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Thread: Armor vs Stam: Effective Health

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    Armor vs Stam: Effective Health

    I did this math a long while back on request, comparing the Emblem of Triumph armor trinket to the Black Heart on passive equipped values. I wanted to re-post and revisit it.

    Here's the original math:
    1792 armor (does not get Toughness or Frost Pres) = X% DR *depending on gear
    126 Stam x 1.06 (Frost Pres) x 1.02 (Imp GotW) x 1.10 (Kings/Sanc) = 150 Stam = 1500 health

    So, we can compare the values based on the composite of armor and health, effective health. Remember, this only applies to physical damage. Here's how we calculate EH based on armor damage reduction:
    Code:
    EH = Total Health/(1-DR%)
    Using a convenient Solver method, we can find the breaking points for some set health and armor values. In the chart I put the armor and health values as if you had one empty trinket slot on the far left. A Rdx% is just the matching amount of damage reduction from that amount of armor. A+T is as if you added the armor trinket in your last slot, so that is the new armor value to go with the base health, and EH (AT) is the matching Effective Health. H+T then, is if you instead put the Stam trinket in the slot, and EH(HT) is the matching EH value. Here is the solver data from the spread sheet:
    Code:
    (Health)  (Armor)  (A Rdx%)  I  (A + T)  (AT Rdx%)  (EH (AT))  I  (H + T)  (EH (HT))
     42000    33541    66.85%       35333     67.99%    131209        43500   131209
     45000    37125    69.06%       38917     70.06%    150276        46500   150276
     48000    40709    70.99%       42501     71.87%    170636        49500   170636
     36525    27000    61.88%       28792     63.38%     99742        38025    99742
     38199    29000    63.55%       30792     64.93%    108907        39699   108907
     39873    31000    65.08%       32792     66.34%    118473        41373   118473
    So, the general decision is, from a standpoint of effective health against physical damage, the equip bonus of the Armor Trinket is better than the equip bonus of the Stam Trinket, so long as you fall on these breakdowns:
    • If you have 42k health, the Armor Trinket is better until you have over 33.5k armor.
    • If you have 45k health, the Armor Trinket is better until you have over 37.1k armor.
    • If you have 48k health, the Armor Trinket is better until you have over 40.7k armor (ha ha, good luck).
    • If you have 27k armor, the Stam Trinket is better so long as your health is less than 36.5k.
    • If you have 29k armor, the Stam Trinket is better so long as your health is less than 38.2k.
    • If you have 31k armor, the Stam Trinket is better so long as your health is less than 39.9k.
    So the armor value is quite respectable against a physical threat, but you lose some of that value in the face of magic damage.
    The math holds up pretty well, and in general, but to add a small bit of flavor I wanted to update the numbers slightly for a 245 level stam trinket, and show the different relative stam multipliers for the different classes.

    Satrina's Impeding Scarab = 192 Stam
    Warrior (Scarab) = 2035 health
    Paladin (Scarab) = 2198 health
    Bear Druid (Scarab) = 2798 health
    DK w/ 3/3 Vot3W (Scarab) = 2096 health
    DK w/o Vot3W (Scarab) = 2035 health

    None of the classes have a modifier that will change the 1792 armor from the emblem trinket on the baseline (only CD buffs).

    In lieu of calculating the value for each class, I'll use 2100 as an average value as the tilt will be very small, even for bears. It will only be on the magnitude of a couple hundred effective health difference for all but bears, and ~1k for bears.

    The new math suggests:
    • If you have 42k health, the Armor Trinket is better until you have over 19.2k armor.
    • If you have 45k health, the Armor Trinket is better until you have over 21.8k armor.
    • If you have 48k health, the Armor Trinket is better until you have over 24.3k armor.
    • If you have 27k armor, the Stam Trinket is better so long as your health is less than 51.1k.
    • If you have 29k armor, the Stam Trinket is better so long as your health is less than 53.5k.
    • If you have 31k armor, the Stam Trinket is better so long as your health is less than 55.8k.
    So, even without considering magic damage, against physical damage, the stamina trinket will give you more effective health than the armor trinket at most reasonable tank stat values.
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    This is survivability only, I assume. There is an inherent value, albeit less than that of survivability, to passive mitigation, in that stamina does not reduce the actual damage done to you, only your likelihood of survival, while the armor will reduce the damage done as well. Very hard to quantify the value of that damage reduction, but if you have sufficient stamina to survive, additional stamina has little benefit, whereas additional armor will always have benefit.

    Maybe I should take on the forum title "Captain Obvious," but I felt it should be said for the few people reading this that don't think about those things.

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    Actually, that's the value of "Effective Health." For physical damage, it's easy to compound health and damage reduction from armor into a single value. So long as the Effective health value is higher than the raw damage from the boss (which you never see), you can survive the hits. The sticky is where it doesn't affect magic hits, so if it were possible to fill your sockets with armor instead of health, you could have the same durability to physical hits and magic damage would be much more dangerous.

    Trust to the Satrina, the Satrina is good.
    The (Old) Book on Death Knight Tanking
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    Quote Originally Posted by Horacio View Post
    Who f-ing divided by zero?!?

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    These are interesting numbers and stuff I've been looking at recently in Rawr calculations and such.

    Of course, it all depends on the fight and how much you value pure EH over average survival/burst time and the like.

    For instance, the Armor trinket (both due to its Armor value and its click-use ability) is probably the best burst time improving trinket in the game, often followed by the Onyxia trinket depending on your existing stats.

    However, for Satrina's (Heroic) Scarab is definitely the best for EH in the majority of cases.

    When it comes to the non-heroic Scarab, it's a bit more of a toss-up, as the average effect from The Black Heart is quite similar both in burst time and average EH--about 3% lower with my stats. However, it is not quite so consistant as it will come in bursts. That said, that has a plus in some fights where the internal cooldown can expire while you are not tanking. At the end of the day, though, they are quite similar for a Warrior.

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    Yes, we're in heated agreement Satorri. What I was trying to point out is that stamina trinkets have survivability value, while armor trinkets have both survivability and mitigation value.

    In other words, the armor trinket will increase your effective health, just like the stamina trinket, but the armor trinket will also reduce your total damage taken over time, reducing the load on the healer.

    While the value of the mitigation may not be as high as that of survivability in most fights, I think there are some situations in which it surpasses survivability. For example, on older fights where we have an EH pool plenty large enough to take the hits, concentrating more on damage reduction rather than stamina may enable a tank to reduce to a smaller number of healers, enabling more dps to be used. The same goes for offtanking situations, where again, damage reduction may count for more than survivability.

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    Damage reduction (aka mitigation) is also better in cases where you're receiving *some* heals, but for whatever reason they might not be enough. Random made-up-numbers example:
    Say there's 90K damage coming in over a few seconds. During that time you'll receive 36K heals. You start out topped off at 50K hp. Adding 2.1K hp will give you 52.1K hp and 36K heals - you're dead. Reducing the 90K damage to 85K by bumping up your armor will leave you happily clinging to 1000 hp, ready to receive additional heals before the next big hit lands.

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    Quote Originally Posted by Reev View Post
    In other words, the armor trinket will increase your effective health, just like the stamina trinket, but the armor trinket will also reduce your total damage taken over time, reducing the load on the healer.
    That's not quite right. The armor trinket increases your EHP BECAUSE it has mitigation over time, whereas the stam trinket is actual visible HP that means you can be healed through a harder it or an attack that isn't physical.

    Don't underestimate a health pool, even if something with more mitigation would hit you harder, saccing all HP for armor still means you have less hps. Healers can't heal armor =P only hit points (ya ya inspiration, but you know what I mean.)

    That's not to say the armor trinket is worse, but if you have 30k hps and 35k armor, steelbreaker and algalon are still gonna kill you.
    "If the world is something you accept rather than interpret, then you're susceptible to the influence of charismatic idiots." -Neil deGrasee Tyson

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    *small note, inspiration no longer provides an armor buff, it is a flat damage reduction %
    The (Old) Book on Death Knight Tanking
    The New Testament on Death Knight Tanking
    -----------------------------------------
    Quote Originally Posted by Horacio View Post
    Who f-ing divided by zero?!?

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    Quote Originally Posted by Aggathon View Post
    That's not quite right. The armor trinket increases your EHP BECAUSE it has mitigation over time, whereas the stam trinket is actual visible HP that means you can be healed through a harder it or an attack that isn't physical.

    Don't underestimate a health pool, even if something with more mitigation would hit you harder, saccing all HP for armor still means you have less hps. Healers can't heal armor =P only hit points (ya ya inspiration, but you know what I mean.)

    That's not to say the armor trinket is worse, but if you have 30k hps and 35k armor, steelbreaker and algalon are still gonna kill you.
    I'm not suggesting anyone sacrifice anything for anything. I haven't made any gearing suggestions.

    Yes, armor increases EH because it increases mitigation. The point is that Mitigation has inherent value outside of survivability and EH, whereas stamina does not.

    I'm not suggesting armor is superior to Stamina, or that people should gear specifically for armor at the expense of stamina, and I don't underestimate the value of a large health pool. However, in this day and age of everyone trumpeting EH all the time (which is a good thing, and correct), I think it's important to remember that more than EH does exist, and Armor is more than just EH.

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    thanks for the numbers Satorri... just wondering if we could get a sticky for this as the nagging question on this will always linger in a tanks mind?

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    Quote Originally Posted by Reev View Post
    , I think it's important to remember that more than EH does exist, and Armor is more than just EH.
    What value does armor have besides EHP? Armor and stam are the straight up EHP stats. Period. You want an EHP set you gear for stam and armor.

    Is what your getting at with armor that it's hit points that healers don't have to heal?

    The extreme example being someone with 30k armor and 50k hps buffed is more healable than someone with zero armor and 170k hps?
    "If the world is something you accept rather than interpret, then you're susceptible to the influence of charismatic idiots." -Neil deGrasee Tyson

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    Yes. In the extreme sense, someone with 50k hp and 50% mitigation would have the same EH as someone with 100k hp and 0% mitigation, but the former would take far less damage, and thus need less healing.

    So the point there is that while armor and stam are both EH stats, armor does have some value in its mitigation (and AP if we want to get technical), whereas stamina does not. I'm not saying that makes it better, but there is some value there.

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    I had intended this to be a small side-comment, not to take over Satorri's very well written thread.

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    Armor decreases the amount of healing needed and thus potentially lowers the window of time needed to be topped back up for the next hit.

    In many cases, this trade-off may or may not be worth it. That said, if you have enough raw health to survive the worst-case burst scenarios, preferring reduction over EH is not always the worst idea to increase your overall chances of survival.

    In an extreme example, a player with 50,000 health and 75% Armor Reduction taking 40,000 damage hits is going to have a much higher chance of survival than someone with 200,000 health and 0% Armor Reduction taking 160,000 hits. :P

    Stacking EH is great, as long as your healers are capable of healing you up at a fast enough rate for the next burst. Reduction increases the effectiveness of HoTs and other periodic heals and reduces some of the strain on healers.

    I won't drag this into a discussion of EH vs. Mitigation/Avoidance or whatever, but Armor does have the positive effect of affecting both sides of the scale.

    EH being equal, you would want Armor over Health on physical damage fights. That's why, for instance, I think there's some value in The Black Heart due to its balance of the two stats into a similar EH value but higher damage reduction value compared to a number of Stamina trinkets.

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    Quote Originally Posted by Kojiyama View Post
    EH being equal, you would want Armor over Health on physical damage fights. That's why, for instance, I think there's some value in The Black Heart due to its balance of the two stats into a similar EH value but higher damage reduction value compared to a number of Stamina trinkets.
    Speaking of this trinket discussion, I'm hereby hijacking this thread =P

    Assuming EHP gear on an all physical fight, what would be the 2 best trinkets.

    Imo the 258 Jug's Vitality is still BiS because of it's on use, passively it's like 2.3k EPH, and on use pushes it almost to 8k EPH when active. That seems good to me.

    However the 258 on use means you cannot use the 245 version's on use, so that part of the trinket is effectively dead and all you have is the roughly 2k EPH.

    The question is: what is the next BiS trinket

    Black Heart, Glyph of Indomitability, or maybe even Fervor of the Frostborn? Fervor's passive dodge is pretty meh for EPH, but the on use seems pretty good.

    Opinions? I don't really have time today to run the numbers, maybe someone else does?
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    Fervor of the Frostborn is pretty terrible, IMO. As far as I know, the Use effect/proc does not trigger from avoided attacks, therefore making it virtually useless and next to impossible to stack.

    Glyph of Indomitability, The Black Heart, and Onyxia Blood Talisman would probably be in my top 3 for a 2nd trinket slot at this point. The value of each would highly depend on the fight.

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    I'd agree with that Koji. I kept wondering at first what Satrina's Impeding Scarab was for a while, until I remembered that the Alliance have different names for the gear. I'm running the 192 stamina trinket (Juggernaut's Vitality) and the Black Heart right now. There are some fights I might switch in my Brewfest Trinket (even though it fills me with nerdrage that a holiday loot piņata drop has almost as much stam as my 245 trinket), and I'm really considering getting the emblem armor trinket for certain fights.

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    Quote Originally Posted by Kojiyama View Post
    Fervor of the Frostborn is pretty terrible, IMO. As far as I know, the Use effect/proc does not trigger from avoided attacks, therefore making it virtually useless and next to impossible to stack.

    Glyph of Indomitability, The Black Heart, and Onyxia Blood Talisman would probably be in my top 3 for a 2nd trinket slot at this point. The value of each would highly depend on the fight.

    Ony Blood Talisman for an EHP set?
    "If the world is something you accept rather than interpret, then you're susceptible to the influence of charismatic idiots." -Neil deGrasee Tyson

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    Quote Originally Posted by Aggathon View Post
    Ony Blood Talisman for an EHP set?
    Well, you stated in an EH set. Not every item has to be stacked with health even in a health-oriented set. Like I mentioned, it's highly dependant on the fight and if you have reached a comfortable EH threshold or not.

    Glyph of Indomitability is most likely going to be your best bet if you are going for pure EH in a 2nd trinket, however The Black Heart is an extremely good trinket all-around.

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