I did the math on my gear which has drastically higher dodge than parry using warloco's formulas.
729 def, 526 dodge, 204 parry
adding 16 of each rating provides,
16 def added = 0.24% avoidance
16 dodge added = 0.23% avoidance
16 parry added = 0.24% avoidance
So you need a pretty extreme difference in your dodge and parry rates for parry to become better, largely due to the much harsher diminishing returns. Oddly enough in my gear I'd have to say that defense would be the best stat for avoidance, since it provides block as well. As others have said though, you really need to run the numbers on your own gear to be certain what works for you.
Course the whole thing is even more amusing to me. After all nerfing avoidance just means that health and bonus armor are just that much more valuable. Going straight blue gems regardless of socket bonus is starting to look attractive in 3.2, particularly considering epic gems.
As of this state of ptr, I'd treat all three avoidance stats roughly equal once your def capped, and stack effective health wherever plausible.
Stamina can not really entirely substitute for avoidance to the point where gemming every socket put stamina becomes favorable. Currently you'll often gear for "surviving an unlucky non-avoidance streak", which is sensible. However as your avoidance goes down, those streaks will become exponentially more frequent. At some point you need to start factoring unlucky healing steaks aswell, such as a paladin / disc priest failing to crit for a while.
Neither one of the 2 should typically kill a tank if both are geared properly, but if you start gearing for nothing but stamina, you'll find yourself at a point where unlucky non-avoidance streaks coincide with unlucky healing streaks so often that either your healers go OOM (IE: The paladin fails to find a time to use divine plea), or you simply just die.
I very much recommend against simply gemming everything stamina, typically socket bonuses are too good to really make that favorable (IMO).
DK's rejoice! I knew I was saving that stupid Saph trinket for a reason......
With blue gems the socket bonuses look decent, and I do match many of my socket bonuses. I really only did so to stay defense capped, which was kinda annoying as I geared through ulduar. But with epic gems the values of the gems all inflate, but the bonus does not potentially shifting the balance some. With the massive increase in ilevel in 3.2 gear, reaching the def cap will be easier, with less gemming and chanting to reach it.
However, the amount of avoidance from your gems and socket bonuses is pretty small. I just counted mine, 36 def, 16 dodge. That's not going to make a significant dent in my avoidance levels, not enough to cause a drastic shift in the amount of 'unlucky streaks'. The vast majority of our avoidance is built into our gear and talents, and the amount from those sources is sufficient for current raiding needs.
Ha ha, me too, I don't have a second dodge trinket from Ulduar yet for my pure avoidance tanking setup (from 10 or 25-man Ulduar, can you believe that? They haven't even dropped once in 2.5 months!).
Oh I believe it.... General hates me, hasnt dropped one yet.
Originally Posted by Satorri
I think it won't be so skewed when you look at people's stats. I know tanks that have 28-30% dodge and 18% parry and other tanks with 25% dodge and 20% parry. I think the difference between the two will be closer.
In a situation where I don't want a stamina trinket, an avoidance trinket is the furthest thing from my mind compared to Mark of Norgannon
You're right, I forgot about switching out some dodge gems for agility a couple weeks back and used my class's base bonus agility. If you'd like to change the numbers to raid buffed, though, using your numbers, I would have:
705 def, 435 dodge, 317 parry, 104 block, 304 agi
I will however disagree with your method of not flooring your defense rating -> defense skill conversion. If you do not do this, you consistently overestimate the value of defense rating as you will never get as much avoidance from it as you calculate. In my case, with 705 defense rating, I have 543 defense skill. If I were to add (somehow) 4 defense rating, it would bump me up to 544 and increase my avoidance. If I were to instead add 8 defense rating through a gem, I would still be at 544 defense skill and gain nothing from the extra 4 points.
Also, in your formulas you are not using the correct paladin agility conversion. Paladin agility conversion = (0.0192 dodge%/agility)/1.15 = 0.0167 %dodge/agility or 59.8958 agility/%dodge.
Given this, my MATLAB code for my avoidance is as follows:
Set the "newAvoidanceFlag" to true for post-3.2 calculations, false for pre-3.2.
function total = avoidance(defenseRating,dodgeRating,parryRating,agility,newAvoidanceFlag)
dodgeCap = 88.129021;
missCap = 16;
parryCap = 47.003525;
k_value = .956;
defConversion = 4.91850;
dodgeConversion = 39.34799;
parryConversion = 49.18499;
agilityConversion = .019200^-1;
if newAvoidanceFlag == true
dodgeConversion = dodgeConversion * 1.15
parryConversion = parryConversion * 0.92
agilityConversion = agilityConversion * 1.15
defense = floor(defenseRating./defConversion);
dodgeUndiminished = dodgeRating./dodgeConversion + defense .* .04 + agility./agilityConversion;
parryUndiminished = parryRating./parryConversion + defense .* .04;
missUndiminished = defense .* .04;
dodge = (dodgeCap.^-1+k_value./dodgeUndiminished).^-1
parry = (parryCap.^-1+k_value./parryUndiminished).^-1
miss = (missCap.^-1+k_value./missUndiminished).^-1
total = dodge + parry + miss;
Now, with these numbers, I get the following post-3.2 raid buffed values (agility is +17 due to BoK, might be 18 if you're lucky):
As you can see, even with the bonus agility factored in, dodge is still preferred to the other avoidance stats unless I were to have even more dodge than I alread do (it's getting close to even), or unless I were to increase my defense rating by the exact amount necessary to get to another defense skill point.
avoidance(705,435,317,304,true) = 31.9134% avoidance
avoidance(705+16,435,317,304,true) = 32.1368% (+.2234)
avoidance(705,435+16,317,304,true) = 32.1523% (+.2389)
avoidance(705,435,317+16,304,true) = 32.1367% (+.2233)
avoidance(705,435,317,304+17,true) = 32.1053% (+.1919)
Not taking into account the stepwise nature of defense rating -> defense skill would make the calculations show +.2421% avoidance for adding a 16 defense gem, erroneously making me believe it is the best thing to socket, which is not at all what I would get were I to actually socket that in my gear (in this case, two points of defense rating would be wasted). Note that since the diminished values of dodge/parry are very close, however, if I -could- make a small change to somehow add only 14 defense rating, that would be better than adding 14 dodge rating or 14 parry rating in terms of avoidance. (see exception 2 that I posted earlier).
On the other hand, you do bring up a good point - if you consider your avoidance raid buffed, the extra Agi any tank will have is worth nearly 200 points of free dodge rating, which you should take into account when considering the two exceptions to the general rule that gemming dodge is best for max avoidance as I stated earlier.
So, in the end... it all boils down to less avoidance? aka another thing to make tanks more dependent on healers and less on what they can do? :(
I think to some extend you are misunderstanding me, you are correct that when the question is: "Should I gem 16 defense, or should I gem 16 dodge", that the anwser should be calculated using floored defense values. This is because, simply put- it's going to give you exact values for your very specific situation.
However if you are comparing stats on a "how good is this stat compared to this stat for a tank at roughly this gear level" as opposed to the context of how to gem 1 specific socket, then you should look at "unfloored" defense values. I'll give you some examples:
The Defense rating "steps" around your level of defense rating are at:
703.3455 (704), 708.264 (709), 713.1825 (714), 718.101 (719), 723,0195 (724)
If you throw a 16 defense gem in your gear, you find yourself at 721 defense. You first bridge a gap of 4 defense rating going from 705 to 709, and then come short 2 defense rating to make it to 724, more or less putting you in a very bad spot to gem 16 defense in.
Let's say you had 3 defense rating more in your current gear- or 2 less defense rating, you'd find yourself getting 1 extra defense skill from that gem, and as such easily pass dodge rating in terms of avoidance.
For that reason, when comparing the 2 stats on a general level- you shouldn't floor the defense, and so long as you don't floor either values (top/bottom) the end result will be the average (read: not specific) value of the stat at your gear level.
In the real world, you'll almost never make a decision between a 16 def and 16 dodge gem, you'd simply go with whichever color the socket has if you really wanted to gem avoidance. If you have 2 items with a similar decision to be made between defense and dodge, you'll most likely want to decide on a case by cases basis, depending on wether or not that particular item pushes you right past a defense skill or leaves you barely short of a defense skill.
Tooltip bugs were very common in the WotLK beta, as well as previous PTR's. I recall at one point equipping a ring with 10 hit rating, gaining 20 hit rating, removing the ring and losing 15, and re-equipping it to gain 20 again. Cycling through the same gear options gave me arbitrarily different stats.
Originally Posted by GravityDK
Then I just gave up, closed my character panel, and relogged. I think it was fixed.
/I do understand what you're saying, but if you're making a generalized statement about the value of defense rating for avoidance based on not calculating what your actual defense skill is, you'll always have to keep in mind the caveat that there is only a 20% chance that it will actually be that good for you. For the most part, when people ask what is better for them in terms of avoidance rating, they're talking about the marginal benifit of adding/removing one gem worth of a certain stat. That's why in my second post above, I said that dodge rating is best barring the two exceptions based on your own gear (if you can almost exactly hit a point of defense skill and dodge/parry have similar post-DR marginal benifits, defense might be better, and if you have way more dodge than parry, parry might be better).
If you really want a generalization, though, you'd need to do something like:
This uses the previous avoidance function to brute-force calculate the best avoidance possible given a certain number of points to distribute (and given that you have 304 agility), while staying defense capped. It also adds in the base 25% avoidance undiminished that paladin tanks get.
totalPoints = 1600;
best = zeros(1,4);
temp = 0;
for defense = 0:totalPoints
for dodge = 0:(totalPoints-defense)
parry = totalPoints - defense - dodge;
temp = avoidance(defense,dodge,parry,304,false);
if defense > 688
if temp + 25 > best(4)
best(1:4) = [defense dodge parry temp+25];
Now, from these numbers you see a strange trend (or not so strange if you think about the stepwise nature of defense). All of the maximum avoidance combinations past defense cap have 728,787,846,910,969 defense rating. If you run the conversion, these are the values of defense rating that result in the minumum wasted defense rating in the defense rating -> defense skill conversion. (on the order of .01 defense skill removed with the floor).
Total Avoidance Points: Best Defense/Dodge/Parry/Avd in 3.1 Best Defense/Dodge/Parry/Avd in 3.2
700 689/11/0/45.2559 689/4/7/44.6078
800 689/111/0/47.2519 689/70/41/46.3973
900 689/211/0/49.1476 728/114/58/48.1398
1000 689/311/0/50.9502 728/179/93/49.8317
1100 689/408/3/52.6666 787/212/101/51.4778
1200 728/451/21/54.3220 787/278/135/53.0819
1300 728/514/58/55.9316 846/311/143/54.6457
1400 787/548/65/57.4952 846/376/178/56.1687
1500 787/610/103/59.0214 910/407/183/57.6550
1600 846/644/110/60.5069 969/440/191/59.1040
I haven't calculated every single value in between, but it is clear that as a -generalization- on the value of defense rating, you want to stack it so that there is as little wasted as possible once it is converted to defense skill, and then stack dodge/parry in an ~2:1 ratio, slightly favoring dodge.
Edit: As an afterthought - these inflated values of defense aren't absolutely necessary. For example, instead of 969/440/191, if you could switch 200 points from defense and split them between dodge/parry (769/540/291), you would lose only 0.07% avoidance. If you put them all in dodge (769/640/191), you'd lose 0.14%, and if you put them in parry (769,440,391), you'd lose 0.16%.
The main point of the 3.2 change (aside from a slight overall avoidance nerf) is that as long as you're not stacking huge amounts of one stat, you'll be fine. In general, though, dodge > defense > parry unless you can minimize wasted defense rating or have a bad dodge-parry ratio.
Great work thanks Xenix and Warloco, best maths-nerd thread I've read in ages.
Originally Posted by Xenix
I tried coming up with a generalisation that incorporates the 'afterthought' balancing, but couldn't quite get there.
Thanks mate. I logged in today, verified the error still exists, filed a bug report.
Originally Posted by Splug
I usually tried to follow the 3:2 or 2:1 def rating:dodge rating and never bothered on parry unless it comes with gear.
Should this change now?
maybe to a 2:1:1 Def : dodge : parry Ratings?
Does this mean Blade Ward becoming superior to other tank enchants in 3.2? (for warrior)
I was going to try and get away with not using a picture, but sometimes a plot of the data is the best way to show these things. The following is a plot where I used the previously posted code to calculate the best possible avoidance for a paladin tank in 3.2 given that they have 304 bonus agility raid buffed.
Note: If you want to convert this for other tanks, think of the agility as 213 dodge rating that I've forced on you, subtract off the equivalent dodge rating from your own agility raid buffed and the difference is how much dodge rating you should add to the numbers in this plot.
For this graph, I assume that you are able to distribute X number of rating points however you chose to get the best possible avoidance. I then calculated what the best spread would be for every value of points from 689 to 1500. (Of course, staying defense capped). From the first plot, you can see three things:
1) Once you have a certain amount of defense rating, you should leave it constant and stack dodge/parry for the best effect.
2) The ratio of dodge to parry is constant for each level of defense rating
3) The ratio of dodge to parry is relatively constant between levels of defense rating
Since I'm sure you're curious if you're reading this, here are the exact ratios:
900-1000 block (728 defense rating): .6542 to .3476
1100-1200 block (787 defense rating): .6519 to .3481
1300-1400 block (846 defense rating): .6525 to .3475
1450-1500 block (910 defense rating): .6527 to .3473
Overall, the ratio is pretty much 1.875:1 between dodge and parry.
The next question then would be what happens if you ignore the defense steps and just keep your defense rating constant while following the dodge to parry ratio? That is what the second graph shows. Each line on the second graph represents what happens when you hold defense rating constant at a certain value and just follow the dodge to parry ratio for that block.
You can see that all of the curves are almost exactly on top of each other, aside from the end of the pink line when it gets extremely far up. Even then, the difference is measured in hundredths of a percent avoidance chance.
So, in summary - what does this mean?
When raid buffed:
1) Stack defense rating until you reach a number that has a minimum of wasted in the defense rating -> defense conversion. (728,787,846,910 and 969 are the best possible ones to hit).
2) Stack Dodge and Parry in an ~1.875:1 ratio
3) If your total dodge+parry rating is getting anywhere near your defense rating, try to hit the next good number of defense rating.
4) If you can't hit the next good number of defense rating, don't worry - keep stacking dodge/parry in the aforementioned ratio and you'll be fine.
Edit: For those who are curious about the "good numbers" for defense rating, I present the following plot of wasted defense skill vs. defense rating:
The best defense rating numbers for each "line" are as follows (I stop at 10% wasted and move to the next line):
These are the numbers of defense rating you want to hit to maximize your avoidance, the further down on each line you can manage, the better.
I must be missing something, when did avoidance/defense ratings have a jagged return on points?
Is this because we're assuming the system doesn't hand defense skill fractions, thus we only gain 1 skill point rougly every 4.92 def rating points? (actually in the middle because while we don't see fractions if they are not factored I'm sure there is still rounding)
But then you're looking at pretty sizeable steps in the defense rating, so, would you mind explaining just how that works? I'm having trouble pulling it out of your math.