Vanshilar's Attack Speed Index and Formulae

[Vanshilar]

So this one will be about monk unarmed attacks.

I don't have a monk, so instead, I LR'ed my assassin tempest to have a monk level on Lamannia (which actually took two LR's due to alignment issues in going from barb to monk). As usual, at the beginning of the test I would cast divine power so the testing was for BAB 20.

Unfortunately, I only did some preliminary testing before Lamannia was closed. However, my testing did cover the whole range of alacrity modifiers; it's just that there are fewer data points (9 total, 8 non-repeating) than for previous styles. As with the other styles, the trend is still additive and linear. The testing results are in the original post, so I won't repeat them here.

The main result is that the unarmed (monk) style has both a higher base attack speed than the other styles, and a better return on any speed modifiers. Whereas THF gets 5% swing speed increase (and hence DPS increase) for each 5% alacrity modifier, and TWF gets 6% for each 5% alacrity modifier, monks get around 6.5% for each 5% alacrity modifier. So monks benefit more from alacrity modifiers than any other class. Consider all weapon types having a 30% alacrity boost. The unarmed style would be swinging about 10% faster than TWF, and about 15% than THF (non-twitch).

The implication of this is that people who are making unarmed DPS builds should highly consider having sources of attack speed modifiers, such as fighter/rogue haste boost. Also, bonuses which are per-attack or per-swing also synergize well with monks, such as opportunist (which gives a doublestrike chance per swing), sneak attacks (which are per-attack), and any sort of +damage bonuses (such as past lives or weapon effects from things like ToD rings). Obviously all melee classes would benefit from them, but the unarmed style would benefit more from these types of bonuses due to the high swing speed.

MrCow puts Qstaff in the Slow THF class, whereas you put it into the fast one. Why's that?

It's because in testing them, they matched the fast THF class (i.e. greataxe) rather than the slow THF class (i.e. greatsword). I think each of the THF weapon types basically will need to be tested again to see how Turbine did them after when they equalized weapon speeds way back when.

Edit: Originally I had tempest on here, but it's been brought to my attention that tempest may not work with unarmed now (in terms of giving the additional offhand proc rate). I did some preliminary testing on this in the past but never got around to tabulating the whole data, so until then, be aware that tempest may not work with unarmed now. However, the opportunist double strike and the fort bypass has been tested to work with unarmed.

[karl_k0ch]

So this one will be about monk unarmed attacks.

If you have the time, I'd be interested in non-monk unarmed attacks, especially if they are considerably slower than other TWF weapons on toons without flurry of blows. To me, it is an interesting question since I want to know if the mabar wraps make also sense on a non-monk.

[Vanshilar]

If you have the time, I'd be interested in non-monk unarmed attacks, especially if they are considerably slower than other TWF weapons on toons without flurry of blows. To me, it is an interesting question since I want to know if the mabar wraps make also sense on a non-monk.

I actually did try out the mabar handwraps on my tempest rogue on the live servers (which is splashed barb instead of monk and so doesn't have any monk levels). However, it looks like your unarmed attacks (without any monk levels) do not have any offhand procs, so you're basically attacking with just your main hand when using unarmed without monk, even when using handwraps. However, the slowest part of the animation is the kick; just like THF twitching, you can also unarmed twitch to get around having that animation come out, increasing your DPS considerably (I would assume). Either way though, it seems like the DPS would just be too low due to not having offhand attacks proc.

[Robock]

First of all, thank you for sharing your research.

It's because in testing them, they matched the fast THF class (i.e. greataxe) rather than the slow THF class (i.e. greatsword). I think each of the THF weapon types basically will need to be tested again to see how Turbine did them after when they equalized weapon speeds way back when.

In trying to figure out which weapon was better, I came to following conclusion regarding Base DPS (literally Base Damage Rating but I read it as DPS).

When first defining the Attack Delay as Average Damage / DPS, the delay varied from one weapon to another. But after including the critical hit chance and multiplier, all the weapons I have came down to the same Delay of 1 sec with the exception of the heavy mace ad the club. But for those last two, if I calculate the DPS assuming a delay of 1, I get the same DPS as the Base DPS with two decimals rounded.

I don't have a greataxe, but the Maul have the same Delay as the Greatsword. The thing to remember is that the text is just a base damage rating. So the delay if equal 1 seconds means damage per seconds, otherwise the damage rating is damage per tic, for however long the game tic last. But in the end, I find that delay to be constant in Great sword, Maul, Heavy mace, Club, short sword, long sword, and throwing axe.

As the item description doesn't seem to adjust to my attack speed modifiers (such as haste), I would go with the base damage rating meaning a damage per tic where its length varies under different buff/debuff. If all this is right, then comparing which weapon is better between different weapon type become easier as all these weapon have the same delay.

[edited out :]
But now if the delay between weapon varies then the base damage rating is only useful within one weapon type. But even in that case there was a point at which they were all the same. For example, I notice that at BAB 0, all weapon category started equal at 3.00. So in conclusion, is the Base Damage Rating any good?
[/edit]
[and adding:]
Rereading the chart and the comment on post #13, I see that at any BAB, all weapon are at the same attack rate. So the difference between weapons Base Damage Rating, is that the DPS is affected differently by haste depending on its weapon type. So a 15% Haste for example, would bring my 8.80 BDR greatsword up by 14.4% to 10.067 while bringing up a 8.25 greataxe of 15.5% to 9.53. In the end a Paladin like me would not see a big difference, the 8.80 even though hasted a bit less, is still better than the 8.25 weapon.

[Kinerd]

Base damage rating is not a good thing to use. It assumes a hit on a 1 (which is an automatic miss), 2 and up (which may not necessarily be the case in your particular situation), assumes 0 Strength bonus and 0 damage bonus, assumes no Improved Critical, and does not take into account any enhancement effects such as Frenzied Berserker or Kensai.

[Vanshilar]

This post covers what twitching is, testing results of THF twitch attack speeds, and its testing history. A future one will cover when it is better to twitch as opposed to the standard standing still and attacking (or, "auto-attacking").

Twitching description
In DDO, twitching refers to interrupting your attack animation by alternating between moving and standing still when you're attacking. The reason is that the later standing attack animations are slower, and so interrupting the animation sequence by moving will reset your attack animation to an earlier, faster one, thereby increasing your overall attack rate (and hence possibly increasing your DPS). It is generally used for two-handed fighting (THF), but can also occasionally be used for other circumstances, such as unarmed without monk levels (because the kick animation is absurdly slow). Note that although your attack speed is increased, you will also receive -4 to-hit on half of the attacks due to moving.

First, let's look at how the attack animations work. When standing, there are four attack animations that are used sequentially: a baseball swing from right to left (1st), a vertical downward swing (2nd), a vertical upward swing (3rd), and a left to right swing (4th). When moving, there are two attack animations: an upper right to lower left swing (1st), and a lower left to upper right swing (2nd). Which animation follows which is shown in the diagram below:



So for example, if you started moving at the end of the 3rd standing animation, you would next do the 1st moving animation. If you stopped moving at the end of the 2nd moving animation, you would then do the 3rd standing animation. And so forth. From the above diagram, you can see the various possible attack animation loops that the game can cycle through.

For the standard THF standing attack animation, unbuffed, the durations of each attack are roughly as follows:

attack	duration (seconds)
1st	0.621
2nd	0.410
3rd	0.938
4th	0.804
average	0.693

The times are based on when the attack's result (i.e. hit, miss, etc.) show up in the combat log. As you can see, the 2nd THF attack animation (a vertical downward strike) has a fast cooldown -- you can do a new attack very quickly after it completes. You can also see that the latter two attack animations are relatively slow. The average duration is around 0.693 seconds, which works out to around 86.6 swing animations per minute.

Twitching relies on using the attack animation loop highlighted red in the above diagram. Rather than cycling through all the standing animations, you move before the end of the 2nd standing attack animation. This makes you do the 1st moving animation, during which you stop moving, and thus returning to the 2nd standing animation. The 1st moving animation is actually not that fast -- around 0.764 seconds -- but the average duration of this loop, the 2nd standing animation + the 1st moving animation, is 0.587 seconds, which then works out to (in this case) 102.2 swing (attack) animations per minute, which is around 18% more animations than if you were just standing still. Because you are effectively having more swings per minute, you are therefore also potentially increasing your DPS.

Twitch testing results
To test twitching swing animation speeds, I basically backed up into a tavern table at the appropriate time. In the videos, it will look like I'm not moving, but actually, the character is trying to move backwards into the table at the end of the 2nd standing animation. Otherwise, the procedure matches that given in the original post. The results of the tests, in SPM (swing animations per minute, or attack animations per minute), are:

fTwitch -- greataxe
boost	0%	10%	15%	20%	25%	30%	35%	40%	45%
none	99.4		118.0	124.9	131.9	137.9			
collar		112.1			131.1	137.1	143.2	150.8	
haste			119.3			137.7	143.2	150.9	156.5
average	99.4	112.1	118.7	124.9	131.5	137.6	143.2	150.8	156.5

sTwitch -- greatsword
boost	0%	10%	15%	20%	25%	30%	35%	40%	45%
none	102.4		119.7	125.3	131.5	137.1			
collar		113.3			131.1	137.3	142.0	149.1	
haste			119.6			136.5	142.4	148.3	154.2
average	102.4	113.3	119.7	125.3	131.3	137.0	142.2	148.7	154.2

Note that the greataxe counts as a "fast THF" weapon, while the greatsword counts as a "slow THF" weapon, and hence "fTwitch" and "sTwitch" respectively. As usual, the linear regression formula that best matches this data is in the original post, and the videos that this testing was based on is in the second post.

The most interesting thing about these test results is that they differ significantly from previous work on attack speeds. Given a 15% attack speed modifier from the haste spell, the following are the estimated attack speeds given by cforce's attack speed estimator for various levels of haste boost:

Boost%	fTwitch	sTwitch	Unarmed	TWF	fastTHF	slowTHF
0%	128.4	128.4	115.5	105.5	102.1	102.1
15%	146.6	146.6	132.2	119.5	112.5	112.5
20%	153.9	153.9	139.0	125.0	116.4	116.4
25%	161.9	161.9	146.4	131.1	120.7	120.7
30%	170.8	170.8	154.7	137.8	125.3	125.3

while the following are the estimated attack speeds given by my linear regression formulae:

Boost%	fTwitch	sTwitch	Unarmed	TWF	fastTHF	slowTHF
0%	118.5	119.5	111.3	102.2	99.9	99.1
15%	137.6	136.9	129.4	117.8	113.3	111.6
20%	143.9	142.7	135.5	123.0	117.8	115.8
25%	150.3	148.4	141.5	128.1	122.2	119.9
30%	156.6	154.2	147.5	133.3	126.7	124.1

The difference, percentage-wise, is below:

Boost%	fTwitch	sTwitch	Unarmed	TWF	fastTHF	slowTHF
0%	8.29%	7.37%	3.71%	3.24%	2.18%	2.98%
15%	6.54%	7.09%	2.18%	1.49%	-0.72%	0.78%
20%	6.90%	7.86%	2.60%	1.70%	-1.12%	0.57%
25%	7.74%	9.08%	3.49%	2.31%	-1.25%	0.63%
30%	9.07%	10.79%	4.89%	3.34%	-1.13%	0.93%

As you can see, most of the results are fairly similar, differing by a few percent at most. However, the twitch swing animation speeds were reported as being significantly faster (on average, by around 8%) than what my testing results indicate. And if you doubt my results, I would recommend that you download the videos and count up the animations yourself -- that's why they're there.

Twitch testing history
The reason for this discrepancy has to do with how the data was originally collected. Unlike some of the other data, the twitch numbers weren't tested by cforce himself but based on a video by Shade, as you can read about in Monkey_Archer's attack speed thread, and in cforce's attack speed thread. However, Shade was using a capped barbarian for his video. Unfortunately, as I documented here and Monkey_Archer confirmed here, it turns out that barbarians were getting a hidden alacrity boost from their capstone. So Shade's attack speed was taken as a baseline speed for twitch, whereas in reality, it was benefiting from an alacrity bonus. Hence, the resulting estimated numbers were faster than the actual numbers.

For example, a pure fighter pre-update 5, with 20% from madstone, 30% from haste boost 4, and 10% from the fighter capstone, is estimated by my formula to have 136.6 SPM while not twitching, and 171.5 SPM while twitching, a 25.5% increase by twitching. By cforce's formula, however, the fighter would be estimated to have 136.3 SPM while not twitching, and 193.7 SPM while twitching, a 42.1% increase. Now looking at Durnak's pre-Update 5 capped fighter + epic SoS video here, taking a long stretch of standing animations (from frame 2986 to 3346 at 29.97 frames/second), he attacks at 139.0 SPM when standing still. When twitching however, such as from frame 2075 to 2116 or from frame 2170 to 2211, he attacks at 175.4 SPM, so by twitching, his attack speed increased by 26.2% -- thus matching my formula much more closely.





(1:10.603 - 1:09.235) / 4 attacks = 0.342 seconds per attack
60 seconds per minute / (0.342 seconds per attack) = 175.4 attacks per minute

In short, twitch has always been at the speed matching my formula above (or at least, since March 2010, so likely since Sept 2009 or so with Module 9, when they last did a major change to attack speed mechanics), just that the current DPS calcs have been using incorrect values for its animation speed and hence, the DPS output for this type of weapon style.

The remaining question then is when is it better to twitch, as opposed to just standing still and attacking (which I'll often shorten to "auto-attacking" since that's all you really have to do), but I guess I'll cover that in a future post, since I think this one is long enough already.

[Feithlin]

On terminology: In Update 5, two weapon fighting (TWF) offhand attacks have become probabilistic, rather than in a set sequence. Furthermore, the main hand can have a chance to strike twice, or "doublestrike". Because of this, there may be some confusion when I talk about "attack speeds", since it may refer to multiple things. For this thread, I will generally be talking about the character's swing animations per minute, or how often they make a new swing animation (while standing still), not the proc rate of different attacks (main hand, offhand, glancing blows, doublestrike) per minute. "Alacrity" also means swing animations per minute, by the way. I will sometimes shorten "swing animations per minute" to "SPM".

The thread is highly interesting, but I would need some more info to evaluate the dps of my characters (and the possible adjustments). Where could I find informations about the proportion of main hand and off hand strikes within the swings?

[Backley]

Where could I find informations about the proportion of main hand and off hand strikes within the swings?

In your Feats and Enhancements
For TWF:
Without any special feats: 20% off-hand attacks on each swing
With Two Weapon Fighting feat: 40%
With Improved Two Weapon Fighting feat: 60%
With Greater Two Weapon Fighting feat: 80%
With Ranger Tempest I enhancement: +10%
With Ranger Tempest II enhancement: +10%

Also you need to factor in Double Strikes on the main-hand attack.

For THF, you may want to factor in Glancing Blows.

I think that covers it?

[Feithlin]

In your Feats and Enhancements
For TWF:
Without any special feats: 20% off-hand attacks on each swing
With Two Weapon Fighting feat: 40%
With Improved Two Weapon Fighting feat: 60%
With Greater Two Weapon Fighting feat: 80%
With Ranger Tempest I enhancement: +10%
With Ranger Tempest II enhancement: +10%

Also you need to factor in Double Strikes on the main-hand attack.

For THF, you may want to factor in Glancing Blows.

I think that covers it?

So the off hand attack test is made for every swing, thanks, that's what I missed somehow.

[grodon9999]

So pretty much any DPS numbers pulled from AO's calc are inflated and should be discounted?

[Aaxeyu]

So pretty much any DPS numbers pulled from AO's calc are inflated and should be discounted?

So it seems.
I'll update the calc with numbers from this thread. Gonna take Vanshilars words as gospel, I'm too lazy to test it myself

[grodon9999]

So it seems.
I'll update the calc with numbers from this thread. Gonna take Vanshilars words as gospel, I'm too lazy to test it myself

You rock! Thank you. I tried to figure it out but my brain can't get around the formulas.

Attack speeds and the haste multipliers to?

[grodon9999]

Need to know if anyone can find confirmation . . . was the bug with Tempest still giving a 10% speed boost corrected in U7 or U8?

[k1ngp1n]

Need to know if anyone can find confirmation . . . was the bug with Tempest still giving a 10% speed boost corrected in U7 or U8?

My basic testing has suggested it has been fixed, but I'm about to check again as soon as I get in game. Gimme 2 or 3 mins.

[cforce]

How did I miss this thread the first time around? +all rep.

Pretty interesting results, and definitely some different characteristics from when I did the bulk of my testing. This looks *much* simpler and cleaner than 'back in the day'. The main thing that drove me away from an additive model and into a multiplicative one was that I consistently got a different speed in testing for, say, tempest (10%) + boost (15%) than for haste (25%) or boost (25%), and that for very high values of boost (say, 25% haste + 30% boost + 10% tempest), the benefit dropped off below linear. It looks like it fits nicely now all the way out 45%, at least. They must have made some changes that affected it back in the Update 2 drop -- I'm glad someone has finally done the due diligence to recheck all the numbers after that drop! (The best I ever did was to leave my model intact, but to update some of the coefficients I was using to best fit observations. Looks like throwing out the model and starting from scratch was a better idea...)

Unfortunately, it looks like TWF getting more benefit than THF from speed bonuses hasn't changed much. Oh well...

Thanks for putting this together!

[k1ngp1n]

Need to know if anyone can find confirmation . . . was the bug with Tempest still giving a 10% speed boost corrected in U7 or U8?

OK, so I just reset my enhancements and went and beat on the training dummy. Then took just Tempest 1, no other damage/speed adds, and beat on it again.

Zero difference in attack speeds. Tempest 1 does NOT add 10% anymore. That little happy bug was fixed.

[cforce]

The remaining question then is when is it better to twitch, as opposed to just standing still and attacking (which I'll often shorten to "auto-attacking" since that's all you really have to do), but I guess I'll cover that in a future post, since I think this one is long enough already.

I plugged these estimates into my DPS estimation spreadsheet (a branch of A_O's model), and initial glance suggests that the scenarios where twitching would be expected to give a benefit are pretty rare. Single target, it looked like it would give a small advantage for a Kensai 20 THF build, but result in a drop-off for a Frenzied Berserker 20, and about a tie on something like an Archon. 2 targets, it's a significant drop-off.

I know there are some folks who still maintain that twitching is a significant single-target DPS benefit. I guess I'd like to see them perform against the airship dummy, twitch and regular, to see some counter evidence. Fraps or it didn't happen?

[t0r012]

don;t know if anyone has point this out yet from your unarmed.

Again, the video was recorded at 10 frames per second. Each attack round was 4 swing animations. The measurement error is 1 frame, so with an average testing length of 17.7 seconds, the measurement error was around 0.57%, or varied from 0.48 SPM to 0.75 SPM (depending on the test).

A couple of conclusions from this:
* Lesser wind stance provides a 7.5% alacrity bonus which does NOT stack with the 15% from the haste spell.
* A linear fit gives that the formula is:
Unarmed swings per minute (BAB +3/+4) = 89.4 * (100% + 1.39*sum of each boost%)

monk attack animations are not 4 they are 5.
step 1 main hand straight punch
step 2 main hand back fist (the one I think you aren't counting)
step 3 off hand swing
step 4 kick #1
step 5 kick #2

[Thanimal]

Since I can't seem to sleep right now, I thought I'd jump in here to give rep and join the chorus saying: Thanks for redoing this.

On a slightly more minor note: I am actually pretty psyched that Turbine had the guts to rip out the cluster of an implementation that cforce and I spent a TON of time trying to fit to all sorts of models and couldn't believe the ridiculous levels of complexity. This new implementation actually makese SENSE!

[Fougere]

t0r012 is right regarding monk unarmed attack speed, they have 5 swings per sequence, not 4.

With 4 bab, I'm getting ~108 swings per minute. If I twitch, I'm going up to ~123.
So including twitching, that's around +55% speed compared to a twf of the same bab!
If it scales to bab 20, and I bet it does, it would change the top dps builds, since the dps calculator sheet is also based on incorrect unarmed attack speed.