Thursday, May 20, 2010

Crit Bad. Damage Good.

My post about rating conversions contains the seed of an argument that I'd like to spell out in more detail. Dps classes in PvE are balanced based on how much dps they do, not based on how often they crit or how much they crit for. If one class crits for double damage and another crits for triple, that doesn't really make a difference to class balance. The class that crits for more will either crit less often or have lower non-crit damage to make up for the difference so everyone is equal1.

So lets say that in cataclysm dungeon blues the developers are aiming for about 10k dps. Let's also say they are aiming with current talents and rating conversions for us to crit about 20% of the time. That means that if you crit for double then without crits you would be doing 8333 dps. At 8333 dps, when you crit 20% of the time, and crits double you damage, you end up doing 80% regular hits (.8 * 8333) and 20% critical hits (.2 * 16666) and that adds up to 10k dps (ignoring the rounding I've done). If you crit for triple damage than without crits you do only 7142 damage. Again, you have non-crits 80% of the time for 7142 damage and you crit 20% of the time for 21428, averaging to 10k.

If you gain 1% more damage from a talent or a buff, then we know how much damage that is. Regardless of what class or spec you are, in our simply and perfectly balanced world of dps, 1% of 10k is 100. A 1% boost in damage means you do 1% more whether you crit or not and it always comes out to 100 more dps.

What if you crit 1% more often? Well, if you crit for double then your it means you do your base damage of 8333 79% of the time, while you do your critical damage of 16666 21% of the time. .79 * 8333 + .21 * 16666 = 10083 dps. So 1% crit means only 83 more dps. If you crit for triple, of course, crit is better, it gives you .79 * 7142 + .21 * 21428 - 10000 = 142 extra dps, making it better than dealing 1% more damage.

The break even point between these two values, where 1% crit is the same as 1% damage is critting for 2.25. At that point 1% crit is worth 100 dps just like 1% damage.

The math here might be slightly unintuitive. If you crit for times two damage then each 1% crit adds 1% of your non-crit damage to your final damage. If you crit for times three then each 1% crit adds 2% of your non-crit damage to your final damage. But in reality critting for times three doesn't make crit twice as good as critting for times two. This is because, in order to arrive at the place where you do the same overall dps, your non-crit gets smaller as your crit multiplier gets higher, given a fixed crit chance.

What happens to the same calculations when you have a 25%, 30% or 35% chance to crit instead of a 20% chance to crit?

In the case of critting for triple, the amount of extra dps you get from critting goes down from 143 to 133 to 125 to 117 as you increase your crit with the same dps number. At 50% crit, a value that is probably a little low for today's dpsers, critting for triple is just enough to make 1% crit as good as 1% damage. Any more than 50% as an expected crit value and you'll need to crit for more than triple to make a crit buff as good as a damage one.

But very few classes actually crit for anything like that much. The physical dps classes get pretty good crit multipliers because they start with times two and so their talents tend to put their crit over that. For casters, though, they start with critting for only 50% extra and their talents tend to take them up to double. The most extreme example of critting is the now defunct frostfire mage, who crit for 2.25 and then put a DoT for 40% of that on the target, making their total crit over triple. Fire mages crit for only 2.45. Hunters can also get pretty big crits with Aimed shot, critting for up to 2.4 with 30% of that becoming a bleed for a total of 3.12.

Almost every class, however, has a fraction of their damage that cannot crit. Almost every class has talents that boost the crit of some but not all of their damage. In the case of hunters Aimed Shot and some other shots might crit for 3.12 (3.21 with the metagem) for Marksmanship spec but their auto-shots and wild quiver shots crit for only 2.3, and those account for a significant portion of hunter damage. This lowers the effective bonus damage from each percentage point of crit.

Developers are concerned about giving out too many crit buffs because crit has interactions with other abilities. But in reality there are few classes that benefit more from a 1% crit increase than they do from a 1% damage increase, and as an expansion wears on the number of classes that benefit more from a 1% crit increase than a 1% damage increase will get smaller and smaller.

Of course this only matters for weighing buffs, talents and glyphs against one another, but it is something that I hope the developers can realize and keep in mind when they are balancing Cataclysm.

1. Everyone is not equal, but assuming they are supposed to be roughly equal, we can go forward.

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