Example for an 18 second rotation with 1 Flame Shock, 2 Lava Bursts and 11 Lightning Bolts:
Total spells cast = 1 + 2 + 11*1.33 = 17.63 or 0.98 spells per second, 1.96 spells every two seconds.
If you have a 45% crit chance then total spell crits will be:
1*0.45 + 2*1.00 + 11*1.33*(0.45+0.05) = 9.77 crits per rotation, or (divide by total number of spells) average crit chance of 55% per spell hit.
Chance for crit per two seconds is therefore:
1-(1-55%)^1.96 = 79%
Average time until a crit/mote is then 2/79% = 2.53 seconds, so pillar fired every 7.59 seconds on average, which is 7.9 PPM.
Myes, I always assumed the mechanics of ICD worked differently and I think you also made a small error; let's discuss:
1) you forgot to divide your 17.63 sec by the number of spells (14). This means 1.26 sec per spell, not 0.98sec. Since we do have EM and BL on bossfights, I would argue that 1.17 sec or something like it is a defendable number for the average spellcast time
2) when approximating the time needed to get a Pillar out, I would say it takes on average 1.17sec/critchance to get 1 mote, and then a period of 2 sec it doesnt matter what happens because any crit produced here is not used. In other words: Pillartime = 1.17/crit + 2 + 1.17/crit + 2 + 1.17/crit +2.
Your method seems to neglect the fact that any crits during the ICD period are wasted and thus I believe this is a wrong representation of how the 2 sec ICD period works, but I would definately like to hear your and other people's opinion
3) I forgot CoE and crit for the dmg per Pillar in my previous post, so the overall dps from the proc would then be 2117*1.13*(1+crit) / Pillartime
4) Taking LO crits into account would increase the crit with ~3% for all LB casts (which is 11 of the 14 casts), so the average crit chance goes up with 2.4%
So with a 45% critchance (raidbuffed etc) this would mean an average overall crit of 55% and a Pillar dps of 280 (so excl the sp contribution).
At ilvl 277 gear we appear to have 58% crit raidbuffed, leading to average overall crit of 66% and a Pillar dps of 334
So question is: what is the proper way to model the 2 sec ICD after a crit/mote? It makes quite a big difference as we see
2) when approximating the time needed to get a Pillar out, I would say it takes on average 1.17sec/critchance to get 1 mote, and then a period of 2 sec it doesnt matter what happens because any crit produced here is not used. In other words: Pillartime = 1.17/crit + 2 + 1.17/crit + 2 + 1.17/crit +2.
this is very wrong.
Instead it means that the spell cast right after a crit cant generate a mote, while the 2nd next spell can cause 2.34 sec will have passed since the last mote was generated.
Thus the formula you get for one Pillar is (3 + 1/critchance) * spelltime.
This is because for every pillar 3 spells wont have a chance to generate a mote cause they happen during the cooldown, and 1 divided by critchance is the number of spell casts it gets to get one crit (critchance here means your average critchance across your rotation).
I haven't teste what happens with exactly 1 sec casts cause then 2 spells might be shut out of generating motes. However I tested with 1.05 cast time and got motes/shards allright on the 2nd spell after the last crit.
Myes, I always assumed the mechanics of ICD worked differently and I think you also made a small error; let's discuss:
1) You misunderstand: 17.63 was the number of spells and 18 was the number of seconds; hence 17.63/18 = 0.98 spells per second. Remember I included Lightning Overload which gives 33% extra Lightning Bolts.
2) The cooldown is simply the period of time after proccing a mote during which you cannot proc another mote. That means the quickest you could possibly proc a pillar is 6 seconds, if you were getting a crit precisely every 2 seconds.
3) Indeed you did, as I mentioned! With a 45% crit chance, the average damage of a Pillar would be 3068. With the maths I used in my previous post its DPS would therefore be 404 for the arbitrary numbers I plucked out of the air.
4) I already included LO in my calculations.
So what is the proper way to model the ICD? What I did was to ask "what is the chance we'll have had a crit at 2 seconds?" and then divide two seconds by that. But let's think about some alternate methods that better account for the ICD, with the arbitrary numbers I used in my previous post:
What if we take average crits per cast and average cast time and work this around the 2-second ICD? We could try to say that 1/0.55 = a crit every 1.82 spells which is like clockwork every 1.85 seconds. Or to put it another way, a 53.9% chance per second to proc a mote. But we're essentially saying that after 2 seconds there's a 108% chance to have procced a mote so now we're getting pillars every 6 seconds exactly.
What if we simply take average cast time and the logical latest point we can possibly get a crit? With our average casting time of 1.02 seconds and Lava Burst's 8 second cooldown, we can say that at 9.18 seconds we'll be guaranteed a crit. So we could say that the maximum time between crits is 9.18 seconds, making the median 4.59 seconds. That'd give 13.77 seconds between pillars.
We could think about the timing of the first spell after the ICD, which would be at 2.04 seconds using my arbitrary numbers. The chance that this spell will crit is 55%. Then at 3.06 seconds there's a 79.75% chance that a crit will have occurred, and after 4.08 seconds that chance is 90.89%. So when do you proc the mote? The crit chance will never reach 100% (remember we're using the average crit values and average cast times, so LvB is irrelevant) so we have to pick a moment to use for the maths. Of course the logical time is as soon as the ICD has expired, which gives 2.04/0.55 = the time between motes is 3.71 seconds or 11.13 seconds per pillar.
All these methods have their merits and all give totally different answers, so which do we use? With hindsight I personally think the last one is probably the best (and wish I'd thought of it sooner, honestly). I see that the most recent version of SEIC used method 1 but without accounting for LO or damage buffs, and apparently factoring in partial resists. The first method I already considered and rejected.
I suppose I should change ZAP! to use method 3 as that seems to reflect a more realistic Reign DPS. For a heroic Reign with 45% crit chance and 50% haste this rates the proc at 282 DPS (one pillar per 10.89 seconds). The existing method at the same stats gives 408 DPS (one pillar per 7.51 seconds).
[e] Comparing with SimulationCraft using the 4t10 BiS list: SimC - 312 DPS, method 0 - 496 DPS, method 3 - 375 DPS. I think SimC factors partial resists, though? Either way 3rd way seems better.
(Sorry that this is going somewhat off the topic of 4t10, perhaps it would be better to move the discussion to the spreadsheet thread?)
Last edited by Zamir : 12/26/09 at 3:42 PM.
Reason: Incredibly serious typo fixed.
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The most logical way to calculate it is this (hopefully a more understandable version of what I posted before):
step 1: calculate the average critchance of our rotation, taking into account everything from lavaburst to lightning overload* and the average cast time of our rotation
step 2: analize what has to happen to get one pillar and how the ICD affects us
previous pillar gets 3rd mote and fires
-> 2sec CD
1st mote
-> 2 sec CD
2nd mote
-> 2 sec CD
3rd mote, fire
-> 2 sec CD before 1st mote of next pillar
...
The true effect of the ICD is simply that it prevents one spell from triggering a mote, since the 2nd spell after the one that triggered the last mote will have happened at least 2 seconds later (unless it's flame shock)
step 3: calculate the average time for one pillar
One pillar consists of 3 crits and 3 ICDs. Therefore the average time for one pillar is:
3x average spell cast (those are the spells that get eaten by the ICD) + 3 x the time it takes to get one crit
=> (3 + 1/critchance) * average spellcasttime.
*basically this would mean modelling the LO proc as an added crit chance for the original lightning bolt. this is somewhat unprecise cause the LO fires later, but in the long run that should not matter. After all, the LO that procced from a LB that was cast during the ICD might fire right after the ICD ends and trigger a mote etc etc..
The clarification was helpful, I see what you're getting at and broadly agree with the methodology. However (3 + 1/critchance) * casttime doesn't work. It'd be 3*casttime+3*castime/critchance which simplifies to 3*(castime+castime/critchance). Also, this only works if precisely one spell falls within the ICD time. You'd need to do some extra maths:
Average spell crit chance (c)
Average spell cast time (t)
Divide 2 seconds by t and round up to give you integer number of spells per ICD (n)
Subtract one from this to get the number of spells which can't proc a mote because they are being cast within the ICD (x)
Multiply this by t to find the "dead time"
Now you want to divide t/c to get the average time until a crit based on the crit chance of the first spell to land outside the ICD.
So the time per pillar could be represented as:
3(xt+t/c)
Using the same numbers as earlier this would be 3(1*1.02+1.02/0.55) = 8.62 seconds per pillar, which is a mote every 2.87 seconds. As you can see this is (a) a more refined example of what I called "method 3" above and (b) giving results very close to the method I was using previously, which I referred to as "method 0". The proc DPS using our arbitrary numbers would be 356.
It's "better" than my method 3 as the maths is more accurate: I actually did nt/c, which is dividing n spells by the crit chance for only 1 spell (wrong). However it's also "worse" because the results reflect reality less accurately.
So the dilemma is: do I use the "correct" maths and the higher PPM figure, or do I artificially pad out the result to reflect "reality" better? On the one hand, the whole point of the spreadsheet is to give an idealized picture free of the capricious twists of reality; on the other hand, if you idealize the picture too much then the usefulness of the tool is compromised. This is, for example, why settings like Cast Delay, Rotation Delay, and "Trinket proc how often?" exist - it's an attempt to allow the user to dial back specific aspects of the maths to try and accommodate the effect of "reality" on specific types of comparison (e.g., is haste really better than spellpower? is a trinket with a chance-to-proc better than a trinket with a use effect? etc.).
I'm not sure what to do with the Reign maths now. I could leave it as it is which is mathematically hard to justify, or I could change it to reflect the above method which is realistically hard to justify.
I don't suppose somebody has a better solution as to how to model Reign's proc in a way that doesn't artificially inflate it past nearly every other trinket out there (or has noticed some mistake in my methods which would fix the problem)?
I see Rawr is rating the proc with 4t10 BiS in the region of 370 DPS, but I can't tell if it's allowing the proc to crit or not. ZAP! using method 3 rates it as 376 DPS, or ~360 factoring partial resists. The output for the method above (I'll call it method 4) is 442 DPS (~420 with partials). Remember SimulationCraft is giving ~320 DPS for the proc under the same conditions.
Every one of us is, in the cosmic perspective, precious. If a human disagrees with you, let him live. In a hundred billion galaxies you will not find another.
Just FYI, after taking into account the new math on DFO and reign, BiS trinkets are going to be heroic Phylactery and heroic DFO, so feel free to update your gearlists as appropriate.
I'm likely going to skip 4pc t10 (at least for now) due to the reasons discussed above, so here is the updated working 2pc t10 BiS list:
So, I didn't read everything in detail so correct me if I'm wrong, but to sum things up, simulations say that 4p T10 bonus is a very little dps increase with respect to 2p + bis offset ? Something like 10 or 20 dps ? It would be very cool for I really don't want to have 4p bonus ^^
Just FYI, after taking into account the new math on DFO and reign, BiS trinkets are going to be heroic Phylactery and heroic DFO, so feel free to update your gearlists as appropriate.
I'm likely going to skip 4pc t10 (at least for now) due to the reasons discussed above, so here is the updated working 2pc t10 BiS list:
Your bis setup only has 239 hit for alliance... Is that intentional?
Perhaps switching out the ring of rapid ascent for [Valanar's Other Signet Ring] would be better then being under hit cap, or worse, having to gem for hit?
It assumes 3 sp/hit gems, and yes, I tried other combinations, this was the highest DPS. You can substitute that ring in if you want, however, since the difference was ~17 DPS.
Gemming for hit isn't necessarily bad - it's only bad if you would otherwise gain more from using the sp (or preferably, sp+haste) gems over the hit ones. I've put the items together as best I can, but it always ends up that using 3x Veiled is better than going over hit via using another +hit item. Things change a lot at the 264 level vs the 277 for us - that's anther topic all together, though.
That said, my analysis of the BiS shows the 4pc on top of the 2pc+offslot items by a fairly considerable amount (same list that Origins posted above, but using T10 pants+shoulders). It seems his principal logic is using rawr or zap! for the calculated results on stat scaling - but unfortunately, both of those resources right now don't include fire totems in the DPS calculations, and that shift is fairly significant. Most notable is the fact that fire totems shift the relative value of haste downward in favor of spell power and crit (since they do scale with the later 2, but not haste). Since the principal gain of not using the 4pc is having the haste pieces rather than the crit ones, this diminishes the difference and puts the 4pc back on top (in theory, anyway).
But, the only resource for calculating with fire totems right now is simcraft, and I'm not sure their method of calculating a couple things (trinkets, mostly) is accurate, so I can't be 100% sure on that. It's likely the difference is on the order of <1% at BiS level either way, and it may turn out that our BiS while using ToW is different than our BiS while not - although I genuinely hope that won't come up often for most of us at this point.
That's a good point, and it's definitely a good thing to add here that this list was made with the assumption that you will be dropping ToW, the fight is single target, and you have all other relevant raid buffs minus Demonic Pact.
Thanks for the replies;
- I understand now you included LO already so that's great. So we have 1.02 sec between casts on average (without EM or Bloodlust even!)
- the 3 methods you are describing are not really arbritary ways to calculate; as you indicate yourself 1 and 2 are pretty bad estimates of a skewed distribution
- my own estimate of casttime/critchance + 2sec is also incorrect since there is 1 mote possible in the 2 sec period which I omitted
- you state the average times between motes is 2.04/critchance, but I think it is more like 1.02 sec + 1.02/critchance (= 1.02+1.86=2.88s for 55% crit) since the first cast is always lost in the 2 sec restriction but the second can crit with its regular chance.
Reading your last post here, this is exactly what you propose as well.
Btw, I filled in my 277 stuff and your new 114 spreadsheet shows only 226 dps for the proc, while here we argued it is about 350+ dps (54% critchance, 2 T10 pieces, 1110 haste without relic, 3605 sp, 1367 int, 981 crit). Is there a formula error in the sheet or is this correct?
Furthermore, I don't think it is a 'worse' representation of reality, but it is more an 'average' that is valid for an extended period of time and not situational. I think this is the best way of representing the dps value for the trinket, so thanks for having this discussion!
@masanbol
I have the same list as you, and expecting LK to drop a more itemized weapon for us. Instead of the Flesh shoulders, you could also go for Shoulders of Mercy Killing if you need the hit (e.g. instead of neck or so).
Things may still change incidentally if he also drops a better hit-belt/helmet, or some uber crit/sp/haste legs or gloves. Likelyhood on this may however be small.
The drawback I see from the list itself is the extreme amount of haste; I'd rather see the dps coming from other sources as we are well in the region of slightly decreased haste effectiveness and it eats mana.
Then again, it will probably be June before we have access to all of this anyway....
$mightrecruitment
You are correct that fire totems are not included and that they may have impact. However, the use of magma or fire elemental is at this time still very situational and rare; maybe in your guild there is no restriction but when I raid I am expected to put ToW 95% of the time since it benefits the raid more then the dps I can do myself with a fire totem.
So I would be strongly in favour of evaluating gear without any significant fire totem usage
Then there's the added "bonus" that increasing the number of LvB casts decreases the number of LB casts, and since LB casts have an impact on the 2pc bonus, you end up reducing the value of that as well.
This right here is what is making me shifty on actually grabbing the 4-pc, I can already picture the 4-pc backlashing the potential dps gain the 2-pc affords us.
@Ravhin:
Well dress me in purple and call me Dorothy, you're absolutely right.
(Though I wasn't calling the methods arbitrary, I was noting that the numbers we were using for our examples were arbitrary - that is, they were just convenient made-up figures and weren't attached to any actual gear set.)
With regard to your findings in v1.1.4, the error is that I'm using method 3 instead of method 4 and that deflates the numbers for Reign dramatically when the player's average cast time goes under one second. The same effect actually happens with method 4 as well - so for people with less haste, the proc's rated higher rather than lower. And if I use "method 4", the DPS of the proc with 4t10 BiS is... 320! Which is very close to what I think it should be, though that's sadly entirely a coincidence. Higher haste should really mean more procs.
Hmm... what I could do is just use the 2-second ICD as the dead time, and then just add t/c to the end of that. That is, instead of:
xt+t/c
replace xt with 2:
2+t/c
That way, getting more haste and crit will always increase the proc DPS. The DPS will also start out fairly low and then scale up with gear. For someone in my gear it'd be about 270. For someone in BiS 4t10, it'd still be about 320. This way it'd still be head and shoulders above all trinkets up to and including T9, but below the 25-man T10 trinkets. That's actually quite an elegant solution.
About the BiS list:
Using DFO instead of Reign and with Glyph of Lava in the 4t10 set (ToW in the 2t10 set), and remembering to add all the spellpower averages from the trinkets and the ring, I'm finding that the 4t10 list comes out on top consistently by 40-60 DPS. This is not much, but it does indicate that 4t10 will be slightly better even with the clunky DoT-clipping rotation. For comparison, the sims I just did were putting the difference at 80 on Patchwerk and 130 on Helter-Skelter using Glyph of ToW for both profiles (Glyph of Lava in SimC actually reduces the DPS of 4t10 considerably).
I see that the haste value of the 2t10 set is pushing it further past the 50% boundary than the 4t10 set, which reduces the value of the haste slightly. In fact, as we've already noticed, 4t10 works better with slightly lower haste. I see that with the higher haste values of the 2t10 list, ZAP! is once again rating the set bonus negative. Maybe we shouldn't be so upset at the crit-instead-of-haste on our legs after all.
I would suggest that what it will come down to is how 4t10 "feels" and how many emblems/tokens we have access to. So long as we don't let ourselves miss Lava Burst crits (which would definitely be a DPS loss) there's nothing to lose except emblems. And, well, a couple of seconds on our Elemental Mastery cooldown.
Every one of us is, in the cosmic perspective, precious. If a human disagrees with you, let him live. In a hundred billion galaxies you will not find another.
I updated the current BIS profiles, again using masanbol's list. Using the DFO resulted in a nice gain over reign. The SimC output is below with scale factors.
The sim is a straight tank and spank, no adds, 5 minutes with variance, and low latency.
Again, SimC is showing that 4pc is worth ~110 dps. Using Chain Lightning is a dps decrease in every way I tried it, which means mana is again a joke, as seen in the HTML output. You can see the complete action list in either output, which is using the default actions as of build 4167.
The scaling factors will need to be taken with a grain of salt, but the use of dps totems again favors straight SP the most and lowers the value of crit slightly and haste, nothing new.
I managed to get hold of the 2pc today and it has been working fine for me so far. Don't know if it's still bugged, meaning that the cooldown could switch over to 7 days for me but at the moment it seem to be working properly.
So, I input the stats of the gearsets used in the simcraft above into ZAP, and got slightly different results.
First off, ZAP said that glyph of ToW was better then glyph of lava for both gear setups.
Secondly, ZAP said that even with glyph of Lava, the 4p bonus was only worth 88 dep in the 4p setup... and worth 55 dep with ToW.
So I wonder, where is the disconnect between Simcraft and ZAP? Which is more accurate? It sims the 4p setup to 11366, and the 2p setup to 11274, yet places almost no value in the 4p itself, as well as stating in both setups that haste has a higher dps value.
It's all in the details (which have been discussed quite thoroughly earlier in this thread as well as in the 3.3 discussion one). Firstly, ZAP! and SimulationCraft do the 4t10 rotations in slightly different ways, which will give a small (~50 DPS) variance in favour of SimC's method (which is harder and riskier to execute in-game). Secondly, the default settings - such as fight length, latency, partial resists etc - for ZAP! and SimC are different. Thirdly, SimC is a simulator and ZAP! is a formulator, so their results will always differ at least slightly: SimC is more concrete, and ZAP! is more abstract.
As to which is "more accurate", if you use them properly then the answer is... neither, and both. Think of them as different perspectives on the same question. In the case of 4t10, both agree that it's a DPS increase. SimC shows that if you can avoid missing a Lava Burst crit then the bonus is potentially worth a little more, whereas ZAP! shows that if you clip your FS DoTs to avoid that problem then the bonus is worth a little less - but is still apparently worthwhile.
(By the way, if the figure is that low without partial resists then I think you've missed out a few things in ZAP! - maybe Flametongue Imbue, the spellpower from Ashen Band, the fight length, CL use (should be off), Bizuri's, etc?)
Incidentally, it seems the T104pc profile linked above is 0.05% shy of the hitcap.
Every one of us is, in the cosmic perspective, precious. If a human disagrees with you, let him live. In a hundred billion galaxies you will not find another.
Incidentally, it seems the T104pc profile linked above is 0.05% shy of the hitcap.
Both of them are. Using a gem to cap it, results in being over the hit cap and actually results in lower dps. Some may choose to gem for it anyway for peace of mind, because missing a FS recast as you queue LvB is annoying. Icewalker is also available to be used, in place of tuskars, if the user so sees fit.
If we decide to make a true BIS elemental list, like they have for enhancement, then we can decide specifically on what things are required. Such as being 100% hit capped or going for what the tools say are the max dps, and whether the use of Tuskars is required.
100% hit is always going to be required, because missing Flame Shock or Lava Burst casts is going to be a big kink in your rotation. Plus I would question how much of a "dps gain" being 2 hit rating under the cap, while gaining another 11 spellpower. Statistically, missing 0.05% of your spells doesn't sound like a biggie, but if you're doing 40ish every minute, missing one spell in a 5 minute fight is actually 0.5%.
0.05% of 10k = 5 dps
0.5% of 10k = 50 dps
Sure, that extra 11 spellpower should be better than the 0.05% miss rate, but when it occurs it's more costly.
I was thinking of taking tailoring as one of my professions, but not if the Lightweave Embroidery shares CD with other similar procs for as for example the ring reputation's proc.
Can someone say to me if this happens this way?
I managed to get hold of the 2pc today and it has been working fine for me so far. Don't know if it's still bugged, meaning that the cooldown could switch over to 7 days for me but at the moment it seem to be working properly.
GC's post says the 7 day cooldown only trigger in cross-realm dungeons. So it works fine in a raid, but if you go into LFD you don't want to equip the 2 piece.
Originally Posted by drusillo
I was thinking of taking tailoring as one of my professions, but not if the Lightweave Embroidery shares CD with other similar procs for as for example the ring reputation's proc.
Can someone say to me if this happens this way?
Lightweave and other item procs like the rep ring do not share a cooldown.
Millions of words are written annually purporting to tell how to beat the races, whereas the best possible advice on the subject is found in the three monosyllables: 'Do not try.'
100% hit is always going to be required, because missing Flame Shock or Lava Burst casts is going to be a big kink in your rotation. Plus I would question how much of a "dps gain" being 2 hit rating under the cap, while gaining another 11 spellpower. Statistically, missing 0.05% of your spells doesn't sound like a biggie, but if you're doing 40ish every minute, missing one spell in a 5 minute fight is actually 0.5%.
0.05% of 10k = 5 dps
0.5% of 10k = 50 dps
Sure, that extra 11 spellpower should be better than the 0.05% miss rate, but when it occurs it's more costly.
Whilst I understand the point you are trying to make, you can't conveniently forget that for every fight where you lose that 50 DPS due to the miss, 9 fights go by where there were no misses at all and that 2 extra hit gained you nothing at all. You also lose the benefits of that 11 SP on all 10 fights. If we assume that the 11 SP is about 20 DPS (0.2%) then what we get is that in 1 fight in 10 you lose 30 DPS but in the other 9 you gain 20 DPS. Are you really saying that you would prefer to lose 20 DPS on nine fights to avoid losing 30 DPS on one?