Combat and Mutilate Spreadsheets (Obsolete as of 4.0.x) - Page 50

Leonoire · 05/29/09, 8:02 PM

Originally Posted by Aldriana

Edit: I should probably add that Dark Matter doesn't take into account either crit capping or the synergy with other trinkets; doing so is somewhat beyond what's easily possible in the current format.

I do not think it is possible even raid buffed to hit the crit cap for white attacks, even with full raid buffs I hit 45.62% on my char sheet in my T8 set (which i am not using currently). Which ends up being 48.62% with the crit buff, that brings the dark matter proc to 61.96% crit chance on white attacks(64% CqC and 77% on mutilate).

I am fairly sure that the special crit cap isn't 80.01% (correct me if I'm wrong on the caps, it's been a while since i've payed attention to the crit caps) like the white crit cap, butt i don't see it being a problem.

As to synergy, If the internal CDs of Mjolinar/BOG and Gretness are the same as dark matter, those may increase(Mjolinar/Blood of the Old God) or decrease(greatness) in value when used with it.

• Aldriana · 05/29/09, 8:17 PM

There is no special crit cap short of 100%, however, there is a *white* hit cap well short of 100%. Basically, the white hit table is one-roll - thus, if there's too much stuff on the table, crits can start getting pushed off. Thus, if your dodge chance, miss chance, glancing chance, and crit chance sum to 100%, your crits are being pushed off the table.

For a specific discussion and example in the case of Dark Matter, see this post.

Feist-Mok · 05/29/09, 8:19 PM

Originally Posted by Leonoire

I do not think it is possible even raid buffed to hit the crit cap for white attacks, even with full raid buffs I hit 45.62% on my char sheet in my T8 set (which i am not using currently). Which ends up being 48.62% with the crit buff, that brings the dark matter proc to 61.96% crit chance on white attacks(64% CqC and 77% on mutilate).

I am fairly sure that the special crit cap isn't 80.01% (correct me if I'm wrong on the caps, it's been a while since i've payed attention to the crit caps) like the white crit cap, butt i don't see it being a problem.

As to synergy, If the internal CDs of Mjolinar/BOG and Gretness are the same as dark matter, those may increase(Mjolinar/Blood of the Old God) or decrease(greatness) in value when used with it.

It's quite possible to crit cap white attacks. The crit cap for white attacks, assuming expertise cap (not always true, and will lower this cap further) is 100% - 25% (glancing) - 24% (default dual wield miss rate) + X where X is the total +hit you have from talents and gear.

In my full T8.5 gear, I sit at 47% crit unbuffed. A feral druid or Fury warrior adds 5 %. An Elemental Shaman, Ret Paladin, or Mutilate rogue adds 3%. So that's 55% before food buff, GotW, Kings, etc. I also run without a huge amount of hit rating on my gear. 5% from talents, 7.75% hit from gear, that's it. I'm not Expertise capped, and have ~1.5% chance to be dodged. So, critcap for me is around 63% crit. I'm dangerously close even without a Dark Matter proc being brought into things.

impi · 05/29/09, 9:26 PM

Originally Posted by Aldriana

Updated combat sheet posted. Should have all the new items + item changes in it, as well as some modeling tweaks and buff selections. As usual, there may be bugs, so let me know if you find any.

Edit: I should probably add that Dark Matter doesn't take into account either crit capping or the synergy with other trinkets; doing so is somewhat beyond what's easily possible in the current format.

Do you plan on updating the mutilate spreadsheet also ?

Mavanas · 05/30/09, 12:50 AM

Based on my analysis of Dark Matter using simulation, it's best in slot but only in armor penetration setup for combat. If you use agility gems and BiS gear, you hit the white crit cap when Dark Matter procs, which effectively means half of the proc is wasted. The impact of the crit cap is so big that it makes DMC:G outperform Dark Matter by 17 dps, which is statistically significant.

Also Dark Matter and Mjolnir have a synergy of 16 dps on top of what an average method would suggest. There are also synergies that I did not estimate between the Dark Matter and Berserking buff procs.

• Aldriana · 05/30/09, 1:16 AM

Dark Matter doesn't really "synergize" with Berserking in any real sense, as your berserking procs are (more or less) randomly distributed in time - thus, time averaging gives a pretty good model of what's going on.

Basically, when two procs uptime distributions are independent - that is, if trinket 1 has uptime U_1 and trinket 2 and uptime U_2, then the expected uptime of the overlap is U_1 * U_2 - time averaging works pretty well for anything that stacks roughly linearly - which is everything except ArPen with itself, more or less.

And in a long enough fight, by the nature of procs, this assumption always holds - for a truly infinite length fight, this assumption will hold very very well. The problem is that fights are not infinite length.

Thus, the question is how long a fight needs to be to make this assumption largely valid. For procs like berserking - and other procs with short or no internal cooldown and a lowish proc rate - this assumption tends to be quite good in fights of any length. And when you're comparing two long-cooldown procs with differing cooldowns - for instance, Darkmoon Card and Mirror of Truth - it's still largely valid, because the periodicity of their overlap is just a couple of minutes, meaning that the assumption is fairly reasonable even on a 5-10 minute timescale.

The problem comes when we start using two trinkets with the same periodicity - notably, any combination of Grim Toll, Mjolnir, Dark Matter, and, to a slightly lesser extent, Darkmoon Card: Greatness. The periodicity of their overlap is measured in hours, thus for any fight of reasonable length, they overlap more than they "should". Hence, any two trinkets on this list will exhibit some degree of synergy - however, relative to any other proc (notably berserking), the usual randomness assumptions hold, so time-averaging should be a good estimate.

Leonoire · 05/30/09, 2:21 AM

Originally Posted by Aldriana

There is no special crit cap short of 100%, however, there is a *white* hit cap well short of 100%. Basically, the white hit table is one-roll - thus, if there's too much stuff on the table, crits can start getting pushed off. Thus, if your dodge chance, miss chance, glancing chance, and crit chance sum to 100%, your crits are being pushed off the table.

For a specific discussion and example in the case of Dark Matter, see this post.

I see, that makes more sense.

Thank you aldriana.

I just did some quick changing on the spreadsheet, and if you are not hitting the white crit cap Dark Matters' value hovers around 380, slightly better than the other currently available trinkets. Obviously the proc is not modeled properly but it is more of a rough estimate, I believe it will be in competition for BiS.

Mavanas · 05/30/09, 8:45 AM

Originally Posted by Aldriana

Dark Matter doesn't really "synergize" with Berserking in any real sense, as your berserking procs are (more or less) randomly distributed in time - thus, time averaging gives a pretty good model of what's going on.

Basically, when two procs uptime distributions are independent - that is, if trinket 1 has uptime U_1 and trinket 2 and uptime U_2, then the expected uptime of the overlap is U_1 * U_2 - time averaging works pretty well for anything that stacks roughly linearly - which is everything except ArPen with itself, more or less.

And in a long enough fight, by the nature of procs, this assumption always holds - for a truly infinite length fight, this assumption will hold very very well. The problem is that fights are not infinite length.

Thus, the question is how long a fight needs to be to make this assumption largely valid. For procs like berserking - and other procs with short or no internal cooldown and a lowish proc rate - this assumption tends to be quite good in fights of any length. And when you're comparing two long-cooldown procs with differing cooldowns - for instance, Darkmoon Card and Mirror of Truth - it's still largely valid, because the periodicity of their overlap is just a couple of minutes, meaning that the assumption is fairly reasonable even on a 5-10 minute timescale.

The problem comes when we start using two trinkets with the same periodicity - notably, any combination of Grim Toll, Mjolnir, Dark Matter, and, to a slightly lesser extent, Darkmoon Card: Greatness. The periodicity of their overlap is measured in hours, thus for any fight of reasonable length, they overlap more than they "should". Hence, any two trinkets on this list will exhibit some degree of synergy - however, relative to any other proc (notably berserking), the usual randomness assumptions hold, so time-averaging should be a good estimate.

By synergy I always meant that the effect of two procs occuring at the same time is different from the value of each proc calculated separately and then summed up. This is undoubtedly true for an attack power proc and a critical rating proc. Under these circumstances it is incorrect to measure the two procs independently of each other since every time they overlap the effect is going to be different from what an average method would suggest.

While average method is inaccurate in dealing with the synergy of any procs with different functional forms, its inaccuracy could be minimal when the overlap of procs is low, which is what you are suggesting. However even over a 5 minute fight the overlap of berserking and dark matter proc is around 13%. That's based on the simulation, but I am sure you can confirm it using a purely theoretical approach. I have compared in the past your approach to calculating overlap between ArP trinkets and my simulation approach, and the two gave very close results. 13% overlap is not trivial. For instance, it is higher than the overlap of Grim Toll and Mjolnir or Mjolnir and DMC:G. My estimate of the dps value of the synergy is 9dps; I obtained it by replacing the trinket and enchants with time average values of their procs and stats. You can independently evaluate it using probability theory. I should note that 9dps difference is not statistically significant using 500 iterations. If I really set a goal of having a more accurate estimate, I'd use 10,000 iterations, like I use to estimate dps/point values of each stat. However, I just wanted to illustrate the the difference is material and it adds to the value of the trinket.

• Aldriana · 05/30/09, 5:34 PM

Right, my point is that that's accounted for by the usual time-averaging approach. If stats benefit is either linear (AP and AP) or multiplicative (AP and crit), time-averaging both procs and using the averaged values throughout gives answers that are a very good approximation of the behavior assuming both the procs occur independently. It's not that it's 100% accurate, but it exhibits no systematic bias in one direction or another - it *is* making a reasonable allowance for the case when both procs are up. Thus, the usual time-averaging approach is a perfectly reasonable approximation - and thus doesn't need a "synergy" adjustment - so long as the procs are independently distributed - such as berserking with any other proc, or any two trinkets with differing cooldowns. It's only in the case where you have two trinkets with similar proc behavior that this model breaks down, and we need to look at doing something different. So yes, there is synergy between any two of DMC, Grim Toll, Mjolnir, and Dark Matter; but there is *not* synergy in any sense not already modeled between those and most other procs.

Mavanas · 05/30/09, 11:21 PM

Originally Posted by Aldriana

Right, my point is that that's accounted for by the usual time-averaging approach. If stats benefit is either linear (AP and AP) or multiplicative (AP and crit), time-averaging both procs and using the averaged values throughout gives answers that are a very good approximation of the behavior assuming both the procs occur independently. It's not that it's 100% accurate, but it exhibits no systematic bias in one direction or another - it *is* making a reasonable allowance for the case when both procs are up. Thus, the usual time-averaging approach is a perfectly reasonable approximation - and thus doesn't need a "synergy" adjustment - so long as the procs are independently distributed - such as berserking with any other proc, or any two trinkets with differing cooldowns. It's only in the case where you have two trinkets with similar proc behavior that this model breaks down, and we need to look at doing something different. So yes, there is synergy between any two of DMC, Grim Toll, Mjolnir, and Dark Matter; but there is *not* synergy in any sense not already modeled between those and most other procs.

It does exhibit systematic bias. It is inaccurate, and it is important to understand if it is material or not. There is synergy between DMC, Grim Toll, Mjolnir, and Dark Matter that has not been modeled by your spreadsheet. If you allow me, I can help you estimate the importance of each synergy.

Or I can help you write the formulas from the standpoints of probability theory, for each combination of procs.

To be perfectly honest, I know that most of the synergies are not materialy significant. And in my very first post related to this topic I suggested making a list of synergies sorted by their material significance, so that you can focus only on the most important ones.

• Aldriana · 05/31/09, 12:35 AM

And what's your evidence that there is a systematic bias? Which way does it lean? And can you provide mathematics to back up this assertion?

Look, calculations of this sort are never going to be 100% perfect. It's the price you pay for determinism - simulators are imprecise even if perfect (and usually inaccurate as well), and calculators are highly precise but somewhat inaccurate. The trick is to have a good handle on the ways in which they are inaccurate. And near as I can tell, there is no synergistic relationship not already modeled between most proc effects, notably including berserking with anything. You're welcome to disagree if you want, but if you're not going to provide math to support your claims you're not being very helpful.

As for actually measuring the few synergies that *do* exist - the reason they're not modeled is simple: the conceptual framework of this spreadsheet simply can't handle them. I do have plans in the works for modeling them, but this spreadsheet isn't going to do it without serious rewriting. It's not a matter of needing assistance in modeling them - I know exactly how to do it. It's a matter of taking the time - which will be considerable - to actually implement it.

Thus, in the meantime, I provide the only piece of information that's useful: DMC, Grim Toll, Mjolnir, and Dark Matter - as well as any other 45 sec cool high proc rate trinkets - will be better when used in concert than this sheet currently reflects. However, every other interaction is adequately modeled. Is it perfect? No. Calculators never are. But is it pretty close? Yes. And is there a systematic bias in play? No, there is not. If you disagree, that's fine - all I ask is that if you're going to do so publically, you provide evidence to support your claims.

ingrizod · 05/31/09, 2:52 AM

[Spaulders of the Careless Thief]

wowinsider tells people new to raiding rogues to get these for the +hit ... I think they would make a nice addition to the chart. I know you all will probably laugh though...

saedo · 05/31/09, 4:14 AM

Originally Posted by ingrizod

[Spaulders of the Careless Thief]

wowinsider tells people new to raiding rogues to get these for the +hit ... I think they would make a nice addition to the chart. I know you all will probably laugh though...

Well don't pick gear just cause of hit, take the entire piece and all its stats as a whole. Anyways, you can add anything on your own. Unhide the Gear Sheet, insert what you want, fill in the stats, etc

Mavanas · 05/31/09, 9:42 AM

Sure, here is the mathematics behind my claim. Assume there is no Seal of Fate, Focused Attacks and Honor Among Thieves for simplicity. If any of these talents are present, the synergy is going to be more pronounced, and the math is going to be more complicated.

Introducing notation:
DPS without any procs = X(1+C) with (1-a1-a2-b) uptime
DPS with AP proc = (X+x1)(1+C) with a1 uptime
DPS with crit proc = X(1+C+c1) with a2 uptime
DPS with both procs = (X+x1)(1+C+c1) with b uptime

Average method:
Uptime of AP proc is a1+b. On average the dps is X(1+C)(1-a1-b) + (X+x1)(1+C)(a1+b) = (1+C)[X+x1(a1+b)]
Uptime of crit proc is a2+b. On average the dps is (1+C)[X+x1(a1+b)](1-a2-b)+(1+C+c1)[X+x1(a1+b)](a2+b) =
(1+C)x+(1+C)x1(a1+b)+c1x(a2+b)+c1x1(a1+b)(a2+b)

Synergetic method:
x(1+C)(1-a1-a2-b)+(x+x1)(1+C)a1+x(1+C+c1)a2+(x+x1)(1+C+c1)b=(1+C)x+x1(1+C)(a1+b)+xc1(a2+b)+x1c1b

Difference:
x1c1[b(1-a1-a2-b) - a1a2]

While the value of the synergy is measured by b (uptime of both procs) and is positive, the difference between the average method and synergetic method can be either positive or negative depending on the sign of the expression in parentheses.

Kitteh · 05/31/09, 1:01 PM

Just a question in relation to the Combat Sheet.

As I understood it armour pen scaled quite a way past Agi/AP in EP once you had a decent chunk of it.

Equipping both Grim Toll and the Runestone (so maximising the potential of any extra ArP) the sheet still gives straight AP as the superior stat.

Has this come from ArP not being fully modelled due to sheet limitations? Is it something we are intended to be knowledgable of (same as the Meta always being assumed active) and "work around"? Or is this a change in mechanics/previous overstatement of ArP's potential?

Previously there was a modified version of Vulajins sheet that seemed to take a different route in modelling ArP, this put Fractured fairly head and shoulders over anything else you could stick in a red slot. I do of course trust your figures to be very accurate, just not sure if this is an intended oversight or previous wrong info.

Originally Posted by Aldriana

Blacksmithing Support
Estimated Work: Medium
Support for the extra sockets from Blacksmithing. The problem with this one is that the current UI doesn't have a good place. What you'd really want to do is, when you select BS as a profession, two extra sockets appear which you may then socket. The problem, of course, is that there's no good way to make sockets "appear" like that - they'd need room in the selection table whether you were a BS or not, which is sort of... clunky. If you have better ideas for how to do this, please let me know (and don't say "rewrite it as a webapp". While it would certainly solve this and many other problems, I'm not quite in the mood to restart that project quite yet). When I have a good design in place, the actual implementation work is probably not that high... but figuring out how to do it is the hard part.

As a solution to this (as messing with sockets directly seems to be causing some issues - all the other sockets start changing colour "bodging it" the way it was suggested previously in the thread. Not sure if it's just the UI colour though. I belive it is) you could just leave a space at the bottom of the glove/bracer section with "BS Gems (optional)". People that don't have them can leave them unfilled?