Wereform Attack Speed Formula

[Tycho Maudd]

||ugh TheDragoon's wereform guides I spent some time looking at his wereform speed formula that he came up with, and while close, it doesn't seem exact(and he says it isn't), but there must be a real formula that the game uses. Looking through other posts, I found this post:

http://www.lurkerlounge.com/forums/index.p...whirlwind+speed

In this post, I saw something interesting to me,

*snip*
delay = a1_frames*256 / ((weapon ias+wsm+100)*anim speed/100)
a1_frames = frame length of normal attack (attack1)
anim speed = 256 for all attacks
weapon ias = sum of fast/faster/fastest attack speed mods on the weapon
wsm = negative 'speed' from weapons.txt
This is then "breakpointed":
delay = real delay
*snip*
bit ot: The formula I gave for 'delay' is also used to determine the very slow-very fast attack speed display on weapons (and it is also used in wereform attack speed calculations)

This formula looks abit like part of TheDragoon's formula for wereform attack speeds, and if my memory serves correctly, the forumula on TheDragoon's site hasn't changed since this post was made, and I am thinking that this might help find out the formula, but I am clueless as to how to derive a formula from given data.


Edit: Messing around abit in Excel, I used the delay=a1_frames*256 / ((weapon ias+wsm+100)*anim speed/100) formula and then used the IAS formula on the "delay" I got and frames I got turned out to be very close, if not the same as the tables on TheDragoon's site, it just seems like the rounding I'm using is off.

[Hammerman]

Try this (btw, I have not, so it might turn out incorrect):

From http://www.lurkerlounge.com/diablo2/inform...s-lemekim.shtml , a bit modified,

Frames = {256*(Base + 1)/[(100 + Speed Increase)/100*Animation Speed]} - 1

Speed increase = (120 * item_ias) / (120 + item ias) + skill ias - wsm

Now, normally 'Animation speed' is 256. But for wereform attack speeds it uses a differently calculated number... here's how. We begin with:

Animation speed = a1_frames*256 / ((weapon ias+wsm+100)*anim speed/100)

Aha, the 'delay' formula. It will, by the way, use the Druids human form values here. If not using a weapon, then Animation speed = 19. We modify the current value:

Animation Speed = (prev frames * 256) / Animation speed

prev frames = animation length of previous mode, wich is always neutral (use the shifted form values here):

bear = 9
wolf = 10

See if you can make anything of this, and always remember to round down after each division.

[Tycho Maudd]

I'm not getting correct values, but I don't think I'm doing it right since I don't fully understand what your saying


You use the words Animation Speed several times in there, and each time it seems its used differently, could you be more clear on how it is used?

Also, what do you mean by: Animation Speed = (prev frames * 256) / Animation speed ?

Is that second Animation speed the speed you get from the delay formula? And is the the first one the one that gets plugged into the frames formula?

Also is that prev frames the shifted values you gave? (9 and 10 for bear and wolf?)

[Dagni]

Well, after much confusion of my own, I think I've figured out what Hammerman meant.

Hammerman:

Now, normally 'Animation speed' is 256. But for wereform attack speeds it uses a differently calculated number... here's how. We begin with:

Animation speed = a1_frames*256 / ((weapon ias+wsm+100)*anim speed/100)

But since he was using the 'delay' formula, he didn't change or explain any of the variable names. So for that we copy from the whirlwind thread:

a1_frames = frame length of normal attack (attack1)
anim speed = 256 for all attacks
weapon ias = sum of fast/faster/fastest attack speed mods on the weapon
wsm = negative 'speed' from weapons.txt

Ah, but what is the frame length of a normal attack for a shifted Druid? That is what Hammerman is explaining when he says:

It will, by the way, use the Druids human form values here.

So a1_frames equals whatever a unshifted Druid will get for 'Base + 1' with whatever type of weapon is being wielded (ie one-handed, two-hand sword, bow, or whatever).

Ok, now we have a value for animation speed, but that isn't the final value for animation speed.

We modify the current value:

Animation Speed = (prev frames * 256) / Animation speed

So that could be rewritten:

New Animation Speed = (prev frames * 256) / Old Animation speed

Where Old Animation speed is the value we just got from the 'delay' formula. And prev frames is:

prev frames = animation length of previous mode, wich is always neutral (use the shifted form values here):

bear = 9
wolf = 10

9 for the bear, and 10 for the wolf.

Now we can finally use that New Animation Speed and plug it into the standard weapon speed formula in place of the usual 256 that goes there.

Frames = {256*(Base + 1)/[(100 + Speed Increase)/100*Animation Speed]} - 1

Speed increase = (120 * item_ias) / (120 + item ias) + skill ias - wsm

Note that because Hammerman copied from two different places, this formula and the 'delay' formula differ in their definitions of 'wsm'. This formula uses the value in weapons.txt, rather than the negative of the value as in the other formula.

The only remaining thing to know is that 'Base' is always 11 for the Bear, 12 for the Wolf.

So here are the formulas again, in the order in which they should be applied, and hopefully clearer (and with the 'wsm' term self-consistant):

Anim speed0 = [a1_frames*256 / [(weapon ias+wsm+100)*256/100]]

a1_frames is the 'Base + 1' value for a Druid using that weapon type

Anim speed1 = [prev frames * 256 / Anim speed0]

prev frames = 9 or 10 (Bear or Wolf, respectively)

Speed increase = [120 * item_ias / (120 + item ias)] + skill ias + wsm

EDIT: Oh, and Speed Increase is capped at 75.

Frames = {256*(Base + 1)/[(100 + Speed Increase)/100*Anim Speed1]} - 1

'Base' = 11 or 12 (Bear or Wolf, respectively)

*[] denotes round down, {} denotes round up.

-------

Anyway, if I interpreted and applied all that correctly, than this formula does not quite fit the observed data. I compared to TheDragoon's Attack Speed Chart (Werebear) for a One-handed Axe with base speed 0. I didn't know what a1_frames would be for a one-handed axe, but given that the value on the chart with no ias of any kind was 22, the only value that would fit is 17. Using that, and 11 for 'Base' and 9 for 'prev frames' the formula was near the chart but differed at (among other places) 25, 35, and 95 wias (with no oias).

- Dagni

[Hammerman]

Dagni,

Anyway, if I interpreted and applied all that correctly, than this formula does not quite fit the observed data. I compared to TheDragoon's Attack Speed Chart (Werebear) for a One-handed Axe with base speed 0. I didn't know what a1_frames would be for a one-handed axe, but given that the value on the chart with no ias of any kind was 22, the only value that would fit is 17. Using that, and 11 for 'Base' and 9 for 'prev frames' the formula was near the chart but differed at (among other places) 25, 35, and 95 wias (with no oias).

Shame. I thought it would match up... as I said, I didn't test it myself but was only speculating. I have, however, made a little speed calculator that gives results matching the ones on TheDragoon's site, in most cases. With oias = 0, or wias = 0, it matches perfectly (for werebear at least), but when mixing high values of those two the results are sometimes off a frame or two. That calculator mimics the games frame counter, and does not use the normal speed formula.

But the process I described is used, and the final value is replaced with the latter 256 factor in the formula. Perhaps I or you made a mistake somewhere. I'm in no mood to go over what I originally posted now, but will hopefully have time tomorrow to check it and try to come up with something that works.

[Dagni]

Well also, if the formula matches all but a very few cases, it always could be a mistake on the table of test results, although that does seem unlikely.

Hammerman:

With oias = 0, or wias = 0, it matches perfectly (for werebear at least), but when mixing high values of those two the results are sometimes off a frame or two. That calculator mimics the games frame counter, and does not use the normal speed formula.

Are you capping the Speed Increase formula at 75? (Or rather, the internal game code that causes the cap in the formula) If not, that would lead to results that were too low for high values of ias. Hmm... but I suppose if that were it, than unmixed high values of either oias OR wias would be off too - unless TheDragoon's tables don't go high enough to reach the cap without mixing....

(EDIT: Added...)
Anyway, I may be way off base here, but that's the one thing that jumped out at me that could cause that sort of problem (or the reverse, if you were applying a cap, and there wasn't one). Also, way back when the diminishing returns was finally figured out, IIRC Jarulf mentioned that he was puzzled about the cap existing, as he couldn't find anything internally that would cause the observed effect described by the cap.

Jarulf @ Aug 01 2001:

As such, I would say the proposed "cap formula" (I still wonder if there really is a cap, not that I doubt it) is similar, an attempt to find a formula matching observations.

- Dagni

[Ruvanal]

prev frames = animation length of previous mode, wich is always neutral (use the shifted form values here):

bear = 9
wolf = 10

When I checked the animation lengths of the wereforms, I had found that the NU (neutral) animations had a length of
Bear=10
Wolf=9

Which is a reverse of what you have listed. Looks like you might be plugging in the wrong numbers.

Also, would the previous mode always be the NU version if you are holding down the attack key to set up a continuous cycle of attacks? It would seem to me that the previous mode after the first cycle would actually end up being one the attack animations for the second and successive repetitions of the same attack. With the wereforms, the animation lengths of their only attack animation is
Bear=12
Wolf=13

[Dagni]

Although I hardly did a comprehensive check, using 10 instead of 9 for the Werebear got rid of the inaccuracies I was experiencing last time. Note that I changed the number I was using for 'a1_frames' from 17 to 19 to match the observed datapoint of 22 frames for 1h-axe with unmodified attack speed. So this formula DOES seem to fit the experimental data.

Also, would the previous mode always be the NU version if you are holding down the attack key to set up a continuous cycle of attacks? It would seem to me that the previous mode after the first cycle would actually end up being one the attack animations for the second and successive repetitions of the same attack. With the wereforms, the animation lengths of their only attack animation is
Bear=12
Wolf=13

Since using 10 for the Bear seemed to work so well, I would doubt it.

Thanks again to Hammerman for demystifying another part of the game. :)

- Dagni

Edit/p.s. Oh, one question: Hammerman I believe said that a1_frames would be the same as for an unshifted Druid. Is a 19 frame animation correct for a Druid with a 1h-axe (So unmod base swing speed =18)?

[Dagni]

Well, it matches every datapoint of TheDragoon's for the Werebear chart with One-handed Axe of base speed 30, and the Werewolf chart with One-handed Axe of base speed 0. So I think it's pretty safe to say that this is the correct formula. :)

delay = [256*(WeaponBase + 1) / [(weapon ias+wsm+100)*256/100]]

prev frames = 10 or 9 (Bear or Wolf, respectively)

Anim speed = [prev frames * 256 / delay]

Speed increase = [120 * item_ias / (120 + item ias)] + skill ias + wsm
if (Speed increase > 75): Speed increase = 75

WereBase = 11 or 12 (Bear or Wolf, respectively)

Frames = {256*(WereBase + 1)/[(100 + Speed increase)/100*Anim speed]} - 1

Note that skill ias of course includes the Werewolf inherent bonus and is 68 (at slvl20) with TheDragoon's werewolf charts.

As one can see, I renamed some of the variables here, hopefully this way is more clear. In particular, I renamed a1_frames to 'base + 1' as that is what it is normally referred to in the standard weapon speed formula, then gave the different Bases different names to differentiate between weapon base animation length and wereform base animation length. Also 'delay' had been called 'animation speed' earlier in this thread, but I switched it to what it was called originally in the Whirlwind thread.

Although this should work for standard Wereform attacks, I don't know how Fury works. I tried changing just one of 'WereBase', 'prev frames', or 'WeaponBase' to a different value and didn't get an exact match (for the same 1h-axe base 0 chart I used for Werewolf standard attack), although 'prev frames' = 15 was close enough I didn't notice the differences right away.

- Dagni

[Ruvanal]

Although I hardly did a comprehensive check, using 10 instead of 9 for the Werebear got rid of the inaccuracies I was experiencing last time. Note that I changed the number I was using for 'a1_frames' from 17 to 19 to match the observed datapoint of 22 frames for 1h-axe with unmodified attack speed. So this formula DOES seem to fit the experimental data.

Also, would the previous mode always be the NU version if you are holding down the attack key to set up a continuous cycle of attacks? It would seem to me that the previous mode after the first cycle would actually end up being one the attack animations for the second and successive repetitions of the same attack. With the wereforms, the animation lengths of their only attack animation is
Bear=12
Wolf=13

Since using 10 for the Bear seemed to work so well, I would doubt it.

Good that was what was needed to clear up the problem. Like Hammerman I did not feel like trying to wade therough the 'mess' of formulas right now (and try to match to the imperical charts).

Edit/p.s. Oh, one question: Hammerman I believe said that a1_frames would be the same as for an unshifted Druid. Is a 19 frame animation correct for a Druid with a 1h-axe (So unmod base swing speed =18)?

Hand axe uses the 1hs animation and the length is 19 frames.

human druid
mode animation_length
hth 16
1hs 19
2hs 21
1ht 19
2ht 23
staf 17
bow 16
xbow 20

Thanks again to Hammerman for demystifying another part of the game. 

I am very much in agreement on this. :D

[Dagni]

Like Hammerman I did not feel like trying to wade therough the 'mess' of formulas right now (and try to match to the imperical charts).

Well, fortunately the first time I 'waded' I wrote a tiny program so I wouldn't have to calculate the values by hand. So all I had to do was change a couple of numbers, and then have it spit out a whole chartful of numbers at once, and I could easily compare the revised formula with the emperical charts.

Like Hammerman, I wasn't about to double-check all my work over again anytime soon. Ugh. But with something new to try, it was happily a quite simple change.

- Dagni

[Hammerman]

So it did work, excellent. Thanks for correcting me there Ruvanal, I thought I remember wich token the bear had and wich one the wolf had (40 and TG). Doh.

And since we're on a speed related issue, I'd like to point out something that most people aren't aware of (at least I noticed that it was incorrect on TheDragoon's site, and the speed mechanics page here). Fanaticisim doesn't add directly to the 'speed increase' value as most ias boosting skills. Rather it modifies the wsm. Chars have a base 100 'attack rate'. When equipping weapons, it subtracts the value in 'speed' column from that (if I understand your concept of wsm correctly, you could say that it adds the wsm to attack rate). Fanatcisism then modifies this value, as:

attack rate_new = attack rate_old + (attack rate_old * fanat %)

Whereas most skills just do:

attack rate_new = attack rate_old + ias % boost

That SHOULD mean (note should, I havent checked this) that if a Barbarian receives Fanat from a friendly Paladin, his attack rate should be:

attack rate_new = attack rate old + frenzy boost ; first do frenzy speedup

Then the fanat bonus kicks in as:

attack rate_new = attack rate_old + (attack rate_old * fanat %)

To apply the attack rate value correctly to the normal speed formula, you'd have to do:

Speed increase = attack rate + item_ias ; item_ias after diminishing returns, that is

Cap this at 175, and add it normally to the speed formula but skipping the '100 +' part before 'Speed Increase'.

[Dagni]

That SHOULD mean (note should, I havent checked this) that if a Barbarian receives Fanat from a friendly Paladin, his attack rate should be:

attack rate_new = attack rate old + frenzy boost ; first do frenzy speedup

Then the fanat bonus kicks in as:

attack rate_new = attack rate_old + (attack rate_old * fanat %)

So let's see if I understand this correctly. First off, Fanaticism is always applied after other skills, not just Frenzy? If so, then the practical effect could be summed up like this (?)

Speed Increase = (100 +)** [120 * item_ias / (120 + item ias)] + skill ias + wsm + [fanat ias*(wsm + non-fanat skill ias)/100]

**Doesn't make any practical difference if you add the 100 now, or in the other formula, as long as you change the cap (75 or 175) as appropriate.

With that final piece in bold being the only difference from normal. So, for example, with a 20% faster base weapon (wsm = 20), and +25% fanaticism, instead of +45 speed increase, or 145 total speed, you'd get 150 total speed (+ 20*25/100 = +5).

- Dagni

p.s. What is the animation length for Hunger/Rabies for the Werewolf, and Hunger for the Werebear? Oh, and Fury if it has its own animation.

[Ruvanal]

p.s. What is the animation length for Hunger/Rabies for the Werewolf, and Hunger for the Werebear? Oh, and Fury if it has its own animation.

Sorry, missed those the first time due to not having much time to even do the post.

Feral Rage, Maul and Fury use the A1 animations sequence.
Fire Claws use the A2 animation sequence.
Rabies and Hunger use S3 animation sequence.
Did I miss any?

For the wolf and bear forms the A1 (right paw swing)and A2 left paw swing) sequence are their normal attack length WereBear=12, WereWolf=13.

For the S3 sequence (biting attack animation) the lengths are WereBear=13, WereWolf=10.

Sorry to miss these earlier but not all of these special sequences are for attacks. some are for things like the shapeshift effect or kicking actions and such. Nor are they always consistent between the different classes either.


You might want to reconsider how you 'renamed' some of those variables. Their orginal designations came from before the .DCC files had been cracked and modders could look at and manipulate the animation files. The term 'base+1' can actually be particularly misleading in some ways. This 'base+1' is the anim_length, which in reality is the true "base" to working off of for many things. Some of which can more readily be seen if you are using that for expressing your figures.

First a quick digression about the repeat attack skills like Strafe and Zeal (Hammerman please fill in with facts ;) ). Most of the attack animation should be set for an appearance like a Golf Swing; the target is hit at some point near the mid point of the swing, not at the end (last frame). As such to run a series of multiple repeat attacks you would not be repeating the entire swing sequence, but in fact only a portion of the the overall attack. From the various posts that I have seen on this it appears that the standard amount of a repeat sequence is to use 1/2 of the frames for the repeating portion. Then this repeat_anim is what is used in the rollback formula to determine the number frames to actually roll back on the repetative cycle. Frames_to_rollback= rollback*repeat_anim/100
(yes this is different than what Jarulf has listed in the past, but can better fit what is being observered from what I can see)
In the case of Zeal the rollback is 100% and this would result in using the full amount of the repeat_anim.

For example lets look at the page that Hammerman first linked to and its example for Zeal. They are listing a Paladins 1 handed weapon base as being 14 (anim_length=15). They then give without much explanation that when using Zeal that a 1 handed weapon should use a value of 6. Does not seem to come from anywhere in particular does it? But if you take into account that Zeal uses a 100% frame rollback and that the anim_length is 15; you can get 15/2=7 as the amount of frames that are being used for the repeating sequence. Note that a Zeal base of 6 which would correspond to the anim_length of 7 (6+1) that is apparently being used in this case.

In a similar manner you can then try checking the repative cycles of skills like Strafe.
Amazon bow anim_length=14, repeat_anim would be 14/2=7, rollback of Strafe is 50%.
Frames_to_rollback= 50*7/100 =3
For Amazon using a xbow, anim_length=20, repeat_anim=20/2=10.
Frames_to_rollback= 50*10/100 =5
Which match the accepted figures.

Ama Fend has a rollback of 60%.
1ht anim_length is 15, repeat_anim=7
Frames_to_rollback= 60*7/100 =4
2ht anim_length=18, repeat_anim=9
Frames_to_rollback= 60*9/100 =5
How well does this fit with a rigourous testing of Fend?

This relationship would be somewhat obscured if one is alway thinking of the 'base' as the real value and not realising why the "+1" is including in certain spots.

The rollback for Fury is 100%.

[Dagni]

Thank you. That was particularly clear and well explained. :)

Yes, I understand how the 'base + 1' can be misleading. I used it because that is the way the original speed formula was written. And that was because of the way a weapon with no speed modifiers swings a frame faster than the true anim_length.

For the S3 sequence (biting attack animation) the lengths are WereBear=13, WereWolf=10.

Interesting, if that were the only number changed in the formula, that would make a wolf's bite much faster than a bear's. But it must not be the only difference, at least for the Bear, because that would make him slower when biting, and that's not the case.

- Dagni

[Hammerman]

Ruvanal,

Very good explanation of the rollback procedure. The 'attack frame' is usually half through the animation, but if not its usually only 2-3 frames before/after the animation is half through. Paladin attack 1 2hs has attack frame = 8, but anim length = 20, as an example. Except the assassins kick animations, where its in the first quarter of the animation.

The exact formula for rollback is:

current frame_new = current frame_old * (100 - rollback %) / 100

But your formula can be used as well, I guess, and it is simpler. Note that the attack is done at the attack frame, or when it has passed. Example:

Necromancer; attack 1; attack frame = 9; wclass = 1hs; anim_length = 19; maxed ias. The frame play order is:

1
3
5
7
8
10 <- attack frame
12
14
15
17

Not really important, kinda trivial info.

Dagni,

Let's take an example with:

25% fanat
10 wsm (wsm = negative 'speed' here)
50% other skill ias

Speed Increase = (100 +)** [120 * item_ias / (120 + item ias)] + skill ias + wsm + [fanat ias*(wsm + non-fanat skill ias)/100]

From this we get:

Speed Increase = 81 (or 181), effectively 75 (or 175)

Using my formula...

[quote]attack rate_new = attack rate_old + (attack rate_old * fanat %)

To apply the attack rate value correctly to the normal speed formula, you'd have to do:

Speed increase = attack rate + item_ias ; item_ias after diminishing returns, that is[quote]

...the result will be:

Speed Increase = 261, effectively 175. Here's how you should do it:

attack rate = 100 + wsm + skill ias

The effect of fanaticism is:

attack rate_new = attack rate_old + (attack rate old * fanat % / 100)
Speed Increase = attack rate + item_ias

Then you skip adding 100 to 'speed increase' in the normal speed formula. Note that I missed adding '/ 100' in the fanat effect fromula in my original post.

No comment on fury attack speeds, exceot that it is a sequence animation (as Ruvanal said) and sequence anims often have different speed calculations based on the skill they are assigned with.

[Dagni]

Hmm... I get Speed Increase = 200, effectively 175 with each formula.

Speed Increase = 100 + [120 * item_ias / (120 + item ias)] + all_skill_ias + wsm + [fanat ias*(wsm + non-fanat skill ias)/100]

= 100 + [120*0 (no item ias) /120] + (25 (fanat ias) + 50 (other skill ias) ) + 10 (wsm) + [25*(10 + 50)/100]

= 100 + 0 + 75 + 10 + [1500/100] = 200

Or:

attack rate = 100 + wsm + (other?)skill ias

attack rate = 100 + 10 + 50 = 160

attack rate_new = attack rate_old + (attack rate_old * fanat % / 100)

= 160 + (160*25/100) = 160 + 40 = 200

Or is it "attack rate = 100 + wsm + (all?)skill ias" with fanaticism included? That would still only get me, umm... 231, not 261

Oh, and quick question:

>1
>3
>5
>7
>8
>10 <- attack frame
12
14
15
17

or

1
3
5
7
8
>10 <- attack frame
>12
>14
>15
>17

Which would be the repeat animation for a skill like Zeal, the second, right?

- Dagni

[TheDragoon]

Well bloody hell! Why did you guys wait until AFTER I had put 20+ hours making the calculator to do this? ;)

Seriously, good job. I'll look through it and compare the results to my tables (which are in handy excel format :) ) to double check all of the tables. I guess this just shows that a lot can happen while you're gone (as I've been camping the past week).

EDIT: In messing with the equations (which appear RIGHT!) I was able to generate a correct Fury table for Scythes by changing the "WereBase" from 12 to 7. :) I'm going to go see if I can generate the rest of the Fury charts with that change, as well. I'll work on getting my calculator up and running everything that's been discovered here tomorrow or later tonight! :lol:

EDIT #2: Alas, it doesn't appear to work for the other charts.. Oh well, I'm sure we'll figure it out eventually!

EDIT #3: I've re-worked my calculator to take into account what's been discovered here. I've been going through the tables looking for errors but I haven't found one so far! If you'd like to check out the info easily, check out my calculator. :) Note that the Fury data points still read off of my charts and so it still has limited data points. Again, great job, guys!

Wereform Calculator

[Hammerman]

Dagni,

You're correct, the result will be 200 from both formulas. I have no idea how I came up with the numbers i posted (well, I tthink I used 35% fanat, wrote 261 instead of 216, and various other typos. Was in a hurry.). Nevermind that, good job.

Which would be the repeat animation for a skill like Zeal, the second, right?

Sorry, are the frames marked with '>' the ones that are repeated? Well, in this case, frames 1-10 would be repeated with rollback = 100% (Zeal). See the formula I (or Ruvanal) provided to calculate the rollback effect.

[Kar0n]

but if not its usually only 2-3 frames before/after the animation is half through. Paladin attack 1 2hs has attack frame = 8, but anim length = 20, as an example

Can I say,in most cases the "attack frame" is the basic animation frame/2?
But those exceptions(like pal 2ht and asn kick),how can I get thier values of "attack frame"?
:)

Btw,a skill's "cast frame" is similar,isn't it?

Can "attack frame" or "cast frame" be modifiered by some factor any way?