Elitist Jerks Damage, Crit, Hit, and Haste: Differential evaluation for item comparisons

 07/11/07, 7:23 PM #1 • Hamlet     Hamlet Tauren Druid   Mal'Ganis Damage, Crit, Hit, and Haste: Differential evaluation for item comparisons 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. -------------- 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. -------------- 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. Last edited by Hamlet : 07/11/07 at 9:08 PM.
07/11/07, 7:44 PM   #2
dedmonwakeen
Bald Bull

dedmonwakeen

No WoW Account
 Originally Posted by Arawethion This is 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.
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.

Last edited by dedmonwakeen : 07/11/07 at 9:23 PM.

07/11/07, 8:08 PM   #3
Juice
Soda Popinski

Orc Shaman

Mal'Ganis
 Originally Posted by dedmonwakeen Says the guy who can just spam one spell over and over and over again.......
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.

07/11/07, 8:15 PM   #4
♦ Praetorian
Mike Tyson

Orc Shaman

Mal'Ganis
 Originally Posted by 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.
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.

 07/11/07, 8:25 PM #5 Disquette doop doop de doooo     Discoepfeand Human Rogue   Sargeras 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. http://us.battle.net/wow/en/forum/to...6766?page=3#41 Let me map a priority list out for you so that you can refer to it in the future: 1. Money 2. Money 3. PvE 4. Mages 5. Companion pets 6. PvP
 07/11/07, 8:45 PM #6 • Hamlet     Hamlet Tauren Druid   Mal'Ganis You're right (above), I worded it too generally. Will change after raid. It's obviously not worth trashing the whole post over.
 07/11/07, 9:01 PM #7 Disquette doop doop de doooo     Discoepfeand Human Rogue   Sargeras 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. http://us.battle.net/wow/en/forum/to...6766?page=3#41 Let me map a priority list out for you so that you can refer to it in the future: 1. Money 2. Money 3. PvE 4. Mages 5. Companion pets 6. PvP
07/11/07, 9:06 PM   #8
Hamlet
<Druid Trainer>

Tauren Druid

Mal'Ganis
 Originally Posted by Disquette 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."
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.

 07/11/07, 10:03 PM #9 Shade Von Kaiser   Shademan Draenei Shaman   Boulderfist 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?
 07/11/07, 10:29 PM #10 Zephriel Von Kaiser     Zephriel Troll Mage   Shadow Council 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.
07/11/07, 10:41 PM   #11
Hamlet
<Druid Trainer>

Tauren Druid

Mal'Ganis
 Originally Posted by 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.
I thought I remembered this board deciding a long time ago that they were additive. Not at all certain, though.

07/11/07, 10:43 PM   #12
Nenormalen
Von Kaiser

Human Priest

Talnivarr (EU)
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:

 I have created a simulation package that currently supports Priests, Mages, Warlocks, Balance Druids, and Elemental Shaman. It allows raid/party creation of arbitrary size and will generate excruciating detail for each player. It also supports Tier 4/5/6 set bonuses as well as a great many unique gear procs. On this page you will find links to the source code as well as a great deal of reference information created by exercising the simulator. Enjoy! -Dedmonwakeen / Wicked Legion / Llane

07/11/07, 11:24 PM   #13
Zephriel
Von Kaiser

Troll Mage

 Originally Posted by Arawethion I thought I remembered this board deciding a long time ago that they were additive. Not at all certain, though.
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. =]

Last edited by Zephriel : 07/11/07 at 11:26 PM. Reason: for clarity

07/12/07, 12:35 AM   #14
Disquette
doop doop de doooo

Human Rogue

Sargeras
 Originally Posted by 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.
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.

http://us.battle.net/wow/en/forum/to...6766?page=3#41
Let me map a priority list out for you so that you can refer to it in the future:
1. Money 2. Money 3. PvE 4. Mages 5. Companion pets 6. PvP

07/12/07, 1:21 AM   #15
Hamlet
<Druid Trainer>

Tauren Druid

Mal'Ganis
 Originally Posted by 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.
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.

 Elitist Jerks Damage, Crit, Hit, and Haste: Differential evaluation for item comparisons