Diablo® III

Attack speed questions for Zero Dogs and RoT

I am currently running a Zombie Bear build, and I am having very little trouble in MP6. I use to run a rain of toads build and often consider if rain of toads still has any advantages.

After looking at the Zero Dogs build, I have noticed there seems to be a huge push for increased attack speed in the gearing. Honestly I am confused on why, because to my understanding that increase to the attack speed will not increase the damage of sacrifice as the damage is not based off your damage tooltip, but instead based off of the equation

Damage of skill per cast = (average weapon damage)*(skill damage)*(1+(primary stat/100))*(1+(passive skill damage/100))*(any other damage/100)

Nowhere in the equation does attack speed play a factor. Attack speed only helps us to find our damage per second, or what the tooltip shows.

So, if I am not understanding this correctly and our attack speed indeed increases the damage of our sacrifice, then comes my real question.

Does attack speed help rain of toads, besides increasing the speed at which our LoH is being applied. From what I have read, rain of toads is a two second DoT, so recasting rain of toads before the 2 seconds is up only starts the timer over, and there for would not increase the damage done.
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It somehow helps you cast faster.
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For Zombie Dogs, the casting animation is sped up as according to your attack speed, which is why people have been pushing to increase attack speed for C4 Dogs. The faster you can cast, the faster you will be able to detonate, receive healthglobes, and heal. There are certain breakpoints to get to though with the attack speed. The casting animations will only really increase at each of the different AS breakpoints. There are several different threads that have the information regarding this. But that's just the reasoning behind it.
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