Saturday, March 14, 2009

Common sense testing of SD

Savage Defense reads as follows:
Each time you deal a melee critical strike, you gain Savage Defense, reducing the damage taken from the next physical attack that strikes you by 25% of your attack power.

What does this not do?
-It does not mitigate magical damage.
-It does not proc if the target is immune to attacks.
-It can not proc while you are stunned or incapacitated.
-Scale with incoming damage.

What does this do?
-Crit% chance to proc a one-time damage reduction equal to 25% of AP.
-This works out to about 40% chance for current gear and around 1500-1700 damage reduced(equivalent to block for paladin or warrior).
-Our combined swingtimer of swipe+maul is about 8 attacks every 7.5 seconds before factoring in haste. This means we're dealing with a about 1.0 swingtimer when correcting for lag.
-It takes on average 2.5 seconds to get a crit against a single target based on these assumptions.
-1500/2.5=600 damage reduced per second on average.
-Multiple mobs will increase the uptime of SD, but never beyond our combined swingtimer, so at best it will reduce damage by 1500 per second.

When will it be good?
-Trash tanking when dealing with a relatively small amount of mobs. More mobs increases the uptime, but beyond having 2.5 mobs(2.5*0.4=1.00=100% chance to crit on atleast one mob every second) there is litle gain. Multiple mobs infact simply scale the unmitigated portion of attacks since when working properly, SD is only intended to block one such attack, regardless of size, for the given amount(1500 low end estimate).
-2.5 second swingtimer boss hitting for less than 37.5k(15k DPS)(based on assumption of 12% protector of the pack and 30k armor post-3.1 as opposed to 37k armor pre-3.1 vs. a lvl83 mob which is a reduction of mitigation from ~73% to ~69%).
-Faster swingtimer reduces the portion of attacks SD reduces, balancing out at 15k DPS for a 1.0 swingtimer being the highest 1.0 DPS for which SD is beneficial.
-Basicly, as long as the physical damage portion of the fight does not go beyond 15k DPS SD is a buff.

When will it not be good?
-Extremely fast swingtimer/multiple sources of very small(less than 4.8k unmitigated) physical attacks.
-Slow, hard hitting bosses.
-Bosses for which physical DPS portion is over 15k.

Logic. Pretty great isn't it?


Marino said...

You calculate it has an average proc per 2.5 seconds. The thing is that you forgot to calculate the double proc change (2 procs between boss' hits), to which you hinted by mentioning slow hitting bosses.

But even with normal hitting bosses you will see that maul and swipe will be done really fast after eachother. If both crit you will loose one shield to that.

Making a guess calculation on a swipe cycle of 1.5 and a maul cycle of 2.5 seconds I guess that 40% (1 - 1.5/2.5) of the time you will have both hits close to eachother (again this math is just a guess, it lacks all scientific prove for this statement, and it heavily depends on how fast the boss hits).
There is a 40%^2 chance both hits will proc. That is 16% chance of a wasted proc.

So I'd say if your calculations above are 100% then recalculate them to 86%.
For instance 1 proc ever 2.5 sec = 0.86 proc every 2.5 sec = 1 proc 2.9 seconds.

In this calculation I failed to factor in dodge. With high dodge nearly every boss known will become a slow hitting boss. I think SD shield will make us very sucky MTs.

Shamad said...

Basicly this is "ideal conditions" for SD, which means assuming no double-procs, no proc-less streaks and no avoidance. It's meant to be the absolutely best possible result for SD. Real world applications will be, as you pointed out, often worse than this best-case-scenario, so in effect SD is weaker than the situation the post outlines.

Suppose I should have explained my methology about these things to begin with. Ah well.

Kalon said...

Just FYI - you can't figure out the probability of a crit by multiplying the chance per hit by all the hits. Each event is independent. The easiest way to figure it out is to figure out what the chances are of not having any crits in that time (which is multiplicative) and subtracting that from 1 (all probability). So in this case it's
(1 - (1-crit chance)^number of chances)

So in the 2.5 second window, you'll have 1.66 chances per GCD attack and 1.1 chances per white/maul attack, or 2.76 chances. If your crit rate is 40%, that means you have
1-(1-.4)^(1.66+1.1)=75.6% to get a crit in that 2.5 second window.

If you raise your crit rate by 10%, you get an 83% chance to get a crit.

Shamad said...

I know Kalon, but over an infinite sample on average you'd get a crit every 2.5 hits, which was the point. What I was looking for was a point where your reasonable expectation to crit approaches 100% over a longer period, and at which point adding more mobs scales the incoming damage without significantly increasing your expectation of getting a SD-proc.