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Quote from Tsukishima

Being able to sustain or cast for longer periods is an advantage but for an equal period of time neither burst nor DPS is different.

That is incorrect. For an equal period? We're always talking about equal periods here to compare them properly.
Question really is: short or long period?

If you say instead that:
"Being able to sustain or cast for longer periods is an advantage but for a shorter period of time neither burst nor DPS is different."

You're correct. In the example this short period where neither burst nor dps is different is 6 seconds.

The first two premisses are correct.
Premise 1: Damage per second of spells is equal for weapons of different speed.
As long as you're casting the same spell yes ofc, same weapon dps, same spell-> same dps
Conclusion2: Damage per arcane power point is higher for slower weapons
Yup and in a strange manner.

Quote from Tsukishima

Premise 3: Weapon speed affects how long you can cast before you run out of resource but does not increase DPS assuming an equal duration
(...)
Conculsion: You get to cast longer (10s vs 3s) if you're on a slow weapon and will have a higher cumulative damage, all other factors held constant, however you do not do higher DPS. The DPS at the 3s mark is equal.

Again: what equal duration?
The dps is the same as long as... it's the same? well...yea

Let's talk about bringing a boss down. A boss takes more than 3 seconds. If you have a wizard, and you're using ray of frost, you can chose to use a slow weapon and do more damage in the fight or use a fast weapon and do less damage.

Using the same setup as usual (17ap cost for the 280% ray of frost, 14ap regen and 120total ap) i'll try to use the 280% version with the fast weapon.

If you chose Snow Blast however you won't be able to sustain your cast. You'll spend 17ap per cicle, 34 per second, only recovering 14. You'll lose 20ap every second, being able to cast during 6 seconds.

Yup you'll be able to cast Ray of Frost during 6 seconds. BUT you can use amissiles after and recover mana. Let's study it.

Arcane Missiles is a free cast. You can chose a rune to make it give you 4 ap, or you can chose a rune that will increase its damage.
Let's start with the 4ap rune. And we'll also take prodigy, a passive that will make it give 8ap.
Now every arcane missile returns 8 ap. But with a 2.0 weapon you can return 16ap every second. So during the recharge time you'll return 14ap+16ap=30ap every second, correct? So it will take 4 seconds of arcane missiles to reach 120ap right?

We have 6seconds of ray of frost(280%). And 4 seconds of arcane missile(110%).
The weapon speed is 2.0 so every second we hit twice. The weapon damage is 50.

6x2x(280% of 50)
+
4x2x(110% of 50)
=(12x140)+(8x55)=2120

So if this is correct over 10 seconds you can do 2120 with this weapon.

Let's compare.

With the slow weapon you used ray of frost (280%) all the time
So it's 10 seconds of Ray of Frost. Remember the weapon damage is 100.

10x(280% of 100)=280x10=2800

Well 2800>2120. Even with both using 280% slow weapon>fast weapon.

Now i also want to prove that using 215% is better than 280% for the fast weapon.

10seconds of 215% of 50 weapon damage x2 (speed)
10x2x(215% of 50)=20x107,5=2150

So we reach 2150, which is a little bit better than 2120. You can see i wasn't "cheating".
In fact we had weapons with the same dps. Be it using the 280% spell or the 215% (that offered more dps) the 2.0 weapon will do less dps.

Edit: to conclude the explanation let me explore the other arcane missile rune.
Instead of returning 8ap, you can return only 4ap and bring arcane missiles to 143%. Let's see how it goes.

4ap per cast, 8ap per second +14ap you'll have 22ap regen every second. So to reach 120 ap it'll take 5 and a half second s(sorry we just wasted 1 arcane power here!).
So we have 6 seconds of 280% and 5,5 seconds of 143%. 50 weapon damage. 2x due to speed.

6x2x(280% of 50)
+
5,5x2x(143% of 50)---11x(50+20+1,5=71,5)10x71,5=715+71,5=786,5
=
1680+786,5=2466,5

So we get 2466,5 but it took 1,5 more seconds. I could compare it properly to the 110% amissiles returning ap but i'm lazy right now. You can already see it's still less than what we get with the slow weapon.

Quote from Tsukishima

I am unable to comprehend/understand. Feel free to insult my intelligence but please do humour me.

Ok i'll try to REALLY explain it. It'll take some time but i'll do it.
I'll use the same weapons.
WeaponA- 100damage, 1.0speed-> 100dps
WeaponB- 50damage, 2.0speed-> 100dps

There are two variants of Ray of Frost.
Snow Blast-increases damage to 280%, but the cost remain 20ap
Cold Blood-reduces ap to 12, but the damage remains 215%

So you have the 280% expensive one and the 215% cheap one. To resume it: with a fast weapon you can't sustain the 280% one, only the 215%.

Now wait a while i'll make all the math and compare all possibilities. Edit coming in a few minutes.

Quote from Peanutz5

Now this is the point that the OP is trying to make, but im not sure if this is correct. Correct me if I am wrong, but I would think that ray of frost would cost 20 arcane power every second, not every cycle, making it so both weapon A and weapon B could be used for 10 seconds, and would both do the same amount of dps. This speculation might be incorrect though.

No the speculation is perfect sir. That's the origin of the whole distortion. When ray of frost cost 40, not 20, ap per second because your weapon is faster, and you still only regen 10 ap per sec no matter what...this happens. You could either correct this by making ray of frost cost x per second, not per cicle. Or you could make attack speed increase arcane power regen, but this would be a big giant ugly mess.

Quote from Tsukishima

Why do you use 280% for weapon A and 215% for weapon B?

Read my post.

Quote from Shadowedtruths7

I would be suprised if that didn't change at somepoint, due to Bliz not wanting to make a huge difference between 1h and 2h. But atm the faster weapon wins just because of the orb.

Well it's actually not hard to correct (make ray of frost and similars cost x per second, not per cicle, and the distortion is gone) . But i don't know if they will.
It seems from what we've seen that they're handling itemization pretty well so if you have a 2h and a 1h+orb of the same level they'll be roughly equal. Unless of course you're a wizard casting ray of frost
But it's not only that. Some class/builds will want a faster setup for x reasons, others will want a slower setup for y reasons. It's just that their reasons generally won't include strange behaviors as this one.

Quote from Shadowedtruths7

Actually the DPS would be the same assuming the Dps on the weapons are the same. (...) So in essence the higher DPS weapon regardless of speed will always do more DPS, It is just a matter of if you want to do it in quick bursts or constantly.

No it's not and i'll prove both your statements are false.

1-"Actually the DPS would be the same assuming the Dps on the weapons are the same"
Same dps situation example inc
WeaponA- 100damage, 1.0speed-> 100dps
WeaponB- 50damage, 2.0speed-> 100dps

WeaponA case: (280% of 100) x1=280
WeaponB case: (215%x50) x2=107,5 x2=215

Result: NOT THE SAME DPS.

2-"So in essence the higher DPS weapon regardless of speed will always do more DPS, "
It was proven that a higher dps weapon can do less dps in this case due to a distortion related to attack speed and arcane power. Gosh some people just can't understand no matter how clear we show things;

"It is just a matter of if you want to do it in quick bursts or constantly"
Maybe you don't understand the concept of dps vs the concept of damage. You see you can do the same damage with a lvl1 weapon and with a lvl60 weapon. Let's say...200 dmg. It just happens that with a lvl1 weapon you'll take minutes and with a lvl60weapon you'll take less than a second. Dps is damage per second, ok? Ok.

The case here, however, is even stranger because you have a higher dps weapon, which is faster, and you should expect more dps and more burst from it. But the case is that you're not only doing less dps. You're also doing less burst. The fast weapon is doing 258 damage every second, and the slow weapon is doing 280 every second.

Read again and pay attention. Try to identify where the mess started (tip: it's related to arcane power cost)

Quote from MADCATX

You should also note that with one handed weapon you'll have orb, which gives you +damage (...)
So overall damage of weapons is about the same, but with wand and orb you can kill things about twice as fast.

You may have a orb, you may have a shield or you may have a pig in your offhand. It doesn't matter: there will still be the distortion. Let me re-explain.
It's not a matter of hitting less but faster or hitting harder but slower. That's not what we talking about. It's a matter of hitting faster and by doing so drain way more arcane power than you should be draining! You double your speed you'll prob expect to drain twice as much arcane power, so that your cast lasts half as much. Right? No.
If you double your speed you'll find some very strange results in terms of how much ap you're draining and how long your cast lasts.
The most simple example is the first.

1.0attack speed: you lose 10ap every second, you can cast for 10 seconds
2.0attack speed: you lose 30ap every second, you can cast for 3.3 seconds. That's the problem.

On a sidenote: +damage is an interesting thing. Did you know that it benefits more faster weapons? How?
You get a +10dmg ring. If your weapon ss 1.0 you'll deal 10 more damage every second, that is, 10dps.
If your weapon is 2.0 you'll deal 10 more damage every half second, 20 more damage every second, that is, 20dps.
That is why you see such huge differences in damage when you check lvl60 weapons. The 2h weapons bring more damage and more dps usually, but that's because they expect this interference from rings amulets and offhands.
But this is another thing, ok?

Quote from Nastai

I do agree with you for the most part, but we should really also be considering signature spells and things such as prodigy, which can be used to regain AP. With higher attack speed, you will regain AP even faster when using these skills.

Yes! So it works both ways. Let's say you pick Attunement and Prodigy. Every am hit will recover 8ap right? Well with a 1.0 weapon that's 8ap every sec, with a 2.0 it's 16ap.
I think the major point is that attack speed is good and maybe should always be good, and that it's really strange when you find a situation where it's not. The really strange thing is this:
Double attack speed...double ap recover!
Double attack speed...not half time casting ray of frost....but actually almost a third due to how you spend every "cicle" but you only recover every second.

Quote from ComMcNeil

And OPs "theory" is based upon no further equippment
As we have seen, there are various ways to increase AP generation which means that the fast you generate, the more "raw" dps you can pump out with faster weapons (or + attack speed items)

1-Not a theory, a fact
2-We did bring a lot of optimization both in ap generation AND reduced cost to demonstrate how it works.
3-There are not various ways to increase ap generation, actually. People think they'll find +ap power generation on gear...they won't. +1 ap regen is way too powerful. You may find AP on crit and more total ap on gear.

Quote from Nastai

In conclusion you mention that more damage will come from a weaker weapon. However, if the weaker weapon is the same weapon speed as the stronger weapon, I don't see how this could be.

You have a irregularity. This irregularity is evidenced when you change a value.
If you don't ever, EVER change the value...the irregularity is fixed!! Right?

Tip: the problem is not with the weapons.

Edit: oh btw in that specific case if the weaker weapon had the same weapon speed as the stronger weapon...it wouldn't be the weaker weapon anymore. Not related, not related. Just a curious magical fact.

Good? No
Fun? Yea

Attack speed is as a dps increase. For some classes it also means faster resource generation, which means even more dps. For the wizard attack speed can be... complicated sometimes. Let's see how this can happen and why.

Ray of Frost- costs 20 arcane power and deals 215% weapon damage. It'll do this amount of damage over a cicle. If you have 1.0 attack speed you have a 1 sec cicle, every second it'll deal 215%. If you have 2.0attack spped you have a 0.5 sec cicle, every second you'll deal 215% twice.

It happens that the cost is also affected by attack speed. You spend 20 arcane power over a cicle. If you have 1.0 you'll spend 20 arcane power every second. If you have 2.0 you'll spend 40 arcane power every second.
One could assume that if you double your attack speed you'll last half of what you used to last casting ray of frost. But it's worse than that.

Every second a wizard will gain 10 arcane power. That is not affected by attack speed. Every second, no matter what's you attack speed you'll regen 10 ap.

Situation 1- Your attack speed is 1.0.
If you cast ray of frost you'll spend 20 arcane power every second.
But you also gain 10 arcane power every second.
The result is that you'll lose 10ap every second, so you can cast ray of frost for 10 seconds before getting out of ap.

Situation2- Your attack speed is 2.0
If you cast ray of frost you'll spend 40 arcane power every second.
But you still gain only 10 arcane power every second.
The result is that you'll lose 30 arcane power every second, so you can only cast ray of frost for 3.3 seconds before getting out of ap. Not 5 seconds.

More attack speed is still a dps gain. But not as much as it should be, because it affects the balance of your arcane power management.

The situation is even worse when you consider runes and other skills.

Let's say you have two choices:
Weapon A -100 damage, 1.0 attack speed ->100dps
Weapon B-60 damage, 2.0 attack speed -> 120dps

If you chose weapon B you can make a proper build to maximize your Ray of Frost usage. If you have Familiar (Arcanot) and the passive Astral Presence your ap regen goes from 10 to 14 and your total ap goes from 100 to 120. You can also use Storm Armor (Power of the Storm) to reduce the cost of every skill by 3 ap.
Now for Ray of Frost you have two choices:

Snow Blast-increases damage to 280%, but the cost remain 20ap
Cold Blood-reduces ap to 12, but the damage remains 215%

Let's try Cold Blood. With this build your regen is 14 ap every second and you're spending 9ap every cicle, 18ap every second. The result is that you'll lose 4ap every second and you'll be able to cast ray of frost for 30 long seconds without interruption.
How much dps? 215% of 60 is 129, double that (speed) and you're doing 258 dps.

If you chose Snow Blast however you won't be able to sustain your cast. You'll spend 17ap per cicle, 34 per second, only recovering 14. You'll lose 20ap every second, being able to cast during 6 seconds.

Now let's think about weapon A. The weapon hits harder, but it's slower and offers less dps overall. With the exact same build we'll try to cast Snow Blast. We'll spend 17ap every second (1.0 attack speed, remember) and recover 14ap every second, losing only 3ap every second. You can cast that for 40 seconds.

Now let's check the dps. 280% of 100 is 280, this time the speed multiplier is 1x so the final dps is 280.

What does that mean? That means you'll do more damage if you chose a weaker weapon. Why? The way attack speed is currently working for wizards is a bit...

..strange

Quote from Antirepublican

Another thing to consider is that the massive number of attacks could potentially trigger procs, like critical mass and +AP on critical hit. Assuming this occurred, the Hydra would be like a little generator you throw out.

Good point. We don't know if Hydra/Familar crits can return you ap. If they do yea it would have a big impact on ap regen.

Loved the familiars

Quote from jungle_woman

Quote from oneoftheorder

I think the intent is to use Meteor for single targets as necessary; in the context of spammability, there's no reason its dps shouldn't be comparable to that of any explicitly-single target spell.

ray of frost is single target

Read again. It's easier now.

Female witch doctor because she seems more accessible