Monday, May 10, 2010

Damage mitigation overview, part 1

There are a lot of different things you can do to reduce the damage you take from melee attacks. For example: Defense, Physical Damage Reduction, Evasion, Parrying, Shield Blocks etc. Of this list Physical Damage Reduction and Defense are the "reliable" ones in the sense that they will affect every single hit that actuall lands. The others are based on chance. I believe this is the reason why tanks prefer to max out these stats before the rest. Even if the law of averages implies (assuming a normal distribution) that the "less reliable" forms of damage mitigation will just as often reduce more damage as they will reduce less damage compared to their average amount.

I believe evasion is severely undervalued as a ways of damage mitigation. However, if you look at the math people use for accuracy calculations (which a lot of melee class players use to great effect) it says that adding Evasion increases your evasion rate by a static amount, namely +0.5% per point of evasion. This is similar to PDT in the way that each point of evasion added has more value than the previous. For example:

Original evasion rate: 50%
+ Optical hat (=+5% evasion rate)
= 55% New evasion rate
55%/50% = 110%
= a 10% increase from original evasion rate

Take this even further and you actually reach the point where a Wind Staff (+10 evasion) gives the same damage reduction factor as an Earth Staff (20% PDT) if you start from 0% PDT and 75% evasion rate. It's a very extreme situation, but it's still pretty crazy, eh? Well it was a surprise to myself when I ran the numbers.

Not only does evasion give increasing returns, the cap is much higher than most other forms of damage mitigation. Namely 80%. That's right, capped evasion reduces your damage over time from melee attacks by 80%. You might ask: "What does this matter? Most jobs can't even get close to capping evasion on anything that matters." This is true. However, most tanking jobs are not at evasion floor when tanking such mobs, meaning that adding Evasion has a small but non-trivial effect. [I have to retract the preceding sentence, this is probably only true for Ninja] Also, what about tanking on things that "don't matter"?

You can get up to -20 accuracy from blind spells. From my experience people don't care to cast blind on mobs since they're perceived to have such high accuracy in the first place. As long as you're not at floored evasion that's still -10% damage taken over time. It doesn't change a lot of play elements for most tanking jobs, but I certainly will consider casting Blind the next time I go RDM to something. It's also made me reconsider gear pieces like Koenig legs and Genbu's Shield (both have +10 evasion).

Calculating how much damage your defense mitigates seems pretty hard at first. Not everyone (including me) is fully versed in the ways of cRatio, p-dif and fSTR. If these terms are unfamiliar to you, it's worth your time to take a look at this page. From what I've seen these functions aren't fool proof or complete and the game will, on occasion, show different values from what you'd expect. Take a look at this graph:
What does p-dif mean? It's what you multiply base damage by to get the actual damage. P-dif has a range and is not an exact value. The value is dependant on the ratio between target defense and attackers attack stat as well as the level difference between attacker and defender.

That's pretty much all you need to know. Looking at the graph with that in mind you will see that the lower left portion is what we are interested when tanking. I find it a bit hard to figure out what the average p-dif would be at atk/def=0 because of how p-dif can never be negative. I want to avoid getting too much into details, because I'm bound to say something wrong. I think it IS safe to say that in between atk/def=1 and atk/def=0, most of the time you can use
1 - 1/(1 + defense_increase/original_defense)
as a decent approximation of how much damage a single piece of gear or defense buff will reduce at the most.

To make a long story short: something like Cocoon, which raises defense by 50% will reduce damage a bit less than 33%. The higher your defense is compared to the attacker the lower the actual reduction is compared to this approximation.

The truth of the matter is that the exact function doesn't actually matter as long as you understand its shape. As long as you know that defense will help an amount relative to your current defense and that its effectiveness decreases as you reach low atk/def ratio's, then you can make better decisions for gear.

Complicating the matter
So, now that I have given myself a way to compare defense, evasion and PDT, I can make gear and buff choices based on some type of data and less on gut feelings and general consensus. However, some types of damage mitigation can't be boiled down to a percentage so easily as others. Take Phalanx. Its damage mitigation factor depends on how much average damage you take from melee hits, something you won't know until you've take many hits to the face. What about Utsusemi? The damage reduction factor can only be calculated for melee hits once you know how many shadow absorbs you get relative to the number of hits you take. This depends on things like spell recast and mob attack rate. I didn't touch on fSTR because of this as well. The more VIT you have the more the attacker's base damage decreases, but the actual percentage depends on the mob's base damage before the reduction.

Remember that this is all for melee hits only. There's a big difference in priority when you bring monsters' TP abilities into the mix. Some of them are magic damage. Some of them are more susceptible to evasion and others to defense.

All reduction factors can be applied in sequence (order doesn't matter except for rounding) to produce the total reduction. Another complication is that there are cases where multiple forms of defense can proc on the same hit. Think of Shadow Mantle, shield blocks and Phalanx. Here the overlap reduces the actual damage reduction factor.

There aren't any. This is not that kind of post. If anything we can summarize this post as:
  • Evasion has increasing returns like PDT.
  • The damage reducing factor of Defense can be approximated.
  • Things aren't as simple as the numbers, but numbers help.

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