For whatever reason, it occurred to me today that the method we've been using to measure the stochastic value of activated and on-proc defensive relics is extremely broken. Specifically, the standard way to measure these sorts of things is to take the rating contribution of the relic and multiply it by its uptime ratio. This allows us to treat periodic effect relics from the perspective of static mitigation contribution, measuring them against things like the old PvP relics and normalizing issues with uptime across relic types.

 

Unfortunately, time averaging is a *linear* process. Specifically, it makes the following assumption:

 

f(x) = k * f(x / k), forall k > 0

 

This assumption is true if and only if the double derivative of f is a constant 0 (proof). Unfortunately, this is absolutely not the case for things like defense, shield or absorb. The double-derivative of defense as a function of its rating (for a shadow) is: -7.91539 * 10^-8 * 0.966667^(0.0151515 * x), which is clearly non-zero.

 

So we have a problem. We can get a much closer approximation of stochastic value by time-averaging the *percentage* contribution of a relic at current rating rather than the rating contribution (e.g. time average defense % rather than defense rating). However, I'm not sure that even that is going to be correct given the way that mitigation stats interact in composite.

 

Thoughts?

Edited April 15, 2013 by KeyboardNinja

I'm not an amazing math person but if you're saying what I think you're saying then it makes sense to me haha.

Here is what I think you're saying:

 

Lets say for simplicity's sake that we're dealing with a tank with 20% Defense Chance and 50% Shield Chance and a shield proc relic that gives 500 Absorb for six seconds with a twelve second cooldown.

 

Before: 500*(6/12)=250 static absorb.

Problem with this ^^, it assumes perfect conditions where the proc will renew the instant the cooldown wears off.

 

You propose: 500 * (6 / (12 + (some calculation involving incoming attacks per second minus whatever is defended and so can't be shielded and shield chance to figure out the amount of time between the end of the 12 sec cooldown and the beginning of the next proc))) = slightly less than 250 static absorb.

 

Makes for better and more realistic time average.

 

Am I understanding you right?

Edited April 15, 2013 by kjmarst

I'm not an amazing math person but if you're saying what I think you're saying then it makes sense to me haha.

Here is what I think you're saying:

 

Lets say for simplicity's sake that we're dealing with a tank with 20% Defense Chance and 50% Shield Chance and a shield proc relic that gives 500 Absorb for six seconds with a twelve second cooldown.

 

Before: 500*(6/12)=250 static absorb.

Problem with this ^^, it assumes perfect conditions where the proc will renew the instant the cooldown wears off.

 

You propose: 500 * (6 / (12 + (some calculation involving incoming attacks per second minus whatever is defended and so can't be shielded and shield chance to figure out the amount of time between the end of the 12 sec cooldown and the beginning of the next proc))) = slightly less than 250 static absorb.

 

Makes for better and more realistic time average.

 

Am I understanding you right?

 

Wasnt it 500 absorb for 6 seconds on 20 sec cd? it makes it 150 'constant'

I'm not an amazing math person but if you're saying what I think you're saying then it makes sense to me haha.

Here is what I think you're saying:

 

I think it's a little more like this... (numbers simplified, for ease)

 

Let's assume that same tank with 20% absorb. Let's say adding 100 absorb would take him to 30%, but due to the DR curve you need to add 400 to get to 40%.

 

If you have a proc relic that adds 400 absorb with 25% uptime, the usual way to measure its value is to say 400*25% uptime=100absorb, and the relic is as good as 100 static absorb. However, the relic isn't adding 4x the absorb PERCENT, just the absorb rating, so it's actually worth (20% extra absorb)*25% uptime=5% average absorb, relative to the 10% a static 100 absorb would give you.

 

I think that's the problem he's talking about.

 

In theory this would be simple to account for, as in my example above you'd just need to find what absorb rating gave 5% and that would be the value of the proc, but it's highly gear dependent (changing the relative value of the proc per user). I also don't know anything about the interaction between mitigation stats that the original poster mentioned, so it may be more complicated than I give it credit for.

Edited April 16, 2013 by namesaretough

Beyond this, time averaging can also be dangerous due to having it averaged over a too long period - for example, IMO you can't time average a clicky relic since the CD between uses is too long, you may have better survivability for 30 second swhile it's up, but if you're relying on that in order for your average mitigation to be high enough, the following 1,5 minutes without it may kill you. When talking about short CDs, like the proc relics, I'm fine with it - the CD should easily be within the TTK when considering that you're getting heals at the same time, so exactly when within that 20 sec window you get the mitigation doesn't matter that much, but over longer periods of times it's vital to consider.

In regards to the OP, correct me if I misunderstand this, but I'm going to try translate it for non-maths geeks.

"We shouldn't look at the time averaged RATING contribution. We should look at the time averaged PERCENTAGE contribution due to DR since a high increase over a short time actually provides less averaged benefit than a small constant increase."

 

That premise I agree with completely, part of the reason I was never a fan of the Absorb proc relic. However, even time averaging based on the percentage increase requires you to be wary. Time averaging the Proc relics based on % increase is fine, short up time, short CD and a fairly consistent proc rate. Damage fluctuations within that CD window are averaged out by damage fluctuation in other CD windows throughout the fight. Basically, you have sufficient sample across the fight that it should tend toward the average.

 

Time averaging on the activated relics is really misleading however since these can be leveraged effectively in above-average DTPS/IHPS scenarios to provide a higher mean contribution, conversely, if used at the wrong time they are worth even less. Personally, I've always been a fan of the activated ones for this exact reason. If DTPS is set to increase or IHPS is set to drop due to increased raid damage: Pop the relic. However you have 2-4 activations across the entire fight and this can cause them to provide a notably above or below average contribution depending on when and how they were used. Essentially, it adds in an immeasurable variable: player skill.

Well - trying to average an on use effect that can be used at most 2-3 times an encounter is a bit ridiculus and I have always ignored it.

 

Although mathematically it entirely makes sense over very large time periods; we are not up against a boss for anywhere near long enough for averaging to be a valid activity.

 

The on use relics are a trade off between a low static dmg reduction versus a high "burst" dmg reduction.

 

The question should not be whats a better avg; it should be a philisophical one of static vs burst. i.e.

 

A small continual decrease in needed heals over time (which may or may not add up to a larger total) versus a large decrease in necesary heals over a short period.

 

As to the proc relics averaging them seems reasonable - but again we can't think of it as static, because we still alternate between needing more heals and less heals when it is active.

 

This conversation should entirely be analyzed from a healers perspective. They are not looking at a flat klandscape when it comes to healing - they are looking at a series of low hills and mountains.

im sure you saw my post about proc relics vs. on use in your thread. of course i do the calc youre talking abobut to give a rough estimate of what kind of mitigation we are talking compared to a pvp relic, but i feel the final method i used to take the time averaged mitigation was suitable since i did not apply to the whole interval an averaged stat value.

 

what i did was calc the post armor mitigation when adding that stat value to a base optimal build, call that mitigaiton relic,a nd the base call base.

 

then we have

 

relic*uptime+base*downtime

 

i think this is a good reflection of what is happening with our stats during the fight.

 

but i could be missing the point.

 

a clear example:

 

for absorb/defense proc i said:

 

the absorb/defense one gives 550 for 6 seconds every 23 seconds or so... time average of 143, so that would be 6624 dps to make this relic bettert than the healing one, and that giving this relic way too uch credit. that is assuming the relic gives a balanced set of points. in reality you get (assuming 2200 mitigation with 790 shield):

 

(6/23)*0.4264+(17/23)*0.4404=0.43679 for defense and 0.43684 for the absorb relic.. defense wins that one.

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so the first part i calc average contribution, which you say is bad, and i agree. if i were to use that number to say that its just like having that much extra all the time i woud have gotten 0.43642 for defense and 0.43643 for absorb. the conclusion would have been they differ by less than 0.00005, but using the mitigation values time averaged gave a larger gap. 0.43679 for defense and 0.43684 for the absorb.

 

also the absorb relic doesnt give static itigation right now, while the defense does... i think,

Edited April 20, 2013 by dipstik