Diablo® III

CM Proc Rate (Testers needed)

Awsome, keep up the good work. The results are definitely looking interesting.
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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.

This is insane. You are experience 1000% more procs than expected. With those stats I would have expected at most 6 CM procs, average of 5. Nothing in my hypothesis comes anywhere close to explaining this.

This does support however that it cannot be a proc coeff. problem (or at least cannot be SOLELY a proc coeff. problem) Even if the proc rate was 1.000 you cant get 52 procs out of 41 crits (the statistical chance of getting 52 crits from variance with that gear is extremely minute).
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While I agree it's probably not just the proc rate, it's also probably a character's "effective" crit chance being enhanced. If what you're hypothesis about clumping is true, we'd also expect to see a lot more crits. It's extreme, but probably reconcilable with a bit more testing. The assumption being made is that there should be only 5-6 crits. That might not be true. Instead clumping of crits, due to correlation, could result in us expecting to see a HUGE spike in the number of crits...
Edited by TekkZero#1963 on 1/29/2013 11:33 PM PST
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Okay, this can't be correct. I don't know what it is, but somewhere I must be making a huge mistake.
Seing that APS scaling for RoF should be the same as for WW, I just tried the Archon test with RoF - Cold Blood and 0.63APS.
Resetting the 100s cooldown took me 39 seconds. Yes, I shaved off 61s of cooldown. I was channeling for around 38 seconds (right until the cooldown was reset). That's around 50 ticks. And that's impossible.
Just as an example for one big "clump", going from half cooldown to a quarter took me around 8 seconds. That's 17s saved, which means more than 2 effective crits per second. In a setup that should give less than 2 hits per second.
I did it again and got to 40 seconds.
0.71APS -> 40s
0.76APS -> 40s
0.81APS -> 43s
0.90APS -> 40s
1.00APS -> 46s
1.10APS -> 39s
1.20APS -> 37s

For each of those you can ssume I channeled ~1s less than what it took to reset the cooldown.

Can anyone please do some tests with Archon CD? The results I'm getting are so ridiculous, I need someone to back this up or disprove it.
Edited by apo#2677 on 1/30/2013 5:56 AM PST
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Those resutls are really really really crazy. Probably the least important aspect of your testing, but one that I'm still interseted in, what was your crit chance? Is it still 43% from before?

So far based on this info it seems any dot or channeled type spell is having some very odd interactions with CM or perhaps just the crit mechanic in general is strange for those skills. The clumping theory doesn't quite fit either, at least for the low APS results. The only thing that I can think of would be there are more damage tics occruing that we expect from the LoH mechanics, but that doesn't make sense because that would make it inconsistant with LoH. It also doesn't explain why higher APS would give different results, but figured I'd mention it in case anyone can use the theory for anything.
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Yes, CC was still 43%. And yes indeed. It's so f'ed up, I don't even know how to proceed.
You are right, clumping can't account for all of this. I actually got more CM procs than hits. In this scenario, RoF is even much further off than WW.
So there must be something completely wrong with either the test or our current understanding of game mechanics.

I guess I'll try some Disintegrate next and vary a bit with my crit chance. And I think I'm gonna build in SA somewhere. See if there is a correlation between SA procs and CM procs.

But to be honest, I'm kinda giving up already. There are endless possibilities of what we could test. And as long as we don't have at least a hint on what to look for, that's gonna take ages. The approach worked for LoH/breakpoint tests, but that was just one variable, 6 seconds per test, no variance in results and then putting two numbers in an excel sheet. Done. Next.
Now this mess right here is much more complicated. More variables, variance, longer tests, different test setups, stopwatching/videos. It's a crapload of effort for searching the needle in the haystack.

So yeah, I would greatly appreciate any theories or ideas for better/simpler testing methodology.
Edited by apo#2677 on 1/30/2013 6:21 PM PST
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I really can't think of anything to explain how you can get more CM procs than LoH tics. As I said, the closest thing that comes to mind is that maybe the crit/damage tics are different from the LoH tics, but even that doesn't really make any sense because the displayed damage for low APS WW is not every 0.5s like with faster APS. If it were simply the case of like 10 tics per second, we would expect to see the damage displayed every half second. Instead, at low APS you only see like 8-10 displayed numbers for the 6s duration.

So I'm completely lost, and I don't really have much time to devote to it either. I'm willing to entertain just about any theories people might have but right now I don't have any that make any sense.
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So what do we think then? I'm pretty confused by all this myself. The most we can do to piece this together is probably to vary things slowly from very low cc to high cc while holding aps constant. And then try vice-versa. We should also try both the Archon and Ghom test, since it's worth seeing the difference of full windup versus just a few twisters. Unfortunately, this seems like a lot of work. I'd be happy to help do a lot of the testing, but I don't think I'll be able to commit for at least a week due to RL being very busy.
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In the absence of any theory to prove or test, the best we can do is collect data and determine an empirical fit of some kind.
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I'm no expert in the maths and the only testing outside the norms I've done are with ET/CC - but I think y'all are missing the FPT rates that must differ from WW than it does with RoF, everything can't be the same.

FPT = Frame per tick, which would have an effect on overall CM calculations. For a better understanding of that formula just look at the RLTW nados which work in the same manner. Bottom of the first thread explains FPT (that differs from ticks per second): http://us.battle.net/d3/en/forum/topic/6037344497

Just a guess, could be absolutely baseless.
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that could make sense since rltw is supposed to be similar to wicked wind
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Isn't that RLTW info basically exactly the same as the WW breakpoint info, just with different speed coefficients (2 for WW, 3 for RLTW)? The point is that if we look at the number of LoH tics and factor in Crit chance, we're seeing much more CM procs than we expect. In some cases 10 times the number of expected CM procs to the point where we see as many or more CM procs than the number of expected crits (for WW at least).

RoF has the same LoH mechanics as WW provided you channel it the entire time (i.e., speed coefficient of 2, meaning it approximately follows TICS = 2*APS, which is the same as WW, just with breakpoints).

The other issue with comparing WW to RLTW is RLTW actually scales in damage with higher APS. In other words, doubling your APS gives you double the effective damage per tornado. For WW, raising your APS does nothing to the actual damage per WW cast. In other words they're slightly different dot effects.
Edited by Loroese#1415 on 1/30/2013 11:22 PM PST
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@Loroese: Actually, the breakpoints are different for RLTW and WW due to frame length differences. That's why I asked earlier about Ray of Frost, since I don't know if we know exactly what the tick frame length is. So MasterJay's point is exactly what I was worried about and I appreciate him bringing it up.

Estimation of Ticks for RLTW:
Tick frame length = (20 / aps); rounded down to the nearest whole number
Number of tornado ticks = (180 / frame length); rounded up to the nearest whole number

Estimation of Ticks for WW:
Tick frame length = (30 / aps); rounded down to the nearest whole number
Number of twister ticks = (360/ frame length); rounded up to the nearest whole number
Edited by TekkZero#1963 on 1/30/2013 11:52 PM PST
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Yeah, that's because they have different 'speed coefficients'. WW and RoF have the same speed coefficients though, so they should behave exactly the same.

The speed coefficients are all listed here: http://eu.battle.net/d3/en/forum/topic/5208511084

To compare WW to RLTW, at 1 APS WW has 12 tics over 6s or 2 tics per second, thus the speed coefficient of 2. RLTW has 3 tics per second so it has a speed coefficient of 3. RoF speed coefficient is also 2 though disintegrate is 3.
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Thanks, I was wondering about that. So if I understand it correctly, then the speed coefficients are just a different way of describing the tick frame length: 20 frame length is a speed coefficient of 3, 30 frame length is a speed coefficient of 2, and 60 frame length is a speed coefficient of 1. So things like RLTW, WW, Arcane Torrent, Disintegrate, Archon Beam, and Ray of Frost should all generally follow the same rough formula for estimating breakpoints. However, if I understand it, this mechanic isn't used for Meteor, Blizzard, or Spectral Blades which are instead fixed tick rates.
Edited by TekkZero#1963 on 1/31/2013 12:27 AM PST
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Pretty much. I'm not sure quite how the speed coefficient applies in those equations. I guess it's something like TFL = floor(60 / Speed Coef / APS) and number of tics is Ceil(60 * Dur / TFL), where floor rounds down to the nearest integer, ceil rounds up, and Dur is the duration. I think those work out to the right numbers.
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Yeah, that should be correct. I'm glad you brought up the speed coefficients, since I wasn't quite sure how to interpret the speed coefficients in light of what we subsequently learned about the wicked wind breakpoints. Now it seems pretty straightforward. :)
Edited by TekkZero#1963 on 1/31/2013 1:17 AM PST
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01/30/2013 06:52 PMPosted by Loroese
I really can't think of anything to explain how you can get more CM procs than LoH tics.

01/30/2013 06:19 PMPosted by apo
But to be honest, I'm kinda giving up already.

Yeah... I got nothing. This is seriously blowing me away here fellas. My theory was based on my understand of the functionality of WW from 2.5 to 3.0 attacks per second. But my clumping theory would create almost a Normal Curve.

My hypothesis can't come anywhere close to explaining this. In fact, its completely destroyed by this. There should be no clumping whatsoever below 1 attacks per second. There is plenty of time for each tick to be calculated individually.

Therefore I would have expected the relative number of 'extra' crits vs 'expected' crits due to clumping to be 0 or extremely small at 1 attacks per second, then slowly increase as you approached 2aps. Peak at some point from 1.8 to 2.2 aps, then (relatively) reduce as you approached 3 aps. The absolute number of 'bonus' crits would increase as you increased in aps, but relative to 'real' crits would slowly reduce due to the fact that crit chance can't exceed 100%.

Expect Apo has just shown that somehow crit chance has exceeded 100%.

There is only one possibility here. At very low attack speeds the game must somehow subdivide ticks. It must split the damage, and the 'hit' effect into several 'half ticks' or 'third ticks' that provide 50 and 33% of the normal LoH. I'm thinking this is in a similar fashion to how one cast of electrify is actually two bolts for half of its damage each.

The chances of actually being able to prove any of this with a reasonable margin of error is such a daunting task however.

Apo, I don't have a low IAS grey weapon. When you are using RoF at 0.63 aps, how quickly do the white damage numbers appear? It should only be 1.3 'hits' per second, but I've never seen white numbers appear any slower than 1.5 per second. If it somehow appear faster that 1.3 times a second, then each white number would represent less than 1 tick.
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My tickrate calculations are based on the formulas as described in the RltW thread. A while back, I built my own google docs spreadsheet for this stuff. If you are interested:
You can make your own copy of the sheet, but you can't download because the magic is happening in a bunch of javascript, not Excel compatible formulas. It's really slow and sometimes randomly dies. But it's the best I got.

That being said, no, the well known APS scaling mechanics are not a valid explanation for what we're seing here.

Damnit, you are right. How could I not see this? The damage values keep popping up every half second. Well, almost. I counted 77 damage ticks in 40 seconds. At 0.63APS.
So I guess it's possible that this unholy fixed interval summing up of damage is screwing with us.
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Okay... Well, it doesn't scale properly with crit either.
I got my CC down to 15% and got 55s at 0.63 APS.
My initial tests at 43%cc got me around 60s reduction during 40s of channeling. To make this work with the LoH formulas, that would need to be somewhere around 60/(0.43*0.333) = 418 ticks in 40s. Or ~10 ticks per second.
Now the 15%cc test would be at 45/(0.15*0.333) = 900 ticks in 55s. Or ~16 ticks/s.

I also did some tests with around 20% and 30% CC, and they don't make any sense either.

So this can't be explained by "too many ticks" alone. I think there must be some kind of RNG confusion when it comes to crits in a channel. In addition to the APS scaling being off, as shown by the damage numbers popping up too fast.
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