Niphredil

I'm trying to create a good frost spec because we will probably kill Al'Ar in the next raid ID and I also have to spec frost for my arena team and a couple of other occasions. It's quite obvious where to spend most of the points, but I don't know how many points I should put in Winter's Chill. I believe 5 points would be too much because with 4 points there is already only a minimal chance left for the debuff to fade while chaincasting frostbolts, but I would like to have exact numbers for the average percentage of time the debuff will be up and the average crit chance increase with 1, 2, 3, 4 or 5 points in WC.
I already tried to do the math myself, but there are so many things to take into account which got me really confused that I gave up and decided to better hope for some genius here to do it for me. In addition to that, I haven't got sleep for 24 hours, which doesn't really help me.


Talent description: "Gives your Frost damage spells a 20% chance to apply the Winter's Chill effect, which increases the chance a Frost spell will critically hit the target by 2% for 15 sec. Stacks up to 5 times."
Each talent point increases the chance by 20%.

How I tried to calculate it (didn't get very far):
Each number at the beginning of the lines stands for the number of frostbolts casted so far. You have 5 chances to reapply the debuff (12.5 sec) before it fades. On the right side is the chance that the debuff will be on the target, not considering the height of the stack (2%-10% increase). I know I could have written it with powers, but I think it doesn't matter because this won't help very much anyway, just wanted to present my result (which consisted mostly of many numbers and big confusion swirling around in my head^^).
0 - 0.2
1 - 0.2+0.2*(1-0.2)=0.36
2 - 0.36+0.2*1-0.36)=0.488
3 - 0.488+0.2*(1-0.488)=0.5904
4 - 0.5904+0.2*(1-0.5904)=0.6928
5 - 0.6928+0.2*(1-0.6928)~0.7542
6 - Here the debuff may fall off for the first time if it has been successfully applied at 0.



PS: Sorry if the English is bad, it's not my native language.

PPS: I used the search function, but didn't find any useful postings about this.

 

• Efejel

Well, you should be able to approximate it by

1 - ((1 - (0.2 * points in talent))^5)

or:

Points in talent: chance to reapply within 5 casts
0: 0
1: 0.67232 = 1 - (0.8^5)
2: 0.92224 = 1 - (0.6^5)
3: 0.98976 = 1 - (0.4^5)
4: 0.99968 = 1 - (0.2^5)
5: 1

Examine the line for one talent point "1: 0.67232 = 1 - (0.8^5)"
With one talent point, you have a 20% or 0.2 chance to apply with each successful cast. You have 5 casts with which to apply the debuff. You have an 80% or 0.8 chance to fail each time. Your odds of failing 5 consecutive independent trials is 0.8^5. Thus, your odds of succeeding are "1 - (odds to fail)", or "1 - (0.8^5)".

Someone please correct me if I'm wrong!

EDIT: Hmm, I just realized that I'm simplifying things a bit too much, probably. I'm not taking into account the fact that your "five-casts" window of opportunity is reset with each successful application.

 

Ithayla

Ejefel's math looks correct, although my math skills are limited entirely to forum browsing and attempting to understand theorycraft posts.

Some anecdotal advice I have seen on the forums is that 2/5 is enough. Allow me to attempt to hammer the math using Ejefel's formula...

...and realize that he's ALREADY done the math. Go me.

As you can see the diminishing returns kicks in heavily after 2/5, so it seems logically the best time to stop adding points.

Q: What are you planning to place the remaining points into?

 

Niphredil

@Ithayla:
I was playing around with frost specs for different purposes.
1. 5on5 Arena - I have about 9800 HP and 170 resilience unbuffed, so I need Ice Block - my favorite specs are atm 17/0/44 and 33/0/28.
2. PvE Spec for Al'Ar - you probably get the most dps if only one mage has Winter's Chill and the rest has more points in the arcane tree, so either 19/0/42 (of course for Al'Ar 2% less fire damage would be better, but the Frost Nova cooldown reduction is better for everything else) or arcane
3. We still don't have a tank with FR gear for Leotheras, so I thought it might be fun if I tanked him because I have 100 badges on my bank for which I have no use, although it's probably much more difficult than as a warlock. This 33/0/28 spec would be really nice, I get 10% less fire damage, have a quick Ice Block + Ice Lance to regain aggro if I have too many debuffs, no aggro reduce and every resist gives me 5% mana back.


Sorry, I just realized that I've used the German calculator because WoWHead is down, but I suppose you know the talents anyway...

 

WibbleNZ

The number of casts to get a full stack going might also be of interest. A negative binomial distribution (see http://en.wikipedia.org/wiki/Negativ...l_distribution) gives the mean number of failures before r successes as r(1-p) / p, thus (after adding 5 successes):

Points in talent : Mean number of casts to stack winter's chill to 5
0: n/a
1: 25
2: 12.5
3: 8.33
4: 6.25
5: 5

You could also investigate the rogue dps spreadsheet's modelling of deadly poison, I believe it uses a poisson distribution (the negative binomial converges to the poisson) to model a very similar mechanic.

 

◊ Malan

Did you check this thread Vontre's Mage DPS Spreadsheet to see if its modeled?

Vyktianity already has over 75 billion followers. The first verse in his book "Gift of the Wild" is "In the beginning Vyk cast lifebloom and then maul."

 

Overhead

Initially I was going to say 3/5 would be good - 2/5 gives too much chance that it'll take forever to stack them up. The thing that makes me want to suggest 5/5 is that you plan to use it for pvp. Having every hit increase your chance to crit by 2% adds up quick. (say 30% crit, and shatter, having it stackedto 5 brings your critrate from 80% to 90% - reducing the chance to not crit by half)

 

galzohar

Try calculating the same thing on fights that ever require you to move for ~10 seconds. You don't need to be forced to move too often to make more than 2/5 look like more than just a neglicible increase. And if you need to reapply from 0 (say if you stopped for 15s or more due to how the fight works, for example), anything less than 5/5 is most likely unacceptable.

At the end, it really depends on the fight. But might as well spec for all fights - if you're making a pure DPS spec getting up there:
http://www.wowhead.com/?talent=of0Vf0cZZVAMcof0oqqt
All you lose is a point in ice flows, and you could still go 4/5 and get 2/2 ice flows.

 

Ithayla

I agree with the second part of the quoted segment, but couldn't you just ice lance the target to keep it stacked?

 

Aoife

Well, for fights like Lurker, you're going to have to reapply it after every time he emerges. This means you're going to lose a bit of dps depending on how many points you have in Winter's Chill.

 

galzohar

Ice lance has problems:
1. When you're not casting it does so little damage you're probably better off staying out of the 5-sec rule.
2. You may have to cast multiple lances.
3. If you're "no attack" time is because you cannot damage the boss for one reason or another rather than just needing to move, your ice lance won't save you.

Ice lance can help, but it's not a solution. If you want to be good for all fights, 4-5 winter's chill is recommended. And you really don't need to gimp your DPS to get it to 4-5.