As a rough guess, I would expect Power of the Storm to increase dps by around 12%. My thought is that AP reduction of 3 means WW costs 32 which is around 10% cost reduction, and CR goes from 20 to 17 which is 15% cost reduction, so if you split the difference it's around 12-13%. That would put the total damage boost around 1.35*1.12 = 1.52 or around 50-55% damage increase for Storm Armor plus Power rune.
This could become very effective when you use Mistral Breeze. Hm... anyone ever tried Mistral Breeze + Prism + Power of the Storm? 10 AP Twisters all over the place... I'm gonna try this tonight.
If you want to go with the near zero cost build, I would advise Meteors. In addition to the 10 AP cost reduction from skills, you can get up to -19 meteor cost from gear (5 from source, 5 from SoJ, 5 from Mara's, 4 from Skull Grasp) leaving star pact with an AP cost of 6.
I'll see if I can do some testing on this with different speed weapons. Tonight is a raid night for me so I won't be able to do much testing until tomorrow unless I lose the roll (we're overstaffed on melee DPS right now =().
Also, despite around a 12% overall cost reduction, the effect has accelerated returns with APoC because more tornados also means more AP per second from APoC, so it is a reduction in cost and an increase in AP regen overall.
Cost reduction gear does absolutely amazing things for Meteor builds, I wouldn't be surprised to see Power of the Storm compete with Shocking Aspect in the right circumstances.
Awsome work. Here is the interesting part to me. Storm Armor with no rune gave you a 36% boost, while adding in shocking aspect brought that up another 29% to a 65% increase. The suggests that the base storm armor does more damage than the shocking aspect triggers, which is something I would never have guessed. With that in mind, it raises a next question in my mind. We can conclude from tooltips that in the same test, Storm Armor (Thunderstorm) would yield a 46.8% DPS gain leaving it still inferior to shocking aspect, Reactive Armor and and Scramble aren't terribly relevant to what we're trying to do, but what about Power of the Storm?
Prism gave us a 13% DPS gain with very minimal uptime, while the base storm armor is worth 36%. This suggests that power of the storm might compete with Shocking Aspect in terms of damage gain, and is very likely to outpace Thunderstorm.
So I'm running with a new video card and finally found some time to investigate the behavior of shocking aspect.
Storm Armor's base damage is annoying and can get in the way, but here is what I have managed to determine:
Shocking Aspect's chance to trigger appears the same as the LoH coefficient of the triggering spell, but I don't have enough data points to say conclusively. I tested this against monster power 10 inferno slow ass zombies using a set with a lot of EHP 30% crit chance, and a static damage range (white weapon and +min damage rings). I was easily able to confirm that it triggers on every critical hit from a magic missile through simple observation. For energy twister I used a 1.0 attack speed weapon and no IAS. I noted the hit point total of the zombie, cast a wicked wind and stood there while it took the damage. When the first wicked wind expired I cast another. I do this continuously while recording. Afterwards I watched the recording, counted the lightning strikes from storm armor and their damage, subtracted that from the total damage done to the zombie over the course of the fight. I then calculated the expected damage output of the energy twisters and subtracted that. The total damage divided by the expected damage of a shocking aspect strike gives a number of procs, which when compared to the expected number of crits from energy twister yields a proc coefficient. I did this for a total of 7 zombie kills and came very close to 0.125 every time.
The Shocking Aspect attack can crit, but does not trigger LoH, Critical Mass, or itself. Base lightning bolts from Storm Armor similarly do not trigger LoH, Critical Mass, or themselves, at least when using the shocking aspect rune.
The range of the shocking aspect shock is short, roughly the same as the radius for frost nova. Shocking aspect will favor the closest target to you, but this isn't guarenteed.
I unfortunately didn't think to write down the number of times storm armor struck, just totalled the damage and subtracted it, would be nice to know how the base storm armor works and how much damage it does relative to tooltip DPS.
This should be very simple to model, even in a closed form rather than a simulation like Matlab. I'm curious for cases of 1 or 2 targets (read here ubers) how much DPS relative to tooltip DPS does shocking aspect provide at a given value of crit. Mainly concerned with the tradeoff between using a Shield and Shocking Aspect versus using a Source and Energy Armor.
I haven't done any serious investigation into its proc rate, I know on live with energy twister it is not possible to read all the damage numbers it generates because it is triggering so often, I'll see what I can figure out this week.
Edit: and my video card at home decided to quit on me last night, so I guess I won't be doing any testing on this very soon.
Well if that is the case it shows that Meteor Cost Reduction gear (rare sources, skull grasp, stone of jordan) is massively more valuable than APoC for single targets and attack speed is almost a dead stat in terms of DPS gain outside of scenarios where you have 5 or more targets getting rocks dropped on them.
I'm also curious how Storm Armor (Shocking Aspect) figures in with either of these specs and if using it makes Energy Twister a clear winner over Meteor (for the content that can be cleared without the use of force armor or prismatic armor).
Edit: Mechanics wise my understanding it is undergoes all of the same processes critical mass does, whenever you crit it rolls against the coefficient and determines if it is triggered. When it is triggered it produces a 35% weapon damage strike against a random single target within roughly the same range as frost nova, weighted towards the closest targets. These strikes can crit, but have an LoH/Crit Mass coefficient of 0. The PTR updated Storm Armor produces a visible lightning strike for the tooltip damage within a longer range roughly every 2 seconds (possibly affected by attack speed) that again can crit but has a coefficient of 0 for LoH/CM.
On live with the 0.5 coefficient on storm chaser it is a prolific damage dealer, so much so that I have considered at times running builds without Explosive Blast because it doesn't feel like I need it with shocking aspect. I'm not sure how well it will add to damage in 1.0.5 but it still seems like a worthwhile switch if you have the survivability.
Thank you for the information. From the results it seems like mistral breeze is out performing wicked wind in most cases. Unless im not understanding the chart correctly. It also seems that ap on crit is a bigger boost to overall performance damage wise and shouldnt be underestimated
It should be noted that these sims aren't taking into account damage that can be gained from Storm Armor (Shocking Aspect). Assuming it can be calculated as simply 35% weapon damage * PPS * CritChance / AttackSpeed, it would adjust the relative cases in favor of wicked wind, which generates more PPS than Mistral Breeze. Not having matlab to look at the code I'm not sure how the implementation of shocking aspect would look like overall.
Also note that there is an assumption in this simulation that you get 50% uptime on mistral breeze casts, 75% uptime on wicked wind casts, and 90% uptime on meteor casts. I don't personally feel that wicked wind would be any less accurate than meteor, in meaningful cases, and I highly doubt anyone is routinely getting 3 full seconds of exposure on average from moving energy twisters, so I suspect that assumption is weighting the math towards mistral breeze and inflating its numbers.
I think those results speak to an important point about how to play CM.
Increases in DPS through increased APoC comes from additional casts of explosive blast, I assume you've modeled this to use explosive blast optimally when enough arcane power is avaliable so as not to interrupt spam of the proc generator. It is important to note however that optimal DPS is being obtained when the user is careful not to delay their next energy twister or meteor by activating explosive blast with insufficient excess arcane power.
With respect to your spreadsheet, I agree that we're basically calculating a soft cap beyond which APoC no longer provides a substantial performance increase, rather than a minimum to run the build.
Some clarifications though. Morphos was running, according to his thread 45% critical hit chance, 1.64 attacks per second, 27 APoC, using Star Pact and Prism. If we assume this gear is the minimum level of arcane power generation to make the build work, we can calculate the percentage of full APoC coverage he is getting to determine what out targets should be when reversing the process to produce required APoC values.
***NOTE: Doing the math on what I observed from the video I am led to believe that I have something wrong in my modeling of Star Pact, or the patch notes coefficient of 0.05 is off base and the actual value is higher than that.***
If we calculate assuming prism is up we find his coverage from APoC amounts to only about a little over 10% of the cost of Star Pact, which leads me to a different conclusion:
His Star Pact is not paying for itself, but his explosive blast is almost paying for itself, and actually pays for meteor casts beyond a certain level of APoC. Under a Prism his explosive blast only costs 13 arcane power, and it is generating about 4 AP per cast from APoC giving it a very low adjusted Arcane Power cost of 9.
Watching a 30 second sample of the keywarden fight (1:10 to 1:40 on the video) where only a single target is present, I count 24 meteors landing, and 13 casts of explosive blast, and prism is up for 27 of the 30 seconds (90%). His total arcane power expenditure during this time is 841 Arcane Power in 30 seconds or 28 arcane power per second. Thats a deficit of 18 arcane power per second from base regeneration. He generates 39 chain reaction blasts, each one has a 45% chance to crit, resulting in an average of 17.55 critical hits, each of which refunds 3 (2.97) arcane power, for a total of between 51 and 54 arcane power. His 24 meteors generate 24 landings and 72 DoT ticks, for a total of 96 chances to crit. On average 43 or 44 of these will crit, and that will generate 1.35 (so 1 or 2 depending on how APoC works with rounding and partial AP numbers) arcane power per crit, or anywhere from 43 to 88 arcane power.
Assuming this rounds very generously, the 122 arcane power APoC covers translates to only 4.067 arcane power per second of the 18 arcane power per second deficit, and with the reported old coefficient of 0.1 it would only be covering 8. This works out to 8 or 9 meteor casts that he should not have been able to pay for, or 50% more meteor casts, or almost five times the AP return from APoC than i would have expected based on the numbers we've been told.
Either I've made a serious error in my math, or the star pact coefficient of 0.05 is bogus, or the mechanics of star pact work substantially different from my understanding of them.
Edit:
While I don't want to base any conclusions on the above since it doesn't line up with observation yet, the calculations above show the net effect of 27 APoC on arcane power deficit to be reducing it by 4.067 (122 arcane power over 30 seconds), running Storm Armor (Power of the Storm), would have saved 3.7 arcane power per second (111 arcane power over 30 seconds), and a single -5 meteor cost item would have saved 4 arcane power per second (120 arcane power over 30 seconds) producing the same effect as three full sources of APoC.
I think what he is asking is at what point does energy twister (or various meteor runes) start paying for themselves and generating excess arcane power that can be funneled into explosive blast through APoC and what builds can accomplish this at what crit, APoC and attack speed values.
The calculation is fairly simple, the expected APoC return of the spell has to be greater than its cost, so:
Cost = Crit * Ticks * coefficient * ApoC
The real question is, how many targets. None of the meteor runes at real gear levels (i.e. less than BiS values) will break even on Arcane Power through APoC or enhanced regeneration on a single target, and it takes close to BiS to do so with two targets, but virtually all of them will generate surplus arcane power on 3 targets with moderate gear levels.
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Also, despite around a 12% overall cost reduction, the effect has accelerated returns with APoC because more tornados also means more AP per second from APoC, so it is a reduction in cost and an increase in AP regen overall.
Cost reduction gear does absolutely amazing things for Meteor builds, I wouldn't be surprised to see Power of the Storm compete with Shocking Aspect in the right circumstances.
Prism gave us a 13% DPS gain with very minimal uptime, while the base storm armor is worth 36%. This suggests that power of the storm might compete with Shocking Aspect in terms of damage gain, and is very likely to outpace Thunderstorm.
Storm Armor's base damage is annoying and can get in the way, but here is what I have managed to determine:
Shocking Aspect's chance to trigger appears the same as the LoH coefficient of the triggering spell, but I don't have enough data points to say conclusively. I tested this against monster power 10 inferno slow ass zombies using a set with a lot of EHP 30% crit chance, and a static damage range (white weapon and +min damage rings). I was easily able to confirm that it triggers on every critical hit from a magic missile through simple observation. For energy twister I used a 1.0 attack speed weapon and no IAS. I noted the hit point total of the zombie, cast a wicked wind and stood there while it took the damage. When the first wicked wind expired I cast another. I do this continuously while recording. Afterwards I watched the recording, counted the lightning strikes from storm armor and their damage, subtracted that from the total damage done to the zombie over the course of the fight. I then calculated the expected damage output of the energy twisters and subtracted that. The total damage divided by the expected damage of a shocking aspect strike gives a number of procs, which when compared to the expected number of crits from energy twister yields a proc coefficient. I did this for a total of 7 zombie kills and came very close to 0.125 every time.
The Shocking Aspect attack can crit, but does not trigger LoH, Critical Mass, or itself. Base lightning bolts from Storm Armor similarly do not trigger LoH, Critical Mass, or themselves, at least when using the shocking aspect rune.
The range of the shocking aspect shock is short, roughly the same as the radius for frost nova. Shocking aspect will favor the closest target to you, but this isn't guarenteed.
I unfortunately didn't think to write down the number of times storm armor struck, just totalled the damage and subtracted it, would be nice to know how the base storm armor works and how much damage it does relative to tooltip DPS.
This should be very simple to model, even in a closed form rather than a simulation like Matlab. I'm curious for cases of 1 or 2 targets (read here ubers) how much DPS relative to tooltip DPS does shocking aspect provide at a given value of crit. Mainly concerned with the tradeoff between using a Shield and Shocking Aspect versus using a Source and Energy Armor.
Edit: and my video card at home decided to quit on me last night, so I guess I won't be doing any testing on this very soon.
I'm also curious how Storm Armor (Shocking Aspect) figures in with either of these specs and if using it makes Energy Twister a clear winner over Meteor (for the content that can be cleared without the use of force armor or prismatic armor).
Edit: Mechanics wise my understanding it is undergoes all of the same processes critical mass does, whenever you crit it rolls against the coefficient and determines if it is triggered. When it is triggered it produces a 35% weapon damage strike against a random single target within roughly the same range as frost nova, weighted towards the closest targets. These strikes can crit, but have an LoH/Crit Mass coefficient of 0. The PTR updated Storm Armor produces a visible lightning strike for the tooltip damage within a longer range roughly every 2 seconds (possibly affected by attack speed) that again can crit but has a coefficient of 0 for LoH/CM.
On live with the 0.5 coefficient on storm chaser it is a prolific damage dealer, so much so that I have considered at times running builds without Explosive Blast because it doesn't feel like I need it with shocking aspect. I'm not sure how well it will add to damage in 1.0.5 but it still seems like a worthwhile switch if you have the survivability.
Also note that there is an assumption in this simulation that you get 50% uptime on mistral breeze casts, 75% uptime on wicked wind casts, and 90% uptime on meteor casts. I don't personally feel that wicked wind would be any less accurate than meteor, in meaningful cases, and I highly doubt anyone is routinely getting 3 full seconds of exposure on average from moving energy twisters, so I suspect that assumption is weighting the math towards mistral breeze and inflating its numbers.
Increases in DPS through increased APoC comes from additional casts of explosive blast, I assume you've modeled this to use explosive blast optimally when enough arcane power is avaliable so as not to interrupt spam of the proc generator. It is important to note however that optimal DPS is being obtained when the user is careful not to delay their next energy twister or meteor by activating explosive blast with insufficient excess arcane power.
With respect to your spreadsheet, I agree that we're basically calculating a soft cap beyond which APoC no longer provides a substantial performance increase, rather than a minimum to run the build.
Some clarifications though. Morphos was running, according to his thread 45% critical hit chance, 1.64 attacks per second, 27 APoC, using Star Pact and Prism. If we assume this gear is the minimum level of arcane power generation to make the build work, we can calculate the percentage of full APoC coverage he is getting to determine what out targets should be when reversing the process to produce required APoC values.
***NOTE: Doing the math on what I observed from the video I am led to believe that I have something wrong in my modeling of Star Pact, or the patch notes coefficient of 0.05 is off base and the actual value is higher than that.***
If we calculate assuming prism is up we find his coverage from APoC amounts to only about a little over 10% of the cost of Star Pact, which leads me to a different conclusion:
His Star Pact is not paying for itself, but his explosive blast is almost paying for itself, and actually pays for meteor casts beyond a certain level of APoC. Under a Prism his explosive blast only costs 13 arcane power, and it is generating about 4 AP per cast from APoC giving it a very low adjusted Arcane Power cost of 9.
Watching a 30 second sample of the keywarden fight (1:10 to 1:40 on the video) where only a single target is present, I count 24 meteors landing, and 13 casts of explosive blast, and prism is up for 27 of the 30 seconds (90%). His total arcane power expenditure during this time is 841 Arcane Power in 30 seconds or 28 arcane power per second. Thats a deficit of 18 arcane power per second from base regeneration. He generates 39 chain reaction blasts, each one has a 45% chance to crit, resulting in an average of 17.55 critical hits, each of which refunds 3 (2.97) arcane power, for a total of between 51 and 54 arcane power. His 24 meteors generate 24 landings and 72 DoT ticks, for a total of 96 chances to crit. On average 43 or 44 of these will crit, and that will generate 1.35 (so 1 or 2 depending on how APoC works with rounding and partial AP numbers) arcane power per crit, or anywhere from 43 to 88 arcane power.
Assuming this rounds very generously, the 122 arcane power APoC covers translates to only 4.067 arcane power per second of the 18 arcane power per second deficit, and with the reported old coefficient of 0.1 it would only be covering 8. This works out to 8 or 9 meteor casts that he should not have been able to pay for, or 50% more meteor casts, or almost five times the AP return from APoC than i would have expected based on the numbers we've been told.
Either I've made a serious error in my math, or the star pact coefficient of 0.05 is bogus, or the mechanics of star pact work substantially different from my understanding of them.
Edit:
While I don't want to base any conclusions on the above since it doesn't line up with observation yet, the calculations above show the net effect of 27 APoC on arcane power deficit to be reducing it by 4.067 (122 arcane power over 30 seconds), running Storm Armor (Power of the Storm), would have saved 3.7 arcane power per second (111 arcane power over 30 seconds), and a single -5 meteor cost item would have saved 4 arcane power per second (120 arcane power over 30 seconds) producing the same effect as three full sources of APoC.
The calculation is fairly simple, the expected APoC return of the spell has to be greater than its cost, so:
Cost = Crit * Ticks * coefficient * ApoC
The real question is, how many targets. None of the meteor runes at real gear levels (i.e. less than BiS values) will break even on Arcane Power through APoC or enhanced regeneration on a single target, and it takes close to BiS to do so with two targets, but virtually all of them will generate surplus arcane power on 3 targets with moderate gear levels.