I found these trade-offs a bit hard to visualize until I drew an equivalent circuit:
which I think is correct. Avoidance of dodge and parry add like resistance in series and parallel, based on the weightings k and c. This makes sense that as dodge and parry grow large, c dominates the parallel component (ie, the dodge and parry 'cap' from gear).
Throwing it up here in case the visual of an avoidance circuit helps anyone else...
I somehow missed the post about the diminishing returns, and as a warrior I'm also trying to figure out how this affects my gearing. The thing that I've read and re-read that I don't understand is the "cap".
Class type c 1/c
Warrior Dodge 88.129021 0.011347
Warrior Parry 47.003525 0.021275
What exactly does 'c' mean? Are those hard coded maximum percents? Are they just per-rating constants for the formula? The fact that druids have a 100+ 'cap' would seem to indicate that it's not percent, and the numbers are way too low to be ratings (it would seem).
So outside of the equation, should that 'c' be evocative of anything to us? Are there hard-coded % maximums we can never achieve?
The closer you get to the cap, the faster the returns diminish. For warriors, pallies, and DK's, the parry cap is lower so the returns diminish faster at the same avoidance. For example, you get the same "bang for your buck" (Ad/A) in rating at the following points.
10% dodge and 5% parry
15% dodge and 6.5% parry
20% dodge and 8.5% parry
So it looks like parry is much more expensive in terms of diminishing returns. So if your added avoidance from dodge is less than twice your added avoidance from parry, go for Dodge, otherwise go with parry. On top of that, parry is more expensive in terms of avoidance/rating so it makes it even more expensive.
I wonder how this is all related to defense and do misses from defense also suffer from diminishing returns?
After reading this post i decided to do abit of math myself, mainly to find a formula that tells me how much rating i need for another % of avoidance for dodge and parry, havent come to do def yet. And use those to find out when it's worth gemming for parry instead of dodge.
Since all data already have been multiplied with 100% omnitting the % sign ill do the same.
To gain an additional % postdimished avoidance of a single attribute post diminishing returns you will need Ax amount of of that stat pre diminishing returns furfilling following equation, where A the amount of avoidance you have in that stat exceding base, as listed in the tooltip:
To convert that to rating pr avoidance post diminishing returns you only have to multiply with the base rating pr avoidance.
To better understand these formulars i have made a graph of how much rating you need to gain 1% avoidance, compared to how much you have in your tooltip (predimished).
As you can see from the graph you need quite alot of dodge for parry to be equally as good, i have decided to calculated this aswell to get the exact.
Ap is the % of additional parry in the tooltip, and Ad is the % of additional dodge. Then lets see what Add must be for both stats to return the same avoidance pr rating.
So you more then twice as much dodge plus 10 then your parry for parry gemming to be worthwhile for avoidance purposes.
P.S. I apologize for any flawed language not used to writing in english.
Sorry for being a nub, couldn't figure out how to post a graph.
If I get this right, Iím afraid spreadsheets are required gear decision.
First, I rewrote the formula to this:
Ad = 1 / [ (1/c) + (k/A) ]
Both c and k are constants, the only variable is A.
In terms of survivability, the only thing that matters is the difference (∆) for Ad. The smaller the denominator the lesser avoidance you lose on the ∆ Ad.
Due to the dodge and parry caps (c) are different, these two types of avoidance do not subject to the same rate of diminishing return. Essentially speaking, due to 1/c for dodge is smaller than for parry, for the same A value, the denominator for dodge is smaller than for parry.
The only general rule that derive from this is to diversify the different types of avoidance and keep each category low to minimize diminishing return (avoid stacking a single avoidance type). While this comes pretty close to stack defense, due to the rates for diminishing return for them are different, there should be more dodge than parry (not to mention the same amount of avoidance in parry cost than dodge, please read Zephyrís post for details).
After saying all these, sorry, you still need to run a spreadsheet with your setups to make the final decision. I blame blizzard for making the math so much more complicated.
An interesting point, when A is an extremely small value, ∆ Ad is greater than A.
When A > 1.02%, A becomes greater than ∆ (parry)
When A > 1.92%, A becomes greater than ∆ (dodge)
Although practically, this makes no difference. Since you need 90 defense skills above base value to eliminate critical strikes against you; you should have A = 3.6% for every type of avoidance already.
Thank you for this post and all the information. It's certainly very useful and thorough
But in my case, my math skills are non-existent. I literally cannot do even basic math well. So when I go to add gems and enchants to upgrade my defense rating or dodge, etc. I often feel very frustrated because I have no way of knowing exactly how much + defense (for example) I will actually get when I apply the new item.
To be honest, I think this is a fault in the game that Blizzard should fix. For example, if an item reads "On equip: Adds 12 defense rating", then it should do just exactly that when it is equipped. I'm a player, this is just a game I do in my past time and I shouldn't be required to do complex calculations to figure out just how much defense (for example) I will get AFTER equipping a BOE item that I could have sold instead.
Having said that, I realize Blizzard may not do this any time soon. So I guess my real question is, is there a simple script/macro/forumla somewhere that I can simply plug numbers into? I used to have one for total avoidance and it was very, very useful before we all leveled to 80 - Just click it and I'd know what percentage I was at.
Anyway, thanks again and I appreciate anyone who might be able to help.
Is one, and while it is not entirely updated, the vast majority of stuff is. If you are familiar with spreadsheets you can edit some things too.
Anyhow, I never used spreadsheets before but now that the value of def/dodge/parry changes based on your gear choices and gear level, it's pretty much required. Take a look, I assume the author will update it more in the future.
Thanks Zephyr for the calculation. One thing I think you may want to clarify in your text though is that Ad and Ap need to be the undiminished avoidance from the dodge and parry tooltips PLUS the undiminished dodge and parry % you get from the defense tooltip, right? For instance, at exactly uncrittable, your additional defense gives you 5% pre-diminishing returns to dodge, parry and miss. Assuming no additional defense or parry on gear, how much dodge rating would you have to stack to reach parity per rating point with parry? Using your formula, you'd need about 20% additional undiminished dodge. You have 5% from your defense, so 15% undiminished dodge. 39.34799 dodge rating per percent undiminished, we get ~590 dodge rating. Any additional parry or defense you have is just going to make this number go up, so the rule of thumb should be: Until you are at 590 dodge rating, point for point dodge is better. Gem for dodge. Once we get that high we can revisit the calculation.
From what I understand is that the diminishing returns for avoidance now work quite similar to the diminishing returns of armor.
By this I mean that a point of dodge rating will yield less dodge percentage the more you add, but that every point of dodge rating will have a linear decrease in the amount of damage received (on average over time).
So what you are saying is that, like armor, stacking avoidance is actually linear now? As Satrina's famous example way back when showed, in Time to Live terms, adding 100 armor benefits you the same whether you have 10,000 armor or 20,000 armor (until you reach the cap). Would the same hold true for avoidance stats now? Is adding 12 Dodge Rating always the same no matter how much you currently have (until you reach the cap)?
It used to be that avoidance had increasing returns, e.g. adding 12 Dodge Rating when you were at 80% avoidance reduced a lot more incoming damage than adding 12 Dodge Rating when you were at 60% avoidance. Is this change meant to offset that (to keep avoidance tanks from stacking too much)?
First let me say this helped me figure things out quite a considerable amount, thank you.
My trouble however lies when I attempted to run your calculations myself, I'll admit that it could be a mistake with my maths but I rechecked it as best I can with identical results or perhaps I've mistaken some of the explanation.
My Paladin, 80th level has 699 def rating, 127 dodge rating and 22 agility from gear. These being the stats used in the calculations of dodge chance.
According to your information this results in 13.79% dodge after diminishing returns, the trouble lies in that according to my in-game character screen I have 18.73% dodge (before diminishing returns).
Now I know that 5% of that is from the Anticipation talent, but how is my in-game before diminishing returns statistic lower than the result of calculating it using your notes?
Surely it should be the other way around?