[MECHANICS] The Big "Attack Speed" Conundrum

[MaxQuest]

"- when not using an ability, and having 1h or wielding a shield incurs a 0.5 penalty"

 

If I understand well, you should re-write it :

"- when not using an ability, and having single weapon (1-handed or 2-handed) or wielding a shield incurs a 0.5 penalty"

"1h" seems to exclude 2-handed, and I don't think this was your intention.

Thanks for suggestion, as indeed I meant single weapon and not one-handed. So, in the end which variant does sound better?:

- "when not using an ability, and having single weapon (1H or 2H) or wielding a shield"

- "when not using an ability and (wielding a single weapon or using a shield)"

- "when auto-attacking while wielding a single weapon or shield"

 

I think DAoM should be greyed out.

If you could also add Nature's bounty too 

Fixed.

Ok, I'll check Nature's Bounty later. (reminder to self: plus durgan enchant (shield))

 

I never tested how spells work and I'm not sure I understand how recovery works for them. Having 2 weapons gives 50% recovery for spells too, or you can have 50% recovery only with fists?

When you use an ability or spell, or when you make an auto-attack while dual-wielding (and without a shield) you don't get a 0.5 penalty coefficient.

When you auto-attack while having a single weapon (1h or 2h) or shield equipped, you do get a 0.5 penalty coefficient.

For spells it doesn't matter what you are wielding in weapon/shield slots.

 

Updated tables:

 

 

 

Special attention to 2*speed_coef:

 

 

 

 

That means 15% attack speed from gloves and 50% from DAoM would allow wearing up to durgan enchanted scale and be able to cast spells with 0% recovery?

Seems so.

 

speed_coef = (1.15*1.5 - 1) + (0.65 + 0.15 - 1) = 0.725 - 0.2 = 0.525

recovery_duration = attack_duration * max(0, (1 - 2 * speed_coef)) / recovery_factor

recovery_duration = attack_duration * max(0, (1 - 2 * 0.525)) / 1.2

recovery_duration = 0

 

Will test it today, but I bet it will be zero.

 

 

P.S. But as peddroelm noted, not all stuff listed in the attack categories list does apply to spells.

Spells are affected only by AttackSpeedMult (and only those which do not come from weapon or shield passives), RangedAttackSpeedMult (if it is a ranged spell), ArmorSpeedFactor and StatAttackSpeedMult (dexterity).

Edited January 17, 2017 by MaxQuest

[JerekKruger]

But yes, those multpliers are increased by 1. That was done to skip an extra step later.

Consider you have swift aim, swift gloves and cautious attack.

AttackSpeedMult should be: [(1 + 0.2) * (1 + 0.15) * (1 - 0.2)] - 1 = 0.104

Instead, it can be presented as:

AttackSpeedMult should be: [1.2 * 1.15 * 0.8] - 1 = 0.104 (that's why I wrote those multiplers that way)

 

 

Looking at your table again, most attack speed bonuses are blue ones i.e. most are multiplicative. That's not how I thought it worked, interesting.

[Dr <3]

Thks for the awesome work maxquest.

I just noted how the reload Speed bonus staks. Apparently with ranger you can stack both gunner and swift aim for a -70% reloading time.

Just asking around: did someone ever tried to build a shotgun ranger with gunner and swift aim? How did it work out?

 

Edit: so dual wielding wizard ( integrated daom) is the new official boss of spell slinging?

Edited January 17, 2017 by Dr <3

[MaxQuest]

Thks for the awesome work maxquest.

I just noted how the reload Speed bonus staks. Apparently with ranger you can stack both gunner and swift aim for a -70% reloading time.

Just asking around: did someone ever tried to build a shotgun ranger with gunner and swift aim? How did it work out?

Reload speed bonuses stack multiplicatively (or would it be right to say divisively? )

 

For example blunderbuss has base reloading speed of 5s (or 150 frames)

150 / (1 * 1.5 * 1.2) = 83.33 frames

Unfortunately it won't be -70% in reloading time, but only -44%.

 

Edit: so dual wielding wizard ( integrated daom) is the new official boss of spell slinging?

Too early to judge, as more testing is required. But it seems so. (also casting speed is independent from weapons, dw or not) Edited January 17, 2017 by MaxQuest

[Boeroer]

Actually a barb with Frenzy + Bloodlust + Blood Thirst is the official boss of spell slinging. Too bad he hasn't that many spells.

[Elric Galad]

DAoM has made wizz the strongest offensive class since 1.0. It was just not as obvious as now as long as people weren't familiar with his unequal low level spells.

 

Alternatively, you can consider Rogue as ultimate spell caster (who said Death Maelstorm Blows ?)

Edited January 17, 2017 by Elric Galad

[Elric Galad]

 

"- when not using an ability, and having 1h or wielding a shield incurs a 0.5 penalty"

 

If I understand well, you should re-write it :

"- when not using an ability, and having single weapon (1-handed or 2-handed) or wielding a shield incurs a 0.5 penalty"

"1h" seems to exclude 2-handed, and I don't think this was your intention.

Thanks for suggestion, as indeed I meant single weapon and not one-handed. So, in the end which variant does sound better?:

- "when not using an ability, and having single weapon (1H or 2H) or wielding a shield"

- "when not using an ability and (wielding a single weapon or using a shield)"

- "when auto-attacking while wielding a single weapon or shield"

 ...

 

IMHO:

"when not using an ability, and having single weapon (1H or 2H) or wielding a shield"

[Dr <3]

 

 

"- when not using an ability, and having 1h or wielding a shield incurs a 0.5 penalty"

 

If I understand well, you should re-write it :

"- when not using an ability, and having single weapon (1-handed or 2-handed) or wielding a shield incurs a 0.5 penalty"

"1h" seems to exclude 2-handed, and I don't think this was your intention.

Thanks for suggestion, as indeed I meant single weapon and not one-handed. So, in the end which variant does sound better?:

- "when not using an ability, and having single weapon (1H or 2H) or wielding a shield"

- "when not using an ability and (wielding a single weapon or using a shield)"

- "when auto-attacking while wielding a single weapon or shield"

...

IMHO:

"when not using an ability, and having single weapon (1H or 2H) or wielding a shield"

IMHO:

"Everytime that you are NOT dual wielding" is more clear

[Elric Galad]

Well, I agree.

Except "not dual wielding OR using an ability"

[MaxQuest]

That means 15% attack speed from gloves and 50% from DAoM would allow wearing up to durgan enchanted scale and be able to cast spells with 0% recovery?

Had time to test it now.

Yeap, a wizard (with gloves, daom and durganized scale) could cast any spell without recovery. (it doesn't matter what weapons he has equipped, or if he dual-wields or not)

And same thing with ciphers powers.

 

---

Also, tested Nature's Bounty, Vielo Vidorio and Durgan Enchant (Shield).

The first two are getting into AttackSpeedMult category and are suppressable.

While Durgan Enchant (Shield) is a completely separate thing, and it can decrease (additively) the penalty a character gets when attacking while using a shield OR not dual-wielding.

 

So, updated tables look like this:

 

 

 

 

 

 

Also, it turned out that full and primary attacks are not considered "abilities" and can be affected by Single1HWeapRecovFactor penalty.

Thus I decided to avoid using the term "ability" and rephrase the penalty condition into "when not casting a spell" or "when performing an attack (auto, primary or full)".

 

P.S.:

Primary attack follows the same rules of an auto-attack.

Full attack with a single weapon does the same.

Full attack while dual-wielding (or using 1h+bashing shield): offhand_attack -> mainhand_attack -> mainhand_recovery

i.e. offhand_recovery is skipped. so if using weapons of different speed; it's better to put the faster one in main hand, if the character has many full attacks.

Edited January 22, 2017 by MaxQuest

[MaxQuest]

Check ^ above post.

 

---

Also have tested spells' speed a little.

 

Generally spells have following "attack phase" durations:

- fast: 35 frames (or 1.1666s)

- medium: 60 frames (or 2s)

- slow: 120 frames (or 4s)

 

And a recovery duration that is equal to: attack_duration / 1.2; i.e:

- fast: 29 frames (or 0.9722s)

- medium: 50 frames (or 1.6666s)

- slow: 100 frames (or 3.3333s)

 

But, there are exceptions:

 

Logged values:

Fast Cast (s):
1.16666 + 0.97222 (aspirant mark)
1.16666 + 0.97222 (holy radiance)
1.16666 + 0.97222 (recall agony)
1.16666 + 0.97222 (mind wave)
1.16666 + 0.97222 (amplified thrust)
1.16666 + 0.97222 (iconic projection)
0.3333 + 0.2777 (eyestrike)
0.3333 + 0.2777 (whispers of treason)

Average Cast(s):
2 + 1.66666 (circle of protection)
2 + 1.66666 (pillars of holy fire)
2 + 1.66666 (despondent blows)
2 + 1.66666 (crow for the faithful)
1.4150 + 1.1791 (interdiction)
0.3333 + 0.2777 (mental binding)


Slow Cast (s):
4 + 3.333 (storm of holy fire)
0.3333 + 0.2777 (ringleader)

As you have noted, some powers were logged to have super fast durations of [0.3333s attack + 0.2777s recovery]. Their real "attack" duration is not THAT fast. The reason I think this is happening is because they are probably codded in a different way, and are... two-phased so to speak? So only their second part is being logged.

These spells have a really long delay before the real cast going off. For example these are the frapsed values for Eyestrike and Ringleader: 

Eyestrike: (naked) (0.3333s + 0.2777s)

0:  unpause, start
58: activate
84: new action | recovery start
92: recovery end

total: 84 att + 8 recovery frames | or 2.8s + 0.2777s
------

Eyestrike: (plate) (0.3333s + 0.5555s)

0:  unpause, start
58: activate
83: new action | recovery start
99: recovery end

total: 83 att + 16 recovery frames | or 2.8s + 0.5555s
------

Ringleader: (naked) (0.3333s + 0.2777s)

0: start
128: activates
143: recovery start
151: recovery end

total: 143 att + 8 recovery frames | or 4.766s + 0.2777s

What does that mean? I don't know really, except that their attack duration is greater than it should be, while their recovery duration is super low, and that a plate wearer can cast them almost as swiftly as a naked character.

 

 

Edited January 21, 2017 by MaxQuest

[Dr <3]

Wow, so finally the dual wielding sabre ( flames of fair rihan) Fire wizard genie theorized by Boeroer will see the light, powered by 0 recovery between the rain of fireballs.

[MaxQuest]

^ Yeap. But generally... 2h or 1h+shield wizard can have 0-recovery with spells, under the same conditions.

 

- If you are casting spells - you don't get the SingleWeapon penalty.

- If you are performing an attack (be it auto-attack, primary attack or full attack) while dual-wielding (bashing shields don't count) - you don't get the SingleWeapon penalty.

Edited January 21, 2017 by MaxQuest

[Dr <3]

Ah , ok, i misunderstood the First part, thanks

[MaxQuest]

No problem)

 

---

P.S. Wanted to write about Dexterity diminishing returns for some time now. It was already discussed, but a visualization wouldn't hurt:

 

 

TL.DR: Each point of dex does not necessary provide a 3% dps increase.

Edited January 22, 2017 by MaxQuest

[Elric Galad]

Dexterity is better for 2 handed swords than for daggers.

At least dexterity does not suffer from diminushing returns WHEN SUMMED WITH ANY OTHER DAMAGE BOOST (only intresic diminushing return).

 

Dexterity has still the advantages to work with about any type of actions, except movement.

But it does not work well with limited ressources. 

[Dr. Hieronymous Alloy]

No problem)

 

---

P.S. Wanted to write about Dexterity diminishing returns for some time now. It was already discussed, but a visualization wouldn't hurt:

 

 

TL.DR: Each point of dex does not necessary provide a 3% dps increase.

 

 

Oh wow, that's really interesting. What's actually causing it to be less than 3%? Is it that there are portions of the attack sequence that can't be reduced by dex -- the "inter action delay" - or the granularity of frames, or what?

 

I suspect this math shifts the DPS benefit back in favor of Might away from Dex for a lot of things. Last time I looked at math on this kind of level, I believe consensus was that Dex was preferable for DPS, because Might didn't increase damage from Lashes, whereas dex would (by increasing attack speed). This difference might be enough to change that calculation though. Thanks.

[rheingold]

So does this mean that putting a couple of points into dex is a good thing ? Don't claim to understand the maths, but suddenly it seems a good idea to put, say 2 or 4 points into dex (12/14) rather than maxing it.You would get some benefit out of it and the rest could go into might.

[fiddlesticks]

If I understand the chart correctly, slower weapons tend to benefit slightly more from all attack speed modifiers than fast ones because the irreducible Delay is a comparatively smaller part of their overall attack animation. So a Warbow/Rod will get the biggest relative DPS boost from additional attack speed.

 

Granted, the difference is vanishingly small and probably unnoticeable when playing the actual game, but it's still kind of interesting on a theoretical level.

[MaxQuest]

Dexterity is better for 2 handed swords than for daggers.

Yes. And it's used to it's fullest with reloading weapons.

 

At least dexterity does not suffer from diminushing returns WHEN SUMMED WITH ANY OTHER DAMAGE BOOST (only intresic diminushing return).

Absolutely right. There are many things that can dilute the effect of might on weapon attacks: weapon quality, crits, soul/bitting whip, deathblows, two-handed style, etc.

 

 

Here is the theoretical model of Might diminishing returns with the same weapons.

* Theoretical, because in practice there is also damage values rounding, and we have to also deal with DR.

 

 

A practical model would include so many variables... like graze/hit/crit rate, enemy DR, 20% min dmg going through, indirect might gain increase via lash enchant,... that table should be 4D

[MaxQuest]

Oh wow, that's really interesting. What's actually causing it to be less than 3%? Is it that there are portions of the attack sequence that can't be reduced by dex -- the "inter action delay" - or the granularity of frames, or what?

Two things:

- the inter-action delay, which happens to be ~5 frames between any two actions. I don't know exactly how Unity works, but there seems to be some onUpdate schedule system which ticks periodically and checks for queued abilities, and that could be it's tick rate. If I am not mistaken it's possible to get into the same tick (i.e. get rid of the delay) but you would need to have 500+ dexterity.

- the intristic diminishing returns. It's like: 3/2 > 4/3 > 5/4 > 6/5 and so on. Add a drop to a drop, and you get twice the amount; throw that drop into the sea, and nothing has changed.

 

I suspect this math shifts the DPS benefit back in favor of Might away from Dex for a lot of things. Last time I looked at math on this kind of level, I believe consensus was that Dex was preferable for DPS, because Might didn't increase damage from Lashes, whereas dex would (by increasing attack speed). This difference might be enough to change that calculation though. Thanks.

Vs zero-DR 1 point of DEX is always better than 1 point of MIG, provided that they are equal at the moment and your character relies on attacking with his weapon a lot.

But for spells; and also for attacks made vs high-DR targets the preference does indeed shifts toward might. But by how much?

 

15x15 > 16x14 > 17x13 - the biggest area is that of a square. But different variables (like enemy DR, abilities, talents, enchants and especially role in the group) askew it toward a rectangle.

And we want to find that sweet spot when we get the maximum benefit.

 

So does this mean that putting a couple of points into dex is a good thing ? Don't claim to understand the maths, but suddenly it seems a good idea to put, say 2 or 4 points into dex (12/14) rather than maxing it.You would get some benefit out of it and the rest could go into might.

It depends.

But shortly: if you was intending to have 10 dex on an attacking character, rising it to just 12 could be worth it, as the first points provide a benefit at higher ration.

 

 

If I understand the chart correctly, slower weapons tend to benefit slightly more from all attack speed modifiers than fast ones because the irreducible Delay is a comparatively smaller part of their overall attack animation.

Correct.

 

So a Warbow/Rod will get the biggest relative DPS boost from additional attack speed.

Correct)

 

Granted, the difference is vanishingly small and probably unnoticeable when playing the actual game, but it's still kind of interesting on a theoretical level.

Well, a bit optimization here, a bit there... and suddenly things start to snowball)

It's way more noticeably in Tyranny than in PoE, but still. Maximizing cipher's focus gain such that he could cast amplified waves back to back; or increase priest's AoE DoT damage is fun

Edited January 22, 2017 by MaxQuest

[Kaylon]

You should put points in dexterity only if you're a class (usually ranged) who can ignore stats like constitution or resolve. The rogue also can work with low might at high level if he's able to chain Death Blows over and over.

 

At high level, the enemies against which your dps counts, have high DR (over 15) which removes 100-150% of your weapon damage (or more if they also have high defenses and you graze often). That means you will deal less than 100% weapon damage and might will increase your dps more than dexterity in these situations.

[Elric Galad]

You should put points in dexterity only if you're a class (usually ranged) who can ignore stats like constitution or resolve. The rogue also can work with low might at high level if he's able to chain Death Blows over and over.

 

At high level, the enemies against which your dps counts, have high DR (over 15) which removes 100-150% of your weapon damage (or more if they also have high defenses and you graze often). That means you will deal less than 100% weapon damage and might will increase your dps more than dexterity in these situations.

 

That's why I favor Dex on classes who already gets big %damages bonus, like Rogues and Ciphers and, to a lesser extand, fighters.

 

And also a bit on priest, because is the only stats apart INT that matters for Buffbots is DEX.

Edited January 22, 2017 by Elric Galad

[Dr. Hieronymous Alloy]

 

Oh wow, that's really interesting. What's actually causing it to be less than 3%? Is it that there are portions of the attack sequence that can't be reduced by dex -- the "inter action delay" - or the granularity of frames, or what?

Two things:

- the inter-action delay, which happens to be ~5 frames between any two actions. I don't know exactly how Unity works, but there seems to be some onUpdate schedule system which ticks periodically and checks for queued abilities, and that could be it's tick rate. If I am not mistaken it's possible to get into the same tick (i.e. get rid of the delay) but you would need to have 500+ dexterity.

- the intristic diminishing returns. It's like: 3/2 > 4/3 > 5/4 > 6/5 and so on. Add a drop to a drop, and you get twice the amount; throw that drop into the sea, and nothing has changed.

 

I suspect this math shifts the DPS benefit back in favor of Might away from Dex for a lot of things. Last time I looked at math on this kind of level, I believe consensus was that Dex was preferable for DPS, because Might didn't increase damage from Lashes, whereas dex would (by increasing attack speed). This difference might be enough to change that calculation though. Thanks.

Vs zero-DR 1 point of DEX is always better than 1 point of MIG, provided that they are equal at the moment and your character relies on attacking with his weapon a lot.

But for spells; and also for attacks made vs high-DR targets the preference does indeed shifts toward might. But by how much?

 

15x15 > 16x14 > 17x13 - the biggest area is that of a square. But different variables (like enemy DR, abilities, talents, enchants and especially role in the group) askew it toward a rectangle.

And we want to find that sweet spot when we get the maximum benefit.

 

. . . .

 

Well, a bit optimization here, a bit there... and suddenly things start to snowball)

It's way more noticeably in Tyranny than in PoE, but still. Maximizing cipher's focus gain such that he could cast amplified waves back to back; or increase priest's AoE DoT damage is fun

 

 

 

Yup, that's the $64,000 question. Plus, raw DPS isn't the sole concern -- Might gives front-loaded damage, which can often be preferable to a higher dps rate over a longer time period.

 

Intuitively then, I'd guesstimate that the sweet spot for stats for a ranged cipher on PotD is probably . . hrm . . 

 

16/6/15/19/19/3 or so. 

 

I could see an argument for higher Might at the cost of Perception, though. Not entirely sure.

 

The real question is probably how to weight Might vs Perception and Int, which is hard because of the opportunity cost of a missed action, etc.; there's a decreasing return on investment with Perception too, of course, but that's less so on PotD and especially so if you're using guns.  With those #'s you'll be able to make most of the stat checks in the game given appropriate gear, too.

Edited January 22, 2017 by Dr. Hieronymous Alloy

[George_Truman]

Are seperate blue categories additive?

 

I was testing AS and was at zero recovery with a 20% speed weapon (no durgan) a durgan shield, swift action gauntlets, and DAoM pot with no armor.

 

1.2*1.15*1.5=2.07, 2.07-1.55=.52

 

1.2*1.15*1.5*.8=1.66, 1.66-1.35=.31

 

Unless I am missing something it shouldn't even be close if vulnerable attack is multaplicative, but it checks out as an additive malus.

 

Version 3.05.1186

Edited March 15, 2017 by George_Truman