Diminishing Returns - Avoidance
Thanks and credit to Whitetooth for doing all the math and analysis to get us the numbers and formula that make all of this explanation possible. (Want math? It's in post #2)
Dodge, parry, and miss are subject to diminishing returns. When you determine how much dodge/parry/miss you gain from rating or defense, it must be converted into the diminished amount. The diminished amount is what is added to your dodge/parry/miss chance.
Diminishing returns on avoidance do not work like diminishing returns on stuns! There's a common belief that if you avoid an attack, your chance to avoid subsequent attacks is reduced. This is not true - read on!
What are diminishing returns? One definition puts it this way: The principle that further inputs into a system produce ever lower increases in outputs. Basically, you get less avoidance for every point of rating than you got for the last one. There's a simple step-by-step "here's how it works" explanation of diminishing returns here: http://www.tankspot.com/forums/f63/4...ns-armour.html.
Some things worth noting:
- Chill of the Throne is applied after diminishing returns. If you get all buffed up outside of ICC to, say, 26% dodge, when you zone in you will have 6% dodge.
- The diminishing returns on dodge, parry, and chance to be missed are independent of each other. Each has its own cap and formula.
- There is no "avoidance cap". If you can get to 10% miss + 20% parry + 70% dodge, you would indeed be completely unhittable by an equal level attacker
- Avoidance contributed by defense is subject to diminishing returns, as will be shown below
- Your base (naked) avoidance and avoidance given by talents and racials is NOT subject to diminishing returns, and are not included in the formulas. Just add them on at the end.
- The cap for miss has been verified for warriors only at this time.
- The dodge and parry numbers shown on your character sheet do have diminishing returns taken into account (see Post #86 for how that works)
- The miss chance on the defense tooltip does not have diminishing returns taken into account (see below for how to calculate miss chance.) The tooltip is also reporting only the non-diminished amount of miss chance that your defense is contributing - it does not include the basic 5% miss chance that an equal level opponent will have against you.
- Block chance is not subject to diminishing returns at all
The total change in an avoidance type (i.e. dodge, parry, or miss) from all sources (rating, defense, agility, etc.) must be calculated together so that the result correctly takes the diminishing returns into account. When considering an item and whether it is an upgrade or not, a total recalculation of each avoidance type using the new item's stats and all stats from other items, buffs, etc. must be performed. To avoid a great deal of tedious calculation and recalculation, an addon like Whitetooth's RatingBuster is highly recommended. RatingBuster will do the complete recalculation for a given item, and display the correct increase or decrease in stats in the item's tooltip. Get RatingBuster: WoWInterface, Curse
Here's a sampling of rating vs. avoidance (pretty graphs are below in other posts).
- We start at zero and just show values for different amounts of rating.
- The expected value for each of dodge, parry and miss is simply the amount of rating divided by the rating needed for 1% (what you would have gotten as a tank in the Burning Crusade era)
- The diminished value for each is what you will actually get.
- See post #2 to see how these diminished numbers are actaully calculated, if you care.
Note that actual avoidance approaches the cap asymptotically as expected. Stacking rating to try and hit the cap will leave you disappointed. All of the above numbers are based on just the ratings. To these you need to add your base chance to dodge, parry, and be missed (don't forget an extra 2% if you're a Night Elf).
expected diminished expected diminished expected diminished
rating dodge dodge parry parry miss miss
0 0.00 0.00 0.00 0.00 0.00 0.00
100 2.21 2.25 2.21 2.20 0.81 0.81
200 4.42 4.39 4.42 4.21 1.63 1.54
300 6.63 6.43 6.63 6.04 2.44 2.20
400 8.84 8.37 8.84 7.73 3.25 2.81
500 11.05 10.22 11.05 9.28 4.07 3.36
600 13.26 11.98 13.26 10.71 4.88 3.87
700 15.47 13.67 15.47 12.04 5.69 4.34
800 17.68 15.29 17.68 13.27 6.51 4.77
900 19.89 16.83 19.89 14.42 7.32 5.18
1000 22.10 18.31 22.10 15.50 8.13 5.55
1100 24.31 19.73 24.31 16.50 8.95 5.90
1200 26.52 21.10 26.52 17.44 9.76 6.23
1300 28.73 22.41 28.73 18.33 10.57 6.54
1400 30.94 23.67 30.94 19.17 11.39 6.83
1500 33.15 24.88 33.15 19.95 12.20 7.10
1600 35.36 26.05 35.36 20.70 13.01 7.35
1700 37.57 27.18 37.57 21.40 13.83 7.60
1800 39.78 28.26 39.78 22.07 14.64 7.82
1900 41.99 29.31 41.99 22.71 15.45 8.04
2000 44.20 30.32 44.20 23.31 16.27 8.25
10000 220.99 63.80 220.99 39.06 81.33 13.47
How much rating?
The most popular question: How much should you get then, and in what balance? Thanks to a bunch of work by Xenix, Jere, Theck and others (see here), we have some general rules for the post-3.2 world:
Warriors and Paladins
Take your total values for dodge and parry from the character sheet. From there, your optimal balance between dodge rating and parry rating is
Of course, if you're outside of your "optimal balance" and you add a parry gem, that may be enough to tip the balance back. The odds of you needing to actively pursue parry are pretty low.
(character_sheet_dodge-10%)/(character_sheet_parry-10%) = 1.88
The parry you get converted from strength is subject to diminishing returns. This means you will always have lots of parry rating. Your optimal balance is
Frequently Asked Questions
dodge is always better
Q What about parry gems?
A If you're a Death Knight, you're never using them. For a Paladin or Warrior, it may be that a parry gem may satisfy the optimal balance for you. Then again, most will only use such a gem to satisfy meta requirements (the greater debate of stamina vs. avoidance gems is not something we'll go into here), so the likelihood of having the "wrong" gem socketed and making a big difference is basically none. As noted, the likelihood that you will need to stack parry gems to achieve your "optimal balance" is pretty low. Even if you did need multiples, the change in your overall avoidance is on the order of fractions of a percentage.
Q Does gear that is itemised with parry suck?
A Nope. The parry you get from itemisation will help keep you in balance as you go. Of course, the old comparisons still apply: if you have iLevel 187 bracers with 20 dodge rating and get iLevel 200 bracers with 55 parry rating, that's an upgrade no matter how you look at it. If you have bracers with 50 dodge rating and get bracers with 55 parry rating, it's a little less clear as to whether that's an upgrade.
Q Does this mean that every X avoidance you add increases time to live linearly, like armour?
A Nope, it falls out differently for avoidance. Being based on probabilities, you can't determine a concrete amount of time to live it would give anyway.
Q Are we sure that chance to be missed subject is to diminishing returns?
A Yes. Daelo told us so on the WoW forums. Whitetooth has done an insane amount of testing to determine what the miss cap is (here: The Miss Cap)
Q Has anyone confirmed the miss cap for Paladins, Deathknights, or Druids yet?
A Not 100% absolutely yet, but it's a good bet the cap is the same as Warriors for Paladins and Deathknights since the dodge and parry caps are the same. Druids may have a different cap given their cap for dodge is different from everyone else's.
Q What's my chance to be missed at 540 defense?
A 9.29% unless you're a Night Elf, in which case it's 11.29%. Example 3, below, breaks down the math for 540 defense (689 defense rating from gear)
QIs the dodge and parry chance listed on the character panel before or after diminishing returns?
AThe dodge and parry percentages have diminishing returns taken into account. It's a bady worded tooltip for sure. See here: Post #86
Q What's the macro for avoidance now?
Q Is there a real example of the calculation I can see?
A These use Patch 3.1 values: Warrior and Death Knight. The method used there is the same as you'll use with the current values, though.