## Considerations on Choosing Crits

In my longwinded missives on choosing a healing template, I dismissed critical hits a couple of times. That’s not necessarily fair, and I thought today we’d look at crits in some depth.

For a change, let’s put the bottom line up front, then dig into detail. For casters, each percent of crit will add 0.5 TIMES the proportion of your heals/damage that’s crit-eligible to your total heals and damage. However, crit-proc talents and gear may make crits far more attractive. Let’s start by unpacking the first half of this statement.

We all know – or should – that for spells a crit adds 50% to the effect of the spell. And we all know that only some of our spells are eligible for crits. We need to do a little work to determine what proportion of our spells’ effects are coming from the crit-eligible spells. At that point we can estimate how much effect an increase in crit will have because it will increase only the crit-eligible proportion. Let’s go with some examples before we go to smaller but important caveats and details.

In a post about being a more mana-efficient spriest, I pointed out that when killing mobs that died before all the dots from SW:P could proc the spriest was smarter (manawise) to just go to an MB-MF-MF cycle. When in this cycle, only the MB is crit eligible — but it’s doing approximately half of the damage. An additional percent of crit would increase this damage by 0.5%. Since the crits only affect half the total damage, the “real” effect of an additional percent of crit is an increase of 0.25%. If the Spriest is doing a nominal 500 DPS, that increases the total to 501.25.

Restated, if half your effects are crit-eligible, then you will get a nominal increase of 1 point (total) for every 400 points of total effect you do. If all your effects are crit-eligible, you get one point per 200 total effects.

In the overall scheme, then, the effect of crits as modifiers of damage or heals is… small. If my GH is 3000 points, a crit will make it 4500 – and that’s pretty nice. But if I’ve got 15% crit potential (5 innate, 5 from Int, 5 from talents) then I’ll only do that 15 out of 100 times then my average return is 3225 – a nominal increase of 225 or 7.5% per spell. And if I’m the ‘lazy’ renew/interrupt cast GH healer, then GH is about half my heals — in which case I’m getting an increase in HPM/HPS of 3.75% for that 15% increase in crits.

So far, then, we see that crits have a small but measurable impact on our spell effects. But there are a couple of hidden ramifications that need noted. The first is probably the most important — the spikes. The irregularity of the effect means it cannot be relied upon.

For DPS this isn’t really an issue — what matters for DPS is more damage in any way it can happen. It’s why the damage-dealers can get such great effect out of damage meters — it’s sustained output, and spikes aren’t really that bad. For healers, it’s a different story. Shortly I’ll be discussing downranking, but the short version is that when you’ve got a proportion of your heals as crits you can either ignore their possibility and suffer from overheals, or you can count on them and then work to fill the gap if they don’t occur. And filling the gap needs to be a non-crit spell or… poof, overheals. Either way, crits actually work to increase your workload.

And that would be the end of the discussion were it not for the additional complications. As discussed in the long-winded talent post, there is a very useful talent that can proc on crits. Inspiration, when it triggers, gives the target an increase in armor. Armor’s benefits are on a diminishing returns curve – that is, going from 10 to 11 armor has a greater increase in damage mitigation than going from 100 to 101 armor. But 101 still reduces more than 100. And inspiration will change the 100 to 108/116/125 armor — not an insignificant quantity. (A brief interjection – though it’s got diminishing returns, we can ballpark. On a tank, a 25% increase in armor will increase the amount of damage mitigated by approximately 5%. Still not too shabby.) Too bad it only lasts for 15 seconds. So… let’s see if we can’t estimate how much time we can keep our tank up-armored, shall we?

For half our heals to come from GH in a two-spell specialist, the GH needs to be approximately 1/3 of the spells cast. If we ignore the 5 second waltz and do a constant spam, we average one spell every 2 seconds (pre-talent, 1.5+1.5+3, all divided by 3) . Since only a third of the spells cast are crit-eligible, we need to cast 300 spells for a 1% spell to crit — 600 seconds (10 minutes) of casting. That means 1% crit gives us 15 seconds per 600 of armor. That’s not as bad as it sounds. Remember that 15% crit is an easy reach even before gear. 15% crit means 15 crits giving 15 seconds of armor over those 300 casts — or about 225 seconds of armor out of every 600 seconds of casting. To restate it, every percent of crit will give our tank increased armor for approximately 2.5% of the time, provided we’re constantly casting. +20% crit – a not difficult gearing option – means our tank will be up-armored about half the time – and consequently taking a (ballpark estimate) 2.5% less damage – when we’re casting a stereotypical healing pattern.

For both shadow and heal-priests, then, the weighting is fairly clear. If all you’re getting is damage, crits add a definite, small, and highly irregular effect. DPS should consider it (though after other damage increasing abilities), while healers should approach it with caution. However, if you have gear or talents that proc on crits, their importance increases immensely. Whether you actually choose to increase your crits is, as always, up to you — your playstyle and interests will be the final determinate. All I’m doing is helping you realize how they fit into your play.

Have fun.

Nitpick: Armor is not on a “diminshing returns” scale if you consider “survival time”. That is, each point of armor has the same marginal gain in how long you will live. The reason the mitigation % has diminishing returns is because going from 0-1% is half as powerful as going from 50-51%, which is half as powerful as going from 75-76% (roughly).

Tanilin said this on August 23, 2007 at 2:28 pm |

Sorry, Tan, but on this one you’re completely mistaken. The formula for armor mitigation (source WowWiki) is ARMOR / (ARMOR + X), where X is a constant based upon the enemy’s level. To use some simplified values merely for easier math, assume X=100 — though the principle will work across the board.

At armor 10, the damage mitigation is 10/110 or .090909…

At armor 11, the damage mitigation is 11/110, or .1

The gain for +1 at this level is .0.1-0.91 (rounded), or .09.

At armor 100, the damage mitigation is 100/110, or .91 rounded.

At armor 101, the damage mitigation is 101/110, or .92 rounded.

The gain for +1 armor at this level is .01.

(note – there is a hard cap of 75%. On the other hand, the constants tend to be in the thousands.)

The same armor bonus gives a cloth wearer (who tends to have low armor) more benefit that a plate (high armor) wearer.

Kirk said this on August 23, 2007 at 2:54 pm |

No, really, Kirk, you’re looking at it backwards.

Suppose I have 10% mitigation. That means that a monster who hits for 100 will hit me for 90 damage. If I get 5% more mitigation, the monster will hit me for 85. If I start with 10k hp, the monster initially can hit me 111.1 times before I die. After, it will take 117.6 hits to kill me. 111.1 / 117.6 = 1.059, so I live 5.9% longer.

Now, let’s suppose you currently have 50% mitigation and you want to increase your living time by 5.9%. With 50% mitigation, each hit is for 50 (I can survive 200 hits). Surviving 5.9% longer means I can survive 211.8 hits. That means that each hit be for 47.2.

Which means to gain an equivilant increase in survival time, I need a little less than half the mitigation increase at 50% as I needed at 10%.

To rephrase: going from 90% mitigation (every hit for 10 out of 100) to 91% mitigation (every hit for 9 out of 100) is a 10% change in what you are hit for. That is massive. That’s why the “armor to mitigation” curve has diminishing returns — because the benefit of mitigation has exponential returns.

Tanilin said this on August 23, 2007 at 7:15 pm |

Ah. Tam, I see where the confusion is. You’ve gone off into apples while I’m still talking oranges. You’re right, but you’re not discussing my conversation which happens to be about inspiration, and how it has diminishing returns for higher levels of armor.

Inspiration doesn’t adjust mitigation (your point), it adjusts armor (my point). ON THE OTHER HAND (sigh) I’ve been trying to treat the adjustment as fixed instead of a percentage. My math was correct, its connection to inspiration was flawed. So… let’s run some (arbitrary) numbers.

Let us use 20 and 100 for our relative armors, with a constant of 200. In each case we’re going to add 25%. (numbers that follow are rounded for ease of viewing)

20 / 200 + 20 = 0.091

1.25*20 = 25. 25 / 200 + 25 = 0.111 : increase 0.02

25% increase in armor increases mitigation by ~22%

100 / 200+100 = 0.3333

125 / 200+125 = 0.3846 : increase 0.0513

25% increase in armor increases mitigation by 15.4%

The cloth (20) armor receiving mitigation gets to live 22% longer. The mail (100) armor extends his life by 15.4%.

As base armor goes up, the effect of an Inspiration proc has diminishing returns. Not negligible, but diminishing.

Kirk said this on August 23, 2007 at 8:29 pm |