Hydra breakpoints in 2.3

Wizard
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* Hydra breakpoints have not changed from 2.2. to 2.3

An easy glance chart for Mammoth hydra can be found here:
http://i.imgur.com/mEALddo.png

APS Breakpoints for Mammoth Hydra (1/22/2015)
min aps ......... max aps ......... fpa .... hydra aps
========================================================
0.969566388 ..... 1.049256775 ..... 78 ..... 0.769
1.049256776 ..... 1.143220069 ..... 72 ..... 0.833
1.143220070 ..... 1.255667945 ..... 66 ..... 0.909
1.255667946 ..... 1.392649902 ..... 60 ..... 1.000
1.392649903 ..... 1.563178462 ..... 54 ..... 1.111
1.563178463 ..... 1.781296387 ..... 48 ..... 1.250
1.781296388 ..... 2.070155261 ..... 42 ..... 1.429
2.070155262 ..... 2.470830473 ..... 36 ..... 1.667
2.470830474 ..... 3.063829786 ..... 30 ..... 2.000
3.063829787 ..... 4.031354982 ..... 24 ..... 2.500
4.031354983 ..... 5.891980359 ..... 18 ..... 3.333
5.891980360 ..... 10.94224923 ..... 12 ..... 5.000

* fpa = frames per attack
* The hydra aps was calculated from D3's programmed 60 fps


Community Corner
1. Atmo's minimalistic Mammoth Hydra APS Calculator:
https://dl.dropboxusercontent.com/u/22021340/mammoth_hydra_aps_calc.html

2. Lance's spreadsheet to optimize gear for the 3.333 aps breakpoint:
https://docs.google.com/spreadsheets/d/1aenrXa9_Ifij7ZXdSeJ2zcX1y2GZizPBlF_PtGqujto/edit#gid=0

3. BDF's hydra mechanic post:
http://us.battle.net/d3/en/forum/topic/17346364984


APS Breakpoints for Unruned, Arcane, Lightning, and Blazing Hydra (1/14/2015)
min aps ... max aps ... fpa .... hydra aps
============================================
xxx ....... 1.045 ..... 78 ..... 0.769
1.045 ..... 1.139 ..... 72 ..... 0.833
1.139 ..... 1.251 ..... 66 ..... 0.909
1.251 ..... 1.388 ..... 60 ..... 1.000
1.388 ..... 1.558 ..... 54 ..... 1.111
1.558 ..... 1.775 ..... 48 ..... 1.250
1.775 ..... 2.062 ..... 42 ..... 1.429
2.062 ..... 2.462 ..... 36 ..... 1.667
2.462 ..... 3.053 ..... 30 ..... 2.000
3.053 ..... 4.017 ..... 24 ..... 2.500
4.017 ..... 5.871 ..... 18 ..... 3.333
5.871 ..... xxx ....... 12 ..... 5.000

Unruned, arcane, lightning, and blazing hydra share the same breakpoints among themselves, which is slightly different than Mammoth. The numbers are right now theoretical. I did a quick check on a few of the breakpoints for each rune and they align correctly. I know some of you wanted these numbers as soon as possible, so here they are. I'll do a complete verification later. I left Frost hydra out because tracking their attack was a bit unclear.


Defining aps (attacks per second)
There are various types of aps so let's take a moment to clarify what each type means.
1. Weapon aps: your weapon aps with no increased attack speed modifier.
2. True weapon aps: calculated weapon aps with increased attack speed modifer.
3. Character aps = This is a rounded aps value shown in Details (in game UI)
4. True Character aps = A more accurate version of Character aps done by calculation
5. Pet aps = This is just your True Character aps with the buff from TnT.

So if you don't have TnT gloves, then your aps is the "True Character aps." If you have TnT gloves, then your aps is your "Pet aps." Clear as mud? Use that aps to check the breakpoints.


True Weapon aps
True Weapon aps = weapon aps + (increased attack speed on weapon *
weapon aps)

So let's say you had a sword (1.40 aps, weapon aps) with an "increased attack speed by 7%" modifier on the weapon.
True Weapon aps = 1.40 + (7/100 * 1.40)
True Weapon aps = 1.40 + 0.098
True Weapon aps = 1.498 (in UI, it will appear as 1.50)


True Character aps
Your True Character aps is calculated with the following equation:

True Character aps = True Weapon aps + (ias on gear *
True Weapon aps)

So if you had a sword (1.40 aps) and 61% ias on gear (in Details in game UI), your Character aps would be 2.25, but your True Character aps is...
True Character aps = 1.40 + (0.61 * 1.40)
True Character aps = 2.254


Pet aps
Your Pet aps is calculated with the following equation:

Pet aps = True character aps * (1 + (TnT buff / 100))
So a perfect 50% TnT with your character's 2.47 aps would yield...
Pet aps = 2.47 * (1 + (50/100))
Pet aps = 2.47 * 1.5
Pet aps = 3.705


What are breakpoints and why are they important?
Overall, your dps increases linearly with your aps. So if you go from 1.0 aps to 2.0 aps, your dps essentially gets doubled. In the actual game, it doesn't really work out that perfectly. Instead of seeing a linear graph of dps vs. aps, you would see steps or "breakpoints." The reason is because the game is based on frames, which is a unit that cannot be broken down further and must be rounded off. In low aps, it doesn't really make that much of a difference, but as we get higher, the changes become a lot more significant.


Verification of breakpoints
A burn test was done to check my sanity in a real game (not just theoretical math) with actual damage numbers. This is as raw as you can get, but I don't have perfect setup and it contained a little cc/cd.

The test was done with Mammoth hydra. The damage for this type of hydra ramps up upon cast and after around 5 seconds, at 4 aps, the damage output plateaus/stabilizes. To improve accuracy, we are going to use those stabilized damage values until hydra stops.

1. 4.0219868 aps -> 18.187 million dmg
2. 4.027321 aps -> 18.227 million dmg
3. 4.0326552 aps -> 24.406 million dmg
4. 4.0379894 aps -> 24.096 million dmg

The delta jumps are 0%, 34%, -1%. Can you guess where the breakpoint is? There should be a breakpoint between 4.027321 and 4.0326552. The chart says yes at 4.031354983. The chart also says at that specific breakpoint, we should expect to see a big dmg jump of around 33.33333% (from 18 to 24 fpa), which we do. Yes!!


FAQ
1. Does TnT and ias gear items work on Mammoth hydra?
Yes, this has been fixed.

2. If you use the stretch time bubble, do you or the hydra have to be in the bubble?
Only you have to be in the bubble to get the ias buff (hydra doesn't have to be inside)

3. Will "snapshotting" work with the stretch time bubble? So if you originally cast hydra in the bubble and then step out, will it snapshot the ias buff?
No. Hydra does not snapshot with Stretch Time. The damage is dynamic, so once you leave the bubble, the hydra reverts back to your lower ias.

4. Is the Zei's legendary gem distance buff based off the player or the hydra?
The distance buff is between the hydra (not player) and target/mob. Despite the limitation, Zei's is still one of the best leg gems for this build.

5. Does the Enforcer gem work with hydras?
Yes it does, but the buff stacks additively on elemental (fire) % dmg. So while it does give extra damage to your hydras, it won't be as good as zei, BoT, or BoP.

Enforcer vs BoP: http://us.battle.net/d3/en/forum/topic/15700027834

6. How long does the fire trail last?
The trail last for four seconds.

7. Is the "increase hydra damage %" on gear additive or multiplicative?
Hydra damage % is multiplicative. Typically, the skill % affixes are additive on gear, but pet damage % is multiplicative across all classes and hydra is no exception.

8. What does additive and multiplicative mean?
This just describe how the bonuses increase with another bonus. Multiplicative is generally better than additive. So let's say you have gears that give you an increase of 10%, 15%, and 20% of a skill.

Additive:
100% + 10% + 15% + 20% = 145%

Multiplicative:
100% * 110% * 115% * 120% = 151.8%

9. I hear the term "AD snapshotting hydra." What does this mean?
This simply means that once you get 5 stacks on Arcane Dynamo (AD), you can drop a hydra and it will always get the buff for the life (15 sec) of that hydra. If you recast another hydra (not 5 AD) that replaces the buffed hydra, then the buff is gone. If you have a Serpent Sparker, you can get 5AD, cast hydra, get another 5AD, then cast another hydra. Now both hydras have the AD buff.

10. Does hydras proc tal meteors?
Yes. Early in PTR, it did not, but this was fixed.

11. Why do a lot of people use Mammoth hydra with the new tal set?
-Hydra damage % can be found on multiple sources: shoulders, chest, and old tal source. And it's multiplicative.
-They benefit greatly from ias breakpoints with ias on gear and TnT bonus
-The damage can be "doubled" with a Serpent Sparker
-Works well with gems like Zei
-Works well with Arcane Dynamo
-Mammoth hydra generally does a lot more damage than the other hydras
-Leave-n-forget damage, so no channeling, no constant clicking, can be placed in danger areas without you being there.
-Hydras are pets, so no reflect damage


Group play and achieving the 4.031 breakpoint
BDF has included some math on how players can attain the 4.031 breakpoint for group play. I copy/pasted his writeup below.

You have both 100% uptime on BBV (20% IAS) and Crusader Law (15% IAS).

The breakpoint calculation works out as follows:

Weapon APS: 1.4
Weapon IAS: 7%

Tasker Bonus: 50%

20% IAS BBV
15% IAS Law
10% IAS Paragon
35% from gear, gems, and skills

(1.4 * 1.07) * (1.5) * (1 + (45 + 35)/100) = 4.0446 (4.032 is the breakpoint)

There are a few ways you can get to that breakpoint without having perfect gear, the extra attack speed from a Gogok gem (15%) or stretch time (10%) can make up for not having perfect 50% tasker or not having perfect 7% rolls everywhere, but you'll always be trading DPS for it.

Optimal gear looks like this:

Weapon: 7% IAS, 10% dmg ancient sparker
Bracers: 7% IAS, lacuni or strikes
Chest: 7% IAS, tal chest
Gloves: 7% IAS Taskers (with 50% pet speed)
Ring1: 7% IAS, 6%CC, 50%CD, Socket Focus
Ring2: 7% IAS, 6%CC, 50%CD, Socket Restraint

If you have the above pieces you will always be at the top breakpoint without having to use a gem or skill to get there, provided group buffs are active.

Being below the top breakpoint is a 33% damage loss from hydra, which does the vast majority of your DPS.
Nice!

How does a wiz get to 5aps? :>
so, need 2.47 base aps with 50% taskers to hit the bp...
11/19/2014 08:19 PMPosted by Ryoka
How does a wiz get to 5aps? :>

I used legacy gear and TnT.
serpent sparker with 7% ias -1.498 aps
x
1.5 taskers
x
7% rorg
7% lacuni/steady strikers
7% witching hour
7% gloves
10% paragon
7% tal chest or mempo or andy's
+20% big bad voodoo
OR
10% stretch time
gogok of swiftness

should get you to 2.47 aps.
I have 49% TnT, so I need 2.48 APS to reach the 3.69 APS breakpoint? I doubt that's realistic.

The 2.53 breakpoint requires 1.7 APS, which is super easy.

Thanks for the chart! :-)
I never considered Gogok.....interesting.
11/19/2014 08:32 PMPosted by KhalARon
I never considered Gogok.....interesting.


Need a good proc skill to get it going though. Options are AT, energy twister, Forked Lightning. Even at rank 50 (100% chance) it goes off proc co-efficient. apoc has abysmal proc rate.

Btw..Pain Enhancer + Gogok ..just saying ;) That will free up some AS required slots and it works well with the new densities. Also good for solo non-WD/Sader groups.
nah. what you want is arcane dynamo fueled hydras. so you will be using magic missile for sure.
11/19/2014 09:37 PMPosted by kokopuffs
nah. what you want is arcane dynamo fueled hydras. so you will be using magic missile for sure.


Oh that's right, with MB duh thank you and thanks Kiza the great for the BPs!
Your breakpoints make no sense.

You're suggesting that hydras follow speed coefficient 6 scaling, yet only get 1.25 attacks per second at 1 aps. It's more likely that you're just not catching the smaller increments in between.

For what it's worth, I'm fairly sure the speed coefficient is either 1.25 or 1.33. I haven't gone back to retest to find a confirming BP for either (1.4 vs 1.41 should determine which). I've been speed testing with Arcane Hydra but all appear to use the same speed factor although I haven't explicitly tested on all runes to confirm universal base speed yet.

I didn't continue testing because I doubt very much that these rates are going to remain in place for the final patch. In which case, mass testing and mechanical breakdown are kind of pointless at this time.

-dolynick
Yah after more testing the BPs are actually inaccurate. I gain hydra frames going from 2.14 to 2.23 APS on character
11/19/2014 10:49 PMPosted by MasterJay
Yah after more testing the BPs are actually inaccurate. I gain hydra frames going from 2.14 to 2.23 APS on character


Well... IF it's actually using 1.25 coefficient then the breakpoints he did post are all real, but a very incomplete list. There will be 4 breakpoints for each step range he listed.

There is a good mathematical case for it using 1.33 coefficient as well.

It's late and I'm not going to calculate and list complete breakpoint charts for both speed coefficient right now.

I also believe that built in delays and/or time limits is going to prevent the full damage of any breakpoint from realizing in game. The pattern of progression will be there, but there is typically some randomness in the final number. I'm already seeing this in my data collection so far. I'm also seeing some other strangeness in the progression too that doesn't mesh with expectations either. Delays may account for that, but I'm not satisfied with that explanation yet.

-dolynick
I am almost perfectly certain this won't make it to live, at least on Mammoth. The FPS ravage is real.
We've survived Lightning DH. I think we'll manage this too.
And yet, in this very same patch, Blizzard is taking Lightning M6 behind the shed and putting a depleted uranium shell in its head.

Blizzard also destroyed the best rune any skill ever had, AT: Cascade, because it wrecked computers. (Seriously, getting a simultaneous barrage from 20+ enemies killed in 1 shot was the greatest).
They didn't destroy Lightning DH because of the lag it caused. They destroyed it because you could be invincible for 1+ minutes, among other things.

Honestly I haven't noticed much slowdown, but I'm not running in a 4 Wiz party either.

So, if they nerf it... well, whatever. Wizard will be total garbage unless they hugely buff the damage (hey, we're garbage anyway compared to Monks and DH).
highly confident the server lag was a big reason it was fixed. otherwise they would have just nerfed nightstalker.
Yep stack Pain Enhancer with Gogok and it's game over frame rate. This isn't making it live, it's basically like M6 on live all over again. Although I must admit getting 37+ trial keys solo is pretty cool, so this is how it feels like to DH XD
11/19/2014 11:19 PMPosted by dolynick
11/19/2014 10:49 PMPosted by MasterJay
Yah after more testing the BPs are actually inaccurate. I gain hydra frames going from 2.14 to 2.23 APS on character


Well... IF it's actually using 1.25 coefficient then the breakpoints he did post are all real, but a very incomplete list. There will be 4 breakpoints for each step range he listed.

There is a good mathematical case for it using 1.33 coefficient as well.

It's late and I'm not going to calculate and list complete breakpoint charts for both speed coefficient right now.

I also believe that built in delays and/or time limits is going to prevent the full damage of any breakpoint from realizing in game. The pattern of progression will be there, but there is typically some randomness in the final number. I'm already seeing this in my data collection so far. I'm also seeing some other strangeness in the progression too that doesn't mesh with expectations either. Delays may account for that, but I'm not satisfied with that explanation yet.

-dolynick


Oh okay that makes more sense and yah I believe the delays are preventing the damage stacking from being too out of control with FB, although I did see a 538M dmg tick but that was a rare exception on a RG.

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