(My apologies for the lengthy post. I wanted to make sure I went in-depth in the first post in this thread because it is usually the only one read by most people joining the thread for the first time. It might be different here, but I'm new so I wouldn't know. >_>)
Since this is the premier theorycrafter's forum, to the best of my knowledge, I'm here to present some results I find...not shocking, per se, but definitely eye-opening. Up until now, it has been understood with absolute certainty that
all melee attacks are based on a one-roll system, in which your combat table is built in order of priority of combat results until it fills to 100%, at which point any leftover results are dropped off.
This fact has been justification for a great deal of theorycraft over the months. Most notably, when Blizzard initially released our new combat talents for the Burning Crusade expansion, we were up in arms over the 41-point talent, Surprise Attacks. The one-roll model told us that preventing our Backstabs from being dodged actually slightly decreased our DPS, due to the greatly reduced energy cost of dodges and the loss of crit frequency relative to attacks landed incurred with the reduction in dodge frequency.
I'm here to throw a wrench into all that, even if somewhat after the fact. I would like to suggest that perhaps all the fools who did no experimentation or reasoning of their own were correct after all. They were not correct for the right reasons, but they may have been correct. I would like to suggest that Backstab and other special attacks are on a two-roll system. Note that I remain convinced just as much as ever that white attacks follow a one-roll system.
In this thread, I intend to present the data I believe to be evidence of a two-roll system for Backstab. I also intend to provide a cursory statistical analysis of these data, and to attempt to head off any potential counter arguments in advance. I don't expect to convince everybody straight out, but I do expect to at least spark discussion.
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The Data
The data I have gathered represents several months of instance runs and solo play. I am not a raiding rogue, nor am I in a raiding guild. However, since September I have run ZG on average once every other week. Although I have a Lobotomizer and Don Julio's Band, I do not PvP on this character anymore. Thus, the data I will present consists of only a negligible amount of PvP (whatever I happened to stumble upon when trying to get places; I play on an RPPvP server, so it's sometimes unavoidable).
Here are the data for Backstab over this timeframe, provided by KombatStats (screenshot available upon request):
Swings: 5924
Hits: 2423 (40.90%)
Crits: 3207 (54.14%)
Misses: 64 (1.08%)
Dodges: 204 (3.44%)
Parries: 20 (0.34%)
Blocks: 6 (0.10%)
Here is a CTProfile of my character's gear, worn for almost all PvE situations (Stratholme is the only exception; more on this later). You may also see my talent build in this profile. With the gear and talents as indicated in the profile, my tooltip crit chance is 27.86%.
Vulajin / CTProfile
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One-Roll Analysis
We have believed special attacks to be a one-roll system for a long time now. Under this model, the combat table for my Backstab looks like this (assuming level 60 targets):
0% miss
5% dodge
57.86% crit
37.14% hit
Given this table, it's straightforward enough to determine that, on 5924 Backstabs, I would expect to crit about 3428 of them. Of course, probability being what it is, it's certainly conceivable that I don't crit exactly 57.86% of my Backstabs all the time. I observed 3207 crits. How likely is that? This is where statistics comes in handy.
I don't know if everyone's particularly well-versed in statistics, so I'll omit the nitty-gritty calculations and just say that, given the assumption of a one-roll system, the sample size of 5924, and the expected frequency of 3428 crits, the probability of experiencing only 3207 crits is insignificantly small (for statisticians, the z-statistic is -5.82).
Clearly something happened here. What might it have been? There are two possible explanations. One is that there was some source of deviation which caused my crit rate over those 5924 Backstabs to "slip" by over 3%. The other is that Backstab utilizes a sequential two-roll system. Let's analyze the former possibility first.
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Sources of Deviation
There are many potential sources of deviation in crit rate. However, we can generalize them all into two categories. First, there are those which affect the crit rate directly. For example, changing gear can decrease your crit rate. I do have a set of gear I wear every time I run Stratholme, consisting of my Undead Slayer's Armor set and my Seal of the Dawn. Switching into this gear reduces my tooltip crit rate to 25.55%.
Aside from my Undead Slaying gear, I do not change my rogue's gear at any time during PvE. Thus, the lowest my Backstab crit rate ever goes is 55.55%. Obviously, if my crit rate never drops below 54.13%, then it is not likely for the average crit rate to drop to 54.13%. Another calculation shows that even if my crit rate were
always 55.55%, the probability of experiencing the deviation I experienced is approximately 2.8%.
While it seems like 2.8% might still be within the realm of possibility, note that most of my time on this character is spent in instances with buffs such as Grace of Air Totem and Leader of the Pack. I also often drink Elixirs of the Mongoose. Considering that I don't spend 100% of my time wearing my Undead Slaying gear, and that I probably have these buffs much more often than I wear that gear, this is not an adequate explanation for the deviation I experienced.
Note also that mob defense skill cannot adequate explain this deviation either. The highest level mobs I could conceivably be fighting are level 63. Even if we assumed that I were fighting level 63 mobs exclusively (not likely, since I don't raid other than an infrequent ZG), my expected crit rate would only decrease by 0.6%. In addition, I should have experienced a 0.6% lower rate of Backstabs succesfully landed (which I did not; more below). Since I assumed level 60 targets, even though I fight lower level targets most of the time, I am actually underestimating the crit rate I should have experienced, and the discrepancy is still quite large.
The second category of sources of deviation consists of those which increase your chance to miss or to be avoided enough that some of your crit rate gets "pushed off" the one-roll combat table. Because miss and avoidance precede crit on the combat table, if I were to have higher than 42.14% chance to miss or to be avoided, I would "lose" some of my crit. There are certain debuffs which cause this effect. Baroness Anastari in Stratholme and Kurrinaxx in Ruins of Ahn'Qiraj both have debuffs which significantly reduce one's chance to hit.
Let's look at the two extremes. On one end of the spectrum, let's say that I was afflicted by some effect on 100% of my Backstabs, causing the 3% drop in crit rate. Since the effect occurs on every Backstab, it must reduce the expected crit rate by approximately 3%. In order to achieve this effect, it must increase my miss or avoidance rate by approximately 45.14%. However, if I experienced such an effect on 100% of my Backstabs, then not only should I have missed a great deal more, but I also should have experienced zero hits. Clearly neither of these things was the case.
Now let's instead say that I was afflicted by some effect which increased my miss rate by 100%, but it only affected exactly as many Backstabs as necessary to reduce my crit rate by approximately 3%. In other words, (0% * x) + (57.87% * (100% - x)) = 54.13%. Solving this trivial equation yields x = 3.73%, the percentage of my Backstabs which had a 100% chance to miss. However, if this were the case, then my overall chance not to land a Backstab should have been (3.73% * 100%) + (96.27% * 5%) = 8.54%. The frequency with which I actually landed Backstabs was 95.04%. The probability of experiencing this deviation, if I were afflicted with that 100% miss debuff 3.73% of the time, is even more insignificantly small than the above insignificantly small probabilities (z-statistic of -9.85).
Clearly, neither hypothetical extreme adequately explains the results obtained. Could there be some magic number in the middle which would explain it? By inspection, you can see that the answer is no. In order to decrease one factor, you must increase the other, and even if you take either one to its extreme, you will find that there are other consequences which do not appear in my data. Thus, there must be some explanation for the observations other than a source of deviation.
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Two-Roll Analysis
What if Backstab, unlike white attacks, were on a system of two sequential rolls? This goes contrary to what we think about simplicity in programming and reducing network load, but let's think about it anyway. In a two-roll system, first there would be a roll to determine whether the attack missed, connected, or was avoided, and then there would be a roll to determine whether the attack was a crit. The combat tables for Backstab would be:
0% miss
5% dodge
95% attack lands
- 54.97% crit
- 40.03% hit
Under the assumption of a two-roll system, given our 5924 Backstabs, we'd expect 3256 to crit. Recall that I observed 3207 crits. The probability of experiencing this much of a deviation, if Backstab uses a two-roll system, is about 20% (z-statistic of -1.28). The observed crit rate is still slightly lower than expected, but 20% is magnitudes better than the infinitesimal probability of experiencing 3207 crits in the one-roll system.
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Conclusion
The data I have collected over these months display a deviation from the expected values that, in my opinion, cannot be explained away as random deviation. Of the external factors which could have influenced my data gathering, those which should have skewed the crit rate
up far outweigh those which could have reduced it as low as it is. The data do not perfectly reflect the two-roll model I have presented here either. However, this model does come a great deal closer to explaining the discrepancy I observed.
I now submit this thread and all its contents to the scrutiny of the theorycrafters around here. I put a lot of work into it, so I'm going to go ahead and hope that someone doesn't come in and disprove it in blatantly obvious fashion within five minutes. :-P
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Addendum
At Kalman's request, here are the data I parsed for melee attacks over the same time period. As with the Backstab data, a screenshot is available upon request.
Swings: 57863
Hits: 25689 (44.40%)
Crits: 15960 (27.58%)
Glancing Blows: 5645 (9.76%)
Misses: 7828 (13.53%)
Dodges: 1846 (3.19%)
Parries: 667 (1.15%)
Blocks: 228 (0.39%)
Note that for almost the entire length of time over which the parse was conducted, I wore a Tarnished Elven Ring in place of the Seal of the Gurubashi Berserker which I recently acquired. Thus, with my talents, my total +hit% was 11%, and therefore my miss rate on white attacks was 13%. The probability of the observed discrepancy is actually somewhat small (z = 3.78). I don't have a good explanation for this being higher than expected; it's possible that I'm underestimating the portion of the parse that comes from when I used the Seal (and thus had 14% miss).
My crit rate, as mentioned, is 27.86%. The chance of the observed discrepancy here is approximately 13.4% (z = -1.50). My explanation for this, again, has to do with the occasional use of my swords, which reduces my crit rate by 4% (loss of the dagger spec bonus, plus 1% from the Dal'Rend main hand). Let x equal the percentage of the time during which I used my swords. Then we can approximate x by solving this equation: (x * 23.86%) + ((100 - x) * 27.86%) = 27.58%. This yields x = 7.00%, which I will attest approximates the frequency with which I use my swords fairly well.
11/15/06, 5:46 PM
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