2h Frost: Mastery vs. Crit - bad napkin math

100 Orc Death Knight
15795
2h frost, crit actually takes over haste at around the 10kish point, for DW, mastery and haste are pretty well tied together, crit just doesnt scale as well as mastery, especially on aoe encounters.

Crits biggest issue, is that it just purely takes too much rating to get a point of crit, and we get nothing special from it. Classes that go for crit have procs or effects, fire mages being the iconic ones, in which their crit gives them much more damage than the original crit damage gain.

Crit is actually of nearly equal power to 2h and DW, Mastery is just much better for DW, as 2h's froststrike hits half as hard and howling blast is only on proc or an aoe situation. Haste and Crit devalue eachother at similar levels, but haste is your 4th stat in this equation, so you don't reach the point that crit takes over (by tier 16, 2h will be on the point of convergence with crit, in the current model) That point is above 10k Haste, but it also is affected by other statistics. Haste generates more crits than crit rating for obliterate.


see this is what i have always wondered with the sims

do they take into account DW frost GCD capping issue (it caps much faster then 2hnd frost) and Crit is generally devalued at a base lvl due to killing machine's base PPM however DW dmg can at times be completely devoid of such an issue since Howling Blast always benefits from crits.

It should be for DW

Hit /Exp to soft cap > Mastery > haste (to 6k break point) > Crit > hit

but at 6k haste

Hit/exp to cap > Mastery > Crit > Haste

Sims do not show that though which is odd
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90 Orc Death Knight
19415
1% of crit rating (600 rating) allows everything you do that does damage a 1% chance to do double damage, so it's basically a 1% dmg increase. However, it's a 1% increase to your base damage before crits. If 1% of the time you do 100% extra dmg, it's the same as doing 1% extra dmg 100% of the time. Let's say you do 1 dmg per hit, and 100 hits every fight with no crit chance. If you increased the crit chance to 1%, you would crit once, and do 2 dmg for that hit, bringing your total to 101 dmg, or a 1% increase. Likewise, if you do 100% extra dmg 50% of the time, it's the same as doing 50% extra dmg 100% of the time. While going from 0-1% crit rating is a straight up 1% dmg increase, going from 50-51% is a 0.67% dmg increase. Back to the first example, doing 100 hits for 1 dmg each in a fight, but this time with a 50% crit chance to start with. Your dmg would be 50 hits of 1 and 50 hits of 2, or 150 total. Going up another 1% would give you one more crit, and increase your dmg by 1, to 151 total, or a 0.67% overall dmg increase.
The formula to find out how big an increase 1% extra crit chance would be is
(crit % +101)/(crit chance+100)
However, this doesn't take 3 special abilities into account. The first of which is howling blast, which, being our only ability that takes the spell crit rate instead of the melee crit rate, crits 5% less of the time compared to every normal ability. Now, howling blast accounts for about 7.5% of 2hand's total dmg. To adjust the above formula, we simply split the HB dmg and the rest of the dmg into
((crit % +101)/(crit chance+100)*.925) + ((crit % +96)/(crit chance+95)*.075)
Now we need to take KM procs for both FS and oblit into account. A 50k iteration sim tells us that, on average, 19.1% of FS's crits and 25.3% of oblits crits come from KM.
Frost strike accounts for 26.2% of the overall dmg, with 170.2 total casts. With 19.1% of those casts being KM crits, that's 32.5 crits from KM, each worth 120200 dmg. That means 33.3% of FS dmg is from km procs, and that's 8.72% of the total dmg from frost that doesn't benefit from crit rating.
Now the same thing with obliterate.
Oblit is 32.2% of frosts total dmg, with 105.7 total casts. With 25.3% of those being KM crits, that's 26.74 crits, each worth 226972 dmg. Which leaves 35.6% of oblit dmg being caused by KM, and 11.46% of frosts dmg not benefiting from crits.
That's a total of 20.18% of frosts dmg not benefitting from crit rating, which gives us the below formula for the value of crit.
((crit % +101)/(crit chance+100)*.723) + ((crit % +96)/(crit chance+95)*.075)
The BiS melee crit chance is 14.5%, which when plugged into out little formula, gives us a
0.631% + 0.068%, or 0.699% dmg increase per 600 crit rating. This is multiplied by 1.06, to account for the meta gem, giving us a final value of
0.741% increased dps.
Keep in mind this doesn't take skull banners into account, which would increase the value slightly but are very difficult to model.

2% more frost dmg (600 rating) is similar to crit in how we can model it. Going from 0 to 2% is a 2% increase for frost dmg, and going from 50-52% is a (152/150) (1.01333%) increase for frost dmg.
Which gives us a similar formula
(mastery% + 102)/(mastery% +100) *(% of dmg total that is frost/100)
Frost damage sources for 2hand are howling blast, frost strike, and frost fever. These total at 37.5% of frost's dmg for the default BiS profile on simcraft.
Raid buffed, BiS lists put us at 36.54% mastery.
Plugging that into the formula says that frost gets 0.549% increased dps for 600 mastery rating.

Sims have crit at 1.4, and mastery at 1.09, so crit's about 29% higher according to the sims. My evaluation puts crit at about 35% higher. Seems about right.

TL;DR
So crit > mastery
Because crit effects more than twice as much of your dmg than mastery, for twice the rating per %.

All numbers taken from BiS 2hand T14 sim 510-9, feel free to sub in a logs numbers if you want. However, I didn't use the scaling feature at all, only pulling numbers like average oblits and crit%s and km procs, and so on and so forth. Formulas also provided, if you want to use them for your gear setup.

Edit: math mistake throwing off crit numbers, old math below for reference, OP updated.

Now we need to take KM procs for both FS and oblit into account. A 50k iteration sim tells us that, on average, 19.1% of FS's crits and 25.3% of oblits crits come from KM.
Frost strike accounts for 26.2% of the overall dmg, with 170.2 total casts. With 19.1% of those casts being KM crits, that's 32.5 crits from KM, each worth 60100 dmg. That means 14.1% of FS dmg is from km procs, and that's 3.69% of the total dmg from frost that doesn't benefit from crit rating.
Now the same thing with obliterate.
Oblit is 32.2% of frosts total dmg, with 105.7 total casts. With 25.3% of those being KM crits, that's 26.74 crits, each worth 113486 dmg. Which leaves 17.8% of oblit dmg being caused by KM, and 5.73% of frosts dmg not benefiting from crits.
That's a total of 9.42% of frosts dmg not benefitting from crit rating, which gives us the below formula for the value of crit.
((crit % +101)/(crit chance+100)*.831) + ((crit % +96)/(crit chance+95)*.075)
The BiS melee crit chance is 14.5%, which when plugged into out little formula, gives us a
0.725% + 0.068%, or 0.793% dmg increase per 600 crit rating. This is multiplied by 1.06, to account for the meta gem, giving us a final value of
0.841% increased dps.
Edited by Mendenbarr on 1/12/2013 3:12 AM PST
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90 Orc Death Knight
9155
That was more or less exactly what I was trying to math out earlier - only your head didn't explode apparently, hats off to you - and thanks for the wonderfully enlightening post.

01/11/2013 06:26 PMPosted by Postonforums
ot sure if you've run Lei Shi's trinket, but when it procs, you find yourself unable to spend resources quick enough, you either cap runic or end up with strikes that overflow (This is actually one of the many reasons blood tap is superior to runic empower) your frost strike mechanic.


You might have more haste than me, but I can usually keep up with my resources with this 491 darkmist on, it's a rare occasion that it gets hectic - but I sometimes kick myself for upgrading it.

Still, probably should switch to blood tap. My old blood tap keybind got replaced by rocket boots so I've just been hesitant for bar spaces sake.
Edited by Solution on 1/11/2013 7:10 PM PST
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