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[Misc]Quick determination of effective health

Discussion in 'Guides' started by omheten, Oct 10, 2016.

  1. omheten

    omheten New Member

    Oct 8, 2016
    Current patch version: 6.88e
    This guide is mostly about performing simple math operations quickly and on the fly.

    This guide does not pretend to be good or complete, it is just the thing I made.
    If you have any suggestions, please leave a comment.

    ~ 1 ~
    Physical damage survivability


    Before you continue, try to imagine how much damage is it possibly required to kill a hero with 3600 health and 47 armor. Given algorithm includes few easy steps that allows to determine the approxime amount of damage required to kill target on the first step and more precise values on each following step.
    1. Determine the armor impact
    2. Extra health for thousands
    3. Extra health for hundreds
    4. High armor calculations
    1. Determine the armor impact​
    On this step you have to determine the percentage of health that is provided by armor. For the further calculation you want to keep it in integer percent value format rather than in floating point format. Here is the formula I suggest to multiply two-digit values by 6:
    • Multiply by ten
    • Divide by two
    • Add original value
    So if target have 47 armor:
    • 47 → 470
    • 470 → 235
    • 235 → 282
    That may be just enough sometimes since you know now that target have 100% + approx extra 300% survivability to physical damage.

    2. Extra health for thousands​
    To find out the extra health target has for each thousand health you want to multiply the value from previous step by number of thousands and by ten. Let's say, you have a target with 47 armor has 3000 health. The extra health would be 282 x 30. You can easily find the answer by multiplying bit by bit and adding in reverse: 2 x 30 + 80 x 30 + 200 x 30 which would be 8460 and thus 8460 extra health.

    3. Extra health for hundreds​
    The hundreds part goes for the same calculations except that you don't multiply by ten and you already have the number for thousands which you can use. So if target has 3300 or 3600 health you know that extra health would be 8460 + 846 or 8460 + 1692. Answering the very first question you have to deal 3600 + 8460 + 1692 = 13752 damage to kill such hero not counting regeneration.

    4. High armor calculations​
    When target has high armor the ignored tens may provide extra thousands health. From previous example if target had 3350 health ignored 50 health will do extra 142 health. What you could do to avoid additional operations is round armor impact up by 5. So instead of 282 you use 285 which is even a bit easier to operate. Extra hp will be determined as 9405 while real extra health is 9447. Without rounding the result would be 9306.

    ~ 2 ~
    Magical damage survivability


    It is pretty straight forward for the most heroes since hero magic resistance is 25 percent. However it gets a little tricky when it comes to additional sources of magic resistance. One way to calculate the approximate resistance is to subtract current magic resistance as a percentage from new source. For example, if Antimage have 25 percent of default resistance, maximum level of Spell Shield, and wears Hood of Defiance the resulting resistance will be next (fraction values are rounded by five):

    25 + ( 50 - 25% ) ≈ 25 + ( 50 - 15 ) ≈ 60 - Adding the Spell Shield
    60 + ( 30 - 60% ) ≈ 60 + ( 30 - 18 ) ≈ 72 - Adding the Hood of Defiance​

    That's all, Folks!

    Q: Did I just read a guide on multiplying and adding numbers?
    A: Pretty much.

    Q: You have nothing else to do, or something?
    A: ☹
    Last edited: Oct 10, 2016
  2. DrEddgarAllenPWN

    DrEddgarAllenPWN New Member

    Oct 9, 2016
    I'm bad at math. This is bad for me. Also, I didn't read the whole thing.
  3. ValveIcefrog

    ValveIcefrog New Member

    Oct 10, 2016
    So armor is normally armor*6*hp/100?
  4. omheten

    omheten New Member

    Oct 8, 2016
    There is a formula of incoming physical damage reduction based on armor, but generally you can think of it as of extension of your health. Each 10 armor grants you additional 60% from your health.
  5. Dr_JP

    Dr_JP Member

    Jun 26, 2009
    For physical dmg, every point of armor gives you 6% more HP, so EHP: HP*(1 + 0,06*armor).

    For mind counts, it's good to remember 16 armor ~= 100% increase or 2x your EHP based on your HP, so 8 armor = 50% increase and 24 armor = 150% increase, e.g.

    For magical dmg, EHP equals (1/1-"dmg which goes through"), so 25% spell resistence = 75% real spell dmg and regular magic resistence (25%) means every HP = 1,33 EHP.

    If you have ~50% spell resistence, you have +100% (or twice) EHP against spell dmg, mostly meaning you're better buying HP to tank spell dmg than buy extra spell resistence.

    In fact, after reading your guide, why don't Valve show EHP for both physical and magical dmg when we hover the mouse over the dmg and armor icons beside portrait?
    Last edited: Oct 13, 2016
  6. Dr_JP

    Dr_JP Member

    Jun 26, 2009
    Importante note: Evasion increases your whole EHP instead of only HP, so it sinergizes with armor as well.

    EHP = 1/1-evasion, so 30% evasion ~= 1.43x your EHP.
  7. andenrx

    andenrx New Member

    Oct 8, 2016
    EHP is more of a made up term than say HP, Armor or Magic Resistance.

    EHP = Effective HP

    A 1k HP, 0 armor Tidehunter with level 4 cracken and anchor smash being attacked by a 100 damage Phantom Lancer with illusions has a lot more EHP than a 1k HP, 10 armor Lina.

    After anchor smash, PL deals ~50 damage to tide, his illusions deal less. Cracken reduces it to ~5 from the hero and 0 from the illusions. This means Tide's EHP is over 20,000. (PL's group is dealing 100 + illusions on paper, but tide only takes ~5. He takes <5%, meaning that he has >95% resistance. 1000/(1-0.95) = 20,000).

    The lina on the other hand would take ~60 damage from PL (and some from illusions). 100/~60 * 1000 = 1,600.

    Would Cracken shell, PMS, Vanguard be included in EHP calculations? What about Underlord Aura? Then what about HP regen (it effects EHP similarly to how damage block does)? An Alch against low DPS has way more EHP than HP/(1-resistance) would show.

    imo, the player needs to make these decisions when they calculate EHP for themself.
  8. Dr_JP

    Dr_JP Member

    Jun 26, 2009
    There's no need to take into account Block dmg, because it doesn't depend exclusively on the holder, thus being an exception.

    EHP taking into account armor, evasion and spell resistence is enough.
    Final values, so auras/spell and item effects, could be listed in your portrait while you are dead, for example, showing the state your were right at the moment of being killed.