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.