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Blade Ward, Analytical Model

Warning: Theorycraft inside.

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Re: Blade Ward, Analytical Model

Postby kirsty » Fri Jul 23, 2010 4:42 am

maybe it was a factor why he bothered to calculate it, but fact is, that theck never even mentions eh in his thread about agi and dodge. if he does, then tell me exactly where. i can only find mitigation here, dmg reduction there and so on. even the first line states:

"...how does agility stack up to dodge for damage reduction/prevention?"

he goes on and on how much damage you avoid with dodge and agility, and how the icc buff affects that, and he brings in the armor component of agility and proves step by step that agility is in icc superior to dodge, if you look at damage reduction. he also says, that agility gives threat, but he never says anything about effective health. there is a lot of a differance between mitigation and effective health, even though both go hand in hand.

so lets say we have damage income x, reduced by avoidance and mitigation, thus resulting in x*(1-m)*(1-a). then you know how much healing you have recieve to be at 100% again. if you take only this aspect, which theck does in his thread, then it doesnt matter in the end if you have more avoid or more mitigation. either way, in the end you recieve damage*(1-damage reduction), which is the healing you will need.

effective health is a whole different matter. it only looks upon how long you live in a worst case szenario (i.e. no heals, no avoids) or in other words, how high can be a damage swing that you will still survive. (without taking ardent defender procc in consideration of course)

from 10 agility you get 22 armor, and looking only at physical attacks, this would give you a little less eh as 2 stam would. that said, 10 agility gives not only damage reduction as if you had 1.04 dodge, it also gives eh as if you had 1.8 stam. (for physical attacks only of course) now THIS is something which makes agility in my opinion even outside icc better than dodge. because of the eh component. thats why i even startet socketing agi before i knew of thecks calculations, and i was amazed that agility outperforms dodge even when looking only at dmg reduction (at least in icc).
anyway, my point was, that i almost never saw the eh component of agi taken into account.

but to get somehow back to the topic: how much gets you a procc based eh actually? i mean, mongoose only gets us eh as long as its active, so actually i am uneasy to call it "eh" because its nothing i can rely on. but as i said before, it CAN procc just the moment the healer sleeps, and it CAN save just in this moment my ass. i mean, its just the same with block value and other stuff like this trinket from prof 10 man.
personally, i dont believe that bladeward will outperform mongoose in icc under any circumstances, ignoring tps. of course, i guess theoretically it would be possible to somehow dump parry and defense, and get a lot of dodge, and then against a boss with very slow attack speed, bladeward would be better. i just would like to see that theory of mine backed up with numbers. maybe of course i am wrong, but then i would want numbers to prove me wrong.
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Re: Blade Ward, Analytical Model

Postby theckhd » Fri Jul 23, 2010 7:04 am

kirsty wrote:on a side note: why does everyone keep forgetting about the eh part that agility gives. the "get the hell out of dodge" does not factor it in, and you did not too.

kirsty wrote:i think you got me wrong there. thecks agi thread of course did factor armor in, but ONLY in terms of mitigation. what i meant is the effective health contribution. armor does, as we all know, not only reduce the damage, but also lets you take more damage until you die (without healing) and thus it increases your eh.

kirsty wrote:maybe it was a factor why he bothered to calculate it, but fact is, that theck never even mentions eh in his thread about agi and dodge. if he does, then tell me exactly where.


Er.... what? First of all, I did mention it in the article:

Get the hell out of dodge wrote:Practically, this means that once we're getting close to the armor cap, we're getting close to the situation we have outside of ICC, where agility is around 98% as good as dodge rating. Most of us considered this a good trade anyway, since we got some free threat and some of the damage reduction came in the form of extra EH.


Second of all, I did "factor it in." Damage reduction due to armor is EH for static sources. They're not two separate effects. The EH from the armor comes in the form of mitigation. It's completely meaningless to say "he considered the mitigation effects, but not the effective health contribution."

If you're asking "Why didn't you compare the EH benefits of Agility and Dodge," it's because dodge gives 0 EH. Outside of noting that agility gives you a little EH, there's not much else to say about it. The only fair way to compare them is via an unbiased metric - i.e. aggregate reduction of incoming damage.

kirsty wrote:i know its a bit fishy to calculate the exact eh part, and that mongoose is not really valid to be countet as eh since its a procc, but everyone keeps just saying "oh, and also it gives a bit eh". but for me, this is the factor that makes agility even outside icc better than everything else, even though it has slightly less dmg reduction.

Again, the proc-based nature makes it tough to really call it EH. In the strict sense, it isn't EH at all. That said, while the proc is up, it will function as temporary EH. The best analogy would be a short-term, completely uncontrollable cooldown.

Saying "I choose agi over dodge because it gives EH," is all well and good, but it's not precise. Will you only do it when provided in equal amounts, like a gem (note that this is not the case for the enchants)? What about 10 agility vs. 20 dodge rating? 50 dodge rating? 500 dodge rating?

There's no easy answer to that question that you can answer with the EH metric, because dodge doesn't give any EH. So you need to go back to other, more universal metrics to answer it - damage reduction, average life expectancy, or something like that.

kirsty wrote:oh, and by the way: due to the high uptime of mongoose,

The latest logs I've seen show Mongoose uptime below 30% in practical situations, often as low as 20%. That's not "high uptime." In fact, even the theoretical maximums end up around 50%, which is still not "high uptime."
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Re: Blade Ward, Analytical Model

Postby kirsty » Sat Jul 24, 2010 4:54 am

okay, i overread the eh part obviously. sorry for that.

and maybe i used a wrong term. what i meant is damage reduction in general, be it from mitigation or avoidance. you compare damage reduction and nothing else. but when i compare 2 items with each other, most of the time i just cant compare 2 damage reduction resources with each other. i have to somehow weight eh against damage reduction. of course you are right if you say that often, having a lot of a weaker stat is better than having a little of a stronger stat, but thats not the point here. the point is (or better to say was, since it has already been calculated) to find out how much exactly which stat is better than the other one, to determine if i compare 2 items, which one would be better.

as i said, i just overread the part where you actually DID say it gets you eh, and i am sorry for that. i read through it more carefully this time, and you are indeed referring two times to eh.

and also, i may have used a term wrongly, namely mitigation. i should have just said damage reduction, or as you said, "why didnt you compare eh benefits of agi and dodge". i know that you just cant mathematically prove something like 15 stam is better than 10 dodge, especially if you want to give generalized numbers. this depends strongly on the boss you are fighting and the current equip.

nevertheless, everyone of us has at least a bit of an idea, how much stam he would trade for how much dodge (or vice versa). for some stam is so good, that they are only socketing one red gem for the meta, and rest pure stam. others take small bonuses, and again othersc (like me) take all bonuses. its as you said, you cant compare eh and dmg reduction in the way of "x eh equals y dmg reduction".

but you CAN note how much eh it gets you, and that its not a tiny tiny bit you can ignore, as you probably wont ignore nearly 2 stamina. and thats what you did, you just didnt mention it in the summary, even though you DID mention crit. i should have read the parts where you DO mention it, but obviously i didnt notice it somehow even though i should have.

and regarding the uptime of mongoose, for me, 50% IS a high uptime. i took the calculated number for that, because i didnt look up any logs for that. as i already said, i am fully aware that you cant really call mongoose eh, because its not something you can rely on. but what DO you call it? raso, for "random arse saving occurance"? okay, i guess it makes sense that you wont calculate it, because it still is too much of a random factor.

anyway, this was actually all not my point. my point was that i think that tlitp MAY have calculated wrong, in the sense that he may have forgotten the armor part of agility. (whom i respect for calculating it in the first place by the way) i just wanted to check if he did think of it in the first place, because it seems to me that he hasnt.

oh, and by the way: sorry for my mistakes, as this is the first time posting in this forum, and my english is far from perfect.
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Re: Blade Ward, Analytical Model

Postby theckhd » Mon Jul 26, 2010 9:33 am

kirsty wrote:you compare damage reduction and nothing else. but when i compare 2 items with each other, most of the time i just cant compare 2 damage reduction resources with each other. i have to somehow weight eh against damage reduction.

As do I. But that's also not a concrete or definite thing. There are a lot of other factors that go into it which make it impossible to give a generic "this much EH is worth this much avoidance" relationship.

The best I can do quantitatively is to show relevant benchmarks like damage reduction or avoidance, and then provide some qualitative advice about the stuff that doesn't directly compare. The conclusion of that article does exactly that.


kirsty wrote:of course you are right if you say that often, having a lot of a weaker stat is better than having a little of a stronger stat, but thats not the point here. the point is (or better to say was, since it has already been calculated) to find out how much exactly which stat is better than the other one, to determine if i compare 2 items, which one would be better.


Actually, that's not the point here, at least for this thread. The point was to develop an accurate analytical model of the Blade Ward enchant so that we can accurately determine uptimes and average avoidance.


kirsty wrote:but you CAN note how much eh it gets you, and that its not a tiny tiny bit you can ignore, as you probably wont ignore nearly 2 stamina. and thats what you did, you just didnt mention it in the summary, even though you DID mention crit.

You're right, I didn't give the direct Agi->Eh conversion in the summary - each point of Agi gives you 2 armor, or ~0.2 stamina worth of EH give or take. That said, EH is mentioned in the summary:
Outside of Icecrown:

* Each point of Agi is still 83% as effective for avoidance, but is now only 98% as effective as dodge rating for reducing incoming damage. Still a worthwhile trade though, since it gives you some of that reduction in the form of EH, and gives you threat as well.


kirsty wrote:anyway, this was actually all not my point. my point was that i think that tlitp MAY have calculated wrong, in the sense that he may have forgotten the armor part of agility. (whom i respect for calculating it in the first place by the way) i just wanted to check if he did think of it in the first place, because it seems to me that he hasnt.


He hasn't calculated the armor contribution of Mongoose at all in his calculation. That's not an error in his calculation - his calculation just determines the uptime and the average avoidance each enchant offers. He has at no point considered net damage reduction, EH/TTL-style metrics, or anything of that sort.

I think you're reading this thread with the impression that he's trying to give you an answer to "Which of these enchants is better." He's not.
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Re: Blade Ward, Analytical Model

Postby kirsty » Wed Jul 28, 2010 2:04 am

as i said: i should not have brought your "get the hell out of dodge" guide up. i somehow didn't notice the eh you mentioned, and said some things i wouldn't have if i had.

but: if this post is about uptime or not, tlitp HAS calculated the avarage avoidance both enchants give. what else would "avarage avoidance post dr" mean? also, later you came to the conclusion that bw CAN pull ahead of mongoose in terms of avoidance, in certain specific situations. (namly, high dodge low parry, slow boss-attackspeed)

now, all i originally wanted, was to know if in the calculation tlitp really meant avoid, and not dmg reduction. also i wanted to know, if there are still situations in which bw pulls ahead of mongoose if you look not only at avoid, but at armor too.
since you already said that it is unlikely for bw to be better than mongoose avoid wise, i can imagine that when looking at dmg reduction and not avoid, the situations for bw to be better than mongoose just wont happen at all anymore. for example, if you just cant get enough dodge without taking parry with it, with a boss speed of the slowest attacking boss in icc, with maybe socketing pure dodge as the only possible way of bw pulling ahead of mongoose.

i would calculate it myself if i had matlab, but i just have open office, which is kinda...bad for such things.

i must say i was even surprised how "good" bladeward actually is. i thought it would be much worse, as i already did small and easy calculations, but they are not really accurate. in the end the result stays the same, mongoose IS usually better than bw, and i therefore will still recommend everyone who asks me mongoose, and i will still enchant it on my weapon.

that said, thanks for answering the first part of my question. now that i think about it, to know if bw is completly useless, or useless most of the time, is actually not really THAT important to know :D
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Re: Blade Ward, Analytical Model

Postby theckhd » Wed Jul 28, 2010 6:18 am

kirsty wrote:but: if this post is about uptime or not, tlitp HAS calculated the avarage avoidance both enchants give. what else would "avarage avoidance post dr" mean? also, later you came to the conclusion that bw CAN pull ahead of mongoose in terms of avoidance, in certain specific situations. (namly, high dodge low parry, slow boss-attackspeed)

now, all i originally wanted, was to know if in the calculation tlitp really meant avoid, and not dmg reduction. also i wanted to know, if there are still situations in which bw pulls ahead of mongoose if you look not only at avoid, but at armor too.

He really meant avoidance. If you look at the code, at no point does he do any damage reduction calculations. He's just calculating the average post-diminishing returns avoidance based on the Markov-calculated uptime information. He also happens to calculate Blade Ward's DPS contribution since that information is easily found while tracking stack levels.

kirsty wrote:since you already said that it is unlikely for bw to be better than mongoose avoid wise, i can imagine that when looking at dmg reduction and not avoid, the situations for bw to be better than mongoose just wont happen at all anymore.

That's entirely possible. The ~120 average armor from Mongoose is about a 0.2% reduction in damage taken for a tank with A=38k armor. DR=(1-(A+120)/(A+120+K))/(1-A/(A+K)) for A=38000, K=16635.

Compare this to the reduction afforded by avoidance. For base avoidance V, an increase of dV gives:
DR=(1-V-dV)/(1-V)
For V=0.505 (50% avoidance plus 0.5% from goose), dV has to be 0.001 to get a DR of 0.998 (0.2% reduction). In other words, if mongoose gives 0.5% average avoidance, then BW has to give 0.6% to offset the armor contribution.

This is very rough math, as I've just guessed at reasonable values of A and V, but I'd expect that the result is still pretty robust, as we don't see BW pulling ahead by that large of a margin.
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Re: Blade Ward, Analytical Model

Postby kirsty » Wed Jul 28, 2010 7:41 am

theckhd wrote:...at no point does he do any damage reduction calculations. He's just calculating the average post-diminishing returns avoidance...


thats why i thought that he probably compared both enchants only avoid-wise, but since i have nearly no idea how matlab works, i couldn't be sure.

and thanks for your rough math. your numbers match at least with my equip, and even if i heigten both armor and avoid, i cant see bw pulling ahead of that.
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Re: Blade Ward, Analytical Model

Postby Awyndel » Sat Aug 07, 2010 12:24 am

Slightly off topic here but this armor cap you're mentioning. We can't reach the lvl 83 cap atm right?
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Re: Blade Ward, Analytical Model

Postby kirsty » Wed Aug 11, 2010 6:16 am

yes we can!

at least with proccs, we can reach the armor cap. passivly we cannot, but with indestructible potion for example its not so hard to reach it, and its even up most of the fight (4 minutes total). most of us also have other proccs like the icc ring, which would add to the time we are at the armor cap.

obviously you still need good gear for that, but its not that hard to reach it, so its worth mentioning it.
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