Calculating Skill Delays

So pretty much every attack skill has a delay in the data, but how exactly is the delay affected by skills like Booster/SI/Yellow Aura/etc? I'd like to calculate the absolute fastest attacking speed possible with every speed buff active but I have no idea what to do with the initial skill delay to get there.

Mostly interested in Phantom Blow for now, which is currently 810ms, but after RED is 720ms.

You take the 10 + your attack speed divided by 16 (which is 10 + 6, 6 being the attack speed "Normal" since all delays are at Normal(6), we divide that factor out) and multiply it by the delay, and round the product up to the nearest multiple of 30. To achieve this you can divide by 30, round the result up to the nearest whole number (the ceiling function), and multiply that by 30.

For example, if you were at Faster(2) and your skill had a delay of 810ms, it'd be 810 * (10 + 2)/(10 + 6) = 607.5ms. 607.5/30 =20.25, ceil(20.25) = 21, 21 * 30 = 630ms.

(* Note that because of the 10s, it's theoretically possible to have a speed faster than 0, since 0 is really just 10 *)

In order to calculate the number of attacks per second, you just take 1000ms (1000 milliseconds in 1 second), divided by the new delay value, which in this case is 630ms, and you get 1000/630 = 1.587.

At this point, you multiply by skill %, number of attacks, your range, etc, in order to calculate damage for a given attack.

The damage increase from increase attack speed is of course due to attacking more times per second, so to calculate the damage increase from the delay reduction in Phantom Blow, we find the new attacks per second by doing 720 * (10 + 2)/(10 + 6) = 540ms, 1000/540 = 1.852.

Then we just do the formula for % change, (new - old)/old (or really, just (new/old) - 1), which is 1.852/1.587 - 1 = 1.167 - 1 = 0.167. That's a 16.7% increase in damage at Faster(2).

You can skip calculating attacks per second and just find the increase in damage using the delays, since you're basically doing (1000/newDelay)/(1000/oldDelay) - 1 which simplifies to oldDelay/newDelay - 1.

[MENTION=1747]Grey[/MENTION]; Thank you so much!

So, if I did this correctly:

Speed (2): 810 * (10 + 2)/(10 + 6) = 607.5ms --> 630ms
Speed (1): 810 * (10 + 1)/(10 + 6) = 556.875ms --> 570ms
Speed (0): 810 * (10 + 0)/(10 + 6) = 506.25 --> 510ms
Speed (-1): 810 * (10 + -1)/(10 + 6) = 455.625 --> 480ms
Speed (-2): 810 * (10 + -2)/(10 + 6) = 405 --> 420ms
Speed (-3): 810 * (10 + -3)/(10 + 6) = 354.375 --> 360ms

Jesus Christ. So with the new Phantom Blow delay, assuming every possible attack speed buff (which, of course, isn't actually possible, but MATH):

Speed (-5): 720 * (10 + -5)/(10 + 6) = --> 240ms

That's 4.167 attacks/second, at 7 + (7 * 1.7) = 11.9 hits/second with Phantom Blow, excluding Venom/Blade Clone = 49.583 hits per second with Phantom Blow.
Whaaaaaat.

Speed buffs I was using were the following:

Base = 4 (is this right? Daggers are almost all Fast(4) so I think it is, Kataras all seem to be (3) but I don't think that actually means anything)
Adv. Yellow Aura = -1
Speed Infusion = -2
Booster = -2
MPE: Green Potion = -1
Dojo Buff = -1
Inner Ability = -1
Zero's Aura = -1


*Using that Christmas Tree (Faster(3)) Gachapon dagger it'd be 180ms delay for Phantom Blow, (which is an absurd 66.1 hits/second), that's Mille Aiguille speed and Phantom Blow isn't even a Hurricane-esque attack.

How does katara speed effect dual blade skill delays?

Also did anyone notice that the sweetwater knife is faster (3)?

You can skip calculating attacks per second and just find the increase in damage using the delays, since you're basically doing (1000/newDelay)/(1000/oldDelay) - 1 which simplifies to oldDelay/newDelay - 1.

It is necessary to put in some ceiling function for the oldDelay stuff because that expression is for an absolute increase in DPS, whereas a real (CPU-gentle) DPS increase really stems from the expression ceil{[BaseDelay * (10 + x) / 16] / 30} where x is the speed stage in question. Therefore if x is the old speed stage and x' is the new speed stage, the expression for DPS increase will thus be:

DPS increase = ceil{[BaseDelay * (10 + x) / 16] / 30} / ceil{[BaseDelay * (10 + x') / 16] / 30} - 1

Note that because the delay is the period of an attack, whereas what we usually do for DPS calculations is the frequency of the attack (which is 1/period), double-divisions make the old delay on top.

For an example of the calculations (with none of the expressions shown) see this post: http://www.southperry.net/showthread.php...ost1213378. I think it should be a ceiling function, not a round function...?

I'm not sure if speed stage can go negative... maybe?

Hadriel

I'm not sure if speed stage can go negative... maybe?

It can.

It is necessary to put in some ceiling function for the oldDelay stuff

I'm not sure what you're suggesting here, at this point in the calculation both delays have already been passed to the ceiling function (delay' = 30 * ceil([delay * (10 + x)/16]/ 30), and substituting in this expression nets you the same thing you have). If you pass the delays to the ceiling function, you'd just get the same thing back.

Generally, it's ceiling, not round; it's weird, there are a few exceptions (which, I don't know, better to err on the safe side).

It's certainly theoretically possible for you to have a negative speed stage, and I'm sure someone has tested, but I have not personally, and couldn't tell you if it actually works as advertised.

[MENTION=1747]Grey[/MENTION]; Thank you so much!

So, if I did this correctly:

Speed (2): 810 * (10 + 2)/(10 + 6) = 607.5ms --> 630ms
Speed (1): 810 * (10 + 1)/(10 + 6) = 556.875ms --> 570ms
Speed (0): 810 * (10 + 0)/(10 + 6) = 506.25 --> 510ms
Speed (-1): 810 * (10 + -1)/(10 + 6) = 455.625 --> 480ms
Speed (-2): 810 * (10 + -2)/(10 + 6) = 405 --> 420ms
Speed (-3): 810 * (10 + -3)/(10 + 6) = 354.375 --> 360ms

Jesus Christ. So with the new Phantom Blow delay, assuming every possible attack speed buff (which, of course, isn't actually possible, but MATH):

Speed (-5): 720 * (10 + -5)/(10 + 6) = --> 240ms

That's 4.167 attacks/second, at 7 + (7 * 1.7) = 11.9 hits/second with Phantom Blow, excluding Venom/Blade Clone = 49.583 hits per second with Phantom Blow.
Whaaaaaat.

Speed buffs I was using were the following:

Base = 4 (is this right? Daggers are almost all Fast(4) so I think it is, Kataras all seem to be (3) but I don't think that actually means anything)
Adv. Yellow Aura = -1
Speed Infusion = -2
Booster = -2
MPE: Green Potion = -1
Dojo Buff = -1
Inner Ability = -1
Zero's Aura = -1


*Using that Christmas Tree (Faster(3)) Gachapon dagger it'd be 180ms delay for Phantom Blow, (which is an absurd 66.1 hits/second), that's Mille Aiguille speed and Phantom Blow isn't even a Hurricane-esque attack.

I believe yellow aura is -2 now

I'm not sure if speed stage can go negative... maybe?

Hadriel

I did some testing in the summer and it looks like it can, or at least, you can stack attack speed buffs beyond 0, which I figured must make it go down to -1, -2, and so on.

[MENTION=10351]MountLag[/MENTION]; just tested it, and you're right! I think they must've changed that with the little Battle Mage revamp with/before RED, since I'm sure it was just -1 before.

Holy pomegranate a BtlM can get to -9 speed... after fly(unless booster is -1 speed for some stupid reason) bringing the delay of thier blow skill to a rediculus 60ms. and thats outside of dojo. in dojo they can break the game.

Holy pomegranate a BtlM can get to -9 speed... after fly(unless booster is -1 speed for some stupid reason) bringing the delay of thier blow skill to a rediculus 60ms. and thats outside of dojo. in dojo they can break the game.

SO OP, I don't think it works like that

I'm not sure what you're suggesting here, at this point in the calculation both delays have already been passed to the ceiling function (delay' = 30 * ceil([delay * (10 + x)/16]/ 30), and substituting in this expression nets you the same thing you have). If you pass the delays to the ceiling function, you'd just get the same thing back.

Generally, it's ceiling, not round; it's weird, there are a few exceptions (which, I don't know, better to err on the safe side).

It's certainly theoretically possible for you to have a negative speed stage, and I'm sure someone has tested, but I have not personally, and couldn't tell you if it actually works as advertised.

Oh bah I wasn't thinking straight. Sorry. 2am in the morning is not a good time to do math. I ended up thinking you were going to reduce the expression to (10 + x)/(10 + x') - 1 for DPS increase.

Hadriel

[MENTION=1747]Grey[/MENTION]; was musing about the skill delay thing, when it occured to me that each speed stage increase could potentially offer greater and greater DPS increases, only that the 30ms ceiling function just annoys me to hell when I'm doing numbers.

Interested people can see this post: http://www.southperry.net/showthread.php...ost1214370

Hadriel