Diablo® III

Paralysis

95 Undead Priest
4945
Posts: 1,023
If 5% of all lightning damage components stun, how many stuns will I get per cast with Paralysis? The chance to proc seems really low but if you think it through the passive isn't so bad.

Think of a Chain Lightning that hits 6 targets:
[1st hit] [2nd hit] [3rd hit] [4th hit] [5th hit] [6th hit]

permutations for 1 stun:
[hit] [hit] [hit] [hit] [hit] [stun] = .95^5*.05 = .039
[hit] [hit] [hit] [hit] [stun] [hit] = .95^5*.05 = .039
...

odds for 1 stun: .95^5*.05*6 = 23.2%

permutations for 2 stuns:
[hit] [hit] [hit] [hit] [stun] [stun]
[hit] [hit] [hit] [stun] [hit] [stun]
...
[stun] [hit] [hit] [hit] [hit] [stun]
[hit] [hit] [hit] [stun] [stun] [hit]
[hit] [hit] [stun] [hit] [stun] [hit]
...
[stun] [hit] [hit] [hit] [stun] [hit]
...
...
[stun] [stun] [hit] [hit] [hit] [hit]

odds for 2 stuns: .95^4*.05^2*15 = 0.031 (3.1%)
odds for 3 stuns: .95^3*.05^3*20 = 0.002 (0.2%)
odds for 4 stuns: .95^2*.05^4*15 = 0.00008 (insignificant)

23.2% of casts stun once
3.1% of casts stun twice
0.2% of casts stun three times
other cases are insignificant, so assume remaining 73.5% stun zero times.
average stuns per cast = .232 + .031*2 + .002*3 = 0.3
On average, .3 stuns per cast, or 10 casts to stun 3 times.
If I have a high APS, say 3 APS, I can get about 1 stun every second off my signature alone.
Since the stun lasts 3 seconds, in that case I could be chaining about 3 stuns at a time.

Not quite so bad once you begin to think it through. Also remember that other spells that passively add damage components will add more stuns (storm armor, lightning hydra, magic weapon electrify - what about mirror images+mirror mimics that use storm armor? not sure, seems far fetched). So even if I spend more time casting my nuke I'll still approach that kind of CC.
Edited by Zakaluka on 5/11/2012 12:41 PM PDT
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85 Draenei Warrior
6480
Posts: 272
its 8%...
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Posts: 1,048
the new version is 5% to 8% and from 3 seconds to 2 seconds
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95 Undead Priest
4945
Posts: 1,023
Also, best possible attacks per second seems to be around 4.0 for a wizard using a wand+source.

Recalculating for 8%/2sec.
Edited by Zakaluka on 5/11/2012 1:10 PM PDT
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I would but i'm to lazy just getting out of work, it was in the unoffical patch notes (because the official ones only include the stuff accessible in beta). Many people have seen it, and in 4 days you can see for yourself.
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95 Undead Priest
4945
Posts: 1,023
1 stun: .92^5*.08*6 = 0.3164
2 stuns: .92^4*.08^2*15 = 0.0688
3 stuns: .92^3*.08^3*20 = 0.0080
4 stuns: .92^2*.08^4*15 = 0.0005

Average stuns per cast: .3164 + .0688*2 + .0080*3 + .0005*4 = 0.48 stuns per cast.

To chain 3 stuns continuously you'd need about 3 stuns per 2 seconds,

(3 stuns / 2 sec) * ( per cast / 0.48 stuns ) = 3.1 APS. Overall uptime is completely unchanged by that tweak, but the proc is more reliable.

3.1 APS isn't even that godly, since the last beta included affixes that would let you get to about 3.8 APS at level 60.

Maybe too mathy for this board.
Edited by Zakaluka on 5/11/2012 1:23 PM PDT
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95 Undead Priest
4945
Posts: 1,023
oh cool, hadn't even considered shocking aspect. That will fit in quite nicely, thanks.
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Posts: 286
http://us.battle.net/d3/en/calculator/wizard#bUQTPS!VYg!cbYcca

Best stun lock build if mimic can proc paralysis.

Every spell scales with APS so faster you cast the more you stun. (crit is a must have stat)
Edited by Silent#1553 on 5/11/2012 1:46 PM PDT
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Posts: 60
Actually there's an easier way of calculating stun chance. Generally what you're looking for is the chance of getting at least one stun. This is equivalent to the opposite of getting zero stuns:
1-P(no stuns)
The chance of getting no stuns is given by the chance of a single no stun (1-.08 = .92 chance of not stunning) to the power of the number of chances to stun in a time period. For chain lightning it would be to the sixth power since, six targets are hit at once.
1 - (.92^6) = ~39.4%
A good value for attacks per second in the mid-game when you focus on attack speed and crit is about 2 per second, so every second you have
1 - (.92^12) = ~63% chance of stunning AT LEAST one enemy.

So how many stuns can you expect to get in 1 second then? Well an 8% chance to stun means that for every 100 hits, you can expect 8 stuns. If you set 8/100 and x/(#of attacks in a time period) equal and solve for x, you can find out.

Basically if you have 2 attacks/second and look at a time period of 1 second, you'll have 12 attacks:
.08 = x/12
x = 12*.08 = 0.96 stuns per second

Alternatively, you can look at the Expected value for the number of stuns. Given an attack speed of 2/second = 12 attacks to find out about how many stuns/second you could get in the mid-game.
This might require a little more knowledge of probability, but if the events weren't so simple, it'd be the only way to do it. In general, the equation that gives us the probability of getting x stuns is:
f(x) = (12 nCr x) * (.08^x) * (.92^(12-x))
The expected value is defined as:
E(# of stuns) = 1*P(1 stun) + 2*P(2 stuns) + ... + 12*P(12 stuns)
or, more simply E(x) = x*f(x) summed from 1 to 12
If you plug all this into a graphing calculator and sum it up you get:
E(x) = 0.96
also note 0.96 = 12*.08

So, in English, you can expect to get about 1 stun which last for 2 seconds every second. The more you increase your attack speed, the more stuns you can get, obviously.

2 attacks per second would mean you stacked +attack speed gear of
1.4*x = 2
x = 2/1.4 = 1.4285
42.85% which is less than half of the absolute max of +93%
source: http://www.diablofans.com/topic/41045-spoiler-diablo-iii-item-affixes/#entry863921

I'm not sure if there aren't going to be any more flat +attacks per second affixes any more. If that's the case, then the usefulness of paralysis endgame isn't going to be all that great, the max # of expected stuns would only be about 1.3 per second. But, if the data for the +attacks per second affix are missing, then paralysis could actually be extremely useful, if both affixes were stacked.
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85 Human Death Knight
6025
Posts: 98
^^^^^^^^^ /thread over! math was actually understandable, good job explaining and not posting a 45 line equation for me to try and follow.

very nice thread to browse, thanx for everyones input here

i had not learned of the 5 to 8 and 3 to 2. i find this to be a very helpful change

edit: oh also, silent, that build is kinda wonky :P lol, you can do better than a "looks good on paper, could chain stun in theorycraftland!" build. i believe in you.
Edited by SolDojo#1716 on 5/11/2012 2:25 PM PDT
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90 Worgen Warlock
10385
Posts: 435
05/11/2012 12:43 PMPosted by Purelust
its 8%...


last beta patch increased it
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95 Undead Priest
4945
Posts: 1,023

I'm not sure if there aren't going to be any more flat +attacks per second affixes any more. If that's the case, then the usefulness of paralysis endgame isn't going to be all that great, the max # of expected stuns would only be about 1.3 per second. But, if the data for the +attacks per second affix are missing, then paralysis could actually be extremely useful, if both affixes were stacked.


Thank you for the general forms of the equations. Your example of:
E(# of stuns) = 1*P(1 stun) + 2*P(2 stuns) + ... + 12*P(12 stuns)
.. this is exactly how I did it, on a per-cast basis (6 hits), neglecting cases 5 and 6 because they go below a threshold for sig figs where they become negligible. It's been a long time since I read anything about statistics, so I appreciate your insights as far as simpler ways to solve the problem.

I wanted to know how fast I'd have to spam CL with no electrify procs to keep 3 targets stunlocked. I'm pretty sure our results agree. Interesting result is that the change (from 5 to 8%, from 3 sec to 2 sec) had almost no impact on its actual effectiveness for chain lightning.

As far as raw APS affixes, the most recent beta patch still had them in its datafiles, though only on certain slots (gloves ring amulet weapon I believe). With optimal rolls and all possible haste affixes that'd allow 3.8 APS.

We will see, though. Some computers might not be able to render a 3.8 APS wizard, and blizzard might have had to lower the haste cap to compensate.
Edited by Zakaluka on 5/11/2012 3:33 PM PDT
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Posts: 60
Yeah I did it the long way before I realized I could just use the shortcut, but whatever, it's useful information still. Also Zaka I always enjoy your posts, I'll be sure to add you whenever this here game finally comes out.

3.8 aps hmm

3.8 * 6 = 22.8 hits/second

22.8 * 0.08 = 1.82 stuns per second

That's not bad.

Even if you only got 1.5 stuns per second and assuming that inferno stun durations are at least 1 second or more, with exactly six enemies approaching you could keep 1/3 of them stunned at all times.

Of course this relies on having packs of six or less optimally, and certainly no more than 9 or 10 at a time.

One thing we're overlooking, though, is that weapons can also have up to a 5% chance to proc freezes, stuns, immobilizes and such. It remains to be seen if these procs are mutually exclusive, like a crit/hit/block/dodge table for tankage in wow and would work additively, or if they're independent calculations and therefore less useful. Either way, though, putting in one or two procs like that along with paralysis could potentially make up a crap-ton of cc. Will be interesting.

Release faster.
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Posts: 476
Shocking aspect procs on critical hits your character does, critical hits from storm armor, or critical hits done to you?

And by nearby does if mean near your character or near the enemy hit?
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Posts: 3,240
1 stun: .92^5*.08*6 = 0.3164
2 stuns: .92^4*.08^2*15 = 0.0688
3 stuns: .92^3*.08^3*20 = 0.0080
4 stuns: .92^2*.08^4*15 = 0.0005

Average stuns per cast: .3164 + .0688*2 + .0080*3 + .0005*4 = 0.48 stuns per cast.

To chain 3 stuns continuously you'd need about 3 stuns per 2 seconds,

(3 stuns / 2 sec) * ( per cast / 0.48 stuns ) = 3.1 APS. Overall uptime is completely unchanged by that tweak, but the proc is more reliable.

3.1 APS isn't even that godly, since the last beta included affixes that would let you get to about 3.8 APS at level 60.

Maybe too mathy for this board.


Heh I've been constantly doing these calculations for this exact build for some weeks now. I don't think i'm going to use anything except chain lightning.

Its my hope that one of the craftable sets will have a IAS set bonus. As it stands right now somewhere in the 4.15 APS is all we can really call "theoretical max". At that speed a chain lightning only build is right on the edge of viable. Something along the lines of...

http://us.battle.net/d3/en/calculator/wizard#UdOjSP!VfY!aacaac

Mage helm can give +11% to electrocute as well, so we'd have...

80% * 1.10 * 1.11 * 1.12 * 1.15 = 125.8% weapon damage to up to 6 targets.

Single target damage = 125.8% * 4.15 = 522% per second to up to 6 targets, theoretical max damage per second of 3132% per second.

Generally such a build will have a very hard time taking down a 15m health boss, however farming around for champion/elite packs and the drops that come with it I think it will be greater than anything. No need to worry about AP, no need to aim very much. Just focus on your movement, and your health and keep mobs close together and you win.

Its my hope that an attack speed in the 5-6 range can be done before frenzy alter though. With current known limitations I may just not be able to do enough damage without an AP dump.
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95 Undead Priest
4945
Posts: 1,023
Shocking aspect procs on critical hits your character does, critical hits from storm armor, or critical hits done to you?

And by nearby does if mean near your character or near the enemy hit?


I interpret this to mean your critical hits, and near where the crit occurred.

There are many other distinct possibilities though, as you've noted. When midnight rolls around, I'll.... oooh shiny!

One thing we're overlooking, though, is that weapons can also have up to a 5% chance to proc freezes, stuns, immobilizes and such. It remains to be seen if these procs are mutually exclusive, like a crit/hit/block/dodge table for tankage in wow and would work additively, or if they're independent calculations and therefore less useful. Either way, though, putting in one or two procs like that along with paralysis could potentially make up a crap-ton of cc. Will be interesting.


Oh, there's quite a lot of other things we're overlooking. What about the rest of the lightning spells? How many stuns will storm armor generate? What about hydra, which might possibly get 30+ hits per cast? What about Electrify tied info a wide-aoe attack like arcane orb/nova, or blizzard - how many electrify procs can we expect per second?

A real build and real play might have more lightning-based damage components than our pretend scenario, or it might have less. We will have to see.
Edited by Zakaluka on 5/12/2012 2:46 AM PDT
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I suck at math, but what does it look like if it was a 4 wizard team that opted to use forked lightning instead of chain lightning assume 2/4 of the bolts hit?
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95 Undead Priest
4945
Posts: 1,023
forked lightning is a more complicated case. To decide if it's superior or inferior, you'll have to look at average # of total hits per cast. I don't feel like going into all the gory details because it's far too dependent on positioning, and even more dependent on RNG than chain lightning. You'll have to get a gut feeling for it.

I will say that to be even capable of outperforming CL, you'll have to carry in the neighborhood of 35% crit. We think right now that base crit is 5% against same-level monsters, but we're not 100% sure whether intellect affects crit rate. Either way, that's a lot of gear to make up the difference. Once you get high enough crit you're just going to have to experiment with it.

Now you have to guess whether 5% crit is actually going to be what we have at level 60. I'm thinking it'll actually be a bit higher. I've looked at a few different crit-related things and based on a few of them (stat budget value for +criticalDamage comes to mind) ~30% crit rate seems to be an important value to reach for. If we could only make up those 25% with gear, frost nova, energy shield, that'd stifle a lot of builds or make +crit gear a little too valuable. I'm willing to bet crit rate scales with int a little bit.
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Posts: 60
Whoah, now. Don't the jumps of chain lightning inflict reduced damage? I had read that each jump would do only 70% of the original.

So total damage would be

.8+.8*.7+.8*.7^2+...
or .8*(.7+.7^2+...+.7^5) = 1.55 or 155% weapon damage per cast

That seemed about right to me and acceptable vs .8*6 = 480% weapon damage

I assumed the rune was mainly for proc fishing. I mean if damage isn't reduced you would have almost no reason to cast anything except chain lightning unless it was a strong single target burst spell. Seems op to me. But then again CL is my sig in almost every build.
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