## [Theorycrafting] LoH and attack speed with wicked wind

• Based on a discussion going in another thread I thought I'd make a new thread solely to theorycraft and discuss how WW is affected by attack speed, both for damage and LoH returns. I'll share my facts, previous assumptions, my new conclusions, and then give the methodolgy and results last, so people not really interested in how I came upon my conclusions can skip the end. Please feel free to do your own testing to verify or attempt to contradict my results. I'm also planning to do similar analysis with Meteor, though anyone else who has some free time is welcome to do so.

Facts
WW LoH coefficient is 12.5%

EDIT: Someone on the official forums went through some testing similar to what I did, only moreso, and made a nice table with # WW procs vs AS.
http://us.battle.net/d3/en/forum/topic/6794871641?page=1

My previous assumptions were that WW does damage 4x per second, regardless of attack speed, but displays damage every 0.5s and that life gain tics always tic every 0.5s.

My conclusions
1) Damage from WW displays every half second regardless of attack speed
2) Damage from WW is independent of attack speed
3) Life regen displays every half second, with occasional slight variations I attribute to server lag
4) Life gain from LoH is based on attack speed and the tics display at most every 0.5s

Note that (2) and (4) are somewhat contradictive, but that was what I observed. Doubling my attack speed resulted in life gain tics that were for 2x as much. I really don't understand why because the damage clearly seems to be independent of attack speed, yet LoH returns are not.

My setup
I had a 0.9 aps white weapon with 18-19 damage range, a 1.2 aps white weapon with 9-12 damage range, a 400 LoH amulet, and a 1.5 aps weapon with 3-7 damage. I also had gloves with 7% IAS, rings with 7 and 5 IAS, an amulet with 8% IAS, and bracers with 9 IAS. With all those equipped I was able to get a 1.4 APS weapon up to 1.9 attacks per second so my range was 0.9 - 1.9 attacks per second.

To test dps I also had a ring with +11 min damage that I could pair with the white weapons to give a consistant amount of damage, in theory. It works great for single cast spells but wasn't as good for WW.

My tests
1) Remove all gear except white weapon and +min damage ring for base case to test damage.
Then equip IAS gear and compare damage to base case. Repeat for both white weapons. Remove IAS gear and equip item with +Int to bring dps close to the dps with IAS gear.

2) Remove all gear except 0.9 APS weapon and 400 LoH amulet, then take a hit so I'm not at full life. Teleport to mob and drop a WW on mob while it's fighting my fracture clone.
Note life gains and frequency of life gains.
Repeat with IAS gear on and repeat with other white weapons.

Results
1) Damage remained same with and without IAS for each weapon. The tics were steady at 2 per second regardless of attack speed. This test was a little difficult to perform because the tics had more varience than I expected so I tried to focus on the min damage tic while the mob was in the middle of the WW. Just to be sure the lack of a change in damage wasn't due to the small DPS increase of the IAS gear, by wearing no IAS gear but a pair of boots that brought my dps about the same as it was with the IAS gear, I was able to conclude that IAS does not impact the damage done by WW because my damage DID increase with the boots on, but didn't for just adding IAS gear. With both weapons the tics were precisely equal to the damage expected from 252% weapon damage done over 6s at 0.5s intervals, further showing that WW displays damage 0.5s apart, independent of weapon speed.

2) With 0.9 APS I saw tics of 50 every half second. When I added a couple pieces of IAS the tics varied from every 1s to every half second and most of the tics were for 100. With the 1.2 APS weapon, pretty much every tic was for 100, but the tics weren't quite every half second. At 1.92 APS the tics displayed pretty consistantly every half second, but varied between 100 and 150.
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My Wizard
• Isn't it the same principle behind the archon beam ? When you add attack speed the ticks have the same frequency but higher damage per tick (or life back).

I think the ticks are constant on 0.5s as long as you have more than 1 attacks/second.
When you hit 2 attacks/second you get the wired ticks where half of the LOH is gained in the first half tick, and the second half in the later tick.

I really would love to test this, but the stupid char copy is still not working for Euro region.

BTW: most people I know switched from LoH to LifeSteal, as the damage gets high enough, it just gives more life back, it seems ...
• That's the usual test, however with such a test it's impossible to conclude if the WW ticks more / faster with AIS - the damage seem to add up per 0.5 seconds according to what community accepts right now. This is primarily based on the belief that the channeled / beam spells do crit but we never get to see the crit damage as a larger yellow number because they tick faster than 0.5 seconds and every 0.5 seconds the damage is added up. According to that post by blizzard - the tick speed scales with attack speed, assuming that the duration of WW would be the same under all conditions - then it would be reasonable to assume that the attack speed increases the number of ticks of the WW as well. However, i really do not see how it could be tested based on the damage numbers appearing on the screen.
"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."
-- Albert Einstein

• I make the assumption here that because LoH numbers did increase that number of critical hits per second were increasing as well.

I'd really like to have solid data on the under the hood pulse rate of wicked wind and meteor's DoTs. I think this can be observed via LoH since the coefficient is known to be 0.125. So my question is this. If the coefficient is 0.125 and you have 500 life on hit, you can engineer a tooltip attacks per second of 1.0, and observe from the half second amalgamated heals how many times the spell is triggering LoH.

With 500 LoH you should see a multiple of 62.5 per tick and that multiple is the baseline pulse rate of the spell.

If possible, doing similar tests with various meteor runes to obtain similar pulse rates for their DoTs would be helpful as well.
• @DrShell
Based on my results, it is NOT the same principle as the Archon beam. For the beam, the tics display at the same rate as WW but when you increase attack speed the tics increase in damage. For WW the tics did not increase in damage or frequency. I realize most people are trying to switch to Life Steal but the idea behind looking a LoH is that is should also apply to how CM procs work since they both use the same mechanics.

@TheDemokin
How is it impossible to determine if the tics are faster with higher attack speed or not? I did tests that ranged from 0.9 to 1.92 attacks per second. It seems to me if some attack speed make the tics faster or slower, I would have noticed it, but they were consistant at 2 tics per second. The easy way to check tic rate is to equip life regen gear since that tics pretty consistantly at 2 per second. WW damage then lines up pretty well with the life gain tics.

@DisposableHeero
I'd also like to get some solid information about Meteor tics to go along with WW, since I'd greatly prefer to use meteor in a CM build if possible.

To all who responded or have any input, could it be that the varience I saw with the tic damage was due to more frequent damage being averaged? If it was due to crits, like I expected, it shouldn't really happen with much frequency at only 5% crit rate. Probably the best way to do the analysis is to take a vid and post it but I don't have any video recording software so I basically just dropped my WW and saw the same damage number tic several times in a row. It really doesn't make sense that the LoH gains would depend on atatck speed but the damage done doesn't. One other thing I could try is finding a 1.5 APS weapon with the same damage as a 0.9 APS weapon, then I can stack the attack speed to over 2x the 0.9 APS weapon and get better results for comparison. Are there any free vid recording software programs that people use for D3?
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My Wizard
• Some more WW info. I downloaded a trial version of Fraps and went to Belial on normal mode since he doesn't move. He also has a decent HP pool so it's a great place to test damage. I bought 2 new weapons and a new ring:
0.9 APS 22-23 damage
1.5 APS 7-21 damage
+27 min damage ring
+12 min damage ring

setup:
0.9 APS w/12 min dmg ring => 34 - 34 damage range. DPS = 125.16 with 0% IAS, so 0.9 APS total
1.5 APS w/27 min dmg ring => 34 - 34 damage range. DPS = 254.50 with 22% IAS, or 1.83 APS total

For each weapon setup indicated I cast 1 WW at a time while recording with FRAPS. I recorded 4 casts for the 0.9 APS weapon and 6 for the 1.5 APS weapon. Since I'm using a trial version, I can only record 30s of video at a time, but I feel the data is decent.

I replayed each cast in slow motion and recorded the tics on a spreadsheet.

Results:
0.9 APS Total Damage
342
342
390
341
Average = 353.75

1.83 APS Total Damage
346
345
362
370
346
378
Average = 357.83

Based on those results I again conclude that WW damage is independent of attack speed since the 1.83 APS setup had twice the APS but the same weapon damage as the 0.9 APS setup.

I'll repeat the experiment for LoH and post shortly. I'll probably also repeat for meteor eventually.
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My Wizard
• LoH results are in. My results indicate that more attack speed = more LoH tics, which is similar to the results shown in my first post. I have quantified it a bit, and it seems there are breakpoints

Results (sorry for horrible formating but I haven't figured out how to put a table in these posts)
procs = total life gain / life per proc = Total Life gain / (LoH / 8) since the coefficient is 0.125 or 1/8

APS, #LoH procs
0.9 11
0.963 12
1.01 13
1.071 13
1.5 18
1.605 20
1.71 22
1.785 23

A couple things to note are that at 1.5 attacks per second, the results indicate you get about 3 procs per second. It appears that at 1 APS you get about 2. The trends indicate that at 2 APS you'd get 4 procs per second, or twice as many as with 1 APS. Thus it seems the approximate relationship is Procs per second = 2*APS, but it is not a smooth relationship. It appears to take the number or procs and round up, but the formula doesn't work for the 1.7+APS cases, though it works for all other cases. In other words,

Procs = Ceiling(2Base procs per attack * 6 Second duration * Attacks per second)

where Ceiling rounds a number UP to the nearest integer.

I'll work on updating the OP later with this information. My next step will be to do a similar analysis with Meteor. I'm thinking of also doing such an analysis with Archon beam to get an idea of how frequently the LoH procs occur, but that I'll save for last if I have time.
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My Wizard
• Quote from Loroese

Are there any free vid recording software programs that people use for D3?

Bandicam is free and I use it for all my D3 videos. The only limitation on the free version (that I am aware of) is that it puts a "www.Bandicam.com" banner on the top of your video and it can only record a video of up to 10 mins. I havn't had any problem with either of those restrictions, so I'd recommend it. It's also pretty lighweight.

Thanks for doing this testing, it's important information. Especially since I think anybody who wants to farm rings in the patch will need to be CM.

Regarding meteor, I am pretty sure you are going to find that IAS has no effect on the spell (aside from actually decreasing the casting animation, which is something), but by all means please do the testing to confirm. My basis for this hypothesis is that IAS was demonstrated, long ago, to have no effect on Blizzard, and essentially these spells operate in the same way: they have an AP cost and no cooldown. I would have guessed the same result for WW, frankly, but a lot of people have been saying that IAS has an effect. I guess it turns out it works on LOH but not damage, which is a bizarre result.

Also, take a look at this thread, although you might already be aware of all the information: http://www.reddit.com/r/Diablo3Strategy/comments/yz2jn/wizard_104_comprehensive_proc_ratios/

http://eu.battle.net/d3/en/forum/topic/5208511084

The proc coefficients are common knowledge, but the interesting data are the cast speed and tick speed coefficients.
• This is very interesting... from here: http://eu.battle.net...08511084?page=4

Also, I don't know if some people already knew but the green numbers does not appears every 0.5 second like some people tested it on 1.02. Instead the game adapt the green number timing on your life on hit. I learned it the hard way and I don't want people to struggle like I did so I am saying it anyway.

About that strange green number timing : I am currently retesting arc lighting... I might lack sleep because the cast animation (cosmetic) speed appears to be at max on 1.2 attacks per second then suddenly decrease at 1.3... But i have seen green numbers pops between cosmetic cast with 1.3 attacks per second and damage seems to be dealt properly. The tick speed coef appears to be near 2.5. There is really something we don't know about this spell !

I'm having trouble following exactly what he's saying, but I think it might explain the disparity in your results re: IAS changing the LOH healing but not the damage.
• Quote from Loroese

Results:
0.9 APS Total Damage
342
342
390
341
Average = 353.75

1.83 APS Total Damage
346
345
362
370
346
378
Average = 357.83

Based on those results I again conclude that WW damage is independent of attack speed since the 1.83 APS setup had twice the APS but the same weapon damage as the 0.9 APS setup.

Nice work so far,

did i miss something or is there 4 ticks in the first case and 6 ticks in the second? At the same time you proclaim that WW damage is independent of APS, well the average damage seems to remain, while the total number of ticks seems to have increased thus increasing the total damage of WW?
"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."
-- Albert Einstein

• @TheDemokin
Those are case with total damage done over the 12s, I just only ran 4 cases for the slower attack speed because the rest of my vids got cut off and I was too lazy to make more since the results were pretty conclusive. Those values are the total damage done for the entire duration of a WW, i.e., 6s. For both weapon speeds and all cases I observed 12 tics total, which matches the 2 tics per second theory. The average there is the average damage done by the WW over 6s. Sorry for any confusion about that.

Basically, the total damage done by the WW is the same for each weapon, despite the char sheet dps being almost twice as much for the faster weapon.

@Morphos
Thanks for the links. I'll take a look at them tonight. I actually haven't looked up any information about this stuff, so I don't really know what all people have examined. I'll also look into Bandicam since the demo version of FRAPS only lets me record 30s at a time.

I didn't expect there to be any difference with WW and IAS because the damage did not change, but I am suprised that there is some sort of correlation with LoH, so naturally I want to examine Meteor also, since it might behave in a similar manner. Even if there is similar results in those links I'll probably do my own testing just to be sure.
Wizard DPS and EHP Spreadsheet, mostly useful for wizards.
My Wizard
• Quote from Morphos

Quote from Loroese

Are there any free vid recording software programs that people use for D3?

Bandicam is free and I use it for all my D3 videos. The only limitation on the free version (that I am aware of) is that it puts a "www.Bandicam.com" banner on the top of your video and it can only record a video of up to 10 mins. I havn't had any problem with either of those restrictions, so I'd recommend it. It's also pretty lighweight.

Thanks for doing this testing, it's important information. Especially since I think anybody who wants to farm rings in the patch will need to be CM.

Regarding meteor, I am pretty sure you are going to find that IAS has no effect on the spell (aside from actually decreasing the casting animation, which is something), but by all means please do the testing to confirm. My basis for this hypothesis is that IAS was demonstrated, long ago, to have no effect on Blizzard, and essentially these spells operate in the same way: they have an AP cost and no cooldown. I would have guessed the same result for WW, frankly, but a lot of people have been saying that IAS has an effect. I guess it turns out it works on LOH but not damage, which is a bizarre result.

Also, take a look at this thread, although you might already be aware of all the information: http://www.reddit.co...ve_proc_ratios/

http://eu.battle.net...opic/5208511084

The proc coefficients are common knowledge, but the interesting data are the cast speed and tick speed coefficients.

After reading those posts, it seems the LoH relationship I found is the same as that posted in the thread. Also, the thread indicates Meteor has no speed coefficient which means it shouldn't depend on IAS, but I'll still check.

Damage isn't mentioned in the thread either, so that's something different I'm doing.

Again, thanks for the links. I wasn't aware there had been an update since the other LoH Coefficient thread I had been using before that is quicky getting out of date.
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My Wizard
• Well my Meteor - Star Pact results are in, and it behaves exactly as expected. The blast and resulting damage tics are unaffected by attack speed. The LoH returns from the blast and tics are also unaffected by attack speed, with the coefficients being 0.25 for blast and tics but with the first tic occuring at the same time as the blast. Note that this proc is being reduced to 0.10625 or 17/160.

Since I don't really have anything to do tonight, I'll probably throw together a rough CM simulator to compare WW and Meteor in the next patch to see if I can determine any sweet spots in terms of attack speed, APoC, etc. I think it will also be interesting to cacluate the theoretical dps output of each build for say a 60s solo fight, i.e., MP10 keywarden type fight. Is the AP cost of Star Pact still 35 on the ptr? If so, I might also look at the other runes since they only cost 50 AP, based on the PTR notes. Liquify in particular looks like a decent possiblity. With 50% crit the average duration is something like 5.5s or 6.5 total procs, compared to the 4 of star pact. The AP cost is only 43% higher but the proc rate would be 62.5% higher, so it seems like it might be worth trying.
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My Wizard
• Loroese, my question here is:

Does attack speed affect the speed of ticks or ticks per second of the WW?

The problem with this is: according to what community believes as well as i recall seeing it stated by Blizzard - the damage numbers for any skill are added up at 0.5 seconds interval. So for example if the skill ticks twice a second or the skill ticks 4 times or even 20 times a second you will only see 2 damage numbers coming up on the screen.

While the overall damage of the skill is going to remain the same, the amount of ticks it performs is...? The larger number of ticks is going to certainly provide for a larger chance to proc CM, hence making AIS a valuable stat for the CM builds using WW.

According to your tests - the LoH values seem to increase based on AIS. That alone, suggests that the number or ticks definitely increased assuming that the coefficient remains the same no matter the APS. Using the same model of healing done added every 0.5 seconds before being displayed - this clearly explains the reason why the numbers increased from 50 to a 100, etc.

So the final conclusion then would be that APS increases the amount of ticks WW performs? Or am i completely lost?
"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."
-- Albert Einstein

• In order to answer your question I have to break up the spell into Damage Tics and Proc Tics.

The Damage Tics are the displayed damage done, which occur every 0.5s regardless of attack speed. The damage displayed from the tics is also independent of attack speed, so a 1 APS weapon with 100 damage will do the same damage per tic as a 2APS weapon with 100 damage. In short, Damage Tics do not depend on attack speed.

The Proc Tics are the CM/LoH procs. It is easiest to see these tics with LoH because they show up as green numbers. The number of tics DOES depend on attack speed and the formula is #Procs = 2*AttackSpeed*6s duration, so with 1 APS you see 12 procs, with 2 APS you see 24 procs, or you gain twice as much life over the same period of time.

So basically the procs follow a different relationship than the actual damage, which makes no sense to me. While you effectively get 24 procs from 2APS, you still only see 12 damage tics.

My conclusions are that IAS increases the number of procs per WW, but doesn't actually increase the damage of WW.
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My Wizard
• Correct, what i was saying is that with 1 APS you get 12 damage ticks of WW and with 2 APS you get 24 damage ticks as well. The thing is that - it is virtually impossible to see that due to the way the damage numbers are shown ingame at 0.5 seconds intervals. The damage of the spell is going to be broken down into smaller more frequent ticks rather than larger bigger ticks instead.

The reason i am saying this is that it would be rather stupid to have 2 completely different formulas working for every spell, if you just use 1 formula for both the damage ticks and the proc ticks - it would be far more sensible and easier to maintain.
"Only two things are infinite, the universe and human stupidity, and I'm not sure about the former."
-- Albert Einstein

• I agree it would make more sense to have 1 system, but what I'm saying is there isn't just 1 system, or if there is, it's not what we're thinking it should be. If attack speed increased the number of damage tics, and the displayed tics were just sums of the individual tics, then the actual damage done would increase with attack speed. As it is, you get 12 damage tics with 1 APS and 12 damage tics with 2 APS.

Otherwise if you got 24 damage tics with 2 APS, for the damage that is displayed every 0.5s to be the same as the 1 APS case, then each of the 24 damage tics would have to do half the damage as each of the 12 damage tics for the 1 APS case, which makes no sense if both have the same weapon damage.

I hope it doesn't make things more confusing to mention this but channeled spells are treated the way you're thinking WW should be. Specifically the displayed damage tics are averaged damage over 0.5s intervals and higher attack speed leads to larger displayed tics while the procs tic at the same rate as the actual damage is dealt. So if you have a beam spell with a speed of 3, you get 3 hits per tic per attack speed. In other words, with APS=1, your beam deals damage 6 times a second, so every 3 hits is totaled and displayed as damage. Your proc rate is 6 times per second, which matches the damage rate. If you have APS=2, the beam still only displays damage twice a second but now it deals damage 6 times between tics and procs 12 times per second. All channeled spells work that way, with their own speed coefficient though.
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My Wizard
• Quote from Loroese

Well my Meteor - Star Pact results are in, and it behaves exactly as expected. The blast and resulting damage tics are unaffected by attack speed. The LoH returns from the blast and tics are also unaffected by attack speed, with the coefficients being 0.25 for blast and tics but with the first tic occuring at the same time as the blast. Note that this proc is being reduced to 0.10625 or 17/160.

Since I don't really have anything to do tonight, I'll probably throw together a rough CM simulator to compare WW and Meteor in the next patch to see if I can determine any sweet spots in terms of attack speed, APoC, etc. I think it will also be interesting to cacluate the theoretical dps output of each build for say a 60s solo fight, i.e., MP10 keywarden type fight. Is the AP cost of Star Pact still 35 on the ptr? If so, I might also look at the other runes since they only cost 50 AP, based on the PTR notes. Liquify in particular looks like a decent possiblity. With 50% crit the average duration is something like 5.5s or 6.5 total procs, compared to the 4 of star pact. The AP cost is only 43% higher but the proc rate would be 62.5% higher, so it seems like it might be worth trying.

I'm very interested to see the calculator. All of the other meteor runes are in fact 50 AP, and I think it is agreed that Liquify and Star Pact are the two best options for meteor.
• Quote from Loroese

APS, #LoH procs
0.9 11
0.963 12
1.01 13
1.071 13
1.5 18
1.605 20
1.71 22
1.785 23
Unless I miss my guess, the third attack speed in your list should actually be 1.026 as you appear to be using a 0.9 attack speed weapon with 0%, 7%, 14%, and 19% IAS, and then a 1.5 speed weapon with 0%, 7%, 14%, and 19% IAS.

This data doesn't quite fit the hypothosis that you simply get 2 * attack speed ticks per second but there is always a tick at the beginning and end of the spell essentially rounding up. If that were the case your final 2 tests should have yielded 21 and 22 ticks.

You can get a slightly better fit assuming that there is rounding ocurring twice, that there is a base number of ticks for each weapon speed of 2*weapon speed rounded up, and then that creates a base tick rate that is increased by IAS% and rounded up again at cast time to determine the total number of ticks for the spell. This yields slightly closer results but still suggests that your final case (1.5 attack speed weapon 19% increased attack speed from gear) should have 22 ticks rather than 23.
• Quote from DisposableHeero

Unless I miss my guess, the third attack speed in your list should actually be 1.026 as you appear to be using a 0.9 attack speed weapon with 0%, 7%, 14%, and 19% IAS, and then a 1.5 speed weapon with 0%, 7%, 14%, and 19% IAS.

This data doesn't quite fit the hypothosis that you simply get 2 * attack speed ticks per second but there is always a tick at the beginning and end of the spell essentially rounding up. If that were the case your final 2 tests should have yielded 21 and 22 ticks.

You can get a slightly better fit assuming that there is rounding ocurring twice, that there is a base number of ticks for each weapon speed of 2*weapon speed rounded up, and then that creates a base tick rate that is increased by IAS% and rounded up again at cast time to determine the total number of ticks for the spell. This yields slightly closer results but still suggests that your final case (1.5 attack speed weapon 19% increased attack speed from gear) should have 22 ticks rather than 23.

You're right about the 1.01 attack speed being off a bit, though it should be 1.008 since I had a ring with 5% IAS.

Regarding the idea of a tick to start and end, I'm not completely sure what the model would be, something like 2+2*5*APS instead of 6*2*APS?

Quote from Morphos

I'm very interested to see the calculator. All of the other meteor runes are in fact 50 AP, and I think it is agreed that Liquify and Star Pact are the two best options for meteor.

I'll finish it later today. I got stuck a bit when trying to figure out how to account for stacking tics of spells but I think I figured out a good way to treat them while making as few approximations as possible. It's basically going to be a monte carlo type simulator. Unfortunatelly it will be made in MATLAB, which is not a freeware program, but if anyone is familiar with other programming platforms, it should be easy to convert to C++ since I'm not using any MATLAB specific functions. I'll make a new thread for that when it's done and include the code for others to look at.
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