Preface: I want to theoretically compare the value of some weapon combinations for barbarians after the 2.0.5 patch. The impetuses for this thread were other recent threads talking about the BK weapon set and Nubtro's Game Mechanics (barbarian) spreadsheet on google docs.
Bul-Kathos's Set
After patch 2.0.5, Nubtro reported that, not only can the whirlwind proc from the BK set now critical hit, but also that the damage itself scales with your critical hit damage and chance (before it crits). The damage amount also scales with your attack speed, but because the BK set seems to have an internal cooldown, attack speed doesn't influence the amount of procs.
Your critical hit chance and damage apply twice to the BK whirlwind proc, so bascially those stats are squared when factoring the average damage. The damage is reported as 1950% weapon damage / 6 seconds, or 325% weapon damage / second. This 325% is multiplied by your attacks per second and critical hit/damage, so if you have 1.55 attacks per second, 40% critical chance, and 400% critical damage, you can expect to do:
325% * (1.55) * (1 + .4 + 4) ~= 1310% weapon damage/second in a circular area around your character
However, the BK proc seems to be on an internal cooldown of roughly about 12 seconds (in my personal experience- 2.0.4, so this may have changed). This means that the average damage over time will be about half the active damage/second, or about 655% weapon damage per second. Because of the internal cooldown, attacking multiple targets doesn't really increase the value of the proc.
So the estimated damage of the BK set proc in these circumstances is roughly:
Odyn Son
According to the information gathered in Nubtro's Barbarian spreadsheet, the reason why the Odyn Son proc seems so powerful is because it apparently scales with critical hit chance, critical hit damage, and attack speed twice.
i.e.: Your attack speed and critical chance/damage values are squared when multiplying the damage of an Odyn son proc.
The base damage of the proc is only around 100-120% weapon damage, but the base damage itself is multiplied by your critical hit stats and your attack speed. After this, the damage amount can be a critical hit, which uses your critical stats again, and of course the higher your attack speed, the more procs you can create (thus scaling with attack speed twice as well).
Let's say you have 40% critical chance and 400% critical damage. You also have 1.55 attacks per second and your Odyn Son does 100% weapon damage per hit (3 hits per proc). Each hit of the proc will do 100% * (1.55) * (1 + 0.4 + 4) =403% weapon damage.
(I think the above calculation is why a lot of people estimate that Odyn Son's proc does about 400% weapon damage. It does about 400% with those values of attack speed, crit damage, and critical chance, but it could do more or less.)
After you get this value, in our case 403%, the proc will hit 3 times, possibly all on the same target. These 403% damage procs can then critical hit again, boosting their damage further (by another 2.6 times in our case, on average), and the faster you attack (and the higher your proc coefficient), the more often you can trigger the proc.
So, say you have a 30% proc rate Odyn Son with the above stats. It does 1209% damage split between 1-3 targets. It will proc 30% of the time on every hit, modified by proc coefficient. Your attack speed dictates the number of proc chances, because there is no internal cooldown, so the damage/second is multiplied by your attacks/second.
Shard of Hate(lightning build)
Shard of Hate apparently does not scale twice with critical hits or attack speed, but it does scale with % lightning skill damage. It also has a roughly 1 second (I think) internal cooldown.
If you have a 225% damage proc on Shard of Hate and 80% lightning skill damage, the proc does 405% weapon damage per bolt and fires three bolts per proc. This makes its damage per proc strikingly similar to Odyn Son using my sample stats. However, Shard of Hate has an internal cooldown, so it doesn't scale infinitely with more targets. It should do about 405 * 3 = 1215% weapon damage, split among 3 targets in the maximum possible case.
So I estimate the damage at:
1215% (1 - (1 - proc coefficient)^((number of targets + 1) * attacks per second) ) (split among 1-3 targets)
Maximum: 1215% weapon damage/second (split among 1-3 targets)
(This means Shard of Hate looks really good with a high proc rate or smallish number of targets, but other procs start to surpass its total damage per second when there are large groups).
Yeah it looks like that's the conclusion of BK vs Odyn/SOH, at least given the dummy stats that I used. In general, it looks like BK offers superior AoE and SOH is great damage, but it has a functional target/attack speed cap due to its internal cooldown.
I didn't account for other factors like Odyn Son's +% lightning damage, or using different skills, as well.
One question though. You work with a 39% proc cance. Is that your assumption for three whirlwind ticks during one second ?
And we should include odyns 20% lightning damage to the equation.
I did not include the 20% lightning damage in any equations.
The 39% proc chance (for non-Internal cooldown weapons) is based on Whirlwind ticking 3 times per "regular attack" roughly. In a continuous model (ie: not the real way the game works with frames and break points), whirlwind would tick at 3x your attack speed.
(I'll add more stuff later, I was just bored at work today.)
It seems your SoH numbers might be a little inflated for single target situations. Are the charged bolts able to hit the same target? In my experience (mostly on rift bosses), one charge hits the boss, but the other two usually go off in random directions. That would mean you only actually gain a single 405% (using your 225% x 1.8 damage model).
Either way, nice post I have the full BK set, and was a little disappointed with its performance pre-patch. I haven't tested them since, but perhaps I will give it a try tonight.
things to take on count: the Soo i get is purely shit, (1980 damage with low stats) and i lost 'bout 120 k damage replacin' my bk set.
I can see how low health monsters die more easily with Soo proc (And TF) i imagine that with a better Soo combing with a SoH (or a SoH&TF combo) it will be more quickly, otherwise, the 12-22 mil crit from bk are just sweet if ur able to hit them all on a big monster.
dunno what combo is way better, but, in my opinion, a good TF&SoH must be quite better.
bye =)
with the BK set i saw crits well over 10m, where as with the other combos i saw u crit for max 3m.. Would be nice to get a view to ur profile. Its hard to say if ur totally build with paper dps or not
I just wanted to chime in and say thanks to the OP and Nubtro for all their work on this. This topic prompted me to make an account here and post for the first time, and I really feel your numbers are spot on, reflected by what I'm experiencing in game.
I've been looking for some good resources out there regarding Lightning-WW barb builds, and ever since the SoH proc fix, it seems we're a rare breed.
Anyway, my experience has been: 1950 DPS Sunkeeper (30% elite) + 1950 DPS Odyn Son (17% lightning / 31% proc). I'm perfectly willing to believe that the rest of my gear (base damage) needs to be much better in order to really enjoy mods like the 30% elite damage (as well as a well rolled SoJ). My SK + OS has gotten me decently through torment 1, into easymode farming it, I know, not that difficult.
Yesterday, I hit a streak of amazing luck, picking up Bul-Katho's Solemn Vow (2250 DPS!) and immediately went to work with the Warrior Blood with it. This was on top of getting Aughild and Asheara's plans all in one day.
I jumped right into Torment 2, and almost feel my DPS is ready to take on T3, not that my toughness is, quite yet. The proc is that incredibly good, IMO..please for the love of all that is Diablo, do not nerf this one. I'm seeing 30m+ WW (proc) crits with Insanity up on elites, quite a jump from the occasional "big" 10m crit procs I'd see with Odyn Son previously.
It's also my firm opinion that if you're looking to really get the most out of the BK weapon set, you should be actually *using Whirlwind*. The biggest reason for this - the "WW Proc" has an extremely small range. You want to be literally on top of your target, on their nuts, and up in their face - Left clicking Frenzy will commonly put me barely outside the range for the WW to hit things, so you really want a free movement skill like WW. I could definitely also see it performing in some Might of the Earth/Leap builds - for the simple reason that it's a good bit of added DPS since you are using Leap (jump right on their nuts, they will be in range for it), but, I have zero experience in this endgame department yet.
PS: rather than make another thread about this/gear check, I'll just ask here. I would appreciate any critique or seeing some Lightning WW profiles if anyone feels like sharing - I'm mainly asking "am I geared enough for *HC* T2-3?" And, I know this isn't the HC forums, but the HC forums I've asked already are dead...I'll take any critique basically. Here's mine:http://us.battle.net/d3/en/profile/Cassiel-1175/hero/47132742
I know what the obvious gear improvements are - just starved for forgotten souls currently since rolling the socket on my BK's. Any suggestions regarding skill changes, passives or what have you, anything appreciated.
EDIT: forgot to list my ingame stats - 850k DPS / 12.5m toughness self buffed.
It's quite possible for SOH procs to not connect, and thus lower the effectiveness of the proc, but when I whirlwind back and forth directly through most medium or large monsters, it's possible to make all 3 bolts connect instantly with the enemy.
I also agree that the BK set seems designed to work exceptionally well with the Whirlwind skill.
I think the reason why BK ticks seem so high right now is because it appears that the actual damage per "hit" scales with your attack speed and critical stats. A tick is either 162.5% weapon damage (the derived value of one 'tick') or possibly 260% weapon damage (if the weapon reports its damage every 48 frames, as has been said of other DoT-type effects). I'll assume the former, because the proc shows yellow numbers, which doesn't usually occur with DoT-style damage.
With the 162.5% weapon damage per tick, we apparently multiply our critical stats and attacks per second to determine the actual, non-crit damage per tick. Let's say you're fairly geared and have ~1.82 attacks per second (40% attack speed), 50% crit chance and 500% crit damage. Let's say you're also using WotB - Insanity. So your critical chance during WotB is 60%, damage is still 500%, and attacks per second go up to 2.145 (65% attack speed). During WotB - Insanity, factoring in the scaling for attack speed and crit, the 162.5% damage becomes 162.5 * 2.145 * (1 + 0.6 * 5) * 1.5 =
~2091% per tick (every half second)
So, assume you have a BK sword that does 1600 average damage and 8500 strength. One tick will do 1600 * 86 * 20.91 =
~2.877 million damage (non-critical hit)
This is a white hit, though, even though we used critical damage stats once, a crit will do more damage: 2.877 million * (1 + 0.6 * 5) =
~11.5 million damage (on a critical hit)
Odyn Son actually works similarly, and hits 3 times for a slightly lower value (100%-120% weapon damage, x3, instead of 162.5% every half second).
BK theoretically more or less ignores proc rates, triggering almost every 12 seconds (I think), hitting 12 times per proc (or an average of 1 tick per second) and hits every mob in a radius.
If you use the stats above during Insanity, Odyn Son with a perfect proc rate (40%) would trigger about 2.145 * (0.39) * (0.4) = 33% of the time each second, or about 1 proc per 3 seconds.
1 proc of Odyn Son is 3 'ticks', so Odyn Son also averages out to about 1 'tick' per second (with a perfect proc %, when using whirlwind).
So, using whirlwind with a perfect proc % Odyn Son, both Odyn Son and BK set would 'tick' about once per second (on average, factoring in the cooldown on BK set). However, the BK set hits harder (162.5% vs 120%). The number of targets doesn't matter, because more targets gives Odyn Son more ticks (but each 'tick' only hits one target). More targets means that each BK 'tick' does more damage (because it's an AoE).
A noticeable difference is that the BK set does reliable consistent damage when its proc occurs, and Odyn Son is rather random- the chance to trigger, targets selected, etc. Even if on average they both 'tick' with roughly the same frequency, BK set will be much smoother and Odyn Son procs could be very punctuated.
Also, I think Odyn Son and BK set both benefit greatly from WotB or any other attack speed / critical hit / critical damage buffs (Crusader Law of Valor - Critical), because they "double crit" and factor attack speed into their damage per hit.
on top of the proc its worth noting that i seems the stre rolls with BK-set seems to be higher then with other weapons. At least for me when equipping BK-set i get an increase of roughly 450 stre (250 from bonus and around 100stre per weapon) so more damage and more armor right?
My BK swords both have about 630 strength individually. This is actually less than my SoH, but about the same as my Odyn Son. The set bonus of 250 strength does add some extra damage (about 3% if you have 8500 strength).
The BK set should be affected by berserker rage and brawler, but not affected by % whirlwind skill damage / whirlwind runes. Graphically it uses the whirlwind particles (flying axes/swords and spiraling winds), but it's not actually a "whirlwind" skill - your barbarian doesn't actually spin around, move at 75% speed, ignore unit collision, etc.
If I had to guess, I'd say the range is about the same as whirlwind, maybe 8-10 yards?
Here is my profile also using the same weps as the OP. I currently have both BK weps but one is only lvl 68. After reading this post I am very interested in doing some further testing of weps. With the current gear and weps equipped I have zero problems with T2 and usually play T3.
Good job on the post, this is the kind of stuff I get on this site for.
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Bul-Kathos's Set
After patch 2.0.5, Nubtro reported that, not only can the whirlwind proc from the BK set now critical hit, but also that the damage itself scales with your critical hit damage and chance (before it crits). The damage amount also scales with your attack speed, but because the BK set seems to have an internal cooldown, attack speed doesn't influence the amount of procs.
Your critical hit chance and damage apply twice to the BK whirlwind proc, so bascially those stats are squared when factoring the average damage. The damage is reported as 1950% weapon damage / 6 seconds, or 325% weapon damage / second. This 325% is multiplied by your attacks per second and critical hit/damage, so if you have 1.55 attacks per second, 40% critical chance, and 400% critical damage, you can expect to do:
325% * (1.55) * (1 + .4 + 4) ~= 1310% weapon damage/second in a circular area around your character
However, the BK proc seems to be on an internal cooldown of roughly about 12 seconds (in my personal experience- 2.0.4, so this may have changed). This means that the average damage over time will be about half the active damage/second, or about 655% weapon damage per second. Because of the internal cooldown, attacking multiple targets doesn't really increase the value of the proc.
So the estimated damage of the BK set proc in these circumstances is roughly:
Odyn Son
According to the information gathered in Nubtro's Barbarian spreadsheet, the reason why the Odyn Son proc seems so powerful is because it apparently scales with critical hit chance, critical hit damage, and attack speed twice.
i.e.: Your attack speed and critical chance/damage values are squared when multiplying the damage of an Odyn son proc.
The base damage of the proc is only around 100-120% weapon damage, but the base damage itself is multiplied by your critical hit stats and your attack speed. After this, the damage amount can be a critical hit, which uses your critical stats again, and of course the higher your attack speed, the more procs you can create (thus scaling with attack speed twice as well).
Let's say you have 40% critical chance and 400% critical damage. You also have 1.55 attacks per second and your Odyn Son does 100% weapon damage per hit (3 hits per proc). Each hit of the proc will do 100% * (1.55) * (1 + 0.4 + 4) =403% weapon damage.
(I think the above calculation is why a lot of people estimate that Odyn Son's proc does about 400% weapon damage. It does about 400% with those values of attack speed, crit damage, and critical chance, but it could do more or less.)
After you get this value, in our case 403%, the proc will hit 3 times, possibly all on the same target. These 403% damage procs can then critical hit again, boosting their damage further (by another 2.6 times in our case, on average), and the faster you attack (and the higher your proc coefficient), the more often you can trigger the proc.
So, say you have a 30% proc rate Odyn Son with the above stats. It does 1209% damage split between 1-3 targets. It will proc 30% of the time on every hit, modified by proc coefficient. Your attack speed dictates the number of proc chances, because there is no internal cooldown, so the damage/second is multiplied by your attacks/second.
This damage is estimated at:
Shard of Hate apparently does not scale twice with critical hits or attack speed, but it does scale with % lightning skill damage. It also has a roughly 1 second (I think) internal cooldown.
If you have a 225% damage proc on Shard of Hate and 80% lightning skill damage, the proc does 405% weapon damage per bolt and fires three bolts per proc. This makes its damage per proc strikingly similar to Odyn Son using my sample stats. However, Shard of Hate has an internal cooldown, so it doesn't scale infinitely with more targets. It should do about 405 * 3 = 1215% weapon damage, split among 3 targets in the maximum possible case.
So I estimate the damage at:
(This means Shard of Hate looks really good with a high proc rate or smallish number of targets, but other procs start to surpass its total damage per second when there are large groups).
I play a lightning WW barbarian (~39% proc chance), so using the fake stats and estimates above, I can expect to do:
655% (per target) weapon damage/second with BK set
220% (per target) weapon damage/second with Odyn Son
882 - 1215% (varying with number of targets) weapon damage/second with Shard of Hate*
(*assuming it has a chance to trigger off every tick of whirlwind activation and whirlwind hit)
So, using these assuptions (not accounting for other weapon affixes or weapon DPS, just the procs):
BK set does 655% per target per second.
Odyn Son + Shard of Hate does (880 ... 1215)% + 220% per target per second.
Assuming no problems with geometry (grouping enemies into AoEs, missing with charged bolts, etc.)
I didn't account for other factors like Odyn Son's +% lightning damage, or using different skills, as well.
Could you make this calculation for TF as well? In addition to your post it would be nice to have a link to each weapon before you the calculation.
http://eu.battle.net/d3/en/profile/Storm-21498/hero/47687845
The 39% proc chance (for non-Internal cooldown weapons) is based on Whirlwind ticking 3 times per "regular attack" roughly. In a continuous model (ie: not the real way the game works with frames and break points), whirlwind would tick at 3x your attack speed.
(I'll add more stuff later, I was just bored at work today.)
Either way, nice post I have the full BK set, and was a little disappointed with its performance pre-patch. I haven't tested them since, but perhaps I will give it a try tonight.
http://eu.battle.net/d3/en/profile/Storm-21498/hero/47687845
I've been looking for some good resources out there regarding Lightning-WW barb builds, and ever since the SoH proc fix, it seems we're a rare breed.
Anyway, my experience has been: 1950 DPS Sunkeeper (30% elite) + 1950 DPS Odyn Son (17% lightning / 31% proc). I'm perfectly willing to believe that the rest of my gear (base damage) needs to be much better in order to really enjoy mods like the 30% elite damage (as well as a well rolled SoJ). My SK + OS has gotten me decently through torment 1, into easymode farming it, I know, not that difficult.
Yesterday, I hit a streak of amazing luck, picking up Bul-Katho's Solemn Vow (2250 DPS!) and immediately went to work with the Warrior Blood with it. This was on top of getting Aughild and Asheara's plans all in one day.
I jumped right into Torment 2, and almost feel my DPS is ready to take on T3, not that my toughness is, quite yet. The proc is that incredibly good, IMO..please for the love of all that is Diablo, do not nerf this one. I'm seeing 30m+ WW (proc) crits with Insanity up on elites, quite a jump from the occasional "big" 10m crit procs I'd see with Odyn Son previously.
It's also my firm opinion that if you're looking to really get the most out of the BK weapon set, you should be actually *using Whirlwind*. The biggest reason for this - the "WW Proc" has an extremely small range. You want to be literally on top of your target, on their nuts, and up in their face - Left clicking Frenzy will commonly put me barely outside the range for the WW to hit things, so you really want a free movement skill like WW. I could definitely also see it performing in some Might of the Earth/Leap builds - for the simple reason that it's a good bit of added DPS since you are using Leap (jump right on their nuts, they will be in range for it), but, I have zero experience in this endgame department yet.
PS: rather than make another thread about this/gear check, I'll just ask here. I would appreciate any critique or seeing some Lightning WW profiles if anyone feels like sharing - I'm mainly asking "am I geared enough for *HC* T2-3?" And, I know this isn't the HC forums, but the HC forums I've asked already are dead...I'll take any critique basically. Here's mine:http://us.battle.net/d3/en/profile/Cassiel-1175/hero/47132742
I know what the obvious gear improvements are - just starved for forgotten souls currently since rolling the socket on my BK's. Any suggestions regarding skill changes, passives or what have you, anything appreciated.
EDIT: forgot to list my ingame stats - 850k DPS / 12.5m toughness self buffed.
I also agree that the BK set seems designed to work exceptionally well with the Whirlwind skill.
I think the reason why BK ticks seem so high right now is because it appears that the actual damage per "hit" scales with your attack speed and critical stats. A tick is either 162.5% weapon damage (the derived value of one 'tick') or possibly 260% weapon damage (if the weapon reports its damage every 48 frames, as has been said of other DoT-type effects). I'll assume the former, because the proc shows yellow numbers, which doesn't usually occur with DoT-style damage.
With the 162.5% weapon damage per tick, we apparently multiply our critical stats and attacks per second to determine the actual, non-crit damage per tick. Let's say you're fairly geared and have ~1.82 attacks per second (40% attack speed), 50% crit chance and 500% crit damage. Let's say you're also using WotB - Insanity. So your critical chance during WotB is 60%, damage is still 500%, and attacks per second go up to 2.145 (65% attack speed). During WotB - Insanity, factoring in the scaling for attack speed and crit, the 162.5% damage becomes 162.5 * 2.145 * (1 + 0.6 * 5) * 1.5 =
~2091% per tick (every half second)
So, assume you have a BK sword that does 1600 average damage and 8500 strength. One tick will do 1600 * 86 * 20.91 =
This is a white hit, though, even though we used critical damage stats once, a crit will do more damage: 2.877 million * (1 + 0.6 * 5) =
Odyn Son actually works similarly, and hits 3 times for a slightly lower value (100%-120% weapon damage, x3, instead of 162.5% every half second).
BK theoretically more or less ignores proc rates, triggering almost every 12 seconds (I think), hitting 12 times per proc (or an average of 1 tick per second) and hits every mob in a radius.
If you use the stats above during Insanity, Odyn Son with a perfect proc rate (40%) would trigger about 2.145 * (0.39) * (0.4) = 33% of the time each second, or about 1 proc per 3 seconds.
1 proc of Odyn Son is 3 'ticks', so Odyn Son also averages out to about 1 'tick' per second (with a perfect proc %, when using whirlwind).
So, using whirlwind with a perfect proc % Odyn Son, both Odyn Son and BK set would 'tick' about once per second (on average, factoring in the cooldown on BK set). However, the BK set hits harder (162.5% vs 120%). The number of targets doesn't matter, because more targets gives Odyn Son more ticks (but each 'tick' only hits one target). More targets means that each BK 'tick' does more damage (because it's an AoE).
A noticeable difference is that the BK set does reliable consistent damage when its proc occurs, and Odyn Son is rather random- the chance to trigger, targets selected, etc. Even if on average they both 'tick' with roughly the same frequency, BK set will be much smoother and Odyn Son procs could be very punctuated.
Also, I think Odyn Son and BK set both benefit greatly from WotB or any other attack speed / critical hit / critical damage buffs (Crusader Law of Valor - Critical), because they "double crit" and factor attack speed into their damage per hit.
http://eu.battle.net/d3/en/profile/Storm-21498/hero/47687845
The BK set should be affected by berserker rage and brawler, but not affected by % whirlwind skill damage / whirlwind runes. Graphically it uses the whirlwind particles (flying axes/swords and spiraling winds), but it's not actually a "whirlwind" skill - your barbarian doesn't actually spin around, move at 75% speed, ignore unit collision, etc.
If I had to guess, I'd say the range is about the same as whirlwind, maybe 8-10 yards?
Here is my profile also using the same weps as the OP. I currently have both BK weps but one is only lvl 68. After reading this post I am very interested in doing some further testing of weps. With the current gear and weps equipped I have zero problems with T2 and usually play T3.
Good job on the post, this is the kind of stuff I get on this site for.