I'm also curious as to why the steps in defense rating are so large. The "stepped nature of defense" suggests the steps should be with each point of defense skill, but instead the leaps are 8 defense skill or more.
I think those figures are simply when the least amount is lost in rounding? (728,787,846,910)
Edit: ah yes, he updated the post.
The DK tank site: pwnwear.com.
I'm also curious as to why the steps in defense rating are so large. The "stepped nature of defense" suggests the steps should be with each point of defense skill, but instead the leaps are 8 defense skill or more.
@Satorri
If you consider the picture I edited in to the previous post, you'll see that those sizable steps in defense rating correspond to the bottom of each of the "lines" in the wasted defense skill versus defense rating plot. What that means is that your total avoidance is maximized when your defense rating has the minimum waste in the rounding that Blizzard does when they convert it.
Let's look at one of the spikes in answer to your question, though. The jump from 727 to 787 rating happens when you go from 728/221/115 to 787/190/88. If you compare the avoidance change versus what would happen if you had instead kept adding dodge/parry, you get (1065 total points):
Notice that to four decimal places, the additional avoidance is exactly the same. You have to go out to much more than this to see any difference, but when you do, you find out that bumping your defense rating to the next step results in a 0.00003556% increase over increasing your dodge by one and keeping defense at 728, and a 0.000033906% increase over increasing your parry by one point.Code:1,064 point maximum avoidance, 304 agility, on a paladin: 728/221/115: 25.8890% 1,065 Points, 304 agility, on a paladin: 729/221/115: 25.8890% - No change due to no increase in defense skill 728/222/115: 25.9054% 728/221/116: 25.9054% 787/190/88: 25.9054%
From this, you can see that my initial plot jumps to the next minimum in the lines of defense rating when the diminishing returns on dodge/parry are such that the jump will give more avoidance. Because the defense rating has to come from somewhere, though, the parry/dodge ratings decrease accordingly.
If you were to calculate every possible avoidance combination at with your defense rating at anything between 728 and 787 with 1,065 total points, you would find that there is no way to get as high of total avoidance as when you use one of those two values for defense rating since they have less than 2% wasted defense skill.
On the other hand, if Blizzard's actual calculations take it out to two or four decimal places only, hitting these exact defense rating numbers isn't essential and you could get the same results by hitting values with slightly more waste, but never >20% since that means you have a full point of wasted defense rating. Those other low-waste numbers are what I posted in my previous post at the end.
-----------
Edit:
You can look at this another way as well. Let's go back and look at what happens when we maximize our avoidance given 1065 points and 304 agility as a paladin. In this case, I am going to start up the 728 defense rating line (548 defense skill) and calculate the maximum avoidance at the best defense rating for each defense skill up to the start of the 787 line (560 defense skill).
These values are:
You can already see that as you go from 728 to 787 defense rating, the wasted amount of defense rating slowly increases until you hit 787 defense rating where it goes back down to almost nothing. What you're really concerned about, though, is the effect this has on your avoidance. As such, here are the maximum avoidance values given the above constraints:Code:548 Skill - 728 Rating - 1.26% Waste 549 Skill - 733 Rating - 2.92% waste 550 Skill - 738 Rating - 4.58% waste 551 Skill - 743 Rating - 6.23% waste 552 Skill - 748 Rating - 7.89% waste 553 Skill - 753 Rating - 9.55% waste 554 Skill - 758 Rating - 11.20% waste 555 Skill - 763 Rating - 12.86% waste 556 Skill - 768 Rating - 14.52% waste 557 Skill - 773 Rating - 16.17% waste 558 Skill - 778 Rating - 17.83% waste 559 Skill - 783 Rating - 19.49% waste 560 Skill - 787 Rating - 0.81% waste
From these numbers, you can see your avoidance decrease with the increase in wasted defense rating. If your defense rating were in between 728 and 787 and -not- one of these minimum waste numbers, you would lose an additional ~.015% avoidance per point of wasted defense rating. The actual difference is barely noticable as long as you stay at the bottom of the defense rating lines, but if you were to further up the line, you would see the change. Keeping your defense rating at values where the waste is <10% should be indistinguishable from keeping it at the actual minimum steps that the overall plot indicates (when rounding to two decimal places).Code:728 Rating - 728/221/116 - 25.9054 733 Rating - 733/219/113 - 25.9045 738 Rating - 738/216/111 - 25.9035 743 Rating - 743/213/109 - 25.9025 748 Rating - 748/211/106 - 25.9013 753 Rating - 753/208/104 - 25.9001 758 Rating - 758/205/102 - 25.8987 763 Rating - 763/202/100 - 25.8973 768 Rating - 768/200/97 - 25.8958 773 Rating - 773/197/95 - 25.8942 778 Rating - 778/194/93 - 25.8926 783 Rating - 783/192/90 - 25.8908 787 Rating - 787/190/88 - 25.9054
Last edited by Xenix; 07-09-2009 at 10:02 AM.
Ok, I'm following your math there, though there's something slightly irksome about it to me from practical consideration.
The smallest increment of defense, dodge, or parry rating I would (could do 6 or go Outlands gems, but...) add is 8 from half a gem right?
8 of any of those ratings will change my avoidance in a visible fashion.
So I struggle to see why I would want to drop defense rating, or only add it to the next (60 rating pt higher) "optimal." We're making this a deal over losing fractions of a % yes?
The (Old) Book on Death Knight Tanking
The New Testament on Death Knight Tanking
-----------------------------------------
Practically, you'll never be able to hunt through all your gear and re-gem it all exactly as you please to get exactly the maximum possible avoidance given your EH preferences. All of this math was in response to two main questions, though - I think this thread has de-railed a bit from those, which were:
1) What do the 3.2 changes mean in terms of avoidance?
2) What is the optimal defense/dodge/parry ratio in 3.2 (and is defense the best avoidance stat to stack now)?
The answer to 1) is that you will lose a small amount of aviodance and parry will no longer be quite as terrible.
The answer to 2) was what caused all the discussion - basically (from my math), the answer becomes:
a) Keep defense rating at a value that minimizes wasted defense skill.
b) keep dodge/parry in a 1.875:1 ratio.
In terms of a practical use, let's say for whatever reason, I get a new piece of gear that has a blue+yellow gem slot and my un-gemmed stats after equipping it are 725 defense rating , 250 parry rating and 450 dodge rating. First, note that with those stats, I have 40% of my last defense skill point wasted. Let's also say that for whatever reason, I decide that I want to add 1.5 gems worth of avoidance and .5 gems of stam (maybe to keep the socket bonus). Now, I look at what I can get from adding 8, 16 and 24 defense rating - those would bring me to either 733, 741 or 749 defense rating. I can instead add 8, 16, or 24 points of parry/dodge.
Based on my previous numbers, I notice that 733 defense rating has very low wasted defense skill, so I would choose to add only 8 defense rating. Also, my current dodge-parry ratio is 1.8:1, so I would add dodge as my other avoidance stat to bring the ratio up.
So, based on the rules, without running the actual avoidance numbers, I would guess that gemming a defense/dodge and dodge/stam would give me the most benefit of all the avoidance/avoidance/avoidance/stam half-gem options. Also, I would speculate that whether I gem dodge or parry would make little difference since the ratio is near 1.875:1 already.
Now, let's check that against the numbers:
It is clear from these numbers that my supposition was correct based on those two rules - all the best avoidances out of the possibilites are when I gem to have 733 defense rating, the defense rating number with the least waste. Also, even if the differences here only range from 0.01%-0.04%, notice that even gemming defense/parry/parry/stam provides 0.03% more avoidance than gemming dodge/dodge/dodge/stam, which in 3.1 would be considered the best avoidance option by many (of course, that would break the socket bonus). Furthermore, the difference between this and the best possible avoidance if you could redistribute every point is only 0.04% - barely an upgrade from keeping your defense rating at 733.Code:Pre-gemmed: 725/450/250/304 - 31.4743% After gemming: 725+24/450/250/304 - 31.8491% 725+16/450+8/250/304 - 31.8179% 725+16/450/250+8/304 - 31.8164% 725+8/450+16/250/304 - 31.8610% 725+8/450+8/250+8/304 - 31.8600% 725+8/450/250+16/304 - 31.8578% 725/450+24/250/304 - 31.8278% 725/450+16/250+8/304 - 31.8283% 725/450+8/250+16/304 - 31.8267% 725/450/250+24/304 - 31.8240% Best possible avoidance given 1449 points: 910/374/165/304 - 31.9010%
A general "keep defense-dodge-parry at X:Y:Z" is inaccurate and it all depends on your current gear - for practical considerations, use these two rules for 3.2 to maximize raid-buffed avoidance:
a) Keep defense rating at a value that minimizes wasted defense skill. (Doesn't have to be one of the best values, but nice if it is).
b) Keep dodge/parry in a 1.875:1 ratio.
Last edited by Xenix; 07-09-2009 at 03:20 PM.
My own workings using differential analysis on the DR equation also confirm the 1.875 dodgep/parry ratio when keeping defense constant. It essentially comes from comparing the first order derivatives of the DR equations of dodge and parry and finding the point where they give the same value. This equation ends up being:
dodge = 1.875*parry
So it matches your findings.
Theckhd over on maintankadin has done some work on this topic as well and came up with the following ratio's as optimal:
The post on it can be found here:Assuming we get 10% dodge and parry from base+talents, and 1.65% dodge from our 90 base agility at level 80, that means that the ideal gearing progression would be to:
1. Add dodge and parry until we reach around 23.6% dodge and 16.35% parry fully raid buffed (96 dodge rating, 64 parry rating, or 11.96% dodge and 6.35% parry from gear alone)
2. Add dodge, defense, and parry rating in a 2.4 : 1.8 : 1 ratio.
Maintankadin • View topic - Some preliminary conclusions concerning avoidance in 3.2
His findings mostly match yours up to a point where he starts adding defense skill. The numbers will be slightly different as he is using some practical assumptions and using iteration to find the values (so there is some error). The point where he deviates is he finds a spot where you basically get the same effect from dodge or parry rating and then starts stacking all 3 in that ratio mentioned above.
I haven't taken the time to go through it completely honestly, but it looks sound on the surface.
Thanks for the confirmation on the ratio - I did notice one problem with my generalization that might be leading to the different numbers, though.
While looking at the previous numbers I had posted, I noticed an inconsistency that led me to notice an incorrect interpretation of the previous max avoidance vs. dodge/parry/defense graph. I stated before that the best dodge-parry ratio is 1.875:1, basing this off the slope of the dodge and parry lines. In reality, those slopes mean that once you have the appropriate amount of dodge/parry to give them equal value post-DR for your defense rating, a ratio of 1.875:1 will keep them at the same relative value. This makes a generalized statement a lot more conditional. Instead of what I said above for part b), the statement should actually be:
b) Keep your dodge-parry ratio above 1.875:1. If your dodge+parry rating total is much less than your defense rating, this ratio will go up (meaning when you have a large amount of defense rating and not much dodge and parry, you want to stack them in 2:1 ratio or greater). As your dodge+parry rating gets closer to your defense rating, the ideal ratio becomes 1.875:1.
As an example of my change, look at the best avoidance ratio for 1449 points:
910/374/165/304
This has a dodge-parry of 2.28:1 because the dodge+parry is ~60% of the defense rating. Were you to look at how to gem additional avoidance from that starting point, though, you would want to add avoidance in a 1.875:1 ratio, which would make your actual ratio asymptotically approach 1.875:1.
Well one thing to consider there is you are looking at it purely from a ratings perspective. If you keep your dodge % = 1.875*parry %, then the amount of defense you have won't affect that equalization (because it is already accounted for in the percents). Once those percents are equal, then you can stack "the rest" of your dodge and parry rating at that ratio.
so for clarification, I am saying while your overall dodge rating/parry rating ratio won't be 1.875:1 due to the effects of defense, as long as your dodge%/parry% ratio is, then you can stack your newer dodge and parry ratings at 1.875:1
EDIT: Talking purely in the scope of the 3.2 changes of course
Last edited by jere; 07-09-2009 at 03:52 PM.
A lot of extremely interesting points are being brought up here, I like the idea of keeping the ratio percentage based- makes the numbers a lot easier to work with.
Yeah - putting it that way makes a lot more sense. If you consider statement b) in terms of the dodge and parry percentages your character sheet shows (subtracting off the base 10% off each from being tank spec), then you should always have ~1.875:1 ratio for best effect, regardless of your defense rating in 3.2. I guess I was overthinking it a bit too much.
I stand corrected then - you can ignore my previous post and just go with the two rules I posted before as the generalization for best avoidance in 3.2, as long as you keep in mind that the dodge and parry percentages are the post-DR totals off of your character sheet minus whatever you have naked.
So, we:
- get the post-DR percentages from the char sheet
- reduce them by 5% dodge (talents) and 3% or 4% (runeforges), then:
- (a) use these figures, and aim for a ratio of dodge%arry% ratio of 1.875:1
- (b) also try to keep defence rating around the optimal steps of 728,787,846,910 and 969
Is that a correct summary?
The DK tank site: pwnwear.com.
Two corrections:
First, You'd reduce them by anything that DR doesn't apply to, which would be talents (5%) + runeforge + base (5% for warrior/paladins, not sure if it's the same for DK's).
Second, while those are the best numbers for defense rating, any of the numbers at the bottom of the defense lines will work equally well:
(these are the defense rating numbers with < 10% waste)Code:689,694 728,733,738,743,748,753 787,792,797,802,807,812 846,851,856,861,866,871 910,915,920,925,930,935
For DK's we get 5% dodge from talents but no parry. We get more than the parry Warrior/Pallies get from talents from Forceful Deflection (should be about 6.5-7.5% after diminishing in ~226 gear), but it comes in the form of Parry Rating so it just shoves us way further down the curve to start.
Essentially, if DK's want to hold to this proportion, chances are they'll never add gems for parry as Strength climbs with gear.
The (Old) Book on Death Knight Tanking
The New Testament on Death Knight Tanking
-----------------------------------------
Honestly, I don't think you're likely to see many warriors or pallies adding gems for parry, either, unless new avoidance plate gear swerves much more strongly towards favoring dodge over parry.
Very nice analysis, though. The 1.875 number is a very convenient way to see if there's a more efficient way to gear up.
Learn to science and stop theorycrapping in its tracks.
I go for a lot of dodge gear so you will probably see me adding parry to my gear set for balance.
True Bonding Occurs when you wipe your raid and then your raid wipes you in return - Tarigar
That's a bit of an understatement >.< with the ammount of parry we get from Forceful Deflection and our Tier gear it would be really hard to get anywhere near 1.875:1.
I'm way off that ratio, so to compare I peeked at your armory and even though you're geared mostly for dodge, you're barely around 1.3:1. You're getting over 300 parry rating from FD, that's without any buffs. You'd litteraly have to have zero parry rating from gear, and I'm not sure that'd be enough to get to the target ratio.
It turns out we must not only avoid parry gems, but avoid parry gear altogether. Parry looks more tragic the more you look into it, lol.
Indeed. =)
Well, the point I think will be simply that DK's will always enjoy the dodge rating benefit more. We've established now that stands for both survival/avoidance, and (*wipes away a tear*) for threat. At least we're getting some more benefit from the parry we just get for free!
The (Old) Book on Death Knight Tanking
The New Testament on Death Knight Tanking
-----------------------------------------
Just an update - I posted my results on the maintankadin thread where Theck was doing his own calculations, and after looking at them, he came to the following conclusion (which I agree with):
Also, using either of the methods posted above should keep you within ~0.05% of the optimum avoidance possible for you. Stacking defense to a good number is nice if you have a consistent gear set you use all the time, but if you change around a lot, it probably isn't worth the hassle - mainly focus on the dodge-parry ratio.Xenix's method is clearly the best way to optimize your avoidance. It may be difficult to do in practice though, especially when juggling multiple gear sets.
Two close, simple approximations are:
- At low gear levels ( defense rating + dodge rating + parry rating < 1150 or so), just ignore defense and stack dodge and parry rating in a 1.88:1 ratio.
- At higher gear levels (defense + dodge + parry > 1150 rating), gear so that your post-DR dodge and parry percentages come out as close to a 1.88:1 ratio as possible.
This is also equivalent to the algorithm I posted earlier for ratings:Note that this method may result in some "wasted" defense rating, but will also ensure that you're within about 0.075% avoidance of the best possible value you can have without forcing you to worry about exactly how much defense rating you have.Theck wrote:
- Take current ratings and subtract out 689 def, 96 dodge, and 64 parry
- Figure out your current ratio of dodge:def: parry
- if one of these is higher than the ideal ratio of 2.4:1.8:1, swap out some of the rating that's above the target ratio for a rating that's below or at the target value.
- Recalculate and lather, rinse, repeat.
As you said, though - DK's are pretty much hosed on choice. Since your parry bonus also scales with raid buffs, you'll be stacking dodge forever, even counting the extra agility from raid buffs as well.
Last edited by Xenix; 07-10-2009 at 01:10 PM.
Hi all my first post here.
I am more confused now than before.
Would someone take a look at my armory and tell me exactly based on the gear I have now, saying nothing will change what is my ration currently.
I am and never was good at this type of maths.
Is it also possible to put this into a marco, so that people could when changing gear click the marco and it would return some information back.
Thanks for the input.
Flavius, this is only in relation to patch 3.2, don't change anything now.
If it's too complicated for you, just gem for dodge and never parry, that's a good enough rule of thumb.
The DK tank site: pwnwear.com.
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