Haste and Crit mechanics?

[Dorcas]

Hi. I'll cut to the chase, is 1%haste 1% more damage? is 1% crit 1% more damage for frost?

The crit question is easy, it is NOT. Unless you have 0% crit, which you don't.

Explaination.
For keeping things simple, let's assume you have NO haste or crit, and does 1k dps. 1% crit would increase that by 1%, giving you 1010 DPS. Another % of crit would give another 10 dps, and so on. Assuming you reach 50% crit, you would have 1,5k dps.

Still with me?

Good! The 51st percentage of crit would (of course) also increase dps by 10, but NOT 1%. A increase from 1500 to 1510 is 0,667% more dps.

If you get 75% crit, your damage would be 1750dps, and 1% crit (still 10dps) would be 0,571% more dps.
If this is wrong, please let me know.


Now with haste. 1% haste is NOT 1% damage, it's 1,01, since the 100ed spell also gets the haste. Thereby the mage would have 1010,1 dps, an increase by 10,1 dps.
No big deal so far.

10% haste would mean your spells take 90% of the original time to cast, giving that frostmage in the crit example 1000/0,9=1111,1dps. Another percent haste would put her on 1123,6dps, an increase by 12,5 dps, meaning that last percent acctually was a 1,13% increase.
Still the numbers are fairly small as you can see.
¨
Lets now assume 30% haste, the frostmage would have 1000/0,7=1428,6dps. Another percent would put her on 1000/0,69=1449,3dps, a 20,7 dps increase (which by the way is TWICE the amount the first percent gave). That 20,7dps is around 1,4% more dps. O_o


I'm NOT trying to prove haste>crit, theres so many calculations on that. I just wanna know if this is true, that crit doesn't scale like 1% is 1% more damage and haste is better the more you get.

Thanks for reading

[Swizzle]

are you asking a question or giving a sermon?

[Selverein]

Alright, I'm not super good at explaining so I'll try my best (and English is my second language so language barrier and all). Numbers will give you different answers depending how you look at them, you just need to compare them in the same way.

On paper, 1% crit is 1% DPS. Even at 80% crit, another 1% will still be 1% DPS.
Let's assume spells crit for 200% (talents), 1k damage spell cast 100 times.

No crit: 100 * 1000 = 100,000/100 = 1k DPS.
80% crit: (20 * 1000) + (80 * 2000) = 180,000/100 = 1.8k DPS.
1800/1000*100 = 180% DPS (80% increase)

81% crit: (19 * 1000) + (81 * 2000) = 181,000/100 = 1.81k DPS.
1810/1000*100 = 181% DPS (81% increase)

That, of course, is an absolute value. You're looking at relative values.
1810/1800*100 = 100.556% (barely more than half a percent increase)

So, in summary, each 1% crit will increase your "baseline" DPS in the same way as the previous 1%, but you can't assume you'll go from 3k DPS to 3.03k DPS because you gained another 1% crit. (It'll be close enough, and thanks to RNG you'll probably never realize it since DPS does vary regularly, but on paper it'll be lower)

Now with haste, it's a bit more tricky. What you say about 1.01 DPS would be true if time was infinite. But it's not, and boss fights (for example) last only so long. So with 1% haste, you'd have to cast 100 spells to see the full benefit (while 1% crit could occur at any point during those 100 casts). Your first cast would set you at 1000.11~ DPS, second 1000.22~ and so on until your 100th cast which would finally set you to 1011.11~ DPS. If the fight ends before that, you "lose out" on part of your haste bonus.

Hopefully that last part was clear. Anyway, all in all, considering the natural fluctuation of DPS, RNG, procs, etc, you can safely assume that 1% crit = 1% haste.

That being said, there are usually numerous factors that make haste a better choice. Spells that can proc or directly apply a debuff, for example, will favor haste as it decreases the theoretical time it'll take to proc the debuff. In the case of Imp Scorch (might have changed in 3.1) it'll take less time to apply all the stacks.

TL;DR
Haste and Crit impact DPS differently but give a similar result in the end. Because of reasons other than theoretical DPS, Haste is usually preferred. (Applying stacking debuffs, getting as many spells in during a proc, mobility due to lower cast time, etc)

[rathok]

1% haste > 1% crit for frost. Most of your big nukes are going to be on frozen targets or with a FOF proc so you'll have at LEAST 70% crit chance. Another 5-8% from stacking crit isn't worth it. Just get haste. I dont have any numbers to back that up but that is just my POV.

[Sprout]

http://code.google.com/p/simulationc...i/SampleOutput

This should answer all your questions.

[Ygorl]

Dorcas got crit right and haste wrong. Selverein sort of missed the point on both of them.

10% haste doesn't drop the casting time to 90% (if it did, 100% haste would drop the casting time to 0!). 10% haste increases the casting speed by 10%. This is slightly different. Imagine a car driving to its destination at 100 mph. 10% haste raises the car's speed to 110 mph. If the destination is 100 miles away, the regular-speed car gets there in 1 hour, the 10% haste car gets there in 100/110 = 0.909090... (repeating, of course) hours. If the car had 100% haste, it would drive 200 mph, and get there in half an hour.

Since Dorcas covered crit correctly, I won't dwell on it. Since haste works the way I just described, rather than the way Dorcas described, it suffers from the same kind of self-relative diminishing returns. If you've got 40% haste, you're casting 40% more spells, doing 40% more damage than if you have 0% haste. But if you raise your haste by 1%, to 41%, you're doing 1.41/1.4 = 1.0071... or only 0.7% more damage.

Now, both haste and crit can do things other than simply increase your damage. Haste, as mentioned, can stack up debufs more quickly, while crit sometimes causes additional nice effects as well. Moreover, abilities that have cooldowns don't benefit at all from haste. A destruction warlock, for example, still can cast Conflagrate only once per 10 seconds no matter how much haste he has. Conflagrate is a hefty percent of his damage, so haste is accordingly weaker.

Finally, due to their self-relative diminishing returns, the best thing is to keep them in balance with each other. For example, say you do 1000 DPS, and you can put on gear that gives 40% crit or 40% haste or anything in between. Not taking into account any of the considerations from the previous paragraph, here's what happens... If you go 40% haste and 0% crit, you'll do 1400 DPS. If you go 0% haste and 40% crit, you'll do 1400 DPS. If you go 20% haste and 20% crit, you'll do 1440 DPS. Better, right? This is why, as Rathok says, haste is better than crit for frost - if your crit is sitting at 70% just from special abilities, that takes a whole lot of haste to match...

edit: since crit is more expensive per item budget point, it's not realistic to have 40% haste vs. 40% crit. More realistic would be 40% haste vs. 29% crit. The underlying math is similar, just skewed very far in favor of haste (not taking into account the considerations mentioned above).