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Thread: Mitigation

  1. #1
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    Mitigation

    What is Mitigation?
    Mitigation is the amount of damage that is reduced by your armour. You can find out what your mitigation against physical damage is against something the same level as you by mousing over your armour total on the character sheet in game. If you have 54% mitigation, then you would take 46% of the damage from the attack when it lands. Using those numbers, if the attack would hit for 10,000 damage with no armour, you would take 4600 damage from it. There's a hard cap of 75% mitigation on armour, easily testable in game, Blizzard has outright told us in past, and as you see in the code below from the basic WOW interface it gets set to 75% if the calculation were to come out higher than that.

    Note that a lot of people call dodge and parry mitigation. We've been encouraging people to distinguish avoidance and mitigation by their definitions for a long while:
    Main Entry: mit·i·gate
    1 : to cause to become less harsh or hostile
    2 a : to make less severe or painful
    Main Entry: avoid
    (...irrelevant definitions...)
    3 a : to keep away from b : to prevent the occurrence or effectiveness of c : to refrain from
    While a dodge or parry (or being missed) technically means you mitigated 100% of the damage, it also leads to confusion when trying to talk about the various gear strategies. Dodge, parry and miss are properly called avoidance.

    When you block, on the other hand, that is mitigation since you are only preventing some amount of damage, and the rest gets through. Blocking can give up to an extra 10% mitigation, depending on what you're fighting and what your block value is.

    But when I dodge I take no damage, so that really is mitigation!
    As noted, that is technically true. The difference between mitigation and avoidance is a pedantic difference, but the big thing is that you can account for mitigation from armour in calculations since it is a constant. The damage you don't take because you dodged, parried or were missed, or because your block value was bigger than the hit, are all based on probability. You can't determine when that reduction is going to happen (and in the case of block you can't always know that your block value will be enough to block a whole hit). Because of that nature, you can't use it in calculations. That's why we separate them in definition because otherwise it gets terribly confusing when trying to show theorycraft, when trying to explain it all to new people - basically everywhere that matters.

    Block is funny since it can act as mitigation when your block value is too low to absorb an entire hit, and it can be avoidance when it is. It's always based on probability, so it is not properly counted with your mitigation. These days it is very rarely a complete avoidance of damage, so it is not properly counted with your avoidance. Generally it is a third term when used in theorycrafting.

    We generally add a third term to be the all-encompassing one: Mitigation for armour, Avoidance for dodge/parry/miss, and damage reduction when referring to the combination of them, including block.

    There's a reason people come here for this kind of information, and not to whatever other place. We have consistent definitions like these because it helps us to describe stuff that can be fairly complex to people in as simple a way as possible.

    How much mitigation does my armour give, anyway?
    Happily, this is a question that is easily answered without needing to reverse engineer anything. We simply look in the PaperDollFrame.lua file in the basic WOW interface. This is the piece of code that displays all your stats on the character frame. It explicitly gives the mitigation formula for armour. (Note that this formula has not changed at all for Wrath of the Lich King):
    Code:
    local levelModifier = attackerLevel;
    if ( levelModifier > 59 ) then
      levelModifier = levelModifier + (4.5 * (levelModifier-59));
    end
    local temp = 0.1*armor/(8.5*levelModifier + 40);
    temp = temp/(1+temp);
    if ( temp > 0.75 ) then
      return 75;
    end
    ...
    We see that the mitigation function is different for levels 1-59 than it is for level 60-80. In all cases, the formula for mitigation as a function of armour takes this form:
    Code:
          A
    M = -----
        A + K
    Where K is a value based on the attacker's level (not your level!). When considering mitigation for attackers under level 60, and attackers level 60 and over, all that changes is the value of K. Let's first visit the old-style mitigation formula, which still applies for all attackers under level 60.

    Under 60
    From the above code, we see that if level is under 60, we still get K = (85*L + 400). Substituting back into the mitigation formula:
    Code:
                A
    M = ----------------
        A + (85*L + 400)
    60 and beyond
    From the above code, we see that if level is 60 or higher, the value of K is modified based on how many levels above 59 the attacker is. With a bit of manipulation, we get: K = (467.5*L - 22167.5). Derivation of that is left to interested readers. Substituting back into the mitigation formula:
    Code:
                    A
    M = -----------------------
        A + (467.5*L - 22167.5)
    That's pretty ugly. Here's the formula solved for level 80 and 83 attackers, which will be the interesting cases anyway:

    Code:
               A
    M80 = ------------
          A + 15232.5
    Code:
              A
    M83 = ----------
          A + 16635
    Mitigation at selected points
    Code:
    Armour	Level 80	Level 83
    10000	39.6%		37.5%
    15000	49.6%		47.4%
    20000	56.7%		54.6%
    25000	62.1%		60.0%
    30000	66.3%		64.3%
    35000	69.7%		67.8%
    40000	72.4%		70.6%
    Wait, what? So when do I hit the 75% cap?
    As always, the 75% cap is hit at 3*K (again, the derivation of this is left to interested readers).
    For a level 80 attacker, 75% mitigation is at 45698AC
    For a level 83 attacker, 75% mitigation is at 49905AC
    Don't forget to read here about diminishing returns.

    Blocking
    Blocking is also a form of mitigation. Every time you block, you reduce the incoming damage by your shield block value (SBV). Depending on what you're fighting and how much block value you have, it can be a pretty significant amount of mitigation. More on blocking

    Defensive Stance
    The warrior 10% mitigation bonus for Defensive Stance is multiplied with your mitigation from armour, (and is not included in the mitigation given in the tooltip for armour). That is, damageTaken = totalDamage x (1-mitigation) x (0.90)

    For example:
    - If you have 50% mitigation from armour, you have an overall mitigation of 55.0% in defensive stance
    - If you have 75% mitigation from armour, you have an overall mitigation of 77.5% in defensive stance

    What about Magic?
    When fighitng something that does magic damage, armour doesn't provide any mitigation at all. That's when we start breaking out the resist gear. The basics of how resistance works are found here. The best you can do with resistance, as with armour, is to achieve an average 75% resist rate. You get this by having a resistance against the school of magic equal to the (5 x mob level). For level 70, that's 350. For 73 that's 365. Note that spells and special abilities cast by mobs cannot be critical hits, so defense isn't nearly as important as resistance for high magic damage tanking where the magic comes from spells and/or special abilities.

    On the other hand, elemental mobs deal melee damage that is elemental, and they can critically hit you with those melee attacks. Having some defense is good here, but it's often very important to maintain the high resistance even at the cost of defense. In general, maxed out resistance will mitigate more damage than the crit reduction would provide while taking more damage overall because of lower resistance.
    Last edited by Satrina; 01-16-2010 at 10:49 PM.

  2. #2
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    "more on blocking" theres no link

    btw tks for sharing all your work
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  3. #3
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    - If you have 50% mitigation from armour, you have an overall mitigation of 55.0% in defensive stance
    - If you have 75% mitigation from armour, you have an overall mitigation of 77.5% in defensive stance
    How come at 75% mitigation from armour you only get 77.5% in def stance?

    50 * 1.1 = 55
    75 * 1.1 = 82.5

    Or maybe I am missing something?

  4. #4
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    you're assuming the multiplier works that way. it doesn't.

    It's actually, post armor mitigation for defense rating.

    It doesn't work addititively, it works multiplicatively.

    At 50% you actually have (1-.50) * .1(defensive stance multiplier) = 5% defensive stance bonus, that + 50% original = 55%.
    at 75% you actually have (1-.75) * .1(defensive stance multiplier) = 2.5% defensive stance bonus, that + 75% original = 77.5%

    So the more armor mitigation you get, the less def stance bonus you get. Otherwise warriors would be able to obtain 85% mitigation, much more than any other tanking class.

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  5. #5
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    Quote Originally Posted by Kazeyonoma View Post
    you're assuming the multiplier works that way. it doesn't.

    It's actually, post armor mitigation for defense rating.

    It doesn't work addititively, it works multiplicatively.

    At 50% you actually have (1-.50) * .1(defensive stance multiplier) = 5% defensive stance bonus, that + 50% original = 55%.
    at 75% you actually have (1-.75) * .1(defensive stance multiplier) = 2.5% defensive stance bonus, that + 75% original = 77.5%

    So the more armor mitigation you get, the less def stance bonus you get. Otherwise warriors would be able to obtain 85% mitigation, much more than any other tanking class.
    If I am reading this correctly then... it would be 100%-50% = 50% not avoided.. So that 50% x by the 10% from defensive stance = 5%.. 50+5= 55%

    100%-75% = 25% then 25% x 10% = 2.5% So then 75 + 2.5=77.5%.

    Which makes sense .
    True Bonding Occurs when you wipe your raid and then your raid wipes you in return - Tarigar

  6. #6
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    Yeah, the short way is just to multiply all the unmitigated portions, to get the final mitigated damage taken.

    (100%-75%)*(100%-10%) = 25% * 90% = 22.5%

  7. #7
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    Just for clarification, while the absolute values for defensive stance do decrease the more armor you have, the relative value stays the same at 10%: I.E. you take 10% less damage with defensive stance up than you did without it, regardless of how much armor you have. The absolute value will be lower, but the "then compared to now" value will remain at 10% due to the multiplicative nature of the equation.

    As an aside. If you were able to "boost" defensive stance somehow, you would see the absolute contribution of armor decrease in the same fashion as you see the absolute contribution of defensive stance decrease when you boost armor.

  8. #8
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    It makes sense for me... I am working on building a full time to live spreadsheet... And this makes a huge difference. What I would like to do is see how each piece.. inherently affects your ttl.
    True Bonding Occurs when you wipe your raid and then your raid wipes you in return - Tarigar

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