Diablo® III

WoL:Empowered Wave looks like the best option

01/20/2013 09:35 PMPosted by Vrkhyz
Kaho has also claimed this as a pair of 0.22 proc coefficients, which is functionally equivalent.

It seems to be .11*4 but for LoH the game displays 2 green numbers at .22 each. When testing on weaker monsters the multiple hits is noticeable. Anyhow, the total proc coefficient is .44.

At 1 APS, WoL takes about 8 seconds to cast 6 times.
At 1 APS, I can fit 8 LTK in 7-8 seconds but definitely less than 8 seconds.

I don't know the rules for mixing either skill into the thunderclap combo but it seems that the game waits for the current animation to finish before starting a different attack. At low APS the delay between using WoL in the middle of thunderclap is very apparent.
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@hong: I'm thinking that the bell will travel farther in the Fields, allowing you to hit more mobs at a distance. Regardless, if you're not killing everything quickly, those extra 45% blasts outside of the bell's drop zone will certainly help in dense areas. I'd say the two skills are on par, given all that, so the buffs look pretty good.

@Kaho: Any WoL calculations probably won't play exactly as well as they look on paper. Thunderclap/Cyclone is easy to maximize: just hold down the LMB. By contrast, WoL has the problem you've mentioned, and the EDPS calculation assumes you activate it as soon as its available, which won't always happen, thereby lowering that EDPS. Overall, though, I think it's a legitimate alternative to Faith in the Light for non-Overawe monks, which is a good thing. It's better than my 1.0.6 EDPS by about 5.5% and my PTR EDPS by about 7.5%, which will help cover these problems.
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I've been using Wave of light for a very long time with a two hander. I have no spirit issues and can farm mp8-10 with it and am able to almost spam overawe + WoL at same time. Just keep blazing fists buff up would take me to 1.5aps or 1.7 depending on gear I'm using.

I pretty much like all the WoL runes however the knockback effect puts me off. Stun one is great for mp9-10 but I mostly use the Pillar of ancient cos no knockback.
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EW does the highest % damage/spirit point of any spender. You can drop 3 1200% WoL with 250 spirit or drop 6 800%. If you pulse overawe it gets better for EW as you hit 5 + overawe vs 2 + overawe.

True, EW has the better damage-to-spirit ratio, but it has an inferior DPS because it does less damage over the same animation time. When you're comparing Wave of Light to, say, Blinding Flash, what you're really doing is deciding which of the following works better:

1. Using FitL all the time and sticking with TC.
2. Ditching FitL, taking lower TC damage, and pumping it with enough WoL damage that your average is better than option #1.

Ultimately, it's a problem with many factors, but the two biggest ones are DPS and spirit regeneration.

I'll use my monk as an example.Here's my build:

Faith in the Light
Hard Target
One with Everything
Seize the Initiative
Beacon of Ytar

If I carry this build into the PTR, my single-target EDPS, once Cyclone is at three stacks, will be 195,292.13. On the live server, it's 199,077.36. (I believe I've already explained these numbers in Fitz's "PTR Challenge" thread, so I'm not going to explain them here.)

Here are my relevant stats:
  • MH weapon: 686.04 AWD
  • OH weapon: 659.39 AWD
  • 2,130 DEX
  • 1.9239 APS (includes Focused Mind, DW bonus, and IAS gear)
  • 27.0% CHC
  • 244% CHD

WoL uses your MH for all damage, and it resets the active hand to the main hand, so you can put the weapon with the higher AWD in that hand and work wonders. For now, I'll assume that I'm using my Fist of Legend and the 686.04 AWD.

Let's assume I change Faith in the Light to Wall of Light, which delivers 1202% weapon damage, plus 45% to all targets in a straight line. (The 1202% is divided into three parts, for the record.) In that case, my Thunderclap DPS, which is now without FitL, drops to 170,666.00. For this first example, we'll also assume that I have no spirit regen on my gear, so my only means of regenerating spirit is attacking with Thunderclap. I get 6 spirit for every attack.

Wave of Light costs 75 spirit, so I will have to attack 25 times to generate enough spirit for 2 WoLs. To keep everything simple, we're just going to boil this down to 12.5 TCs per WoL.

How long does it take me to attack 12.5 times with TC? Well, my paper APS is 1.9239. Thunderclap has a 1.5 haste modifier, so my Thunderclap APS is actually 2.886 (all numbers rounded, of course). Each TC attack therefore takes 0.346514 seconds, and 12.5 of them take 4.33 seconds. At 170,666 DPS, this generates 739,227 damage. Remember these numbers; we'll come back to them later.

How much damage does Wall of Light do?

686.04 AWD
x 12.47 (1247% damage)
x 22.3 (DEX)
x 1.6588 (1 + 0.27 CHC x 2.44% CHD)
= 316,457

And how loing does it take me to attack with WoL? Well, Kaho shared some numbers, and he believes WoL has a haste modifier of 0.75. My paper APS is 1.9239, but my Fist of Legend's APS is 1.8304 (1.40 + 0.03, multiplied by 1.28 for my IAS bonus). Multiplying this number by 0.75 gives me a WoL APS of 1.3728, which means that this attack takes 0.7284 seconds.

So, let's recap:
  • Total damage: 739,227 + 316,457 = 1,055,684
  • Total seconds: 5.05986
  • DPS: 208,638.85

I'll save you the trouble of reading the same calculations for my Az'Turrasq, which does less damage but has a faster attack speed. Ultimately, it does around 1,043,390 damage in 4.99 seconds, which gives it a DPS of 209,136.49. (Surprise! How many of you thought the weapon with lower AWD would be better? I know I didn't. Didn't rule it out, though.)


So that's Wall of Light. What happens when we examine Empowered Wave? Only two things are different:

1. The number of times we need to attack with Thunderclap to use EW
2. The amount of damage EW does

The activation time is the same, which is why EW's DPS is inferior to Wall of Light's. The real question is whether I can spam it frequently enough to make up the difference.

First, Thunderclap. My attack speed is the same, and my Thunderclap DPS is the same, but I need to make 20/3 attacks. I need 2.31 seconds to do that; at a DPS of 170,666, those 2.31 seconds will produce 394,254 damage.

Next, Empowered Wave. I'm going to start with the Fist of Legend again, after which I'll calculate the Az'Turrasq damage, and we can pick the better option.

Because all the factors in Empowered Wave's damage are identical to Wall of Light except for the damage multiplier, I can take that number and reduce it as follows:

x 8.74 (EW's 829% plus the 45% straight-line damage)
÷ 12.47 (Wall of Light's damage)
= 221,799

Note that the animation time doesn't change; this attack still takes roughly 0.73 seconds.

That leaves us here:
  • Total damage: 394,254 + 221,799 = 616,053.5
  • Total seconds: 3.04
  • DPS: 202,747.10

My Az'Turrasq does around 607,437 damage in 2.97 seconds, which gives it a DPS of 204,682.13, which makes it the better choice for Empowered Wave, too. Probably not a surprise, given that it was better for Wall of Light, too.

So, let's recap for my monk:
  • Wall of Light EDPS: 209,136.49
  • Empowered Wave EDPS: 204,682.13

This is an edge of over 2% for Wall of Light. It's not a knockout punch, obviously, but it's certainly no worse. But Empowered Wave is "far and away the winner" only if you're worried about overkilling enemies constantly with an extra 85K per activation. I don't think this is a legitimate claim, however, as using EW means you'll use your burst skill more often. And what does that translate to? Right: more overkill situations! The extra TC attacks make it less likely you'll "waste" DPS if you're playing a low farming level and are worried about that sort of thing.

Oh—I almost forgot the tornado damage from the bells! According to a website I've used for proc coefficients, WoL has a procC of 0.11 for each of the first three hits, plus 0.11 for the straight-line shot. Kaho has also claimed this as a pair of 0.22 proc coefficients, which is functionally equivalent. Therefore, each bell generates the following tornado damage:

672.715 AWD (because tornado damage on the PTR changes as you alternate weapons)
x 22.3 (DEX)
x 1.6588 (CHC and CHD)
x 0.26 (26% per zap)
x 6 (six zaps)
x 0.44 (sum of proc coefficients)
x 0.27 (CHC to spawn)
= 4,612

This obviously benefits Empowered Wave more than Wall of Light because of the former's shorter cycle. The revised DPS figures:
  • Wall of Light EDPS: 210,060.87
  • Empowered Wave EDPS: 206,236.12


Now, spirit regeneration matters, too, but it doesn't necessary favor Empowered Wave. I'll give an example tomorrow. Also, remember that stats matter. What is true for one monk might not be true for another. Overall, though, I've analyzed enough cases that I feel somewhat comfortable saying that Overawe users should just stick with FitL over WoL because (1) they can't reasonably spam both and (2) they lose too much DPS if they choose not to spam Overawe. For non-Overawe users, however, I'll be mildly surprised if Empowered Wave turns out to be a "clear winner" for somebody, however we're defining that. Overall, I think the skill needs a damage boost (say, to 895% base damage), a better cost reduction, or both. The only advantage I see is that you could conceivably activate Faith in the Light and fire off three EWs, usually at the start of combat. (Of course, I dropped FitL for WoL in this example.) That advantage doesn't seem very large, though. If anyone spots any errors in my math, or can explain what makes EW better than Wall of Light, please let me know.

First, props for effort - there is valuable info above.

BUT, 27 crit chance?! Boom, your analysis for WoL vs. Overawe becomes nearly useless. Go do your testing with 55-60 (maybe 50) crit chance. Then spam TIMES 2 OR MORE bells ;). It's faster than spamming Overawe, my timed testing and quick math show significantly improvement. So much so that even when I got lazy and didn't spam Overawe while doing bells during a run, it was STILL faster than just spamming Overawe & FoT-TC (instead of FT-Quickening). I'm running 2.09 attack speed and 56.5% crit chance for what it's worth.

And, yeah the 45% line-damage is pretty important. Will be interesting to see exactly how WoL and it's runes go from PTR to Live.

So yes if you are under ~50% crit, stay with spamming Overawe & Thunderclap for maximum damage though even with low crit (~30%) it's much closer now.

I'm interested in seeing more math for dual wielding vs. a shield. Obviously a 8%+ shield is going to give you more spirit than 15% attack speed but how does the melee mitgation vs. "possible" added DPS compare (because a shield will give you more bell drops). If I find the time, I'll gladly share my work.

Slightly confused here -->

Multiplying this number by 0.75 gives me a WoL APS of 1.3728, which means that this attack takes 0.7284 seconds.

So the WoL APS is a damage multiplier? Because with a full spirit globe and Empowered Rune, you can drop multiple bells in less than a second. Visually there seems to be no delay with spirit generators (attacking) or between the bells drops where as with something like LTK there is a "visual" delay with LTK AND spirit generators.
Edited by blhotz#1823 on 1/21/2013 8:39 AM PST
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Slightly confused here -->

Multiplying this number by 0.75 gives me a WoL APS of 1.3728, which means that this attack takes 0.7284 seconds.

So the WoL APS is a damage multiplier? Because with a full spirit globe and Empowered Rune, you can drop multiple bells in less than a second.

No, it's not a multiplier. Every attack skill in the game has a haste modifier built into it. For Fists of Thunder, it's roughly 1.5, which means that a monk with a 2.0 attack speed will actually get 3 attacks per second; for WoL, it's roughly 0.75, which means that the monk will get 1.5 attacks per second. In the first example, the monk attacks every 0.33 seconds; in the second, he attacks every 0.67 seconds.

More in a minute, but hold on to that concept, because I'm going to use it in the next post.
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I think the word "better" needs to be situationally defined. I can see that there is a debate about eDPS between EW and WoL rune, but isn't there also value in using the Blinding Light rune to stun enemies for 3s at a time? I haven't tried this, but wouldn't WoL/BL interrupt enemy attacks? I'm looking specifically at the maigewraiths (or whatever you call the spinning ones from A2). Having two skills (BF & WoL) to interrupt those attacks can have a utility that can go beyond measuring DPS.
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We're talking about different things, that's all. My example was a Hard Target monk, not an Overawe monk.

But I considered your theory interesting, so I decided to test it. I took your monk's profile and fed him into my spreadsheet, which correctly pegged your paper DPS at 117,694.92, which is a match for your profile's 117,695 DPS. I then set about looking at how you might do on the PTR with Quickening, Overawe, your 1.67 SpS AzT, and one of the two WoL runes.

First problem? Trying to figure out how many times you need to attack with Quickening for each bell spam, assuming you're trying to keep Overawe up every 3 seconds. This broke my balls, honestly, but I worked out the formula, which is essentially . . . well, it's complicated! But the gist of it is that the sum of these:

1. The number of Quickening attacks times the spirit generated per attack
2. Your SpS times (the amount of time spent attacking with Quickening plus the amount of time needed to activate WoL)

must equal the sum of these:

3. The cost of activating WoL
4. 50 times (the amount of time spent attacking with Quickening and WoL, divided by 3)

Basically, you will need 8.715 Quickening attacks to activate Wall of Light and spam your mantra every three seconds. A quick proof:
  • Your attack speed is 1.54 x 1.36 (36% IAS), or 2.0944. Fists of Thunder has a haste modifier of 1.5, which brings your attack speed to 3.1416. So one attack takes 1/3.1416 seconds, or 0.3183 seconds.
  • You have 56.5% CHC, so each Quickening attack will give you, on average, 14.475 spirit: 6 spirit for the base, plus 56.5% of 15.
  • Wave of Light has a haste modifier of around 0.75, as far as anyone can tell. So we take your 2.0944 APS, multiply it by 0.75 to arrive at a WoL APS of 1.5708, and take its inverse to determine that you need 0.6366 seconds to activate WoL.

So here's the time part of the equation in the "8.715 Quickening attacks per Wall of Light" scenario:
  • Time spent attacking with Quickening: 8.715 x 0.3183 = 2.774 seconds
  • Time spent activating WoL: 0.6366 seconds
  • Total time per cycle: 2.774 + 0.6366 = 3.4106

Here's your spirit gained:
  • Spirit from Quickening: 14.475 x 8.715 = 126.15 spirit
  • Spirit from 1.67 SpS AzT: 1.67 x 3.4106 = 5.70
  • Total spirit gained per cycle: 126.15 + 5.70 = 131.85

And here's how much spirit you're spending:
  • Spirit from Wall of Light: 75
  • Spirit from spamming Overawe: 3.4106 ÷ 3 x 50 = 56.84
  • Total spirit spent per cycle: 131.85

I'm sure everyone here will excuse my rounding error in the information I'm presenting here; the decimals are quite messy :)

So! Established: 8.715 Quickening attacks per cycle, followed by Wall of Light; lather, rinse, repeat.

Your Quickening EDPS on the PTR will be 697,751. Quick check:

Quickening EDPS:

117,695 paper DPS
x 936.581 ÷ 809.435 (FitL mod, up 25% of the time with BoY selected)
x 1.48 (Overawe spam)
x 1.10 (Fists of Thunder bonus)
x 1.50 (haste modifier)
= 332,558

Vortex EDPS:

x 936.581 ÷ 809.435 (FitL)
x 1.48 (Overawe)
x 0.6 (60% for full stack)
= 120,930

Tornado EDPS:

x 936.581 ÷ 809.435 (FitL)
x 1.48 (Overawe)
x 1.5 (FoT haste modifier)
x 0.26 x 6 (26% per tornado, six tornadoes)
x 0.565 (CHC to spawn)
x 275 ÷ 300 (Quickening has proc coefficients of 100, 100, and 75 for each attack)
= 244,264 (non-rounded)

Total EDPS:

332,558 (Quickening)
+ 120,930 (vortex)
+ 244,264 (tornadoes)
= 697,752

The actual figure, according to the spreadsheet, is 697,751.03.

How much damage does Wall of Light do for you?

936.851 (AWD)
x 1.48 (Overawe)
x 25.18 (DEX)
x 2.88155 (CHC and CHD, includes 4.0% WoL CHC bonus on your shield)
x 12.47 (Wall of Light)
= 1,254,167

It might crit and produce a tornado, too:

936.851 (AWD)
x 1.48 (Overawe)
x 25.18 (DEX)
x 2.75715 (your usual CHC and CHD)
x 0.26 x 6 (tornado zaps)
x 0.605 (CHC spawn chance, includes shield bonus)
x 0.11 (proc coefficient)
x 4 (four separate hits and proc chances)
= 39,963

Your Quickening EDPS is 697,751, and you have to attack 8.715 times at 0.3183 seconds per attack:

8.715 attacks
x 0.3183 seconds per attack
x 697,751 damage per second
= 1,935,499 damage

So your total damage is this:

1,935,499 (Quickening/Cyclone damage)
+ 1,254,167 (Wall of Light damage)
+ 39,963 (WoL tornado damage)
= 3,229,629.40

And this takes 3.4105 seconds, which makes your Wall of Light EDPS 946,966.54.


I'm just going to skip to the important parts about Empowered Wave:

1. You have to attack 5.107 times with Quickening to cover EW and mantra spam.
2. You end up with an attack cycle of just over 2.26 seconds.
3. You deliver ~879K with each Empowered Wave, plus ~40K in tornado damage.
4. You deliver ~1,134,250 damage with Quickening.

Your final Empowered Wave numbers:
    [/li]Damage: 2,053,244[/li]
  • Seconds: 2.26219
  • EDPS: 907.635.52

This number is just under 96% of your Wall of Light EDPS. Meet the new math, same as the old math! :)

Now, let's put these numbers in perspective on the PTR:
  • Quickening/Wall EDPS: 946,966.54
  • Quickening/EW EDPS: 907,635.52
  • Thunderclap/(defensive skill) EDPS: 892,387.88
  • Thunderclap/Blazing Wrath EDPS: 982,832.59

Thunderclap is still the best single-target option, but its advantage over the Quickening/Wall combo is less than 4%, which is much smaller than it is on the live server.

Given that even your uber-WoL model monk, with his high CHC, WoL shield bonus, etc., didn't outperform Thunderclap/BW, I think it's safe to say that spamming Overawe and carrying Thunderclap is still the best approach, although not by much. Also, these numbers seem to strengthen what I saw on my monk and another monk when I tried calculating Quickening: the faster your spirit regeneration, the more Wall of Light seems to edge ahead. Is that always true? No, it can't be—if I had enough spirit to activate Empowered Wave every second, I'd be delivering 874% damage each second, versus (40 ÷ 75 x 12.74 = ) 680% damage each second with Wall of Light. But, within certain parameters, Wall of Light is going to outperform Empowered Wave. I think that's pretty clear.
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I think the word "better" needs to be situationally defined. I can see that there is a debate about eDPS between EW and WoL rune, but isn't there also value in using the Blinding Light rune to stun enemies for 3s at a time? I haven't tried this, but wouldn't WoL/BL interrupt enemy attacks? I'm looking specifically at the maigewraiths (or whatever you call the spinning ones from A2). Having two skills (BF & WoL) to interrupt those attacks can have a utility that can go beyond measuring DPS.

Absolutely, absolutely, yes! There are a lot of factors at play for each monk, and utility is one of those factors. I don't mean to suggest that it's all about EDPS; I'm only going through the calculations here because the original post labeled Empowered Wave "the best option" and "far and away the winner." And if that's not true from an EDPS perspective, you'd have to look at something else, like its ability to deliver more frequent knockbacks (which might not be the best option with Quickening, but I digress).

So, sure, Blinding Light will be great . . . unless you're already carrying a lot of crowd control. For example, I have a 5.1% freeze belt, Faith in the Light, and 4.7% stun on my AzT. The more CC I add, the more resistance the mobs will pick up throughout the fight, and the less effective it will become. It's really toon-specific, and people need to see these runes in-game to determine which is best. I'm only illustrating that Empowered Wave is not the best for DPS—Wall of Light, which is intended to be a high-DPS rune, is almost certainly the best for DPS.
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Here's a pic - basically a crit damage/dex/fire resist -->


Can do 15 million. Could be a steal if these take off as quality -4/-5 LTK are really hard to find.

I'll msg you later thanks.
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The problem with pure DPS calculations is that is not how it works in the actual game environment. It's all well and good for killing azmodan but in actual fights? Well firstly, FoT: Quickening gives 15 spirit on crit for every enemy crit. That 3rd attack can easily get 5+ enemies in a close area. Against large packs of monsters spirit is basically infinitely available and very few attacks are needed between bells.

Also what the calculations don't look at is burst damage from bells being able to instantly remove monsters from a fight making the fight easier. Single target DPS should not be the only thing you use to determine what build you use.

The reason I put empowered at the top is because it offers the highest burst damage from a full spirit bubble. It also has less "wasted" damage (ie overkill) which saves spirit. It is more efficient. Efficiency is important. It is why TC + cyclone monks are so good, they basically don't need spirit and are stupidly easy to play: they are super efficient. It is also why so few people use combination strike since less skills = less utility = less options = more deaths. They have poor efficiency on the skill bar.

Do the math of pulsing overawe and dumping all your spirit and see how long it takes WoL to catch-up in DPS. That is a much more true to game situation than starting at 0. You miss a WoL bell you could screw yourself, you miss an EW and you're probably ok to cast another.

I don't disagree with EDPS calculations I just think you need to throw some more math showing burst and how long each build takes to overtake the others starting from a full spirit bubble. Try it with 150 and 250, with overawe pulsing and not.

There is a lot more interesting math that can be done here that just a very basic pure EDPS calculation. I, unfortunately, am far too removed from my math courses to do it properly. My guess is that we'll find a gearing curve based on DPS where EW or WoL or TC + cyclone is best based on enemy HP and the TTK of elite packs. Wouldn't it be cool to have these numbers and say: you have 100k DPS and want to do MP5, based on your gear WoL is the best choice, if you go up past MP7 you should just run TC + cyclone.

That would be a ton of work. Much praise to anyone who wants to figure it all out.
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01/21/2013 02:06 PMPosted by Fitz
Monster density will also have a huge impact on these numbers. The dps of WoL is a very large AoE effect. I don't believe the real numbers can be calculated at all due to this.

It would be so hard that it wouldn't be worth the effort, sadly. I've had enough math for the day; it's time for some actual playtime :)
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It would be so hard that it wouldn't be worth the effort, sadly. I've had enough math for the day; it's time for some actual playtime :)

Say it ain't so! Vrkhyz has had enough math? :P
Edited by Nameless#1537 on 1/21/2013 7:39 PM PST
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just wanted to pop in here and ask ppl to help support this thread

basically on the PTR they changed the base damage of Wave of Light to 829% (good stuff)
they also changed the Wall of Light rune to 1202% (really nice!)
however, they didnt change Explosive Light and Pillar of the Ancients. these need to be scaled up to match the new changes. ive posted my suggestions on their damage in the thread.
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