• frmorrison

Sweet data, I think another 1k scorches would start to show the crit depression due to the 2 roll system.

29.88% should be your expected crit, DrDamage may have some error in its code.

 

chase

You have to look at the way WWS reports crit.

WWS crit = crits/total casts = 230/1000 = 23%
Percent difference (29.88-23)/(29.88+23)=13%

A two roll system = crits/landed casts = 230/(1000-167) = 27.6%
Percent difference=(29.88-27.6)/(29.88+27.6)=4%

Looks a little less decisive to me.

I'm unsure why we are using a 65 mage vs a 68 target. Don't we already know that there is no "crit depression" on +3 mobs? (i.e. boss mobs are +3)

 

PSGarak

We never actually knew if there was one or not, we just assumed there wasn't =/. At only +3 it's small enough that it's hard to notice, but I would expect it to start at least as soon as +3 if it does in fact exist. Could the crit depression be as high as a 13% modifier at +3 levels? Possibly--the miss chance reduction is higher than that.

 

Mageborn

Dangergnome's tests are conclusive for me!

In the two roll system I outlined earlier, if your crit chance is 29.88%, and your miss rate is 16.7% (as reported by your WWS) then your expected crit rate would be 24.89%. A crit rate of 23% after 1000 casts is an indicator of the loss of crit as a result of the 2 roll system.

It's not a surprising result.

 

BeeLz

Wouldn't this be pretty easy to test on loatheb?
Take a firemage with 50% crit, no hit, and chaincast scorches on him?

 

Soul

So I did some testing of my own using a level 65 Affliction warlock with 103 crit rating and 294 int, which yields a crit chance of 11.77%. I cast 1000 Searing Pains on Dr. Boom. Results were as follows:

Hits: 720
Crits: 107
Misses: 173

With a one-roll system, we'd expect to see 117.7 crits. With a two-roll system and with 173 misses, we'd expect to see 97.3 crits. We can approximate the distribution of crits over this many trials as being normally distributed regardless of whether it's a one-roll or two-roll system because the expected value and approximated variance are appropriately large, so let's test against that. Standard deviation is 10.19 if we assume one roll and 9.27 if we assume two rolls.

We are 95% confident that the results are significantly different from expected if the results we observe are more than ~1.9 standard deviations away from the expected value. Which basically means that there is no real difference between the trials and the expected values and I need to collect more data :-P.

SeanDamnit's data shows that there is a significant difference between the observed data and the expected data if one assumes a one-roll system, but there's no difference if you assume a two-roll system.

EDIT: So I did another 1000 casts, bringing the total number of casts up to 2000. Totals are as follows:

Hit: 1488
Crit: 191
Miss: 321

For one roll, expected number of crits is 235.4, variance is 207.7. For two rolls, expected number of crits is 197.6, variance is 174.4. So, at the 95% level, the number of crits is significantly different assuming a one-roll system and it is not significantly different if it follows a two-roll system.

This indicates that if spell use a one-roll table, then target level plays a role in the crit rate. If target level does not play a role in crit rate, then it must be a two-roll system.

If someone has a level 65 with a ton of +hit, they could probably settle this by running their own trial (2000, 4000 spellchecks?) and seeing if the crit rate differs from the paper doll crit rate or not. Probably best to use a level 65 mage with 5/5 Arcane focus and some hit gear spamming arcane missiles on Dr. Boom.

 

SeanDamnit

I can do this within the next week or so. Possibly tomorrow. I can obtain the 16% hit cap with the Arcane Focus talent and some gear that I've been collecting.

 

SeanDamnit

Ok, so first I gathered more data with rank 1 scorch against Dr. Boom as a level 65 mage.

Stats:
139 Crit Rating
0 Hit rating
342 Intel (self buffed with AI rank 5)
Molten Armor

25.88% fire crit according to the paperdoll. That would make 29.88% crit using scorch.

Results:
2010 casts
1196 Hits
463 Crits
351 Resists

Assuming 1 roll, that would make my crit 23.03%. Assuming 2 roll, it would be 27.90%.

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-=-=-=-=-=-=-=-=-=-=-=
Then I respec'd to get the Arcane Focus talent, and put on hit gear to reach the hit cap. I then spammed rank 1 arcane missles on Dr. Boom.

Stats:
85 Crit Rating
70 Hit Rating (7.15% at level 65 on the paperdoll)
359 Intel (self buffed with AI rank 5)
Molten Armor

13.97% Arcane Crit according to the paperdoll

Results:
2039 Casts
1782 Hits
238 Crits
19 Resists

Assuming 1 roll, that would make my crit 11.67%. Assuming 2 roll, it would be 11.78%

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-=-=-=-=-=-=-=-=-=-=-=

I'll let you guys draw the conclusions, as I'm not that good at that kind of stuff. But I do find it weird that both tests had enough data to make the expected resist rate accurate within half a percent, but crit rate (assuming 2 roll) was short 2% in both tests.

Do you guys think they are just unlucky rolls that would even out with more data, or maybe it has something to do with crit suppression?

 

vokzhen

Maybe I'm missing something, but I still don't see how versus a +3 mob differentiates between crit depression and a 2-roll system. There's definitely one of the two it seems, but we already knew one of the two was happening. What we need is something that distinguishes between them - as in, lots and lots and lots (and lots) of casts against an equal-level mob.
Right now it's easy to chalk it up to a 2-roll system, but we still can't say for sure which it is. There's a fairly significant difference in hit rating, the introduction of glancing and crushing blows, and so on against mobs of higher levels, and there's no way we can just assume one way or another on crits without actually testing it to figure it out.

 

SeanDamnit

so you think I should re-gather the data at 66, 67, and 68? Or just 68?

 

Soul

Now this is an interesting collection of data. For both sets of data, the indication is that at the 95% level, the measured crit rate is significantly lower than the expected crit rate. This indicates that your target's level plays an important factor as to what your crit rate is.

I'm sure this is getting expensive for you, Sean, but could you do one more test? Try doing the arcane missiles test again with the exact same gear and spec, but with 0/5 Arcane Focus. This would give you a much higher miss rate... With a miss rate of ~1%, the crit rates of one-roll or two-roll are very close to each other (like to within 0.1%). With a miss rate of ~10%, the crit rates should differ significantly depending on whether you assume one roll or two rolls, but odds are, one of the assumed systems will give you a crit rate of around 11.7%, while the other will be out, which will tell us whether casters use a one-roll system or a two-roll system. Or they both could be out and we'll have a lot more theorycrafting to do.

Well, no, the tests that Sean has done show that crit rate is depressed regardless of whether you assume one or two rolls, so it's pretty certain that your crit rate is lower versus mobs that are higher in level than you. We don't know whether it is a one-roll system now... if Sean's tests had shown that there was no "crit depression" then you would know we have a two-roll system. However, Sean has shown that there is crit depression and that with a 13.97% crit rate, if you take hit out of the equation, your actual crit rate versus a mob 3 levels above you is 11.7% or so. Now, if you put hit back into the equation (by keeping gear the same, but having about 10% lower hit by removing just Arcane Focus), you can to see which assumption (one or two rolls) gives you that 11.7% crit rate.

 

PSGarak

Now we get awesome-fun happy-time trying to figure out just *how* much crit gets depressed by. Just as a starting point, what would a level 68 mages with those stats read as their paperdoll crit rate? My two "logical" suggestions for crit depression are that it uses the target's level for rating->% conversion, or that it's a straight additive or multiplicative penalty (like hit rate). Seeing a correllation on a level 68's crit chance wouldn't "prove" anything but it would be an interesting coincidence.

Obviously, this is of great importance to the number-crunching community as it changes the valuation of crit in a raid setting, assuming 73's already have their own rating conversions--bliz may have left them out until WotLK.

Just FYI, using the defender's level for calculating hit, crit, and armor mitigation always benefit the higher-level player, while using the defenders block/dodge/parry always benefits the lower-level player.

 

Jamax

This is the most relevant thread I could find for this, and i can't create a new thread yet. I don't know if I'll be posting ten posts since I basically just registered to share this.

This might be common knowledge around here, I don't know, but the resist damage printed on the combat log is not correct -- it is calculated before some or all damage modifiers (CoS, Shadow Vuln, etc) whereas the damage is not.

An example:

"Your shadowbolt crits Magtheridon for 4340 (522 resisted)"
ie 10.8% 'resisted'

Blizzard is not lying about resists being 0.25, 0.5, or 0.75. This is clearly a 25% resist, so 4*522 = 2088 damage that would have been done by an unresisted bolt, but before modifiers are applied (or 2088-522=1566 damage after resist but before modifiers). So the ratio of actual damage to expected is 4340/1566 = 2.77 (this ratio includes crit w/ ruin, CoS, Shad&Flame(?), and other after-resist effects). Applying this to the printed resist 522*2.77 = 1446 -- this is the actual amount resisted because had the resist not happened this bolt would have hit for 4340+1446 = 5786 damage.

I base this on 65 partial resists of shadowbolt from 4 boss encounters (gruul and mag). I could not figure out why my resists would be '20%' or '66%' when blizzard says they are in quarters until I made this assumption about the modifiers being applied after the resist, and then just using a gross estimate resist of 1.32 for shadow and flame and CoS the numbers immediately lined up really close to the 25, 50, 75 (S&F might be applied first and what I was seeing was imp sb, idk). I think you'll find this easily to confirm in any case.

It is somewhat relevant to the 1-roll vs 2-roll system since it pretty conclusively shows that crit is applied after resist. It could still be one roll and then if it's a crit they just run the same calculations and add in crit at the end, but in this case it might be likely from a programming standpoint for them to 2x or 1.5x the damage before calculating resist.

In any case, if confirmed, this is a way to measure the total amount of spell damage modifiers, which could be useful for something... it would also mean that anything simply adding up resist amounts and comparing to dmg done is underestimating the amount of damage mitigated by a great deal in the case of crit-heavy damage.

 

Dustwhisper

This has been proven/calculated before in multiple threads including a pretty nice page on wowwiki...

It's simple. 90% to hit, 30% to crit, 0,9*0,3 = 0.27 = 27% realistic crit. Two roll system demystified.

 

Amonra

Well thats it guys, end of discussion. The man has spoken.

Although... no links were provided to these proofs/calculations from multiple threads. I looked at the page on wowwiki and it simply makes statements about how the system works, with little backup.

The only backup referenced is to an admittedly fairly informative page on the WoW-Europe website. But that really doesn't settle matters for me because testing was done on PvP and CoS, both of which could potentially use different mechanics.


Looking over the data we have so far, I have made up the following table:

The crit in the data set is simply whatever the data provider has given (presumably paper doll + any spell specific talents).

The observed crit rate is calculated as the percentage under each of the particular systems.

My Conclusions

The most noticeable thing is that the observed crit rate is lower than the expected rate under either system. This could be due to either crits being depressed against higher level mobs, or innate full mob resists (which I understand show up as misses). However from other dps threads I understand that full mob resists are a pretty small factor so I'm going to discount this.

If a 1 roll system is in operation then the crit rate is depressed pretty significantly (between 15% and 25%) on a mob just 3 levels higher. If a 2 roll system is in operation then the crit rate is depressed by about 5-15%.

Unfortunately this isn't a lot to work with. We know that spell hits are depressed by 16% on 3 level higher mobs and if we were to assume that spell crits operated on a similar scale (a pretty big assumption I know) then this would fall pretty much right between the range of results.

The only way to test this properly would be either an enormous number of data points against same level mobs (i.e. enough that the 1% miss rate wasn't drowned out by random fluctuations) which isn't really feasible, or to find a way to artificially reduce hit rates on a same level mob (i.e. some kind of debuff on a pretty long fight).


Edit: Thinking about this again, I think it does show one additional detail. It shows that if a 1 roll system is in operation then crit rates are reduced multiplicatively rather then by subtraction amount. If 3 levels difference reduced crits by a fixed amount then from the results at about 30% crit rate it reduces it by subtracting 7%, whereas at lower crit rates it isn't being reduced by anything like 7% (on a subrtaction basis). So it would have to be a multiplicative reduction of about 0.8. Which would be a little surprising given how other combat mechanics work.

For a 2 roll system the results aren't really different enough to tell either way. Its either about a 2% subtraction or about a .93 multiplier.

For this reason I'm leaning towards the 2 roll system but can't really conclude either way.

 

Devnex

Question: Do traditional hit rating requirements still stand on old world bosses for level 70s? Bloodlord Mandokir is an excellent fight for long-term testing as he can easily be three manned but IIRC he doesn't give soulshards (at 70) so I'm not sure if there are non-traditional factors in play.

 

SeanDamnit

How much data do you believe is necessary? I plan on continuing to level my mage, so at level 68 I can gather data on Dr. Boom.

I'm curious to know why it is necessary to test this on a same level mob?

 

PSGarak

Well, we've conclusively answered the question of level-based crit depression (<3 to you, sean), but the question of the one-roll or two-roll system, which we were originally wondering about, still remains unanswered. Basically, we need to control out crit depression to get useful data, so we need to test against an even-level mob. We need an absolutely *massive* data against a same-level target because the standard miss chance is 4%, so the difference between a one-roll and two-roll expected result is very small.

I'm saying that, even with know level-based crit depression, Attumen's curse is the easiest way of confidently confirming one/two-roll system. While you won't hit either of the expected values dead on, you can easily see the qualitative difference in a one- or two-roll system when your miss chance is in excess of 50% and your crit chance is over 30%. Getting ten people together in a testing frame of mind is probably less time and effort than shooting Dr. Boom for days.

 

Leveret

Actually, it seems to me that it is a two roll system with no other effect of crit depression.

I think this is the case thanks to what Amonra has said. Against higher level targets, crit chances are not subtracted by a value, but rather multiplied by a percentage. This is completely in line with what we expect crit rates to behave under a two roll system. But is is inconsistent with how crit depression would work. All other statistics that are effected by level differences are additive in nature, such that gear that grants bonuses to close the gap shows the absolute percentage of bonuses they would give. However if crit depression is multiplicative, then additional crit gear would not show the correct amount of bonuses. While this is not conclusive evidence, I think it is a very strong indication that the observed crit depression is a result of a two roll system, and not an inherent crit depression mechanic.

 

Soul

But wait, we do have a controlled set of measurements: the measurements that Sean made with his Arcane Focus mage. We know that in his gear with a 1% miss rate, the crit rate he has is about 11.7%. If he did not have arcane focus, but kept his gear, the mage would have a 10% miss rate, but the crit rate would still be about 11.7% for the right system. So, if he were willing Sean (thanks for all the data so far) could get another mess o' data and find out which assumption gives a crit rate closer to 11.7% if his mage kept his gear the same, but removed Arcane Focus.

 

PSGarak

Lev: the crit rate is lower than you would expect for a two-roll system without crit depression. There is crit depression of some sort going on, so we need to control that out before we can make conclusions.

Soul: you're brilliant! I had not thought of that way to control it out, because I was too dead-set on fighting attumen for an hour and a half =P. PS, <3 Sean.

 

SeanDamnit

Very well, I'll get you all some data soon.

 

chase

SeanDamnit could you continue with posting links to the WWS reports of your testing?

You list:
Casts
Resists
Hits
Crits

But miss is nowhere to be found. I assume you mean resists are misses, but assumption is the mother of all evil.

Plus it just makes it easier to copy data in excel and flush things out there.

 

Dustwhisper

And do minimum of 1k casts with each, preferably 10000 casts with each.

 

SeanDamnit

There is no such thing as a missed spellcast, only resist.

The problem with WWS is that it won't parse more than 12 hours worth of data, and I am not always able to do 2000 casts in one sitting.

I am willing to send anyone my combat log if they wanted to confirm my numbers, however. Just let me know.