Diablo® III

Does CM have a hidden multiplier?

So today got me curious. How does critical mass actually work? My understanding is that it lowers the cooldown by 1s per proc. However, is there a hidden multiplier that makes it proc more often?

For SNS wizards, I'm assuming the following formula governs the critical procs with Wicked Wind: crit per second = [number of energy twisters out at full windup]*[tick rate/second]*proc_coef*crit_chance. Now while that sounds good, it seems like the standards SNS wizard (2.73aps/50cc) is only procing 4 crits per second at full wind up:
#of Energy Twisters at full windup = [(2.73-.95)*6] = 10.68
Proc Coefficient = 0.125;
Ticks Rate = 6 per second (for 2.73aps)
Crit Chance = 50%
Critical Procs: 10.68*6*0.125*.5 = 4.0050 crits per second

Doesn't 4 crits seem very low? I'm pretty darn sure we can reduce the cooldowns of spells a lot faster than that. At least by twice that much.
Edited by TekkZero#1963 on 1/21/2013 11:16 PM PST
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You also need to calculate Shards and EB I think. FN too. There are 4 skills that proc.
Edited by novice#1750 on 1/21/2013 11:15 PM PST
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But can that truely explain the disparity.

My understanding is that Shards, Frost Nova, and Explosive Blast are not nearly as good at procing as Wicked Wind (which is a DoT):
*Diamond Shards = 0.125 Proc Coefficient - Which means with 50%cc that's 1/16 of the time it'll generate a proc.
*Explosive Blast = 0.111 Proc Coefficient - With 50%cc that's 1/18 of the time you'll generate a proc per blast (fortunately you get 3)
*Frost Nova = 0.167 Proc Coefficient

If we assume Diamond Shards+Frost Nova trigger once per second and Explosive Blast twice a second, that gives us approximately (0.125+6*0.111+0.167)*.5 = 0.4790 procs per second. That's nowhere near enough to explain how we can generate enough procs to bring our cooldowns down, on say a single elite. So I have to think something else is at work to explain how we can do it.
Edited by TekkZero#1963 on 1/21/2013 11:27 PM PST
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This stuff... you may have to pull Shandlar out of his grave to discuss lol
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i had a shandler sighting i believe today, he was actually runnin a3 i think :)
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LOL, okay hopefully someone has a good idea, like maybe Shandlar or Loroese. I saw that Steve's DPS simulator uses a 2xMultiplier for Critical Mass, which sounds kinda reasonable but I hadn't heard of something like that bought up before: http://us.battle.net/d3/en/forum/topic/7709121181 . The reason I'm curious about it is that if there is a multiplier, it might potentially make skills of ours that have a proc chance greater than or equal to 0.5 become effectively 1.0. And so for example Magic Missile would be as good as most runes of Shock Pulse.
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I just checked if Shock Pulse (Piercing Orb) was really good at procing CM (ie as good as Magic Missle) and it wasn't. So I guess I'm at a loss where we're getting enough procs... :lol
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Yes, CM procs about double what you'd expect using the skill proc rates that have been established by testing LoH. 2.0 is the CM proc multiplier that my simulator uses.

Edited by Steve#1523 on 1/21/2013 11:51 PM PST
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curiosity killed the cat. delete and lock
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I've done this math like 1000 times now. It gets complex cause the number of CM procs effect the number of frost novas you can cast, which effects the number of twisters you can stack, which effects the number of CM procs....etc etc etc.

So in a single target situation for your theory...

CC = 50%
APS = 2.73
Proc = 0.125
Tick/s = 6

You made the assumption that you had 'perm freeze', a nova cast every 1.05 seconds, thus eating 0.95 aps. This is false, because 4 CM procs per second cannot get you Novas that fast.

You can do it guess and check style, I made up an excel sheet to do all the math for me, I just adjust the numbers until 'CM Procs/s Produced' = 'CM Procs/s Required'

So its actually closer to a nova every 1.58 seconds than it is every 1.05 seconds.


Nova every 1.58 = ( 12.0s * 0.85 / 1.58s ) - 1.58s = 4.875 CM Procs/s Required

1 / 1.58 = 0.63 aps
2.73 - 0.63 = 2.1 * 6 * 6 * 0.125 * 0.50 = 4.725 CM procs per second from WW

4.875 CM procs per second means...

Chain Reaction
4.875 / ( ( 6 * 0.85 ) - 1 ) = 1.19 CR casts per second * 3 = 3.57 CR blasts per second
3.57 * 0.111 * 0.50 = 0.198 CM procs per second

1 / ( ( ( 15 * 0.85 ) - 1 ) / 4.875 ) = 0.415 Shards per second
0.415 * 0.167 * 0.50 = 0.035 CM procs per second

0.63 * 0.200 * 0.50 = 0.063 CM procs per second

4.725 + 0.198 + 0.035 + 0.063 = 5.021 CM procs/s Produced.

So somewhere around 1.56/1.57 seconds per frost nova or a ~67% freeze strength vs a single target.
Edited by Shandlar#1961 on 1/22/2013 12:27 AM PST
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Most excellent, I can see where you're going with that Shandlar! :) MANY THANK YOUS. It was having me worried something bizarre was at work for explaining single-target freezing.

One minor quibble though. Wouldn't you need about 5.45 CM/ sec, instead of 4.8? If I understand the idea, you would want something like: (12s*0.85-1.58s)/1.58 = 5.45 CM/sec, instead of 4.8. It doesn't invalidate what you're saying, just that probably it's slightly longer than maybe even 1.58s.
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Yeah, your correct. In my haste I was backward and subtracted the 1.58 seconds of 'elapsed time' after dividing by the seconds for CM procs per second not before.

So long hand would be...

12s * 0.85 = 10.2s - 1.58 seconds elapsed = 8.62 CM procs needed over 1.58 seconds.
8.62 / 1.58 = 5.456 CM procs/s Required.

You are correct sir, my apologies for confusion.
Edited by Shandlar#1961 on 1/22/2013 12:57 AM PST
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Not a problem! I just appreciate you writing it all, as it definitely seems more feasible. I was getting a little worried tonight that I was missing something. And so it just looks like I was assuming an unfeasible refresh rate for the Frost Nova cooldown. If anything this goes to show how tenuous our stutterfreeze really is.

But I should really sit down sometime this week and see what the difference between Cold Snap and Bone Chill really is, since I can see it's actually pretty complicated. If you're casting faster Frost Novas with Cold Snap, that means you're also decreasing the total amount of procs you can use to reduce your cooldowns; thereby, "paradoxically" slowing your Frost Nova cooldown by a bit.
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