Diablo® III

CM Proc Rate (Testers needed)

Actually, it's worth noting that I used Crystal Shell for 2.59aps (27APoC) and Prism for 1.88aps (17APoC). I was forced to use Prism for 1.88aps as it was the only way to cast twisters without running out of AP, since I had to drop my Chantodo's Will for my Sunkeeper (so 10 less APoC). I probably wouldn't read too much into the difference between the two measurements.
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Here's Ray of Frost with Cold-Blood (similar setup to WW):
Ray of Frost (2.59aps) with 6 Diamond Skin Refreshes --> 27s and 28s
Ray of Frost (1.88aps) with 6 Diamond Skin Refreshes --> 29s and 30s

I dunno though how to estimate the hits per second for Ray of Frost.
Edited by TekkZero#1963 on 1/29/2013 12:37 AM PST
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RoF uses the same tic mechanics of WW with a coefficient of 0.333 per tic for all runes except sleet storm. So with 2.59 APS if you channel it for 6s you should see 33 tics. You can scale it from there.
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That's really weird, since my results between the two attack speeds are almost the same. That then suggests attack speed isn't important for Ray of Frost and it's a constant tick rate. I have to go to bed, but maybe someone else can take a look at Ray of Frost. Else I think I'll have to give that one another try to confirm whether the two attack speed setups result in the same answer.
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01/29/2013 12:40 AMPosted by Loroese
RoF uses the same tic mechanics of WW with a coefficient of 0.333 per tic

So here's what I'm thinking. The things we know...

1) The LoH is not giving us ANY wierd results whatsoever. Its providing the exact amount it should across all spells and across all attack speeds.

2) 1.000 proc spells (none of which are channel or DoT) provide exactly the right amount of APoC return, CM procs, and SA procs. These, unlikely LoH are 'on crit' and not 'on hit'.

3) As per Loroese's earlier testing, as you increase in IAS, the relative number of 'bonus' SA procs lessens.

With these pieces of information, to me it seems reasonable to say the issue is NOT a proc coefficient issue. These are checking out to be accurate in duplicate through the two above tests.

Hypothesis : DoT/Channeled spells are registering too many critical hits due to the nature of 'tick rate' breakpoints clumping them together.

I say this cause it seems certain to me now that this must be an issue of the way critical hits are being registered by DoT and Channeled spells. They don't show yellow, but they do crit.

One possible explanation I can think of for there being too many crits happening would be that for every white number displayed there are 2-4 'ticks' occuring. What if one of these 'crit' they are all consider 'crits' toward the 'on crit' procs? When doing these tests did you guys notice how CM seconds seem to 'clump' together?

Meaning at high attack speeds again a single target its rarely a stream of reliable procs, but instead has alot of droughts and monsoons. I'm thinking perhaps this is because when we're running 2.73 aps its not 6 independent ticks per second, its actually two groups of 3 hits.

For 'on hit' functions this results in 6 hits/s, but for 'on crit' its either 0, 3, or 6 crits/s only. If any of the 3 'hits' in each group crit, all three are consider 'crits' toward CM/APoC and SA.

So if I'm 50cc and 2.73 aps. Instead of 6 * 0.50 = 3 crits per second, its actually more like 3 * 0.875 * 2 = 5.25 crits per second. That would result in 75% more crits than expected. As you gained more IAS or CC however, this 'bonus' amount of crit procs would reduce.

I'm going to have to get the timer out and test this, its not going to be easy, but I think this may be whats happening. Each of the white numbers showing is an even number of 'ticks' that are being grouped together somehow. Thats why we don't see white numbers at exactly 2 times per second and also why we have these crazy breakpoints.

At 2.728-2.999 aps, we get exactly two white numbers per second comprised of exactly 3 ticks each. Then past 3.001 aps we get exactly 5 white numbers every 3 seconds comprised of exactly 4 ticks each. So the white numbers are slightly longer apart, but remains a constant number of ticks each.

This is only a theory. I'll see what gear I can get together to start testing hard on the PTR.

The best testing method I can think of is to use the two channeled spells and APoC. I'll pick runes and gear set ups where the 'expected' AP recover from my base AP/s and APoC return (from the LoH coefficient * CC ) = perfect balance between recovery and consumption.

I can then test to see if it translates to a stable AP pool. If it goes up instead then I'll be recovering much APoC than I should be (and therefore support the link that this is an issue of too many crits, not too many procs).
Edited by Shandlar#1961 on 1/29/2013 2:07 AM PST
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Watching this thread now.

Keep up the good work fellas
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The best testing method I can think of is to use the two channeled spells and APoC. I'll pick runes and gear set ups where the 'expected' AP recover from my base AP/s and APoC return (from the LoH coefficient * CC ) = perfect balance between recovery and consumption.

I can then test to see if it translates to a stable AP pool. If it goes up instead then I'll be recovering much APoC than I should be (and therefore support the link that this is an issue of too many crits, not too many procs).

APoC may not be a good idea. For CM, the coefficients work on the chance of stuff happening. For APoC, they work on the amount of AP you get back. That's a quite different situation.
A while back, I did some tests with RoF - Cold Blood at 1.0APS to see if there was any rounding involved in APoC returns (turns out there isn't). At 7 APoC, I saw returns of 2 and 3 AP (expected 2,333). There was no clumping.
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I'll give you some data when I get online next, I very much like the direction this thread is going.
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As far as I'm concerned, you guys are OP in the theory-crafting and hypothesis-testing. Am bookmarking this thread.

I would hate to lose IAS ^^
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My weapon helps alot with proc rate.
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Okay, a few thoughts on WW:
I did some tests in the very first area of A1, where the zombies stop attacking before they kill you. That's the only area where my crappy gear can survive and monsters still have enough life^^
So, skill setup:
- Archon with reduced cooldown - 100s.
- NO Evocation
- WW
I hit Archon, cancel it immediately and cast WW. I cast exactly 12 of them (arbitrary number) on a single target and wait for my Archon CD to reset. I make sure to wait with each WW cast until I have enough AP, so I don't melee. I'm not using APoC, so it's far from a chaincasting scenario, but it's always 12 twisters total.
For each of those tests I note down how long it takes until Archon is available again.
I'm at 43%CC, did this for 0.63 APS:

0.63APS: 55s -> 45s saved
0.63APS: 48s -> 52s saved
0.63APS: 56s -> 44s saved

The total number of ticks in this case was 96 (12 twisters * 8 ticks/twister). Expected number of crits 41.
So with 41 crits I got up to 52s of cooldown reduction. What the hell? I did the test 3 times because I couldn't believe my eyes.

And when I look at the cooldown animation, there really is a lot of clumping up, like Shandlar suggested. I can see mostly 2, 3 or 4 reductions in a row and then a pause.

I really don't know what to think of this. Further tests suggests that the number of procs is rapidly going down between 0.63 and 0.8APS and then slowly rising again. Still all of my tests up to 1.75APS indicate 3-4 times the number of procs I'd expect.
But because of the clumping, there seems to be a lot of variance which makes it hard to test.

Could anyone check their own testing scenarios with a <0.65 APS weapon (search for grey 2hand hammers)? Just to make sure I've not gone insane.

I'm pretty sure, somewhere at the Blizzard headquarters, there's a bunch of developers gathering around a desk, reading through this thread and then bursting into evil laughter.
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I think we need to be wary of over-interpreting clumps visually. That can lead us down a road with confirmation bias, since humans tend to notice the extremes of even ordinary, random noise. But based on the data we have thus far, I still think the idea is a feasible explanation.

Perhaps we could use a tractable method to see whether ticks tend to be correlated together, such as that if one crits then the others do. Because if this hypothesis were indeed true, then it stands to reason that there might be a non-linear relationship with crit chance, in which the extra crits should scale with: 1-(1-cc)^n, where n is the approximate average number of crits that tend to co-occur. I'm thinking that it might be similar in nature to how Meteor (Liquefy) works, in which the chance for its duration to be increased scales nonlinearly with the number of enemies hit by the initial meteor impact (ie 1-(1-cc)^n, where n = number of enemies hit).

And if this relationship were true, this effect should have the effect of asymptoting at high cc (since there's no way to crit more than 100%). Thus, the disparity would also be much more apparent if someone were using lower crit chance (see below for cc):
*For 50%cc (max possible multiplier would be 2):
n = 2 --> Effective cc: 0.7500 --> 1.5x multiplier
n = 3 --> Effective cc: 0.8750 --> 1.75x multiplier
n = 4 --> Effective cc: 0.9375 --> 1.875x multiplier
n = 5 --> Effective cc: 0.9688 --> 1.9375x multiplier
*For 25%cc (max possible multiplier would be 4):
n = 2 --> Effective cc: 0.2500 --> 1.75x multiplier
n = 3 --> Effective cc: 0.4375 --> 2.3125x multiplier
n = 4 --> Effective cc: 0.5781 --> 2.7344x multiplier
n = 5 --> Effective cc: 0.6836 --> 3.0508x multiplier
Edited by TekkZero#1963 on 1/29/2013 8:27 AM PST
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Wow @@

Powerful thread ! Thanks all of you guys :D now following.
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You guys are nuts. I love it....since I'm a scientist.....but nuts!

Actually, I'm just jelly, and wish I had the free time to test on my own as well. But with kid and wife I find I'd rather be playing....than testing.

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01/28/2013 06:46 PMPosted by atinybug
I can't help but fear this will lead to a nerf of some sort in the future.

01/28/2013 07:54 PMPosted by chrisloup
this topic should be redacted/deleted. it can only lead to bad things

If these results really are specific to WW, my conspiracy theory is that Blizzard put in special case handling for WW procs at the time of the 0.25 --> 0.125 nerf, in reaction to the huge outcry from wizards claiming they were going to quit the game. Rather than admit they were caving in to the reaction from the forums and return the WW proc rate to 0.25, they left it at 0.125 for LoH so we'd think that was the proc rate, but increased the proc rate for other effects so that people would see that CM/WW was still effective and stop making so much noise. I guess we'll never know though, there's no way to go back and do these tests in patch 1.0.3.
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That sounds like as good a hypothesis as I can think of. The best way I can think of testing is to run a series of tests, varying APS and CC. We'd also have to run several repetitions to reduce the varience.

There's also the question of how to carry out the test. Do we use a long fight and cound DS refreshes or use the Archon refresh approach. I'm inclined to use the Archon refresh since it is more consistant across all testing and we can directly count the number of WWs cast and compare with CM procs pretty easily and without as much approximating as we might have to do with the DS method. Also, it works much better at low APS since AP might be an issue for those tests.

I'd still like to see some confirmation on the sig spells to make sure they're behaving as we previously thought.
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I've done a ridiculous amount of testing to establish that my number of Frost Nova casts matches up with an 0.25 WW+CM proc rate over all attack speeds and skill configurations, I put it at d3cmww.com/test_results to prove that the simulator is accurate. I can't say anything about other skills though, WW accounted for around 90% of my procs in all the testing I've done. My simulator is set to 2x CM proc rate for all skills (WW, Chain Reaction, Frost Nova, Diamond Shards), but I'm sure it could also easily match up with the increased proc rate being specific to WW if I tweaked some parameters a little.
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Interesting data point that I got on a work break:
2.59aps with just 26.5CC (did not run out of AP at full wind up due to Prism and Astral Presence) --> Took 35s for 16 refreshes

That means a measured proc rate of 0.2586 or a 2.0688 multiplier! It definitely increased past 2x as I hypothesized it might with low cc. So then we very well might be looking at the clumping artificially raising a character's effective crit chance. Based on this one datapoint (we need more), the clumping seems to predict that ~3 hits are probably correlated together. And that's pretty close to what Shandlar predicted above with it being 3 hits.
Edited by TekkZero#1963 on 1/29/2013 1:20 PM PST
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01/29/2013 01:01 PMPosted by TekkZero
with just 26.5APoC

Do you mean 26.5% Crit? We'll definitely want to repeat the testing to make sure the results are repeatable, probably 3-5 times should be sufficient for an approximation for now.
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@Loroese: Sorry my bad. I meant cc, not APoC. I think the Ghom tests are still valuable from the perspective that we can see how crit chance and attack speed effects these multipliers. From what we know it's either a hidden proc coefficient or what Shandlar is proposing about clumping. I personally find Shandlar's hypothesis compelling since it predicts diminishing returns from crit chance.

And here's some more prelimary proof in favor of Shandlar's hypothesis. I just did the test again at 2.59aps with 67.5%cc and got 19s. That's a measured proc coefficient of 0.2016 or a 1.612x multiplier. Now the multiplier is a lot smaller than my previous tests! And that's what we'd predict from Shandlar's hypothesis of clumping.

Now I definitely want to repeat these tests, but even this preliminary data is pretty exciting. I'll do it 3-4 times each again (hopefully tonight); however, I think we have some evidence now that there is a declining impact if your crit chance is high. This is EXACTLY what we would predict based on Shandlar's hypothesis. What I want to do is see if we can use this to predict the average clumping and if it's consistent across all datapoints.
Edited by TekkZero#1963 on 1/29/2013 1:38 PM PST
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