[Mad PTR Theorycraft] No Crit Chance WW-RLTW

Barbarian
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02/26/2015 03:34 AMPosted by Cayenne
There is definitely no internal cooldown in the effect.
You da real MVP.

02/26/2015 06:51 AMPosted by page
the big question is: do dots that do not visually crit count as non-crit attacks?
As DieHard mentioned, everything that ticks for LoH, also ticks for crits...except that it isn't shown on each tick number...because it would be incredibly spammy.

Quickly digging Nubtro's mechanics, here are the ticks per secondd of other DoT skills:
- Avalanche [Volcano]: 25 ticks over 5 seconds = 5 ticks per second
- Avalanche [other runes]: 10 ticks over 3 seconds = 3.33 ticks per second
- Earthquake [all runes]: 16 ticks over 8 seconds = 2 ticks per second

The only exception is Rend / PE / Toxin, which use the formula: 1 + (CC * CDam/100)

They should also be greatly boosted by running the ring because you'd be passively recasting PE / Toxin and actively casting Rend while the buff is up.

The difference between 50% CC and 100% CC for them at 400% CDam:
50% CC multiplier stays at: 1 + (50% * 4) = 3
100% CC multiplier stays at: 1 + (100% * 4) = 5 [66.67% damage increase]

That ring will obviously be BiS for RendWind builds.
02/26/2015 07:47 AMPosted by Samir
Zodiac will be given the Ess of Johan treatment - in ROS PTR, Ess of Johan had neglibile internal cooldown, it was literally insane. With today`s Raekor, you woud use that amulet with frenzy and mirinae 10 times out of 10 and drop ground stomp.
Zodiac is (or will be) as restricted as Taeguk when it comes to getting the procs.

What I'm saying is...it scales with sheet attacks per second so Frenzy's 75% IAS won't work and neither will WW's insane spending per second. The formula probably is: 1 / attack speed

So...considering everyone runs 2Hers, best case scenario would be 1.5 attacks per second...which means 0.67 procs per second, or 2 procs every 3 seconds, or 29.85 procs per WotB.
Um yeah, anyone else remember the 1st Taeguk?

Remember alk using a level 117 taeguk and fire whirlwind and just melting everything in GR40?
02/25/2015 10:30 PMPosted by Eduw
There is a 77.38% chance that 5 consecutive hits won't Crit.

May I ask where that number comes from? Each hit has a chance of 5% to crit, so why would that change for 5 hits in a row? The chance to not crit is always 95%.
02/25/2015 10:30 PMPosted by Eduw
There is a 77.38% chance that 5 consecutive hits won't Crit.

May I ask where that number comes from? Each hit has a chance of 5% of being a crit, so why would that change for 5 hits in a row? The chance to not crit is always 95%.


because it's consecutive Crits, so your 95% is on initial, 2nd is ~47%, 3rd is ~23%, 4th ~12% and 5th ~6%.

Then you average it out to ~36.8% to not Crit 5 times in a row.
huh?

0,95^5=77,378%

You have a 95%chance that you miss the first, and a 95%chance to miss the second, so to miss them both, you have 95%*95%
edit.. forget it, i was wrong, it's indeed 95%^5
LOL I did the math while playing poker, where you get less cards every hit. Sorry my bad.
It's a matter of Binomial Probability. I'll try to explain:

You are looking at 5 consecutive hits at 5% chance, so you can't look at them alone.

So the chance of getting 2 consecutive non-Crits is: 0.95 * 0.95 = 90.25%
Likewise, getting any extra non-Crit is a simple matter of multiplying by another 0.95

Basically, the formula for X consecutive non-Crits is: [1 - %CC]^x

At 5, 6 and 7 the odds are: 77.38%, 73.51% and 69.83%.

Tt's not that big of a difference at really low CC, but it becomes harder the more CC you have

Example with 30% CC:
At 5, 6 and 7 consecutive hts the odds are: 16.81%, 11.75% and 8.23%
02/26/2015 08:57 AMPosted by page
huh?

0,95^5=77,378%

You have a 95%chance that you miss the first, and a 95%chance to miss the second, so to miss them both, you have 95%*95%


Another example is "Compound Probability". Like Eduw was saying , it's all math. You can liken it to "diminishing returns".
02/26/2015 04:38 AMPosted by page
hm ... 1,54 aps 4 nados out at 5 ticks per s + ww 5 ticks per s -->25 ticks/s
at 18%CHC with 37% to non-crit 5 times

-->0,28s downtime for single target

Yep working as intended. And nerf inc :p
I think it's the other way around.

0.20 sec (time to get 5 hits) * [1 + 0.63] = 0.33 seconds

Haven't really created the real logic yet but the counter-logic is:
If we multiplied the chance to non-crit (instead of the chance to crit), having lower chance to non-crit would be more beneficial when it's actually the other way around.

Example with 5% Crit (77.4% NC vs. 22.6% Crit) and 1 second to get 5 hits:
Using NC: 1 * 1.23 = 1.77
Using Crit: 1 * 1.77 = 1.23 <--- better because of higher NC chance

Example with 18% Crit (37% NC vs. 63% Crit) and 1 second to get 5 hits:
Using NC: 1 * 1.37 = 1.37
Using Crit: 1 * 1.63 = 1.63 <--- worse because of lower NC chance

Minor calc stuff...I'm just bored.

On a side note for people playing on Live:
If you find items that could be good without %CC, hoard them just in case.
All of the math about the chance of 5 consecutive non-crits aside, what other ring options are going to compete with this slot?

This ring is very powerful, and allows you to gear entirely away from crit chance. There are a bunch of other rings that are also strong though and need testing, but after sleeping I'm in a 3 hour queue to create a game.

Personally I want to find out tick rates and damage potential of the arcing rings.
Obsidian Ring of the Zodiac, for sure.

Cooldown reset is the most overpowered perk in the game and Devs are insane for bringing it back. There is a monk streaming (twitch.tv/quin69) with 5% CC + Broken Promises + CDR + Zodiac for permaSerenity and high crit chance.

I feel barbarians can do the same thing but better (except for no invulnerability).
Just imagine running with the following:
- Permanent Ignore Pain (replaces Unity 50% DR)
- Permanent WotB with all runes (should easily replace SoJ in damage + 50% DR too).

It's sort of the perfect combination because Zodiac requires spending resource and a WW-RLTW is non-stop resource spending.

If you find one, make sure to report back with how well it scales with WW channeling or increasing attack speed from low (like 1.0) to average (1.5 - 2.0).
Obsidian ring definitely sounds promising. I'm watching Quin while I wait for my game queue.

In the other thread discussing the IK revamp, a few people were suggesting the obsidian ring could make the 6 piece bonus completely void in a whirlwind/sprint build. That sounds really promising since it opens up so many options for the IK set, like furnace and taskers which completely outclass the IK weapon and gloves.

It does also make blizz adding a 6pc almost completely pointless though.

There's also the skull grasp ring to think about, and soj and unity are still strong rings too, but broken promises + obsidian right now sounds the strongest.

Just need to create a damn game...
lol fail at greater rift 49 @ http://youtu.be/DcN1txo9Vpk

TT :(

Will maybe try more tomorrow with a better optimized build...
Was gonna say that Ancients survivability is great but then I looked at your Toughness.

Still...since WC is barely recasted and CotA unless they die, my suggestion is dropping 6pc IK + RoRG for Zodiac and try getting permaWotB from resetting it.

Good side is that you'd be able to either run TnT + 2pc Aug or 3pc Aug.

Oh! Yea...the more CDR stacked, the easier the reset should be...but you would probably lose some significant Toughness. A difficult trade-off.
02/27/2015 07:34 PMPosted by Eduw
Was gonna say that Ancients survivability is great but then I looked at your Toughness.

Still...since WC is barely recasted and CotA unless they die, my suggestion is dropping 6pc IK + RoRG for Zodiac and try getting permaWotB from resetting it.

Good side is that you'd be able to either run TnT + 2pc Aug or 3pc Aug.

Oh! Yea...the more CDR stacked, the easier the reset should be...but you would probably lose some significant Toughness. A difficult trade-off.


In my current implementation of the build, i'm already running with TnT instead of HS.

I will try what you are suggesting, changing from 6set IK to 4set IK for (still) perma WotB by the help of the Zodiac ring..

Which will allow me to run TnT gloves + HS.

But i need to test if its even doable to get perma WotB with my lowish CDR..

Which bring me to my next point, even if i can manage to sustain perma WotB, iam not sure its worth it..

The trade-off is basically: (if i even can sustain it, and thats big if)

+30% physical damage VS 15% elite damage reduction + 15% elite damage (and this is the only +elite damage i have)

170/140 = is only a 21% damage increase.

Guess it could be more worth it if i had my ancient furnace on the ptr, but old snapshot import made me lose it..

*edit*

Just tested this.. And it seems you need atleast 45% CDR (in inventory) to make this work consistently..

In my ~20% CDR build , i was able to get the WotB cooldown to almost half before it ended..

Gonna leave the testing with this, for someone with a higher CDR optimized build. (already running low on mats from all the rerolling:)
I've posted it already somewhere, but since your post is more detailed than the other guy's post who just predicted that the ring will be nerfed, I will post it again here.

You want theorycraft? Lemme bring the math behind this ring.

Step 1: find average number of attacks to trigger.
We are essentially interested in the distribution of how many attacks you have to deliver until the effect triggers. A statistic of special interest, as it will decide on the overall efficiency of the build, is the average (mean) attacks delivered until the effect procs.

Let q be your crit chance. Let p be the probability of a favorable hit, that is, a non-crit hit, be 1-q.

Now it just so happens (see http://www.cs.cornell.edu/~ginsparg/physics/INFO295/mh.pdf for details but you could work it out for yourself) that the average hits you have to deliver to get n consecutive favorable hits is:

Average number of hits to trigger = [(p^ - n) -1]/(1-p)

For our specific purpose, replace n by 5. As an example, for a minimal crit chance q = 0.05, and thus p = 0.95, we get Average number of hits to trigger = 5.84.

Now, as you rightfully mentioned, the average time to wait until the effect procs depends on attack speed (rather trivially as we will see), whereas the time of the effect is fixed (3 sec). So more attack speed means more uptime.

Let's see that formally. Keep in mind that henceforth, I talk about averages. Enthusiasts could work out the same things for higher moments, but I propose we stay at a pragmatic level here.

Step 2: find average time to wait to trigger

Let aps denote attack per second. To find the average time to wait, simply divide average attacks by attacks per second:

Average time to trigger ATT = {[(p^ - n) -1]/(1-p) } / aps

From our previous example, say you attack at 2 attacks per second: aps=2, n=5, p=095. Then, on average, you have to wait 5.84/2 = 2.92 sec to have 3 sec of full crit.

Step 3: find the average effective crit chance

To find the average effective crit chance, note that we can separate the cycle in two parts: the effect part and the wait-til-effect part. During the effect part, we have 100% crit for 3 sec, during the wait-til-effect part, we have q% crit for ATT sec (see above for ATT).

the Average effective crit chance (AECHC) is thus:

AECHC = (ATT * q + 3* 1) / (3 + ATT)

Replacing ATT by its above value and q by 1-p, we get:

AECHC = (({[(p^ - n) -1]/(1-p) } / aps )* (1-p) + 3) / (({[(p^ - n) -1]/(1-p) } / aps) + 3)

This simplifies into:

AECHC = (({[(p^ - n) -1] } / aps ) + 3) / ( ({[(p^ - n) -1]/(1-p) } / aps) + 3)

Step 4: Find the CHC coming from the ring

This is simply AECHC - q

A sheet-calculator can be obtained here: http://goo.gl/Xd7Bdz, where you can get create some figures with different APS/BASE crit.
You can also derive the first order condition to find the best crit-to-attack-speed-ratio, which is a non-linear function of attack speed, that is, set

d AECHC / d p = 0

and solve for p. This gets pretty messy, but I'd be interested if someone had the patience to do it (while it is not technically difficult, I don't have the time yet to do this. to your pens, ladies and gents).

What you'll find in general is that with a very low attack speed, the ring has little effect, because the 3 sec of effect is not enough if your attack speed is low. However, the higher the attack speed, the better the ring, for obvious reasons already mentioned.

What would be nice to do is for any APS, find the optimal CHC. This is a cost function, that is, CHC must be costly, else you'll find 100% CHC is optimal, with or without ring. Assume CHC is exponentially more costly as it gets closer to 1, and solve for optimal CHC given attack speed.

Get on with the tables! :)

TL;DR : this ring effectively transforms attack speed into crit hit chance, giving one-handers a small boost, for instance.
@ wiwh

From our previous example, say you attack at 2 attacks per second: aps=2, n=5, p=095. Then, on average, you have to wait 5.84/2 = 2.92 sec to have 3 sec of full crit.


While your math looks solid, you have simply overlooked one simple mechanic for the barbarians specially.. :)

Attacks per second - Ticks per Second - Cycle - Crits to NonCrits Ratio - %ECC

1.00 aps - 15.00 ticks per sec - 3.33 sec - 9.00 Crits per NC - 90% Crit Chance
1.25 aps - 20.00 ticks per sec - 3.25 sec - 12.00 Crits per NC - 92.3% Crit Chance
1.54 aps - 25.00 ticks per sec - 3.20 sec - 15.00 Crits per NC - 93.8% Crit Chance
1.82 aps - 30.00 ticks per sec - 3.17 sec - 18.00 Crits per NC - 94.7% Crit Chance
2.22 aps - 37.50 ticks per sec - 3.13 sec - 22.50 Crits per NC - 95.7% Crit Chance
2.50 aps - 42.86 ticks per sec - 3.12 sec - 25.71 Crits per NC - 96.3% Crit Chance
2.86 aps - 50.00 ticks per sec - 3.10 sec - 30.00 Crits per NC - 96.8% Crit Chance
3.33 aps - 60.00 ticks per sec - 3.08 sec - 36.00 Crits per NC - 97.3% Crit Chance

I don't get it! What does that table mean?!

It means that as you stack attack speed (or find more enemies), it takes less and less time to proc the legendary effect through using WW and 4 RLTW tornadoes...which will make all your subsequent hits Crit.


The key thing to notice here is "ticks per seconds".. We are able to get "30 attacks per second" with a slow 2-hander And thats from rltw alone..

On top of that we have the ww ticks :)

Oh and before i forget to mention it, the (TnT) ancients can also proc this for us, (showing that at the end of the video).

Will end with this little video :)

Diablo RoS 2.2 PTR: Greater rift 50 with pure 100% CC WW/nado build @ http://youtu.be/J6JYD69dxsg

Showing stats + gear and build at the end of the video

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