[BOOMKIN] Comprehensive BiS List (1.11/Naxx)

[Keftenk]

Using the first derivative above, you should find that 1 spellpower will increase your dps by x (something around 0.35-0.42ish, depending on your gear). To find how much spellpower 1 crit equals, just divide dps/crit by dps/sp. The terms cancel out and you get sp/crit. You can calculate sp/hit in the same way.

So, if you wanted to make a spreadsheet of gear upgrades, you would want to list how much hit (listed on the item), spellpower (listed on the item), and crit (listed on the item + int/60), determine the dps increase from each of those 3 stats (using the respective derivative above), and add them together for the total damage provided by that piece of gear.

It's worth pointing out that this is just for maximizing your potential dps, with no regard to silly things like mana regen. There's no way to reliably model that, so I would suggest gearing for maximum dps and then swapping regen items if you're finding yourself perma-oom before the end of a fight.

So the initial testing was quite close, nice. This formula should match for the things that I had mentioned in almost every post about the discrepancies and Predicted DPS/Actual DPS not matching up. The above should give us a more precise number for gear values.

[Lorilay]

Is there a base amount of crit before int is calculated?

No, but your crit is non-zero at lower levels because the int/crit ratio is dependent on your level. It takes more int to get 1 crit as your level increases. See: http://wowwiki.wikia.com/wiki/Spell_critical_strike

[Taladril]

Thanks for this info and the clarified calculations. I'll need some time to mull it over and try to get some kind of sense of quantifying it all or at least better visualizing it for how to optimize. I'm sure we can all agree on an accurate approach with enough consensus.

[Lorilay]

Is there a base amount of crit before int is calculated?

No, but your crit is non-zero at lower levels because the int/crit ratio is dependent on your level. It takes more int to get 1 crit as your level increases. See: http://wowwiki.wikia.com/wiki/Spell_critical_strike

Also, you have a base intellect before gear is applied, so you would have a base level of crit that would be a constant to be added to your total crit from gear.

[Imbaslap]

wut

[sumail]

Sorry if this seems like a dumb question but where does the (3 - 0.5*crit) in the denominator come from?

nvm I see it's from Nature's Grave.

Also if you differentiate that function with respect to crit you have to also account for the crit in the denominator right (ie that crit in the denominator is also a variable)?

Using quotient rule it becomes:

3.5*(StarfireBase+spellpower)(1-miss) / (3-0.5*crit)²

0 < miss,crit < 1 (crit & hit range between 0 and 1 to get rid of the need to divide by 100)

[Keftenk]

So, is this right?

Bloodvine Goggles: 3.418327759
The Hexxer's Cover: 3.579733333
Mish'undare, Circlet of the Mind Flayer: 3.595986622

What did I do wrong? Lol..

[Lorilay]

So, is this right?

Bloodvine Goggles: 3.418327759
The Hexxer's Cover: 3.579733333
Mish'undare, Circlet of the Mind Flayer: 3.595986622

What did I do wrong? Lol..

Assuming you have pretty good gear equipped: 659sp, 22.67% crit, 10% hit (7% miss)

dps/crit = (485.5 + 659)(1/100)(1-7/100)/(3-0.5*22.67/100) = 3.69
dps/hit = (485.5 + 659)(1+22.67/100)(1/100)/(3-0.5*22.67/100) = 4.86
dps/sp = (1+22.67/100)(1-7/100)/(3-0.5*22.67/100) = 0.40

Note that the values above will change slightly if you swap in other pieces of gear below (I calculated them with Mish equipped). I was also too lazy to change the value of int from 55 to 60 per crit (mages get +int talent), so the math doesn't add up perfectly.
Mish: (24/60 + 2) crit * 3.69 + 35 sp * 0.40 = 22.82 dps
Goggles: 1 crit * 3.64 + 2 hit * 4.65 = 12.94 dps
Cover: 10/60 crit * 3.69 + 41sp * 0.39 = 16.51 dps

[Keftenk]

Oh, I see now.
Well let's hope Taladril and/or Kraken can update their spreadsheets with the new formulas.

[sumail]

You might want to consider looking at crit algebraically. The method you are using is linear approximation and it works 100% well with hit and spellpower since the function behaves linearly with these two parameters. However the function behaves nonlinearly with respect to crit so a linearly approximation will only approximate the gains you get from crit. However if you do it algebraically you can obtain the gains exactly.

I typically like to work in terms of spellpower so you can solve for how much 1% crit gives in terms of
spellpower.

DPS = f(x,y,z)

x = spellpower
y = crit
z = hit

f(x,y,z) = (A + x)(1 + y)(0.83 + z) / (3 + 0.5*y)

note A is base damage of the spell, also I prefer to using 0.83 + hit as opposed to 1 - miss since you typically are looking to add hit and miss = 1 - (0.83 + hit), therefore 1 - miss = 0.83 + hit.

Doing the algebra spellpower equal to 1% crit is:

delta_x = (3-0.5y)*(A + x)*(1 + y + 0.01) / [ (3 - 0.5(y + 0.01))*(1 + y) ] - (A + x)

this is obtained by equating:
f(x+delta_x, y, z) = f(x, y+0.01, z) and solving for delta_x

delta_x is the change in spellpower you would need to achieve the same dps as if you had 1% crit instead. This method always works but is perhaps more tedious.