As before, the game uses this formula,

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

however, now 'Speed Increase' is not simply all of the different speed bonuses added together. Now only the base weapon speed and fanaticism are straight added in (possibly other skills as well; unknown),

Speed Increase = Base Weapon Speed Modifier+ Fanat + [IAS/(1 + IAS/120)]

Also, the Speed Increase is capped at 75%. For Cast Speed, with nothing that's exempt from the diminished returns, the formula can be simplified to

Speed Increase = [Cast Speed Bonus/(1 + Cast Speed Bonus/120)]

For each formula, the [ and ] are for rounding DOWN whatever is inside them. The { and } are for rounding UP whatever is inside them.

In other words, all equipment that gives +X% Faster ____ Speed (even IAS on your weapon) is now subject to this diminishing returns formula.

Effective X = [X/(1 + X/120)]

e.g. If you have a two items each with 10% IAS (total of 20% IAS) then your effective IAS would be:

[20/(1 + 20/120)] = [17+1/7] = 17

I assume that Faster Run/Walk, Hit Recov, and Faster Block are subject to this as well, same as IAS and Cast Speed items.

This formula matches the Zeal data collected by Heri here, the data in the Pike speed thread here, PapaSmurf's data for the Paladin here, and all but one point of the cast speed data provided by VenemousVixen here. Hopefully, VV's Zon chart is off when it says that 175% is 12 frames, and 176% is 11 frames. I got a switch from 12 to 11 frames going from 151% to 152%.

-----

Ok, some examples: You are a paladin, wielding a Broad Sword (base speed of 14 frames for paladin with 1hw, no base speed modifier). Obviously you currently have a 14 frame swing animation. You equip +30% IAS gloves (Sigon's), now:

Effective IAS = [30/(1+30/120)] = 24, so..

{256*(14+1)/[(100 + 24)/100*256])} - 1 = 12

You now have a 12 frame attack. Suddenly you remember to turn on your slvl 10 Fanaticism, which gives +30% Attack Speed. That adds straight on to your effective IAS, so it's now..

Effective IAS = 30 + [30/(1+30/120)] = 54

Plug that into the basic formula..

{256*(14+1)/[(100 + 54)/100*256])} - 1 = 9

Not shabby, down to 9 frames.

Now you decide to attack with Zeal for a little while, your effective IAS doesn't change, so..

{256*(6+1)/[(100 + 54)/100*256])} = 5

Darn, not good enough for a 4 frame Zeal. Now you switch to an Amazon wielding a Repeating Crossbow of Alacrity (base speed of 19 frames, a '-40' base speed modifier, and 20% IAS). For that:

Effective IAS = 40 + [20/(1+20/120)] = 57

Plug that into the basic formula and you get a 12 frame attack. Not too bad. Now a Paladin with slvl20 Fanaticism joins your party, and so what is your speed with him? Well, slvl 20 gives a 35% bonus, so:

Effective IAS = 35 + 40 + [20/(1+20/120)] = 92?

...except that there is a cap of 75% on your effective IAS, so it is 75% instead. So that gives an 11 frame attack, not a 10 frame one. Therefore, that 20% IAS on your Repeating Crossbow is completely useless, so you switch that x-bow for a different repeating x-bow with slightly better dmg that doesn't have the 'of Alacrity' suffix.

- Dagnirauko

Edit: Rewrote the cap info according to how Tenchi described it and added a couple of other minor details.

That's amazing that you figured it all out so fast, and what you have discovered should prove to be extremely useful to so many people too. Congratulations, and thanks for solving this - and thanks also goes to all those who helped to get this

May the wind pick up your heels and your sword strike true.

The Unofficial LL Forum Etiquette
The Unofficial LL FAQ

Thanks for working out the formula!

SL

Tonight I will review the Zon data I came up with. When I posted it, it was like 5:00am and I needed sleep. A typo or an accounting error of some sort may have crept in unnoticed.

VV

In the Arreat Summit, for each character it's listed as a word: e.g. v.slow, slow, normal, fast or v.fast, but how do I know how many base frames that means?

This was prolly aready figured out, so can someone post a link on this? Thx a lot in advance.

- Dagnirauko

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

Ther is no such formula and none even close to it. That formula is an attempt (very good since it seems accurate) pf people to calculate the actual frames that the game will end up showing. That is why there appears the "strange" round up thing, the game never rounds but rather truncate in cals. It is a result of the game mechanism of keeping track of frames.

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.

Finally, I still have a hard time grasping that fanaticism would add straight in with the weapon modifier. That is just not what I see. Oh well, people seem to claim this is correct and in accordance with what they see, and experience when playing.

This is absolutely splendid work, and it was just the sort of thing that I've been waiting (anxiously) for. Thanks so much for doing all of the legwork for us... it's much appreciated for us lesser mortals who just program calculators and such.

Do you mind if I incorporate these findings into a new LOD version of the Bow Damage Calculator, please? I will, of course, be sure to give you due credit for your hard work.

Best,
Smarty.

Our effective IAS is <194/(1+194/120)> = 74

so {256*(6+1)/<(74+30+30+100)/100*256>} = 3

Heri quoted IAS speeds of 290, so I'm sure he can reach 195 for our speed cap test.

Thanks,
oneko

My query: is an IAS modifier on the weapon treated just like any other IAS modifier (subjecting it to diminishing returns) or does it actually modify the base speed of the weapon?

--
Imagine the most witty and concise verbal gem ever uttered. Now imagine I said it, and quoted it here.

However much time you wasted, it is less than the sum total of time the ~20 people working on this problem around here would have wasted before figuring this out. So, if you have a charitable bone in your body (and clearly you do) you can consider it time well-spent.

-dok

Assuming 13/7 and 15/9 is correct, than max weapon speed increase has to be between 75% and 77.8%, so I think it highly likely that 75% is the IAS cap now.

Works for zeal and pike speed too... it's almost surely 75%.

Anyway, would you (or anyone else) happen to know the base swing speeds for the Druid and Assassin? Also, have there been any changes for the original 5 classes?

Addiction's Diablo II Statistics Guide -- New Expansion Pack version coming soon!

-----------
Speed Kills

You can't believe how many emails I've gotten with "has anyone found the new weapon speed formula yet?"

-Bolty

Pat
"Oh, look, another unique morning star."
-Darth DeGaussia

Also, any idea how Double Swing attack speeds might work- it's clearly not just a doubling? I'm guessing that the Assassin's dual-claw and the Barb's skill have similar mechanics.

Great work. Thanks again- word.

I'll be off to update my speed calculators based on it,
and will provide link to the archive.