[Druid]The net threat value of faerie fire

In the Bear FAQ, Bludge said this:

FF seems odd because of the fact that it's based off spell hit. I notice mine missing more than any other ability I have. So using it in a rotation seems like a bad idea except to refresh it. I might be able to imagine a bear that is melee hit capped, but a bear that is spell hit capped? Now you're smoking.

You bet I'm smoking! I'm smoking the sweet smell of awesome threat, baby. Let's go to the numbers and figure out whether I'm smoking, or he's listening to anecdotal evidence.

First off, the hit numbers: melee miss rate against a level 83 mob is 8%. Spell miss rate is 17%. So faerie fire misses more than twice as much as melee attacks. Making it even worse, the crit multiplier for spells is only 1.5, spell crit is typically much lower for ferals than melee crit, and for this test we're going to assume that you're totally expertise-capped too.

We'll take a typical AP value: 6000. A crit rate of 50% for melee, and 15% for spells (this is pretty correct when raid buffed). And let's go with 0 hit total. Not really realistic, but who cares - this is bold theorycrafting when smoking time.

So the value for various bear attacks in terms of damage is:
mangle: (base damage * 1.15 + 299)*naturalist * master shapeshifter * savage *armor *(2*crit rate + 1*(1-crit rate))* (1-melee miss rate)
swipe: (AP*.063+108)*naturalist*master*feral instinct*armor*(2*crit rate + 1*(1-crit rate))* (1-melee miss rate)

lacerate: (AP*.01 +88)*naturalist*master*armor*(2*crit rate + 1*(1-crit rate))* (1-melee miss rate)
Faerie fire: (AP*.15+1)*(1.5*spellcrit rate +1*(1-spellcritrate))*(1-spell miss rate)

After using 6k AP, 50% crit rate, 15% spell crit, and no hit - we get this:
mangle: 2239 damage
swipe: 698
lacerate: 163
FFF: 803

Okay, so mangle wins big on the damage - but FFF even with all of that is coming in second. Even with a 17% miss rate and a bad crit rate, it wins. But what about TPS?

Mangle TPS: Mangle damage * 29/14
swipe TPS: swipe damage * 29/14*1.5
lacerate TPS: 29/14*(damage+1031)/2
FFF TPS: 29/14*(damage+632)

So the final TPS is:
mangle: 4638
swipe: 2169
lacerate: 1237
FFF: 2974.

But wait! What about higher AP? Turns out that FFF wins at any level over swipe. Well, okay - at around 240,000AP, swipe beats FFF.

But what about a better armor reduction? After all, 30% armor is pretty high...right? Not really, but let's just take that out entirely. If your target has 0 armor, swipe will do about 120 more threat per application. But at 0 armor, your swipes are hitting for 722 damage each. I don't know about you, but that's not what mine hit for. And while you can get 0 armor as a cat under certain circumstances, chances are you'll never hit that as a bear.

What about higher crit? Even with an 80% crit rate, swipe still loses by a few hundred.

What about more hit? That's funny - because hit actually makes FFF stronger. Why? Because the hit rating to 1% hit conversion is 32.79 hit rating per 1% - but the spell hit rating only costs 26.3 hit rating per 1%. And remember - this assumed expertise capped, which means 14% reduced parry and dodge or 56 total expertise skill. Again, not really realistic; chances are against bosses you're going to have a lot less.

So for pretty much any numbers that you can think, faerie fire beats swipe, and it scales insanely well with AP. Also, if you don't have things like master shapeshifter or even naturalist, faerie fire does even better by comparison.

So yes, every time you can you should be faerie firing for maximum threat and for maximum damage. Mangle beats it, and keeping up a lacerate stack beats it - but lacerate by itself doesn't come close, nor does swipe.