• Arawethion

I'm going to keep this simple, and a bit abstract. This thread exists as an explication of a simple concept that I often see grossly misunderstood. The application is most simple when applied to a Mage casting one spell (to some extent, this thread is a reaction to the Mage +hit one elsewhere on this forum), but the concept is extensible to any class. At the very least, this is the sort of analysis most applicable to comparing different stat choices.

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The following are fixed parameters:
A: Base damage of a shot, with 0 +dmg (substitute AP if you wish, everything which follows is identical).
B: Damage coefficient.
C: Critical bonus.

The following are variables:
d: +dmg
h: chance to hit, i.e. 1-(chance to miss)
c: chance to crit
s: haste

Expectation damage per unit time is:
E = (A+Bd)*(h+Cc)*(1+s)

Taking partial derivatives:
dE/dd = B*(h+Cc)*(1+s)
dE/dh = (A+Bd)*(1+s)
dE/dc = (A+Bd)*C*(1+s)
dE/ds = (A+Bd)*(h+Cc)

These derivatives, whatever form they take for your class, are all you need to know to evaluate gear options. Further analysis (such as using a spreadsheet to compute expected absolute DPS taking a variety of different factors into account) serves only to muddy the results.

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A fully-worked example:

In my 10/48/3 build, let's say I have +1000 to Fire, 0 haste, 130 HR (10.3%), and 300Int/240CR (16.9%).

Evaluating parameters (note that all multiplicative bonuses, such as Fire Power and Imp. Scorch, are irrelevant):
A = 719
B = 1.05
C = 1.1 (Ignite)

Variables:
d = 1000
h = 0.963 (Elem. Precision)
c = 0.259 (Critical Mass, Pyromaniac)
s = 0

Results:
dE/dd = 1.05*(0.963+1.1*0.259) = 1.310
dE/dh = (719+1.05*1000) = 1769
dE/dc = (719+1.05*1000)*1.1 = 1946
dE/ds = (719+1.05*1000)*(0.963+1.1*0.259) = 2208


Dividing out relative itemization costs, I find the value of each stat:
+all damage: 1.31/0.855 = 1.53
+Fire damage: 1.31/0.7 = 1.87
Hit rating: 1769/(12.62*100) = 1.40 (factor of 100 because these things are expressed as a % in-game).
Crit rating: 1946/(22.08*100) = 0.88
Haste rating 2208/(21.0*100) = 1.05

Which is all I need to keep in mind when evaluating or comparing items.

Carrot Cake Soup is like the taste of watching girls make out.

 

dedmonwakeen

Doing the same for a Shadow Priest spell priority (can't even use the word "rotation") is considerably harder.

Certainly not impossible....... but perhaps just a little more complicated.

Personally, I prefer to write simulators..... but I can understand why folks would want to "plug-n-chug" with a pre-made spreadsheet.

http://code.google.com/p/simulationcraft

 

• Juice

How can you tell? The subject thread doesn't indicate class applicability nor does the OP have his/her profile properly completed. I'd summarily ignore this thread.

 

◊ Praetorian

Uh, what? The OP has an armory link in his profile, and the post is quite clear about how to apply it -- you're looking at the effect on single spells as per the parameters. Obviously you can't summarize a SPriest rotation with this system, but for any class that primarily uses a single spell to DPS, it's a good guide.

On the contrary, I'd rather recommend not ignoring Arawethion's posts/threads.

 

• Disquette

FYI, I reported this post. Maybe Praetorian is correct, but if so, the subject line and/or the begnning statement should be completely reworked.

This does not make sense for melee attacks where weapon speed, weapon skill, set bonuses, and procs are very important as well.

Please make very obvious that this is not supposed to be a generalized formula in any sense, and take out statements such as "This is all you need to know to evaluate gear options."

I hope other people get a lot more value from your post than I did, and if you rework the verbiage to reflect what I wrote above, perhaps other people won't immediately say "this is a complete waste of a post" like I did before reading Praetorian's defense of it.

----- sig ---------------
Discoepfeand - rogue / Disquette - shaman
A stormstrike / shocks /watershield timer-bar addon: http://www.curse.com/downloads/details/9729/
"Moogle has mentioned this in passing a few times but never elaborated on it. Perhaps we can entice him to respond." - Malan

 

• Arawethion

You're right (above), I worded it too generally. Will change after raid. It's obviously not worth trashing the whole post over.

Carrot Cake Soup is like the taste of watching girls make out.

 

• Disquette

Yeah, I can see that now. It was what seemed like a gross oversimplification, without realizing up front that it was indeed about a simple topic. Good luck to you in making it a bit more clear, because it does seem like a good use of differentials.

----- sig ---------------
Discoepfeand - rogue / Disquette - shaman
A stormstrike / shocks /watershield timer-bar addon: http://www.curse.com/downloads/details/9729/
"Moogle has mentioned this in passing a few times but never elaborated on it. Perhaps we can entice him to respond." - Malan

 

• Arawethion

No, this is part of the whole point. Though the computation may be much more difficult for some classes than it is for Mages, all of the things you mentioned can be incorporated somehow. I'd imagine it's not extremely difficult for, say, Rogues; you'd just have two terms in the basic equation except one. Especially in the cases where everything is linear (nearly everything in this game), the only thing standing in the way is a little algebra.

Carrot Cake Soup is like the taste of watching girls make out.

 

Shade

I think it's really useful for elemental shamans - we really do use only one spell for dps. I always thought about change in dps / change in crit, holding AP constant, or vice-versa. The same obviously applies with spell damage.

Question is, when selecting gear - how do you weight int, stam, mp5, and other non-damage stats?

 

Zephriel

Correct me if I'm wrong, Arawethion, but shouldn't your damage coefficient (B) for the 10/48/3 build be 1.035 [((3.5/3.5)+.15)*.9] instead of 1.05 [(3.5/3.5)-.10+.15]? Most of the theorycrafting I've seen has treated Improved Fireball's coefficient penalty and Empowered Fireball's bonus as multiplicative instead of additive.

 

• Arawethion

I thought I remembered this board deciding a long time ago that they were additive. Not at all certain, though.

Carrot Cake Soup is like the taste of watching girls make out.

 

Nenormalen

I am not sure if this has been mentioned, but a very knowledgeable guy has made a quite impressive wow raid simulator, check it out here:


SimulationCraft - Shadowpriest.com Wiki

 

Zephriel

I did some additional searching through the mage theorycraft thread (105 pages! eep) to find an answer, but the posts dealing with fireball's damage coefficient all appear to be pre-2.0.6, when Improved Fireball didn't alter the spell's coefficient, rendering the distinction meaningless (1+.15 = 1*1.15). Can anyone confirm which of the two (additive or multiplicative) is correct?

Apologies if I'm derailing your thread, but I imagine this would be important to mages who wish to use your evaluation method with the best possible accuracy. =]

 

• Disquette

you can deal with 3 second lock outs of shared wf procs using this? I believe you if you say you can, but I'd have to see it to understand it.

----- sig ---------------
Discoepfeand - rogue / Disquette - shaman
A stormstrike / shocks /watershield timer-bar addon: http://www.curse.com/downloads/details/9729/
"Moogle has mentioned this in passing a few times but never elaborated on it. Perhaps we can entice him to respond." - Malan

 

• Arawethion

The average proc rate per minute can still be calculated, right (I'm not saying that I've done it)?

Or for the Shadow Priest example, assume that your DoT's are always up, and use an empirical approximation for how many Mind Flays you cast per minute, and throw it all in.

--------------

DPS spreadsheets exist for basically all classes at this point. In order for them to exist at all, the computations for the more complex abilities in the games have been performed to at least some degree of accuracy. When people compare gear options, they usually look at a DPS spreadsheet for a computation of their theoretical absolute DPS output in a variety of setups, and compare the gross values. This has a number of problems:
1) The underlying reasons why one item is better than another are not self-evident. Thus people choose items without a real understanding of how each stat contributes to their total output.
2) Many factors that might be entirely unnecessary to answer the actual question at hand may be taken into account. This not only might throw an arbitrary bias in favor of certain stats or items, but introduces computational or other propagating errors due to the frequent approximations in the process of overall DPS estimation.
3) Ultimately, it doesn't teach people to take a logical approach to item selection. There are tons of people who can't correctly and coherently explain to you whether 1 crit or 1 hit would be better for them at the moment. Much more frequently, in my experience, you get an answer which is more along the lines of, "well I have Ruin, so I just want to stack crit out the wazoo" or "spell haste is great! It makes all my spells faster!"

Instead, if the tools to exists to at all model the DPS of your class, the capacity will exist to throw some simple calculus at them and have a set of coherent results that not only further your understanding of your class, but allow you to objectively evaluate gear options in a direct and accurate way.

Carrot Cake Soup is like the taste of watching girls make out.

 

Luc

I totally agree with your last statement.
I think its far better to pick every item on its individual merits using a simple stat weighting system than to have some 'stat' that you decide is the good one, and try to pick a set of gear with that in mind.

I hear so many melee DPS talk about how good 'AP' or 'Hit' or 'Crit' is for their class/talent and then use a one eye'd aproach to gearing up that stat.

 

dedmonwakeen

Casters may find the following tables useful:

SimulationCraft/Scaling - Shadowpriest.com Wiki

http://code.google.com/p/simulationcraft

 

Desiderata

Hi, long time lurker, first time poster. I may be wrong, but here's my take on the current Windfury.

Since Blizzard linked the MH/OH Windfury procs, I've been modeling it as a single Poisson distribution. To calculate the average time between procs, you merely need the MH weapon speed, OH weapon speed, and a rough estimate of the percentage of time you spend in Flurry. From these, you can calculate the swings-per-second you generate with each weapon and from there, the mean time between WF procs:

MH = Main Hand Speed
OH = Off-Hand Speed
F = Time Spent in Flurry

MHS = MH swings/sec = F*1.3/MH+(1-F)/MH
OHS = OH swings/sec = F*1.3/OH+(1-F)/OH
Mean time between WF procs = 1/(MHS+OHS)/0.2

Since a Poisson distribution is memoryless, we can factor in the 3-second internal cooldown by just adding 3 to the mean time:

Actual mean time between WF procs = 1/(MHS+OHS)/0.2+3

For MH=OH=2.8 and F=0.6 (corresponding to about a 30% crit rate - there's a formula for F if you're interested), the proc rate is about once per 8.93 seconds.

Okay, back on topic: I've been using the same concept of differential analysis for my mage spreadsheet, and am very glad to see that my weighted values correspond closely to Arawethion's. SPriest and Warlock calculations will be more complicated, but not grossly so: after figuring out the weights of the stats for each spell, they merely need to weigh them further by the percentage of time spent casting spell X, spell Y, etc.

This tool was very valuable in the days of DM blues vs. Arcanist, however Blizzard nowadays is much more adroit with its stat allocation. Unless the item has an overabundance of Int/Stam or if there's Spirit (hello mage sets!), you generally can't go wrong with grabbing the highest ilvl item available.

 

• Disquette

regarding windfury in calculations...

and

First off, assume all of the above is correct (and I'm pretty sure it's not, but I'll take your word for it until I do some testing - I may very well be wrong, and will happily admit so if it means somone has a good way of making the formulas work). Now, let's look at the differential formulas that can make stuff "easy" to compare.

Take an offhand weapon with 1% crit and 1% hit, 1.7 speed, compare to an item with a currently equipped item which grants you 5 AP and is 2.5 speed.

Before the bulk of the "objections", realize that an offhand like the first item will now be taking a lot of the windfury procs from the main hand and using them in the offhand instead, but will also be falling inside the 3 second rule a lot. This is the reason that epic daggers from Kara do not out damage auction house slow green weapons. If that's in your formulas, I'm missing it. I'm guessing your formulas would show the differential affect of going from a 65 dps 2.6 item with stats to a 83 dps 1.5 speed weapon with stats to be a major upgrade, though in reality this is far from the truth.

Ok, so back to the main part - in order to evaluate the first item, you would need the general white-swing formulas, and the increased amount of white damage from the time in flurry from the 1% crit, and the increased WF proc chance from the 1% hit, and the increased WF proc chance from the extra attacks that the extra time in flurry grants you. Now add the self (and group if you want) bonuses that the 1% crit gives you from unleashed rage additional uptime (for each crit, you get 10 seconds of 10% increased attack power, which in turn will affect the crits and hits that you have from the first item). Add in the extra weapon procs you get from the 1% hit that the first item which will also interact with the extra crit rating you have.

Now, if the base formulas can easily accomodate all of this, I think that would be super! My issue is that it doesn't seem (to me) to easily accommodate interacting effects of multiple variables. In each of the examples in the preceeding paragraph, 1 stat begets results which affect the other stats' relative value. This interaction affect is what is muddying the waters of my mind in understanding how this can work.

This is already long, but it comes down to this:
As I see it, this cannot be the case because we have more than one type of attack, and each type of attack interacts with the other attacks in a non trivial manner. Stormstrike (which has a different miss/hit/crit table than normal attacks) can proc Windfury which can proc Unleashed Range and Flurry, which in turn affect normal attacks and WF/Stormstrike attacks.

The fact that you have only one "hit" number makes this incorrect from the get-go. 1% hit for me means 0 increase hit rate in Windfury and Stormstrike, but a 1% increase in white hits.

If you say "it's all taken care of in the formulas, and Disquette, you're just not getting it", then I'll have to take your word for it. Sometimes things go over my head. Perhaps this is one of them.

----- sig ---------------
Discoepfeand - rogue / Disquette - shaman
A stormstrike / shocks /watershield timer-bar addon: http://www.curse.com/downloads/details/9729/
"Moogle has mentioned this in passing a few times but never elaborated on it. Perhaps we can entice him to respond." - Malan

 

tedv

While it's difficult to use this information to determine the optimal DPS cycle for a shadow priest, I'd assume most priests have a good feel for that already: keep DoTs up, then use cooldown damage spells, then mind flay.

Even though this just gives relative stat values, you should be able to convert all stats into "X points of stat = +1 DPS" for every spell you use in a rotation. Then using a mod like recap you can determine what percent of combat time you spend casting each spell. Just compute the average of each stat for each spell, weighted by the percent of time that spell is cast. That should give a single composite stat rating for an spell cycle you actually use.

 

galzohar

I actually use (partial) differentials to calculate DPS increases from gear too. Heck I even did it before even knowing what partial differential is (very long time ago), but knowing how to do it makes things even easier - especially when everything is linear when you keep the other variables constant.

Another thing to point out is that the other variables aren't really constant, however when you upgrade your gear the change in your DPS is pretty much always << your current DPS, therefore if E = (A+Bd)*(h+Cc)*(1+s), then you can say that if you change s enough to give X DPS increase or change d to give X DPS increase - while changing s enough to give X/2 dps increase while also changing b enough to give X/2 DPS increase, the DPS increase may be more than X, but in reality it'll be almost X, as if the change in dps is << the actual dps then the difference between the real dps increase and X is of the same scale (X/DPS)^2 which since X<<DPS means (X/DPS)^2<<X so X+(X/DPS)^2~=