Papajan

Let me start off by saying that I think the state of mage theory and practice have diverged in TBC (at least the slice of it that I've seen). More and more fights seem to have a mix of 73 and sub-73 mobs (the +hit overrated thread touches on this at times), more and more have periodic aoe components or low-HP adds, and proc-based gear seems to be much more common. The current state of theorycraft will pretty accurately tell me what damage I can expect to do on a boss mob given a particular set of gear/talents/buffs. We can use things like Vontre's spreadsheet or fine-tune gear/talents/group setup and it'll work well for fights like Gruul, Prince, Leotheras, and Void Reaver (maybe more, those are just the ones I've seen).

A second example of what's been on my mind is the endless stream of threads on the WoW mage forums that say something along the lines, "My dps is lower than everyone else, help!" I feel bad cause I genuinely want to help, but they haven't told me which fight and role their dps is low on. Some fights just aren't mage fights. Some fights favor certain gear choices, etc.

So I figured I'd list out some things I'd love to have accurate models for and some thoughts about how to start going about it and hopefully we can collaboratively come up with solutions. I'm more interested in discussion of ways to handle things than anything else; my ideas about how to tackle things aren't all fully developed and someone else might come up with better ways to address them. I also want to clarify outright that I don't intend to criticize current models or current TCers; we are at our current understanding because of them and I'm grateful for their efforts. If I've come across as critical in this post, I apologize in advance.

Also note: basically all of my examples are from SSC, since Kara seems uninteresting to me and I haven't gone higher really.

1) Single-target sub-73 mobs, potentially low HP
Examples: Hydross adds (depending on your strat), Lurker adds, Karathress adds, Leotheras demons (sortof), Vashj striders/nagas/elementals
Note: I just want to talk about the add dps by itself at the moment, not about how it fits into the larger picture quite yet.

First off, the big change is the hit cap, which is modeled for arbitrary levels just fine in Vontre's spreadsheet, DrDamage, etc. Optimal dps for sub-73 adds would use different gear at least.

There are a few other problems, related to the lower amount of HP they have compared to bosses. Unlike bosses, you may not have dps-boosting debuffs like CoE. Things like that are currently modeled. But in addition to those debuffs, you have things like Imp Scorch and Winter's Chill. You're looking at a situation where you could, for instance on Hydross or Karathress totems, get 4 Scorches off or 2 Fireballs. In that case, it's difficult to model the impact and I'm not quite sure what to do about it except maybe compare different spell rotations for for 3s, 6s, 9s, 12s and see how things come up (it's a little trickier to thing about it when you have multiple mage with Imp Scorch or WC). In addition to Fire Vuln making things a little more complicated, travel time on Fireball/Frostbolt is significant for the last spell you cast on the mob. For instance, common sense would say that if you expect a mob to die in roughly 6s and you're limited to fire spells, you'd want something like (Fireball or Scorch x 2), Scorch x 2 so that your last spell doesn't have travel time. If all the mages/locks/whatever do this, maybe the mob could've died in 4.5s instead.

Secondly, since they have low HP, the exact amount of damage done by each spell becomes significant. If a spell costs 150 mana and does 1000 damage, normally it's 6.67 dpm. But if you're using it to finish off a mob with 100 hp, you're looking at 0.67 dpm. In that particular case, it's usually best to get one wand hit for the remaining HP. But I'm just trying to say that dpm isn't what it appears to be on the last hit against a mob. If you can do 105% of the mob's HP with your normal spell rotation in 3 spells, adding a moderate amount of +damage won't increase your dpm at all. Another factor is whether you'll reliably get the killing blow (that one mushroom trinket is the only KB effect I can think of, but if there are more, this might warrant modeling).

So on single-target dps, our current methods of TC are acceptable for some aspects (level, CoS/Misery being present or not) but not quite there for others (the time to stack debuffs being significant, travel time being signficant, over-dpsing, KBs, etc).

2) AoE dps
Examples: Hydross adds (some strats), Morogrim adds, Solarian adds
AoE seems *a lot* more common in boss fights compared to pre-TBC. However, it doesn't seem common to consider gearing for AoE in current models of TC. The basic things that change are the +damage coefficient and the total damage cap. Gearing for AoE dps would likely focus on +hit until capped, +crit, then +damage. AoE is a bit fun with spell rotations too, like rotations that keep the Flamestrike DoT up. Specs seem to be flopped around in terms of AoE dps, like a spec with Shatter, Ignite, Flamestrike, and Blastwave is likely to do very high dps (until it pulls aggro and dies).

Part of the problem in modeling AoE dps is that there isn't a standard number of targets. Hydross would be 4-5 targets depending on strat, Morogrim is maybe 10, Solarian is 12. As you move up the number of targets, the relative values of crit/damage shift around, as the damage cap becomes more significant. But I wonder if what would happen in the following 10/48/3 situations whe AoEing 10 targets:
a) You base your gear around Fireball spam or 9:1 Fireball/Scorch
b) You base your gear around the AoE rotation of your preference (say Flamestrike/BW/DB/AExN) for 5 targets
c) You base your gear around the AoE rotation of your preference (say Flamestrike/BW/DB/AExN) for 10 targets

Assuming (c) is the optimal approach, I'd guess that (b) would be around 5-10% of optimal and (a) would be around 20-30% of optimal. Is there some value for the number of AoE targets such that models based on that number of targets will tell you to gear correctly for a most other numbers of targets? If there is some average number of targets that works, then we could model AoE in general. If not, then I'd guess it'd be more of a pain to deal with, so most people wouldn't bother.

Also, the values of different things change with AoE. On one hand, if you have a miss/full resist on a target, it's a huge loss, especially on a FN if you plan to Shatter, so all the mobs but one die on time but then you focus-fire the last one. On the other hand, if you crit a lot on one target, that target dies far before the rest of the pack and then 1 more target worth of potential AoE effect is wasted. Like had you worn more +damage, not only would you have done about the same damage to that target in the end, but you'd also deal more damage to the other targets. I think ideally, all mobs in AoE would die at the same time. If one dies early, that's wasted dps. If one dies late, that's time you could've spent regenning or dpsing something else.

Also, AoE has some tight aggro constraints. I wonder how possible it would be to try and have an evaluation metric for backloaded aggro (possibly per-target). Like say you make a graph of aggro vs. time and compare it to a straight line from 0 to your final aggro, seeing if it's above the line in the first 10s at all. If there were some sort of TC way to evaluate frontloaded aggro, it might be possible to choose gear/talents/rotations/etc to habitually minimize the risk of AoE aggro.

The first problem of dealing with different mechanics for AoE seems solvable. The second problem of knowing a good number of targets to simulate has potential to be solved. The problem of having your gear effect the number of targets seems complicated; I can't think of how to model that. The problem of aggro and AoE seems like it has potential solutions, though I'm not entirely sure.

3) Mixed-level/role/importance fights; combining stuff
Probably the easiest example is Karathress. All the adds (aside from totems) survive a while, so stacking debuffs isn't really significant. They're all alive for quite a while and whatnot, so you'd use basically the same spell rotation for the adds and Karathress. The trick is picking gear for it. It's possible to say something offhand like 60% of the dps is on the adds, 10% on totems, and 30% on Karathress. And then you'd take a weighted average of the dps, dpm, damage, etc for each role and use that to pick your gear. I *think* that would get you the optimal gear assuming you don't have a whole lot of alternate gear.

But could we take it a step further? If we said (generally) that add-based fights are 50% sub-73 and 50% 73 (all single target) and you only have maybe 2-3 pieces of gear per slot available to you, would that pick the optimal gear for the more accurate ratios? If so, then we could have standard sub-73/73 ratios and use that to help pick optimal gear for single-target add fights.

Similarly, is there a prototypical dps split for AoE fights? Would it be possible to derive some percentage split such that you pick the optimal gear/talents/etc?

Also, the issue of varying importance comes into play. On Vashj, I dps Striders in phase 2. My success or failure in doing that affects the end result (kill/wipe) far more than my dps in phase 1/3. So for people downing striders on Vashj, I usually suggest doing the TC purely on the striders as an approximation to saying that it's 90% of the fight from your dps perspective.

4) Variance of dps
First off, the mage +hit thread danced around the idea of variance and I realize that. The question I'm interested in is this: Given that a fight (say even a spam-fight like Patchwerk) that have a hard dps requirement, can you select gear such that the probability of randomly being below the dps requirement is minimized? As was pointed out in that thread, +hit reduces the variance of your dps. I *think* focusing on +crit (unless it's very high) would increase the variance, so some fights you might be below the requirement, hoping that some other dpser is above it. Crit rates tend to be high enough so that I'd doubt that would cause you to dip below a dps requirement.

What I'm more interested in is procs, such as Clearcasting, Spellstrike, Quag's Eye, Mark of Defiance, etc. My experience is similar to Manly's in the +hit thread: in two consecutive Dr. Boom tests of Scorch spamming with identical gear and no CDs, one time I did 94k (some sub-20%) and the other I did 144k (no sub-20%). Where am I going with this? Well, we can compute an average equivalent +damage that Spellstrike equates to, for example, but if we had that equivalent +damage instead (or say a comparison like T5 vs. Spellstrike), I think we'd have less risk of dropping below a dps requirement on the small sample of spells in any one particular attempt. Clearcasting is probably similar, but usually you can spec so that you have Clearcasting, but don't sacrifice important dps talents for it.

Summary
I'm interested in ideas about how we could bring the state of Theorycraft closer to the fights we have to deal with. It seems like Blizzard has (maybe deliberately) tried to stay away from the Patchwerk model and that we might be able to use more realistic theoretical models to help give better gear and talent choices. Like I wonder if it would be possible to bring current models close enough to practice that gear/talent selections would be identical between theory and practice, even if the exact numbers don't always line up. That's basically how I evaluate theoretical models: would I have made different gear/talent decisions if I had a more accurate model? If not, then it's good enough!

 

• Xei

I think most Mages wear slightly different items if the adds are +/-73 or if the fight involves AoE. I know for Fathom-Lord I used to wear normal gear for all the adds, then switch to a higher +hit off-hand/wand (those I could change in combat) for the boss himself. On Tidewalker I would wear substantially more stam as often I found myself getting insta-gibbed by earthquake -> tomb or AoEing the murlocs then getting tombed - or just plain sucking and having the murlocs hit me a lot (Mages are a squishy class and Spellfire has no stam).

AoE cycles would be an interesting discussion - I would imagine most people would use the Nova -> Flamestrike -> BW -> DB -> IAE spam (or some similar variant). This is the cycle I use when AoE farming out in the world as well as on Tidewalker.

I do think a lot of caster DPS is lost on the last few hps of an add during an encounter. I almost always leave the last add and move onto the next or boss at a certain % where I think the mob will die in the next few seconds - to save myself the lost DPS time due to casting as I know the melee will finish it off with the ever so OP white damage :p This also allows me to stack scorch debuffs on the next target faster.

Personally, I don't like proc's all that much - I prefer to be in control over my own DPS rather then rely on a random proc to increase it (I would suck as melee waiting on WF proc's). I think some proc's can be more valuable for AoE encounters (LC, Spellstrike) whereas some are not (Quags, increase cast time on instant cast AoE?). Again it comes down to a few smart gear choices on the part of the Mage per encounter.

While I do love reading about theorycraft, I think that sometimes in the strive for perfection people try to model too many things.

"Being a leader is not a position of power. It is a position of service." ~ Barestomper

WTB Oceanic Horde PvE Players

 

Kavan

I think this is an interesting topic and I'd like to hear how other approach (or would approach) the problems.

I think it comes down to how you represent/model an encounter in the spreadsheet. In my modeling I specify fight duration, level of main target, level of aoe targets, number of aoe targets, spell sequence for aoe/main target or leave it to LP optimization. Another thing that is only important in combination with gear optimization is minimum health needed, expected incoming damage/healing which can be satisfied through resistances/armor/hp5/pure hp. I can capture most of encounter specifics with this parameter set, although there are certainly exceptions. I remember for example in BWL days I modeled Firemaw debuff and average time till one had to hide+time lost.

 

Papajan

Xei:
Definitely for fights like Karathress, I focus entirely on sub-73 dps, cause if you down the adds in a timely manner, Karathress himself is easy. Same story for Morogrim (but my role on him is 90% add dps, so of course I'd focus on that). And yeah, definitely stamina gear is useful for certain fights to make sure you live long enough to be healed.

As for switching targets, on trash I just switch to the next target at like 5% to not waste my dps, which basically avoids having to rush to beat the kill shot. On bosses though, it depends. Getting those Spitfire totems down ASAP is important. Things like Striders or the hunters on Lurker usually have plenty of DoTs, so I'll swap targets like you're saying on those. I'll swap early on Hydross adds too, cause I know they'll be killed one way or the other, so I just maximize my dps.

As 10/48/3, my AoE rotation would be like you said, Flamestrike, blow CDs, AE until FS DoT is gone, and use CDs whenever up. As frost, I do FN, Flamestrike, CoC, then usually AE until it's FS time again. I did some modeling of AoE schema/rotations back at lvl60, but it was really hand-crafted stuff, not automated at all.

As far as the strive for perfection... well, I think it'd be useful to see gear comparisons for not just single-target but also AoE. But more importantly, at present it seems that there are a lot of people in the WoW community that plug numbers into some formula or system from the Internet and then just do something without even thinking. You see people saying things like "3 damage = 2 crit rating" or whatever, without any reference to the situation, I guess cause they don't really understand TC themselves. If there were some nice way to programmatically account for the weirdo things in TBC, then maybe that would help those people. But I'm not even sure how to model the important things well yet.

Kavan:
LP stands for linear programming, right? Do you estimate your mana pool and feed it a bunch of cycles like Hamlet in his thread? Or are you talking about something completely different? If it's Hamlet's thing, how does AoE fit into the model? Would you say it's time-consuming to do as preparation for progression fights?

I hadn't really thought of maximizing my dps subject to stamina constraints. I don't have a whole lot of stamina pieces though, so usually I only have like 3 decisions to make, which aren't usually hard. But it's very interesting to think of a method where I could feed in arbitrary constraints and not have to stress to do it.

 

dedmonwakeen

I must sound like a broken record, but I'll say it anyway......

* Low-HP targets that break the classic "assume all the debuffs maxed"
* Mixed role/target that may change multiple times of the course of the encounter
* Interest in the dps-spread..... the shape of the bell curve around the avg
* The introduction of more and more proc-based gear with higher proc rates

These problems seem far more suited to simulation. Mathematical formulation can be elegant, even beautiful..... but sometimes its just easier to reach into the toolbox and get the sledgehammer.

I am a recent newcomer to these forums, but there almost seems to be a stigma associated with simulation and I must admit that I really don't understand it.

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

 

Kavan

LP as linear programming yes. I've searched for posts by Hamlet and I can't find anything relevant so I'm not sure if we're talking about the same thing. The most recent posts regarding the topic was by Arawethion if I remember correctly and I've seen the first posts about a year ago when I also started posting here.

In my LP formulation I have constraints for mana gem cooldowns, drinking time before encounter (think chain pulling), evocation time constraints, starting mana pool, health, time constraint, threat limits, target hp (if using this I'm optimizing for time to kill instead of total damage done), constraints for regaining hp/mp (for farming).

Next there are constraints for spell/cycle cooldowns and 2 constraints that determine mix of LP optimized spells and fixed spells. Here is where AOE comes in. For example I specify that a certain percentage of time or some total time has to be spent on a specific aoe cycle. Adding such a constraint automatically fixes the value of some LP variable, leaving the others free for optimization.

For variables I have fixed cycle casting, drinking, wanding, evocation, mana gems/pots, and a number of cycles used (currently I use 6). For determining which cycles to consider in optimization I usually do some manual processing every so often going through encounters and seeing if adding a new cycle to the mix would increase performance. Since each encounter only uses up to 2 cycles 6 total usually covers all needs.

Next comes the time consuming part and how simulations fit in. Solving the LP is very fast, more or less in real time (it's a very small system in LP world). Where the time consuming part comes is in gear optimization. I'm using genetic programming for optimizing gear, using the LP solver as a evaluation metric. Depending on how much gear you have this runs on the order of several hours. Here the fact that LP solver is very fast is very important. Imagine you'd have to wait half an hour or as much as it takes to get a reasonable number of simulations to get a good average for evaluating gear sets in GP, you immediately start talking about several weeks to solve the problem which is just not practical.

Another thing which I do is I grab item data from wowhead and evaluate uprade paths. Here I can't afford to use GP to obtain the true upgrade value and I just use a greedy optimization (you can't just swap an item and see what's the change because of singularities in the form of to hit caps and similar).

 

Papajan

Just to be clear on what I meant, I'm not really interested in the shape of a Bell curve. Given that it's a normal distribution, it has a particular shape. I'm not so interested in the standard deviation by itself, but when you take the mean and standard deviation together and compute the area under the curve below the target dps threshold to find the likelihood that you've violated a dps requirement. It would be fairly easy to do if I knew how to compute the mean and standard deviation of a given spell rotation with a few procs going on, but it's stricky enough to get the mean with procs, let alone the standard deviation.

As far as simulation, I think the somewhat unspoken criticism is that the hard part of both simulation and exact computation is the same, so why bother being dependent on how many iterations you run? I've done some work on evaluating some machine learning by repeatedly taking random training/testing sets and it sometimes took quite a while to converge to a solution. The worse problem though is that you don't really know if you've converged to a solution cause you can randomly get the same value multiple times in a row. I'm not completely against it, but I think knowing when to stop iterating is a serious issue. Even if you say a million casts or whatever, it's tough to guarantee that the variation between random runs is much smaller than the variation between slightly different pieces of gear.

 

Papajan

yeah, we're thinking of the same person. You looked at the account name and I looked at the character name, just a miscommunication on my part, I should've linked the thread.

I have to admit, I'm not quite clear how some things work in representing the decision as an LP optimization. If I understand correctly, the way you're using it, it'll tell you the optimal amount of time spent in each cycle, where cycles are things like "Fireball spam", "9:1 Fireball/Scorch", "AB x 2, Scorch x 4", "Flamestrike, AE x 3" and whatnot. And you say you pick which cycles to add in there by (I assume) using one LP for AoE and finding the best of the proposed AoE cycles and using another LP for finding the best of the proposed single-target cycles. Am I on track so far? Where I can't seem to follow you is constraints on cooldowns or gems, as I think those are very different from Arawethion's LP setup. I remember him building gems into the base mana pool. Also, if I remember correctly (though I might not), when things like the time taken to stack Scorch are significant, that can't be represented cause it isn't exactly a linear function of the time spent in that cycle.

I think your setup probably works very very well for dealing with general AoE and dealing with adds like Karathress' or Vashj's striders. I imagine for low HP adds, if you're specifying a specific amount of damage to them as a constraint along with optimizing for total damage over the course of the fight, it would know to pick between max dps and max dpm on the add.

Still, it'd be awesome to have something to save a little computation for you in combat, by doing something like linking DrDamage and MobInfo, telling you the optimal cycle for max dpm within the constraint of being within 30% of max dps. Or alternatively, showing a chart based on expected mob lifetime, assuming no debuffs or something. I guess that winds up sounding a bit harder than I originally thought... well, back to the drawing board I suppose.

 

Kavan

You're on the right track regarding the LP formulation. I haven't really done much optimization of AOE cycles as being full arcane AE spam is more or less the only option. But yes it wouldn't be too hard to set constraints so that you limit total time on AOE and total time on main target and optimize both at the same time.

It's true that I'm taking a bit different approach on some things. For example Evocation takes significant amount of time and I find it better for LP to tell me whether I should use Evocation at all. For gems I probably wouldn't have to go that far because there isn't any actual time lost (although I model it as 0.5 sec per gem).

Nonlinearities are definitely something where simulation is a lot better and the way I approach it is to use first order approximation. For example I'll have scorch uptime as part of encounter parameters and then solve LP. From the results I can calculate true uptime for that spell sequence and use it to update encounter parameters. Similar for other abilities that are harder to model as a set of constraints.

I haven't really done much work on optimizing damage on low hp mobs. I think this is one area where simulation would be preferred because of the discontinuities.

 

dedmonwakeen

I've found simulation to be falling-off-a-log simple. Pedestrian, yes. Random, yes. Oh-so-boring, yes.

Formulation, on theother hand..... I've found that "exact computation" can be something of a misnomer. It is "exact" in that it is deterministic, returning ONE number..... but I see far too much hand-waving and approximation. Forgive me: It's easy to throw stones at other folks formulations without supplying my own. My point is that more often than not..... it is rather inexact.

What I like about formulation is the ability to re-write the equation to solve for other variables. A simulation has inputs and outputs..... It is computationally difficult to hold individual outputs constant to see variance in the inputs. I believe that -this- is by far the greatest strength of formulation and that we perhaps are too generous in our interpretation of the "exactness" of our equations........

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