Hunter Stat Scaling

There have been a lot of comments about scaling and how our stats scale lately, and then I got into an email conversation with a reader about it, which got me playing with some numbers. This conversation starts back in Wrath, when we saw some very large hunter scaling issues.

The first was that all hunters scaled a bit more slowly with gear than other classes. The reason for this was that our pets only inherited a percentage of our AP — and did not inherit our haste, crit, or armor pen. Thus our overall dps didn’t scale linearly with any stat increase other than attack power.

Secondly, we had the wonky armor pen stat that scaled exponentially. Thus your second 100 armor pen gave you a lot more damage gain than the first 100 armor pen. At very high levels this scaling was very, very extreme.

I’ve stated before that right now it doesn’t look like hunters have any kind of crazy non-linear stat scaling. Of course with all the complexities involved with stats, talents, and glyphs, it’s always possible, but if there is any non-linear scaling, I suspect it’s very small. Of course, I could always be wrong. I do that from time to time, usually in regard to very obvious things as well : )

So I thought it’d be fun to go over some simple stat scaling examples. Specifically we’re going to look at crit and mastery — well, mastery for SV and BM at least. MM mastery is complicated beyond simple examples. My goal here is to point out that both crit and mastery scale linearly but combine to scale a bit better. There’s been a lot of thought out there that SV’s mastery will get crazy huge exponential increases when stacked. And I know it seems like it should somehow, but it doesn’t. At least, as far as I can see.

Let’s take a look.

Crit scaling

We’ll start with crit to get a baseline, and we’ll look at the simplest possible scenario. Let’s say that when we shoot something we do 100 damage. When we crit, we do double the damage — so that’s doing 2o0 damage! Awesome! It’s good to be a hunter!

Now we shoot something 100 times. We are starting off with 0% crit, so all 100 are just hits. They each hit for 100 damage, so we do a total of 10,000 damage. Go us.

Now let’s get 1% crit on our gear. We shoot 100 times, only now 99 of them hit for 100 damage, and one crits for 200 damage. We now do 10,100 damage total. This is a 1% dps gain, because crit rocks my socks.

Now lets get another 1% crit. We shoot 100 times, and now 98 are hits for 100 damage, and 2 are crits for 200 damage. We do a total of 10,200 damage. This is an increase of 0.99% to our dps — not the 1% we saw last time. Our extra 1% crit still gave us the exact same 100 damage increase, but since our total damage done went up, the percentage of the damage of our increase was smaller.

This holds true for any crit values.

If we have 50 crit rating we’re now doing 15,000 damage (50 hits for 100 damage, and 50 crits for 200 damage).

If we increase that by 1% crit we do 15,100 damage. We still increased our damage by the same 100 damage, but now that’s only a 0.66% increase from our previous 15.1k damage.

This is a perfectly linear scaling.

It’s worth noting, however, that crit is a bit more complicated than that. We still have our DoTs that are only doing 150% damage on a crit (we’re pretty certain this is a bug, btw), and when they fix our meta it will add 3% to our crit damage multiplier. On top of that every spec has abilities that proc off crits, adding to the value of crit a different bit for each spec.

SV mastery scaling

Okay, so we know how crit scales, and we know it’s linear, so now lets take the same example and look how SV’s mastery works. Every 1 mastery will increase our magical damage done by 1% — that’s percentage scaling! Woohoo!

Let’s take the same setup. We fire a shot that does 100 damage. It’s  magical, so our mastery affects it. We fire that shot 100 times. With no mastery at all we’d be doing 10,000 damage from those shots.

If we now add 1 mastery, we take that 10,000 * 1.01 to get 10,100 damage. A 100 damage increase, boosting our dps by 1%. Sweet… but somehow strangely familiar…

Now lets add another 1 mastery, for 10,000 * 1.02 to get 10,200 damage. This is now a 0.99% increase to our dps — not 1% anymore, even though the extra 1% mastery gave us the same 100 damage increase as the first 1% did. Exactly like crit, this scales identically through all levels.

If we have 50 mastery, we’re doing 15,000 damage. With 51 mastery we’re going up by that same 100 damage to do 15,100, which is now just a 0.66% increase.

SV’s mastery scales perfectly linearly, and in fact nearly identically to the crit scaling. But, there’s a but. While crit boosts all of our attacks and our pet’s attacks, mastery only increases the damage of our magical attacks. Admittedly, for SV, this is the vast majority of them, but it’s still not helping auto-shot, Kill Shot, or the pet’s thousands of dps. And it doesn’t have the advantage of crit to all those proc talents like Sic ‘Em.

The BM mastery works in exactly the same way. The scaling uses 1.7% instead of 1%, but the scale is also perfectly linear, with the percentage gain from later 1 mastery smaller than the first, but the numerical gain always the same for each 1 mastery. And of course this only affects the pet’s attacks, which is less than 50% of our dps, which is why mastery is worst for BM hunters.

Stat interaction

Of course, our stats don’t exist in a vacuum. Each stat is affected by other stats. But crit and mastery affect each other identically.

You could argue that as crit increases, mastery increases exponentially. After all, all those 200% crits are now increased by 1% per mastery in addition to the hits. That makes mastery way better!

Of course the opposite is also true — you could argue that as mastery increases crit scales exponentially, which makes crit way better! So let’s have some more fun and play with some more numbers. Let’s say we can have a crazy high 50 mastery, or 50% crit, or 25 of each mastery and crit. Does combining them provide a greater increase than they do alone?

Again we’re firing our 100 damage shot, 100 times. With zero of everything we have 10,000 damage done.

With 50% crit we have 15,000 damage done.

With 50 mastery (SV) we have 15,000 damage done.

With 25 crit we get 12,500 damage done, which our mastery then boosts to 15,625 damage done!

Or wait… perhaps it’s when we have 25 mastery that we get 12,500 damage done, which our crit then boosts to 15,625 damage done!

My point is that it’s not one stat scaling better than the other — it’s that both stats scale better in the presence of the other. So by combining the two, we get a total that is greater than stacking any one separately! Exciting! And this total is best at a certain magical ratio of crit to mastery — in our simplified example it’s best with half crit and half mastery (20% crit and 30 mastery, or vice versa, yields only 15,600 damage, for example), but reality is a bit different because crit scales in larger steps, changing the ratio.

So with this interaction, the combination of the two stats does actually scale non-linearly, though very, very slightly.

What does it mean?

Before everyone runs out to reforge to have exactly the same crit and mastery, don’t do that. Let’s recap and clarify a bit.

Crit scales linearly. Mastery scales linearly, but with a smaller scaling. By themselves, one crit will always be equally better than 1 mastery.

Crit and mastery interact to scale very slightly non-linearly, to our advantage. This is where math serves us up cookies drizzled in awesomesauce.

Because crit alone is better than mastery alone, the magical combination of the two would favor crit slightly — so you’d always want a higher net crit chance than mastery percentage, but always a combination of the two in the right ratio. Of course even with zero mastery rating on your gear, you start with 8 mastery for free, whereas with zero crit (or agility) you’d have a negative crit chance (yeah, really). So you also need a big chunk more crit (9.5%ish more) just to catch up to make the percentages the same, let alone favoring crit a bit for that magic ratio.

But, there’s a another but. A big one.

We don’t just have these two stats — we also have haste, which also interacts in interesting ways with both crit and mastery. But happily it’s not that complicated to figure any of this out, thanks to a lovely dwarf named Zeherah.

Zeherah’s dps analyzer does indeed take all of this stat interaction into account. As long as you do a lot of variants on the spreadsheet to take into account odd haste and crit swings, the values you get from Femaledwarf.com are indeed your stat weights. If it says crit is better, then go for crit.

And for SV, it says crit is better. So do the target dummies.

I haven’t played around with all gear combinations yet, but when I first checked it out with all first raid tier of gear, crit was still well ahead of mastery. But we’ll continue to keep our eyes on the ratings to see if we ever manage to compile enough crit for the two to start switching positions (which should happen eventually — after all, that agility is giving us crit as well, so we’ll be gaining crit faster than other secondary stats).

Hopefully this explains a bit about how our stats scale, and hopefully you find these though experiments fun as well. Mastery does not become magically better once you have tons of it, and neither does crit (or haste, for that matter). They both go up in the same steps, but a combination of the two, with a bit more crit than mastery, makes them go up even more, and combine for a multiplicative advantage.

Update: Check out Corwyn’s math in the comments. He did some playing on Zeherah’s spreadsheet to find where the magical ratio is, then calculated the balance. Upshot is you probably want to stack crit until you’re around 44% crit or so (and realistically probably more, since as your gear improves, you’ll end up with more mastery).