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-   -   Extra Attacks, Haste, and you. (http://elitistjerks.com/f15/t9180-extra_attacks_haste_you/)

 LordVoid 11/25/06 4:06 PM

So primarily I'm concerned about Flurry + Sword spec.

Assume:
2 2.0 speed, 50dps weapons
30% crit rate.
1 minute interval

Ignoring yellow damage so we have,
60 swings per minute.

1-(1-c)^3 * 30% is the amount of haste you have over an interval.
.657 * .3 = .1971

This is to say, we have 19.71% more swings essentially.
This raises our swings per minute to 71.826.

Although this is not the focus of what I wanted to establish, I'll see what adding 5% more crit does.

1-(1-c)^3 * 30% is the amount of haste you have over an interval.
0.725375 * .3 = .2176125

21.761235% more swings,
73.05675 swings a minute.

So what do we get with the 30% crit rate, and 5% chance to proc a sword proc?

Well first we have to understand how sword spec works. What I'm having trouble modeling is the effect sword spec has in this situation. Even if we assume sword spec doesn't make you "lose time" when we look only at white damage (meaning it does not reset swings that have not completed). It seems like it will have different effect depending on the state you are in. So you have either crit, or you have hit; and then the sword spec has crit or hit itself. What's more you may or may not be in flurry time when this occurs. This is very difficult for me to make into an equation. While I think on this, does anyone else have any ideas?

So the Extra attack:

Hits:
- Outside of flurry: gives an extra attack - nothing special.
- Inside of flurry: eats a flurry charge.

Crits:
- Outside of flurry: starts flurry.
- Inside of flurry: refreshes flurry.

Grr. Still thinking...

 alcaras 11/25/06 6:52 PM

Does or does not sword spec reset swings that have not completed? For 2h? For dw?

Assuming it doesn't...

You want to model a Markov chain with four nodes.
http://en.wikipedia.org/wiki/Markov_chain

So you'll have something like this (but with Sword Spec added in):

(No Flurry) -p(Crit)-> (Flurry 3) -p(Hit)-> (Flurry 2) -p(Hit)-> (Flurry 1) -p(Hit)-> (No Flurry)
| | | |
p(Hit) p(Crit) p(Crit) p(Crit)
| | | |
(No Flurry) (Flurry 3) (Flurry 3) (Flurry 3)

I hope that helps :)

 Sleign 11/25/06 7:55 PM

It should be reasonably simple. At 60 swings per minute, with 5% additional swings, you get 63 swings per minute. At 30% crit rate in your math, 75.4173 swings per minute. A sword spec swing, for all intents and purposes over a given time interval, should act as a normal swing in regards to flurry. It will either eat a charge or refresh the timer and take its place in the probability over the interval, just like a normal swing.

The main difference between 5% crit and 5% doubleswing would come into play based on what your % crit is. At lower values 5% crit will be superior in terms of swings over time. The equation (1+(1-(1-(c+.05))^3)*.3)*60 = (1+(1-(1-c)^3)*.3)*63 where c is your crit value before your weapon spec would give the value for which you would get equal benefit from 5% crit and 5% extra swings in terms of swings over time (represented by the 60/63 base swings respectively)

 LordVoid 11/25/06 9:45 PM

Ok so I'm fairly sure that the chance to be in a swing that has made use of flurry when sword spec is involved is:
1-( (1-c)^2 * (1 - (c(1-s)^2)) ) where c is crit rate and s is your sword spec chance. This is the chance that any of your last 3 attacks crit, and if the attack that crit was the third one prior, then the following 2 attacks were not sword spec procs.

so with my previous values, we have

0.6426675 * .3 = 0.19280025

19.280025% avg haste.

71.568015 attacks * 1.05 extra attacks gives us 75.14641575
extra swings.

Sword Spec does not significantly affect flurry, but it does decrease its effect slightly at this level of crit.

edit: The problem is that the previous formula for flurry did not take into account the effect sword spec would have on flurry.
edit: This formula also assumes sword spec cannot proc itself.

 LordVoid 12/02/06 10:11 AM

Ok so I've made an error. For an attack to currently be hasted by flurry, the last attack must have crit, or the two attacks before it must have crit, and the attacks since those attacks must not have had sword spec proc on them.

So the formula is looking like:

1- ((1-c) * (1- (c(1-s)) * (1- (c(1-s)^2)) )

so with my previous values, we have

0.635010375 * .3 = 0.1905031125

19.05031125% avg haste

71.43018675 attacks * 1.05 extra attacks gives us 75.0016960875
extra swings.

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