### Melee Crit Chance

Recently, I wrote about the Attack Speed (haste) modifier, and how the math of it worked, and it's implications. This time, I want to explore the Melee Critical modifier.

This modifier is on a diminishing returns curve exactly like the Attack Speed modifier. The nominal value is translated to a percentage, which represents the probability of a normal hit being a critical hit. So, what does a critical hit do for you?

To explore this, I took a sample of 66 normal hits and 66 critical hits from a night my bruiser spent in Chelsith with a group. My bruiser was using the Bo of Flowing Blood, from Unrest. My critical hit chance was NOT 50 percent, by the way, but I've stacked up the data this way because I want to visualize the relationship between a normal hit and a critical hit.

You can look at the data if you want to. The data points are sorted by size, so we can see the trends. They occured consecutively in the dataset, but not in this order.

The first thing of note is that the critical hits have a definite minimum value. That's the flat part of the red curve on the left. In this dataset, that value is 604. The average damage, in this dataset, of a normal hit was 376 hit points, while the average damage of a critical was 703, which is nearly double.

Let's try to cancel out the effect of the floor. We'll do this by taking the average of those critical hits bigger than 604, and the average of the normal hits corresponding to them (underneath them in the graph). The average of the critical hits in this subset is 788, while the average of the corresponding normal hits is 501. Others have claimed that the raw critical hit ratio is 3 to 2, this is pretty close to what we see in the upper half of the data, where the minimum damage value is not in effect.

So how is the mininmum crit damage determined? The claim is that is is the maximum weapon damage, plus one. No criticals can do more damage than that.

However, in our dataset, there are 6 normal hits larger than 604. This is a very odd tail to this curve, with a much steeper slope. There are 3 points on the critical curve with a similar slope.

It appears that there is a special kind of "normal" hit, that exceeds the normal maximum damage. This is in agreement with raiders expressed experience with certain raid mobs, which sometimes do very large hits which aren't logged as critical hits.

I'm willing to support the notion that melee crits have the following model. For all normal hits, roll damage, including a small chance of a "super normal" hit. Then roll the chance that the hit is a critical. If it is a critical hit, multiply the damage by 1.5. If the result is less than the maximum damage for the weapon, increase it to the weapon maximum damage, perhaps plus one or two points.

So, the bigger the damage spread, the more a critical hit will help your damage. In this dataset a critical nearly doubled the amount of damage. At a minimum, a critical will improve your damage by a factor of 1.5.

Ok, what about combat arts, are they affected by "melee crit chance"? I made the following chart of all outgoing damage for the same instance crawl, plotting the percentage of hits that were criticals.

Here's the entire dataset for that chart.

Most of these ratios look pretty good. Savage Bruising is a DOT, only the first tick of a DOT can critical, so that accounts for it's lower ratio. Engulf is very low, and Master's Strike is low as well. My guess is that these skills are treated differently. Engulf does fire damage, that might well be treated as a spell. Master's Strike does slashing damage, but since we are calculating the ratio of crits to melee *hits*, any difference in crushing skill versus slashing skill should be factored out. But it appears to critical at a rate different from the other combat arts.

Melee Critical chance does not affect ranged attacks, whether autoattack or combat arts. For those kinds of attacks, Ranged Critical chance works exactly like Melee Critical chance works for melee attacks.

Ok, bottom line time. Melee crit chance affects both autoattack damage and combat arts, at least most of them. But not ranged or spell attacks. Which makes it extremely valuable to classes that do mostly melee damage. Conservatively, figure that a +1 to Melee Critical is going to be worth a 1.5 to 2 percent increase to your overall dps. That is, if you are averaging 500 dps right now, then a +1 will be worth 8-10 extra dps.

Labels: eq2, EQ2 dps, Everquest 2

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