character's head.

 

How were your tests conducted? Mine were mere frame counting; the latest can be found here.

 

I could never get the math to be 100% accurate (mostly because DEX doesn't really apply a full 3% action speed bonus for some reason) but it was fairly close.

 

 

You don't need armored grace, just durgan reinforced plate - which has 35% recovery penalty - that's enough to see if you have some recovery or not... Of course negative recovery doesn't make you attack faster but it allows you to use abilities or armors that otherwise would slow you down...

 

PS. For tests I used a character with 10dex and counted frames for various speeds and items combinations and then I found the formula.

[Kaylon]

So what about adding dual wielding (+20%) to the mix? If you had two speedy weapons which are both durgan refined? Would you end up with  1.2x1.15x1.15x1.5x1.2 = 286 (186%)?

 

And what about the durgan reinforcement for shields? Does this omnious -15% attack speed penalty also improve your attack speed (1.2x1.15x1.15x1.5x1.15 = 274 = 174%)? Because then it would be somewhat stupid to take Two Weapon Style. Nearly as fast as dual wielding while having lots of deflection and reflex? Deal!

 

Only exception would be all the special attacks that work with "Full Attacks". 

Bonuses from different categories are additive. If you add two weapons style you would have 138%+20%=158% recovery.

For the shield enchantment I can't say yet how it works precisely, but I can say it allows swinging with no recovery while wearing durgan reinforced plate and using vulnerable attack. However it doesn't add speed,it's some kind of negative recovery working with abilities that slow your attack speed.

[Boeroer]

Ah - so it reduces armor recovery penalty or makes things like Vuln. Attack faster (kind of)?

 

I see I have to think about a new build that exploits these things to a maximum.

 

I also wanted to do a monk build that focuses on reflecting ranged attacks like you wrote the other day.

 

Now I'm torn... maybe that's a good thing since I promised not to touch this game until WMII.

Edited January 16, 2016 by Boeroer

[AndreaColombo]

You don't need armored grace, just durgan reinforced plate - which has 35% recovery penalty - that's enough to see if you have some recovery or not... Of course negative recovery doesn't make you attack faster but it allows you to use abilities or armors that otherwise would slow you down...

 

Trying to reconcile your math with my earlier test (from the link above):

 

Plate Armor (+50%)

Vulnerable Attack (+20%)

Armored Grace (-15% penalty*)

Durgan Steel armor (-15% penalty)

 

*this was before 2.03.

 

These should be additive, which means (50+20-15-15)=40% recovery penalty.

 

Then we have:

 

Durgan Steel weapon (+15% attack speed)

Speed weapon (+20% attack speed)

Deleterious Alacrity of Motion (+50% attack speed)

 

These should be multiplicative, which means 1.15x1.20x1.5=2.07 or 107% recovery reduction.

 

So, 140% - 107% = 33% recovery before DEX.

 

50 * 33% = 16.5 frames.

 

25 DEX (+45% action speed; applies to both attack and recovery)

 

Then we apply dexterity: (16.5 / 1.45) = 11.37

 

Et voilà: 11-frame recovery + 4-frame delay (which apparently can't be eliminated and doesn't factor in any calculation.)

 

 

This is a major breakthrough—Kaylon, you are a genius!

 

Now my LoP is not only the ultimate single-target melee DPS machine, but even has the flexibility to forgo Armored Grace and take a different ability (which is great, seeing as TWM pt. II is going to add new mid-level abilities for all classes.) I'm going to enjoy my next play through quite a lot, bwahahah!

Edited January 16, 2016 by AndreaColombo

[AndreaColombo]

I like! 

 

So, I've just run a test.

 

Two characters with the same DEX score, both wearing clothes and wielding non-durgan-enhanced weaponry. Both had the same shield, except one of them was durgan-reinforced and the other wasn't. I placed them at both sides of a third character, paused the game, and ordered both to attack.

 

While the first attack was simultaneous, the character with the durgan-reinforced shield gradually gained a time advantage over the other. This suggests that even in absence of any actual recovery penalty, durgan-reinforced shields still speed up your attack even though their description clearly states "-15% single-weapon Speed penalty."

[Boeroer]

Maybe single weapon usage (one hander with and without shield, two handers) has an inherent speed penalty? Could it be that using two sabres (even without two weapon style) is faster than using only one? Then it would make sense.

Edited January 16, 2016 by Boeroer

[AndreaColombo]

When you dual-wield, your recovery time becomes should become equal to your attack animation, so you're faster even without the Two Weapon Fighting talent. However, I've come to consider that more of a bonus you get when you dual-wield, rather than the norm to which a penalty is applied when you don't. If there's a speed penalty for not dual-wielding, I'm not sure how to make the math work.

 

* Just run a test with a 10 DEX character dual-wielding sabres and got 30 frames for the attack animation, 26 frames for recovery (22 + 4-frame delay.) No idea why recovery is faster than 30 frames.

Edited January 16, 2016 by AndreaColombo

[Boeroer]

Thanks for the testing - it's highly appreciated. Same goes for Kaylon's research.

[Kaylon]

Ok, I did a few tests and durgan reinforced shields give indeed another 15% attack speed which stacks additively. In other words you can reach 158% bonus recovery while using a shield (that explains my observation from my previous post).

 

I discovered also a nice bug involving Cautious Attack - the speed penalty will be suppressed when using any attack speed buff (meaning you get no speed reduction at all). A ranger with Swift Aim could use for example Cautious Attack without any drawback. 

[AndreaColombo]

Kaylon—if it stacks additively, wouldn't it result in 138+15=153% rather than 158%?

 

As for Cautious Attack ... I don't know, do we want to report it?

[Kaylon]

Kaylon—if it stacks additively, wouldn't it result in 138+15=153% rather than 158%?

 

As for Cautious Attack ... I don't know, do we want to report it?

Yes, it's 153%... As for Cautious Attack I consider it a feature... 

 

PS. Melee rangers can achieve perma 0% attack recovery with Swift Aim while wearing durgan reinforced leather+shield.

Edited January 16, 2016 by Kaylon

[Boeroer]

Oh - I have to retrain my Tidefall-Ranger into a Drawn-in-Spring-Ranger now.