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# Crit depression and combat table

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### #21 Mavanas

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Posted 29 November 2009 - 06:46 PM

What am I missing then, I mean which 5% am I double counting?

- Was the crit cap not 100-D-M-G+5% under the crit depression hypothesis before the existence of Hellord's tests? Maybe we need numbers. Let's say D = 5%, M = 15%; we know G = 24, so 56% is left for crit and hit. If my crit rate with all buffs and debuffs is 61%, only 56% is used against bosses under the crit depression hypothesis. So I am at maximum of my crit, i.e. the crit cap is now 61%. Adding anything else is a waste for autoattacks.

- Is the crit cap not 100-D-M-G-5% now when we know 5% of crits are converted into hits? Using same numbers, 5% are dodges, 15% are misses, 24% are glances, and 5% are forced hits. Thus we have 100%-5%-15%-24%-5% = 51% left for crit and hit. So now adding any crit beyond 51% is not adding anything to my autoattack crits, so the new crit cap is 51%. Thus it seems to me there is a 10% difference between what we believed before and what we believe now.

I think when you say the difference in crit cap is only 5%, you are assuming there is both crit-to-hit conversion AND there is still a crit depression against bosses. While that may be true, I am advancing an alternative hypothesis that there never was a crit depression against bosses in first place, but instead there was always a conversion of 5% crits into hits when fighting against bosses. When we tested the crit depression before, we simply observed 5% less crits (and 5% more hits). That observation is consistent with both crit depression and hit conversion.

So in short, if the difference is not 10%, there should be some flawed logic in my calculation of crit caps before and after. Which one is it?

### #22 Aldriana

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Posted 29 November 2009 - 08:03 PM

Before, the computation was the solution to the equation

(Crit-4.8) + Dodge + Miss + Glance = 100, so crit cap was 100-D-M-G+4.8, in your notation.

Under this theory, the equation is (Crit-4.8) + Dodge + Miss + Glance = 100 - 4.8 - that is, our crit is still reduced by 4.8, and we can't go up to 100% crit, only to 100-4.8 due to the forced misses. Rearranging to your notation, we get that the crit cap is simply 100-D-M-G, for a difference of 4.8. To look at it another way: when your "tooltip" crit, prior to crit depression, gets to 100-D-M-G, that indicates that all attacks, neglecting crit depression, should be Crits, dodges, misses, or glances; because of crit depression, 4.8% of attacks would instead be hits, but crit is just as capped.

That said: I'd hasten to point out that this is merely a theory right now - I don't think any comprehensive testing has been done to demonstrate that that's actually how it works. I just don't feel like we understand the problem well enough to comment definitively on what's going on.

### #23 Aldriana

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Posted 30 November 2009 - 12:38 PM

So, per my previous post, I was not wholly confident in this theory, largely because warrior testing has indicated some manner of funkiness (particularly at low crit levels), which makes the mechanics there less than wholly understood. Hence, I opted to do some testing on a rogue, given that we have a decent handle on how rogue crit reduction seems to work - Vulajin's initial testing makes it pretty clear that it's a straight 4.8% reduction, even at low levels of crit. So, I hopped on PTR tonight (just in case there are any changes, and to save the cash I spent on un-speccing) and did some testing.

My gear setup had 20 expertise and 0 hit, and I specced out of all hit and expertise talents; thus, while dual-wielding, I have an expected miss rate of 27%, an expected glance rate of 24%, an expected dodge rate of 5.89%, and an expected parry rate of 13.39% (assuming the accepted values of 6.5% base dodge and 14% base parry). Thus, when attacking from the front, the available space for crit and miss is 29.8%. Under the old theory of crit reduction, I'd need at least 4.8% more than this to be capped, or 34.6%. And there is some uncertainty in the glance/parry rate numbers, so to be safe it would be good to have tooltip crit several percent above this. Well, in the test gear, my tooltip crit rate is 43.77%, a good 9% over the amount needed to cap even by the old theory. As such, if I exhibit any regular hits at all while attacking from the front, we know that there's some minimum "hit" rat - and indeed, in 6250 swings, I got 308 hits. Hence, the theory that there's a minimum hit rate seems pretty plausible.

However, there are multiple possible ways that such a minimum could be implemented - the next step is to test the conjecture that the minimum hit rate is precisely the 4.8% crit of crit depression we suffer; if this new theory is correct, we expect our hit table to be as follows:

Miss, 27%
Crit, 24.92%
Glance, 24%
Parry, 13.39%
Dodge, 5.89%
Hit, 4.8%

Using these, we can make a table of observed and expected attack counts for each result:

Miss|1666|1687.5
Crit|1575|1557.5
Glance|1452|1500
Parry|878|836.9
Dodge|371|368.1
Hit|308|300[/table]

Clearly the agreement is pretty good - but *how* good? Well, fortunately there's an easy statistical test for this - we have 5 degrees of freedom, and a Chi-squared value of 4.263, which works out the a tail probability of 51.22%. Or, in English: assuming our theory is correct, we will get data with at least this much variance just over half the time, and less variance just under half the time. This is what's known in the business as "a stupidly good result". Basically, we couldn't ask for a better match to our theory than what we have. As such, while we certainly can't definitively prove our theory, it's definitely looking pretty good.

As such, the funkiness that warriors have been seeing notwithstanding, it's reasonably probable that rogues, at least, are having crit reduction applies as a forced conversion of 4.8% of our combat table from crits to hits, and that these 4.8% hits cannot be removed through any means - that is, the proposed theory is looking pretty good.

I do think there are still open questions in terms of what happens to warriors at low levels of crit (and similar effects) - but I'm at least feeling a bit more comfortable on the whole about this theory.

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Posted 30 November 2009 - 04:16 PM

My gear setup had 20 expertise and 0 hit, and I specced out of all hit and expertise talents; thus, while dual-wielding, I have an expected miss rate of 27%, an expected glance rate of 24%, an expected dodge rate of 5.89%, and an expected parry rate of 13.39% (assuming the accepted values of 6.5% base dodge and 14% base parry). Thus, when attacking from the front, the available space for crit and miss is 29.8%.

Don't you mean "available space for crit and hit is 29.8%"?

Ignore the italicized part, see edit.
The question is, I think, whether those 4.8% forced hits come from our crits or simply exist in the table the same way glancing blows do. In other words, if your crit rate had been exactly 24.92%, would you have observed 4.8% hits or 9.6%? This does matter because it would mean the crit cap in your example is effectively 24.92%, not 29.72% (or as Mavanas put it, 9.6% lower than previously thought).

If your testing answered that, I apologize, because I'm not seeing it.

EDIT: Having re-read Vulajin's testing, the conclusion was that he was not getting any crits with 4.8% crit chance on the paperdoll, so those forced hits do indeed come from our crits. Which means the crit cap is 4.8% lower than previously thought, not 9.6%. In your previous example, the crit cap would be 29.72%.

### #25 Aldriana

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Posted 30 November 2009 - 08:54 PM

Okay, to clarify: yes, I meant crit and hit, not crit and miss. I'm not entirely sure what you're trying to say in the second part, so let me just review the logic to be clear what we think is happening.

Based on accepted values and testing, we have 27% miss, 24% glance, 13.39% parry, and 5.89% dodge. The total amount of hit table taken up by these options is 70.28%. Thus, there is 29.72% remaining for the last two outcomes, crit and hit. Thus, if no crit reduction existed, and there was no minimum on the number of hits we get, we'd expect all 29.72% of the table to be crits. Since tooltip crit rate is 43.77%, even if crit reduction were as high as 14.05%, we'd still expect to see no plain hits. Since we *do* see hits, we are forced to conclude that we *are* crit-capped, but are still seeing some hits anyway.

The obvious followup question is "how many" - well, the data (which matches hellord's warrior testing) is that there's around 5%. And we *know* that rogues experience an across-the-board crit reduction of 4.8% against boss level mobs. And it seems mighty suspicious that the number of hits we're seeing is very very close to our crit reduction.

Thus, the conclusion we draw is that crit reduction is implemented by a forced conversion of 4.8% crits to hits, which cannot be removed. Or, phrased alternately: the crit reduction is applied *after* crit capping is considered - which is perhaps the simplest way of seeing what the numbers should be. The logic then looks as follows: we've used up 70.28% on glance, miss, dodge, and parry. Thus, our crit is capped at 29.72%, and we have enough crit to hit that. And then, after our crit has been reduced from 43.77 to 29.72 due to crit cap, then and only then does crit reduction kick in and convert 4.8% crits to 4.8% hits, leaving 24.92% crit and 4.8% hit - which gives us exactly the hit table listed above.

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Posted 30 November 2009 - 09:48 PM

I was trying to figure out if we should gear towards those 29.72% to hit the cap, or simply 24.92% since 4.8% won't crit anyway. It turns out that those 4.8% forced hits are converted from our crits, they're not simply always there on the attack table, so we do need to gear all the way to 29.72%. If we only geared to 24.92%, we'd see 4.8% hit plus another 4.8% from the forced conversion, for a total of 9.6% hits.

This, I think, is Mavanas' misunderstanding, above, which I was trying to clarify.

### #27 Aldriana

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Posted 30 November 2009 - 09:58 PM

Correct. If we geared to 24.92, we wouldn't reduce at all to the crit cap and still be at 24.92 - and *then* the 4.8% reduction kicks in and drops our actual crit to 20.12.

In short: the crit cap would now appear to occur when your "tooltip" crit is 100-24-dodge-miss. I say "tooltip" because it does need to include crit-increasing debuffs on the boss, so it won't be the number actually in your tooltip - the point is that it's the value without worrying about any crit reduction. Once we get to that point, we do start losing crit to the crit-capping check, which is performed "before" the 4.8% crit reduction. So, say, if our miss is 10% and we're at the dodge cap for expertise, when our "tooltip" crit reaches 100-10-24 = 66%, we are crit capped, even though this only works out to 61.2% *actual* crit due to crit reduction.

### #28 Allev

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Posted 01 December 2009 - 04:27 PM

It's fairly concrete that crit reduction is due to the difference in levels between the attacker and the boss-level mob. It seems that the absolute test between crit depression and an inherent combat table issue would be to test on level 80/81/82 targets. Ferals cannot get to the crit required to overcome the lack of glances on the 80 dummy (with Live gear). Can rogues?

Do players glance on level 81 mobs, or just bosses? Is there a good place to find only level 81 mobs to test against them?

### #29 Dontmindme

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Posted 01 December 2009 - 05:47 PM

I think I recall glances on equal level mobs. If I am remembering correctly, I did a little testing awhile back and decided that it was probably 6% vs 80; 12% vs 81; 18% vs 82. I didn't spend a lot of time on it, but it appeared to be the trend.

Assuming one can hit the crit cap on a 80 target dummy with only 6% glance; 5% parry; 5% dodge, it would determine if this 5% hit is ever-present or based on boss level.

### #30 Aldriana

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Posted 01 December 2009 - 08:28 PM

Such testing would almost certainly need to involve a dual-wielding class, as the extra 19% miss rate is going to be pretty important for getting there; even so, even assuming no hit or expertise, it's going to take around 60% tooltip crit to get there, which I suspect isn't really feasible for anyone unbuffed; however, with raid buffs, such a thing might be possible to put together.

### #31 Mavanas

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Posted 04 December 2009 - 07:08 AM

Ok Aldriana seems to assume that crit depression coexists with crit-to-hit conversion even though his test is by design incapable of proving one way or another. You observe the conversion which you could also see in Hellord's tests but what about crit depression? You do not actually see it. To test if crit depression is present alongside with hit conversion you need to test it with specific crit rates that are not well above the crit cap level.

So for instance if you have 30% left for crit after dodge, miss, glance and the forced 5% hits, test this with exactly 30% crit. If you observe 30% crit on the dummy, then there is no crit depression above and beyond the 5% crit-to-hit conversion for bosses 3 levels above you. If you observe 25%, then you know there is a crit depression on top of the 5% conversion. If you test this with 44% crit, you won't know one way or another.

I am pretty confident that there is no double crit depression. Meaning that only 5% of our crits are converted to hits, which we thought of crit depression all along. There is no further reduction to our crit once that conversion is done. If you have evidence to prove the contrary, do share. Aldriana's latest tests do not prove it one way or another.

P.S. I am pretty confident I have done tests with low levels of crit, and I observed around 5% reduction in crit rate. If 5% of our crits are converted to hit, and 5% is all the reduction to crit rate we see, then it leaves no room for crit depression above and beyond the crit conversion.

Therefore (unless someone can prove me wrong with a well designed test), our previously known formula for crit cap 100%-D-M-G+5% has to be adjusted by 10% not 5%. The new crit cap formula, based on crit-to-hit conversion and no crit depression on top of that is going to be 100%-D-M-G-5%.

### #32 Aldriana

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Posted 04 December 2009 - 08:47 AM

I have no idea what you mean about my test assuming crit conversion and crit reduction both exist. I don't see how I assume anything of the kind. I may use both terms, but I don't believe I in any way suggest that there's two separate reductions occurring - I'm fairly sure what I said, and what I was testing, was that what we have previously called crit reduction is really implemented as a forced conversion of 4.8% crits to hits. Really, I think the salient facts are as follows:

1) Against boss level mobs, our observed crit rate is 4.8 lower than our "tooltip" crit rate - that is, lower than we might "expect".

2) No matter how much crit we may have, 4.8% of our attack table will still be regular hits.

Vulajin's testing shows the former pretty conclusively; my testing is reasonably strong evidence for the second. So, what does this mean in terms of the mechanic? Well, there's two different ways of phrasing it - please note that they are completely identical in practice. There is no functional difference. They are two different ways of saying the same thing.

Crit Reduction
Crit is reduced by 4.8%, but the hit table had 4.8% hit on it which cannot be removed. Thus, the amount of room in the hit table for crits is 100-G-D-M-4.8, with the 4.8% representing the hits that we cannot get rid of. Thus, we our capped with our tooltip crit rate, C, after being reduced by crit reduction (4.8%), matches this value - that is, when C-4.8 = 100 - D - M - G - 4.8 - that is, when C = 100 - D - M - G.

Crit Conversion
4.8% of crits are converted to hits, after the crit cap is imposed. That is, we our crit capped when 100-D-M-G = C, and our hit table consists of 4.8% hit, C-4.8% crit, and the expected D + M + G of other stuff.

Note that either way, the crit cap occurs when C = 100 - D - M - G; note that our observed crit rate in this case is 100-D-M-G-4.8. This is different from the prior theory, when we believed ourselves capped when 100-D-M-G=C-4.8, by 4.8%.

So, yes, our *actual* crit is 100-D-M-G-4.8 when we're capped. But this is when our *tooltip* crit satisfies C=100-D-M-G. And this is only 4.8% lower than it was before.

Also note that either way, the theory is consistant with the observed data - positing that the crit cap is otherwise does not - we *observed* 100-D-M-G-4.8 crits, meaning that we would be capped with 100-D-M-G crit. And I really don't see how any other interpretation can be valid if it doesn't give the same crit cap, given that the data is an excellent fit for this one.

Like, consider your test; if we have 35% left for crit after dodges, misses, and glances, and we test at 30% crit, what do we expect to see? Well, we expect to see our crit reduced by 5% to 25%, and thus 10% misses. There's the 5% forced reduction/conversion/whatever-the-heck-you-want-to-call-it, and the 5% we didn't even try to remove because we didn't have enough crit. I'm not seeing any reasonable theory that proposes otherwise, so I'm not sure what testing in this case would actually demonstrate.

### #33 Mavanas

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Posted 05 December 2009 - 03:55 PM

Thanks I found my mistake. The crit cap is 100-D-M-G now, which is only 4.8% lower than the what we thought before.

### #34 landsoul

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Posted 14 December 2009 - 10:30 PM

ok so..
1. Crit cap is 100-D-M-G. If Cap is 42.5% (without any antidodge or hit, DW), and you have 45% crit, your crit rate will still be 42.5%
2. 4.8% of all crits are converted to hits. If you are over the 42.5% Cap, your observed rate will be 42.5%-4.8%, and you will see 4.8% hits instead of 0.
3. Double-Roll system (yellow, special) is affected by #2, but since no cap, can be overcome if you have 104.8% crit

That's the consensus I am seeing across all the theories in this post. Would it be safe to use this theory in spreadsheet calculations?

Also, I would be interested to know if this "conversion" comes from the level difference, and also how resilience reductions apply to this. Maybe the crit reduction from resilience also applies in this matter, but I'm not sure how you would test it because there are no glances when testing resilience.

I'm going to test this out myself and should post the results later tonite.
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### #35 Aldriana

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Posted 14 December 2009 - 10:52 PM

I'm not sure I'm 100% confident that 100% crit rate is achievable with strikes; all the testing I've seen go by is with spells, which have a different amount of crit reduction and, therefore, it's quite possible that they have a different mechanic as well. I'd be interested to see testing done with 104.8% critical strike chance on a strike. I'm not sure how much it actually matters, given that I'm not aware of any classes that are getting dangerously close to the strike crit cap at this point; but it's probably worth confirming.

For rogues intending to test this, the easiest way seems to me to be Ambush; talented, it gives +50% crit rate, which means you only need 54.8% elsewhere, which should be possible to assemble for testing.

### #36 BWarner

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Posted 14 December 2009 - 11:19 PM

 Whoops, you can feel free to delete this. My apologies.
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### #37 landsoul

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Posted 15 December 2009 - 01:46 AM

with +3% hit (precision)
48.34-53.34% crit (rampage) it's way over cap so it doesn't matter.

Across 6400 attempts
[table]type|number|percentage|expected
crit|1665|26.01|26.50 or 26.70
miss|1545|24.14|24.00
glance|1540|24.06|24.00
parry|888|13.875|14.00
dodge|444|6.94|6.50
hit|318|4.97|4.8 or 5.0[/table]

So there's definately some conversion action here with white melee attacks.

I made a DD forums post here: World of Warcraft - English (NA) Forums -> Testing Reveals New Melee Hit Table Behavior prompting a blue response to clarify cryptic mechanics
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### #38 Rallik

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Posted 15 December 2009 - 10:12 AM

I'm not sure I'm 100% confident that 100% crit rate is achievable with strikes; all the testing I've seen go by is with spells, which have a different amount of crit reduction and, therefore, it's quite possible that they have a different mechanic as well. I'd be interested to see testing done with 104.8% critical strike chance on a strike. I'm not sure how much it actually matters, given that I'm not aware of any classes that are getting dangerously close to the strike crit cap at this point; but it's probably worth confirming.

For rogues intending to test this, the easiest way seems to me to be Ambush; talented, it gives +50% crit rate, which means you only need 54.8% elsewhere, which should be possible to assemble for testing.

Hellord's post on page 1 shows testing with Imp. OP(+50% crit) and 54.78% crit; he saw 1535 crits with no hits. That puts the odds of crit depression working the same for specials as whites at about 1/impossible.

### #39 Aldriana

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Posted 15 December 2009 - 09:26 PM

Ah, I missed that. Okay, then, yes, I agree with Landsoul's summary.

### #40 mschietinger

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Posted 17 December 2009 - 09:09 PM

I've been thinking about this crit conversion effect for the last day or two, and thought up what might be a posible explanation for the 4.8% crit to hit conversion we are seeing.

What if the effect is caused by bosses having resilience?

A lvl 80 player would take about 470 Resilience to get 5% crit converted to hit. It wouldn't be unrealistic to think then that a lvl 83 mob with 500 resilience would have about 4.8% crit converted to hit.

As I understand it, This mechanic is in game already and could easily have been used to reduce dps from excessive crit scaling. The fact that resilience as a mechanic was added after the core combat table was built could explain this crit reduction interacting with the crit cap in an weird way.

For example, if the process was:
Generate combat table
Generate random number
Check result
If Crit was it countered by resilience? if yes then result = Hit

Then we would see pretty much exactally what has been observed.

The only thing I am not clear on is what happens to say a player with resilience getting hit by someone thats crit capped. Wowwiki only uses the example of a player with 100% crit hitting someone with 5% resilience and beign reduced to 95%, but what abotu a player with 105%?

I would think that a rogue or DW warrior attacking a Prot pally or warrior would do it. Unfortunately As a resto druid I don't have access to either to test with.

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