Diablo® III

CM Proc Rate (Testers needed)

Interesting results apo. So how far did you repeat the test? What I feel I'm missing from the simplified "timeline" is how often you're getting APoC (ie what was your average return) and what the temporal dynamics look like. For example, what is the situation immediately prior to when the "2" apoc return events happen. Do they always follow a previous half-second gain (either "1" or "2"). I'm try to get a sense for whether previous half-second APoC "crits" are correlated in some way, in which "2" events only happen if they were immediately preceded by another half-second APoC return. Because if I understand it, technically we shouldn't see ANY "2" apoc return events. You're only getting 2 ticks per second with Ray of Frost at 1aps. And with a proc rate of 1/3 and 3APoC, the return should only be 1 tick per half-second period. The presence of any "2" apoc returns definitely suggests something is bugged.
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So once again we have some results that don't make sense based on what we thought we knew about the mechanics.

Are you seeing a LOT of AP returns from your APoC? As in more than is expected based on your crit chance? Not the amount of AP returns but the frequency.
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I think this is a recent change, maybe even that they did on purpose to start testing apoc synergies. Something happened in 1.07 to make it easier on ranged wizards, but since you cannot really program what a ranged wizard and a CM wizard has for skills maybe they just changed the entire CM equation instead of messing with skill's proc co-efficient for the 100th time.

It's definitely a 1.07 change, because I did the same test for a different reason in 1.06. And I didn't see any "double procs".
Anyways, I think they even said themselves that they are not particularly keen on adding more hidden game mechanics.
And now they are adding a completely intransparent modifier to parts of existing mechanics just to avoid changing proc coefficients gain? I really hope that's not true.

02/27/2013 03:05 PMPosted by TekkZero
Interesting results apo. So how far did you repeat the test? What I feel I'm missing from the simplified "timeline" is how often you're getting APoC (ie what was your average return) and what the temporal dynamics look like. For example, what is the situation immediately prior to when the "2" apoc return events happen. Do they always follow a previous half-second gain (either "1" or "2"). I'm try to get a sense for whether previous half-second APoC "crits" are correlated in some way, in which "2" events only happen if they were immediately preceded by another half-second APoC return.


For both tests I looked at about 90 seconds of channeling. I'll do some more for the 6 APoC test, because I really really really want to see a proc that gives me less than 4 AP.

I did not focus on the actual number of procs. Because this is something that varies heavily. I think in my tests it was something around 6 or 7 during 90 seconds (counting 2 AP as a single proc).
At 5% crit I'd expect a total of 90*2*0.05=9 crits.
So that's okay I guess. But it's not a large enough sample size to draw any conclusions.

And no, there was only one situation in which a proc was directly preceded by another one. Usually there would be quite some time in between them. Which is not surprising, because I intentionally lowered my critchance to 5%. Analyzing the videos is much more comfortable when there is some time between two crits.

02/27/2013 03:05 PMPosted by TekkZero
Because if I understand it, technically we shouldn't see ANY "2" apoc return events. You're only getting 2 ticks per second with Ray of Frost at 1aps. And with a proc rate of 1/3 and 3APoC, the return should only be 1 tick per half-second period. The presence of any "2" apoc returns definitely suggests something is bugged.


That's exactly right. "2" is absolutely impossible in our previous model.
But it gives us a lead. The only two scenarios I can think of, in which a "2" return for 3 APoC is valid are
a) Proc coefficient of >1/3
This would be a different proc coef than the one for LoH - which definitely is 1/3.
Also, it can't be 2/3 or bigger, because that would lead to returns of 2 only or 2 and 3.
Only with a coef between 1/3 and 2/3, the calculated AP return per crit is 1.x and the actual AP returns would therefore be 1 and 2 in a certain ratio. This I verified in 1.06. With 7 APoC, I would get returns of 2 and 3. Because 7*1/3 = 2.333

BUT if this is true, I can't see 4 AP only at 6 APoC. Because constantly getting 4 AP means a proc coefficient of 2/3. And that doesn't fit the 3 APoC test in which I did NOT constantly get 2 AP.
So I really need an AP return of less than 4 @ 6 APoC for this option to make sense. Additional tests with different APoC Values could then tell us the exact proc coef being used.

b) Bug / hidden mechanic for increasing AP returns
This would have to be something new which is unrelated to proc coefs and follows it's own rules.
Obviously I wouldn't know how it works exactly. But I imagine a separate, possibly varying multiplier to the proc value (as opposed to tick frequency or proc chance).
And as sad as it sounds: If it can be proven, that's more of an explanation than anything we have so far.

I will definitely do some more tests with different APoC values to see if I can find more evidence for one of the options.

02/27/2013 03:14 PMPosted by Loroese
Are you seeing a LOT of AP returns from your APoC? As in more than is expected based on your crit chance? Not the amount of AP returns but the frequency.

See above. Not really, but it's also something I don't really want to get into right now. Looking at crit chance and proc frequency could prove if there's something wrong with the crit RNG or tick frequency.
But I think the unexpected Ap return values are enough to screw things up on their own. Could be the same on CM. Who says we're not getting 2 seconds cooldown reduction most of the time, instead of 1? That would explain a lot.
Edited by apo#2677 on 2/28/2013 10:09 AM PST
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I'm skeptical of a proc coefficient change, because then it wouldn't make sense why you'd sometimes get 1 APoC versus 2. As far as I can see, we're "haphazzardly" gaining twice the APoC. But teh real question is are we?

Here's a clue that maybe we have our model wrong. It's interesting to me that APoC is scaled at all by the proc coefficient. Let's say for a moment you were intuitively looking at APoC, one possible model is that you'd always gain the full 3 APoC per crit, but only 33% percent of the time. Another possible model is that the APoC returns are scaled by the proc chance, so we'd see maximum of 1APoC for Ray of Frost. BUT you're seeing much less than the full 3 and it's not constant (in fact usually only 1 and 2). Thus, the APoC is being scaled, but interestingly it's not always the same.

So APoC returns seemed to be scaled out, presumably metered out by the RNG and based on the proc coefficient. But keep in mind, we're dealing with small numbers here unlike LoH returns. So how do you deal with a situation, where very small numbers remain below 1? The Blizzard proc coefficient was 0.01 in previous patches. Well even at 30APoC, the expected maximum APoC return would be 0.3. Well, that's less than 1, so the game never registered an APoC return (presumably because it was a round down mechanism).

So a possibility of what we're seeing is a new "round up" mechanism that was put in place to "fix" APoC returns on Blizzard. However, because we're dealing with small numbers, a round up mechanism, versus round down mechanism, would generate a notable-increase in APoC returns. Thus, instead of "0, 1, 2, and 3" apoc return returns being possible in your Ray of Frost scenario, it's now "1, 2, and 3". The best way to verify if this might be happening is to observe the frequency of the APoC returns.
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One easy way to test if this hypothesis is even reasonable, and you probably know the answer apo, is that you should observe more variation in APoC returns with more APoC. For example with 6APoC returns, you should see an amalgamation of 1, 2, 3, 4, 5, and 6 APoC returns. I'm a little unclear from what you you saw at 6APoC, so it's not obvious to me if this hypothesis can be right. I think you mentioned it was always 4, which would be evidence against my hypothesis. And if so, how long did you test? Because it'd be even more puzzling if you observed something weird at 3APoC, but not 6ApoC.
Edited by TekkZero#1963 on 2/28/2013 11:05 AM PST
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But one third of 3 is 1. Its not like they made it so they no longer truncate APoC * coefficient. If Apo was testing a case where APoC returns per crit wasn't an exact number than that could be an explanation for the '2' ticks. Since there IS no remainder to round, down or up, that doesn't really fly.

Also considering that blizzard now works with APoC as they say, then its already pretty certain that APoC gives at least 'tenths' of an AP where appropriate.

Apo: I know you only did 90s tests, but are the '2' APoC returns regular? Do you always get a '2' after a certain number of normal '1' returns in between?
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But one third of 3 is 1. Its not like they made it so they no longer truncate APoC * coefficient. If Apo was testing a case where APoC returns per crit wasn't an exact number than that could be an explanation for the '2' ticks. Since there IS no remainder to round, down or up, that doesn't really fly.

Also considering that blizzard now works with APoC as they say, then its already pretty certain that APoC gives at least 'tenths' of an AP where appropriate.

Apo: I know you only did 90s tests, but are the '2' APoC returns regular? Do you always get a '2' after a certain number of normal '1' returns in between?
I'm saying that he's getting 1s and 2s because he has 3 APoC. With a sliding return of APoC, you could see a variation of 1, 2, and 3 APoC returns (presumably weighted downwards due to the proc rate). I'm just trying to come up with a model in which APoC returns might be scaled, so they are more smooth. The two basic models that I would expect to predict APoC returns don't seem to agree with apo's observations:
*Always full APoC return - If you have X APoC, you receive X APoC exactly Y% of the time, where X is your APoC and Y is the proc coefficient. This would predict APoC returns to be always 3 for Ray of Frost.
*APoC returns are scalled by proc rate - If you have X Apoc, and you have Y% proc rate, you receive Y% of your total X APoC per crit (rounded up or down). This hypothesis would predict APoC returns to be always 1 for Ray of Frost.

But I have no idea if my suggestion is correct. My hypothesis would predict a varied assortment of APoC values and that it'd never be precisely constant (ie always greater than 0, but never higher than your APoC).
Edited by TekkZero#1963 on 2/28/2013 11:14 AM PST
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The problem I'm having with coming up with any kind of theory for the results is the results themselves contradict each other. With 3 APoC he sees 1 or 2 AP returns. With 6 APoC he only sees AP returns of 4. To be consistant I would expect to see 2, 3, and 4 AP at times.

At a first glance at least the AP return frequency seems consistant with the crit chance, so I'm reasonably sure it's still only working off crits, which is about all I can say with any degree of certainty at the moment.
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@Loroese: That's what my worry is. If I understand what apo said, the 6APoC returns don't quite seem to agree with the 3APoC results. Right now we have some scaling going on or it's a bug. Unfortunately, we probably need more data to ascertain what's the most likely hypothesis.
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No, that's not it. As I said, I already did this test back in 1.06. Because I was curious if there was any rounding involved in APoC calculations.
What I did was the same test with RoF, just with 7 APoC. At 7 APoC and a 0.3333 proc coefficient, I'd expect a return of 7*0.3333 = 2.3333
I wanted to find out if I always get 2 AP back (=rounded down), always 3 (=rounded up) or 2 and 3 (=no rounding).
I got mostly 2 and sometimes 3.

So the conclusions at that point were:
- The proc coef affects APoC value and not probability. Something that was aparently well known at the time, but I hadn't verified it myself or seen anyone presenting any actual test results. So I tried it myself.
- It was not always rounding up or always rounding down. So either the AP pool was internally using fractions and just displaying non-fractional values, or AP returns are precalculated and placed in a certain order or happen with a certain probability.
Either way, in the long run, I wouldn't get any more or less than I deserve. That was enough for me, didn't analyze it further.
I don't know what was wrong with Blizzard, but based on what I saw with RoF, in your example I'd expect you to get 1 AP every 3 to 4 crits. In theory, it shouldn't have been a problem.

Back to 1.07 and my recent tests. Now the way I see it, the above is not even relevant, because I chose the APoC values of 3 and 6 for the one reason that there can't be any rounding or varying values, as long as the proc coefficient is still the same.
That's part of my reasoning. The varying values at 3 APoC can only be explained by a changed proc coef or a completely different mechanic. It can't be a rounding issue, because the proc coef is 1/3 and 3 APoC multiplied by a proc coef of 1/3 obviously means exactly 1 AP per crit. Not more, not less.
Same for 6 APoC - I should see exactly 2, instead I'm seing 4. Even if the proc coef was not as precise as we previously thought AND they changed the APoC mechanics to always round up, I'd see 3 AP at max. 4 AP can't be explained by rounding.

Now the thing is: If they did change the proc coef to, let's say 0.6
Then my AP returns at 3 APoC would be 3*0.6=1.8
At 6 APoC it would be 6*0.6=3.6

So now the system has to do something. Either rounding up/down or handling fractions. Based on what I saw back in 1.06, I'd expect to see AP returns of 1 and 2 (3 APoC) and 3 and 4 (6 APoC).
So for my 3 APoC test, a changed proc coef is a valid explanation. For the 6 APoC test, I'm missing the "3" return value. It could be that I just didn't look long enough to find one, or it could be that there never is one. If there definitely is no "3" return value, the theory of the changed proc coef is dead.

[edit]
Apo: I know you only did 90s tests, but are the '2' APoC returns regular? Do you always get a '2' after a certain number of normal '1' returns in between?

I got a 1 at first, then a bunch of 2's, then a single 1 again and then I stopped. So I don't have enough data to tell if there's a fixed order.
Edited by apo#2677 on 2/28/2013 11:49 AM PST
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Yeah, basically your results seem to contradict themselves.
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I wouldn't say so. Not gonna dismiss the theory of the changed proc coef before doing more tests with 6 APoC. It is still possible that I just didn't see a 3 AP return, because of bad luck and a relatively short test duration.
Once I do like 5 minutes of testing and still see 4 AP only, I'm gonna say it's something different.

PS: If any of you want to try and replicate the results. You have to place RoF on a number key. If you have it on a mouse button, you won't be able to see the AP globe tooltip.
The beam will still follow your mouse cursor, so then you have to place a target on the lower right of your toon. So you can place the cursor over your AP globe and still hit the target.
Then you will be able to see the current AP value using a video recording software like Bandicam and an appropriate player like VLC for frame-by-frame or slow motion watching.
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https://docs.google.com/spreadsheet/ccc?key=0AgL5S3Revw9ddEhScEpSLWhnRDZKV25OaWZJcHdkN0E#gid=0
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02/28/2013 12:09 PMPosted by aztecwarrior
https://docs.google.com/spreadsheet/ccc?key=0AgL5S3Revw9ddEhScEpSLWhnRDZKV25OaWZJcHdkN0E#gid=0

We're all very well aware of the LoH proc coefficients and the mechanics related to them. The thing is, APoC and CM behave differently. That's what we're trying to figure out right now.
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I guess it's possible that the proc coefficients have changed, but I'm at an extreme loss to say why we would see this. And the patch notes do mention some proc coefficients for wizard skills being changed. Why would Ray of Frost not be mentioned? There's no logical explanation for an increased or changed proc rate. If anything I'm challenging that we actually can use past precedent as the best guide.

A lot of things feel off in 1.0.7. Aand from the Patch Notes the only thing mentioned that seems potentially relevant is a "fix" to Blizzard's chance to proc APoC. To fix that, we may have seen either a rehaul for how the system works or a massive bug. I think I might be convinced of a proc rate hypothesis if we observed only 2 values for APoC returns across multiple APoC values. The clumping theory we discussed earlier doesn't appear as particularly relevant, since you mentioned that the APoC events are pretty far apart in time.
Edited by TekkZero#1963 on 2/28/2013 12:48 PM PST
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... ok, this has already been solved. APOC works just like LOH only you have to have crit chance.

example, 50% cc and WW with 30 apoc.

50 percent of the ticks (which is .125) will be crit. Every crit tick gives you .125 of 30 apoc which would be 3.75 Arcane power on return.

lets go with something simpler. magic missile (seeker). with 50%cc and 30 apoc. When you crit, you will get the full 30 AP.

See, same thing. Only with WW you only get back 3.75 per tick IF you crit. You don't get 30 APOC. But you need 30 APOC to get 3.75 AP back.

Works the same way with less.

That is why i use Increase Atk Spd, to increase chance of APOC. It use to be (before nerfs) atk spd was not necessary. But because of nerf, it is, because you need more than 2.0 atk spd to sustain AP with more than 20 APOC and decent CC.
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... ok, this has already been solved. APOC works just like LOH only you have to have crit chance.

example, 50% cc and WW with 30 apoc.

50 percent of the ticks (which is .125) will be crit. Every crit tick gives you .125 of 30 apoc which would be 3.75 Arcane power on return.

lets go with something simpler. magic missile (seeker). with 50%cc and 30 apoc. When you crit, you will get the full 30 AP.

See, same thing. Only with WW you only get back 3.75 per tick IF you crit. You don't get 30 APOC. But you need 30 APOC to get 3.75 AP back.

Works the same way with less.

That is why i use Increase Atk Spd, to increase chance of APOC. It use to be (before nerfs) atk spd was not necessary. But because of nerf, it is, because you need more than 2.0 atk spd to sustain AP with more than 20 APOC and decent CC.


Except we've already shown that to be not the case.
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Ok, imagine the following:

AP is returned from some linear function that combines APOC, CC, and a coefficient.

A fractional value is returned, let's just say 1.33

Only whole number AP is returned.

1 tick
1.33 - 1 AP = .33

2 ticks
.33 + 1.33 = 1.66 -1 AP = .66

3rd tick
.66 + 1.33 = 1.99 - 1AP = .99

4th tick
.99 + 1.33 = 2.32 - 2 AP = .32

etc.

That gives us 1) variation in AP return per tick and 2) can explain why it isn't a set sequence per ticks.
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@Ossian: The problem with carrying the remainder along is that you would then expect only occassional spikes that are "too high." And then presumably it would go back to normal as you build up towards another big number. Apo instead saw a bunch of sequentially high numbers.
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Muhaha. After some further testing, I finally got my 3 AP return.
It was actually the first of my third try. I was starting at 20, climbing up to 25, falling down to 20 and so on. Then at one point it fell down from 25 to 23 and started climbing up to 28. Then again falling down to 23, etc.
The next one, after several seconds was 4 AP again. Falling from 28 to 27, then climbing up to 32.

So an increased proc coef is now a valid explanation for both my 3 APoC and 6 APoC test.
If this is true, the actual APoC coefficient is X, where 1/3 < X < 2/3
With different APoC values we should be able to figure it out, BUT then there are still many open questions.
This could explain the better performance of APoC since 1.07. But it can't be the only thing responsible for what we previously saw with CM and SA. Because some of the results we got there were so far off that even a proc coef of 1 couldn't explain them.
Also, all APoC tests were done with a single spell and at 1 APS only. So we can't know if the APoC coefficient is a completely separate value or based on the LoH coefficient, if it scales with IAS and so on.

@Ossian: That's one of the options how I suspected APoC to work in 1.06. Very good example.
But the sequence is fixed in this case. It doesn't allow a random order of 1s and 2s. Not saying it's wrong, because I have no idea if the sequence is random or not. But it's something that should be verified.
Another option would be throwing a dice for each proc to decide if it's a 1 or a 2. With the probabilities for either one set so that over time it averages out at 1.33 AP per proc.
But I like your idea better, because it's simpler.

@TekkZero. That depends on the actual values. Imagine the same example with a fractional value of 1.9 instead of 1.33:

1. tick
1.9 - 1 AP = 0.9

2. tick
0.9 + 1.9 = 2.8 - 2 AP = 0.8

3. tick
0.8 + 1.9 = 2.7 - 2 AP = 0.7

4. tick
0.7 + 1.9 = 2.6 - 2 AP = 0.6

etc.

So it is possible to get a bunch of high values with only an occasional low value.
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