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Can someone please explain stacking magic resistance?

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  • Can someone please explain stacking magic resistance?

    Quote from Dota 2 Pedia: "These bonuses stack diminishingly, means the higher a unit's magic resistance currently is, the lower the effects of another bonus will be...".
    http://dota2.gamepedia.com/Magic_resistance

    So today i did some testing in a dota 2 lobby:

    Tester: Elder Titan lvl25 with all the abilities skilled, has Dagon lvl2 (500 magic damage)
    Titan's aura completely removes the base 25% magic resistance that Doom has - meaning that Doom has 0% magic resistance WITHOUT items.

    Subject: Doom lvl25 with all the abilities and stats skilled (total 2468 HP).
    Has only 3,9 HP regen per second, which is rather insignificant for this test since Doom dies in less than 4 seconds.

    Items used to test:
    Dagon lvl 2 (deals 500 magic damage) - has no cooldown because WTF mode is on.
    Multiple Cloaks (gives 20% magic resist)

    Results:
    Doom without any items (0% base magic resistance due to ET's aura) died after 5 Dagon (lvl2) casts.
    Doom with one Cloak died after 7 Dagon (lvl2) casts. two more than previous
    Doom with two Cloaks died after 8 Dagon (lvl2) casts. one more than previous
    Doom with three Cloaks died after 10 Dagon (lvl2) casts. 2 more than previous
    Doom with four Cloaks died after 13 Dagon (lvl2) casts. 3 more than previous
    Doom with five Cloaks died after 16 Dagon (lvl2) casts. 3 more than previous
    Doom with six Cloaks died after 20 Dagon (lvl2) casts. 4 more than previous

    I admit i am no mathematician, but after the 2nd Cloak the amount of survival Doom got with every new cloak grew significantly.
    I verified every test result multiple times, so there was no error in collecting the info (at least as far as i can see).

    Can anyone please explain why do the above test results conflict with the Dota 2 Pedia's statement about stacking magic resistance?
    Last edited by Bogdanov89; 10-14-2015, 08:56 AM.

  • #2
    Don't count casts. Use the combat log and check the damage values done.

    Magic resist stacks exactly as explained in the wiki: diminishingly. The table listed there is utterly useless and confusing though. It works like the following (MR1 meaning magic resist source 1 as a value between 1 and 0):
    Total magic resist = 1 - (1 - MR1)*(1 - MR2)*...*(1-MRX)
    The outcome of this formula is that each new magic resist item lowers the remaining magical damage taken by the amount written in the tooltip.

    Example: 100 damage negated by 25% base magic resist results in 75 remaining damage. A new source of 20% magic resist now lowers that remaining 75 damage by 20%, resulting in 75-15=60 damage taken.
    With the formula: 1-(1-0.25)*(1-0.2)=0.4

    A Doom with 6 cloaks has 1-(1-0.25)*(1-0.2)^6=1-0.1966=0.8034 => 80.34% magic resist. Dagon 2 deals 500 damage before resistance but in this case only 98.3 damage. 20 casts means doom had 1966 HP. This seems to fit.

    EDIT: Forgot that you added Elder Titan. HP from Doom was 25% higher than, 2621.
    If you think I've closed or deleted a post unjustified, feel free to PM me and I'll explain it to you/discuss it with you further.

    Comment


    • #3
      Thank you for replying!
      So if i understand you right, in simple terms magic resistance from separate sources kinda works like in layers.

      Please correct me if i am wrong (assuming 0 base resistance and 4 cloaks of 20% each):

      Doom with 4 cloaks get hit by a single 1000 damage magic nuke.
      That 1000 dmg hits the first "layer" of 20%, reducing it to 800.
      Then that 800 hits the second layer of 20%, reducing it to 640.
      Then that 640 hits the third layer of 20%, reducing it to 512.
      Then that 512 hits the fourth layer of 20%, reducing it to 409,6.

      If that is correct then i understand the concept, but it still seems weird to me that the 6th cloak (in my test) gave 4 additional dagon casts - compared to the previous ones that benefited less.

      Comment


      • #4
        That's why I said you should not check "dagon casts" but "damage done".

        Doom on level 25 has 2468 HP. Assuming Elder Titans aura removing his base resist you can use the following formula to calculate the damage required to kill him:
        HP/((1-0.20)^(amount_of_cloaks))
        Basically every cloak increases his effective HP against magical damage by 20%.

        1 cloak: 2468/0.8=3085 => 7 dagon level 2 casts (85 HP after 6 casts)
        2 cloaks: 2468/0.8^2=3856=> 8 dagon level 2 casts (356HP after 7 casts)
        3 cloaks: 2468/0.8^3=4820 => 10 dagon level 2 casts (180HP after 9 casts)
        4 cloaks: 2468/0.8^4=6025 => 13 dagon level 2 casts (25 HP after 12 casts)
        5 cloaks: 2468/0.8^5=7531 => 16 dagon level 2 casts (31 HP after 15 casts)
        6 cloaks: 2468/0.8^6=9414 => 19 dagon level 2 casts (414 HP after 18 casts)

        You can see that the irregular increase in dagon casts happens due to the remaining HP left after the previous ones. You can also see that you were quite slow to cast dagon 20 times, as 6 cloaks require 19 dagons but Doom regenerated 86.1 HP before you did it :P

        EDIT: Ha. Ha. But a good explanation by bu3ny.
        Last edited by Kryil-; 10-14-2015, 10:26 AM.
        If you think I've closed or deleted a post unjustified, feel free to PM me and I'll explain it to you/discuss it with you further.

        Comment


        • #5
          There are 2 things.

          Each source of magic res increases your magic resistance value by less, the higher your magic res is. This means it can never reach 100%, unless a source grants 100%. This is what the stacking section says.

          What you are having in mind is effective HP against magical damage.

          Effecive hp is, how much damage after reductions can you take before dying. In this case, magic resistance is against magical damage, so this is about your effective HP against magical damage.

          If you have 0% magic res, your effective HP against magical damage is also 100%. (e.g. if you have 1000 hp, you die to 1000 magical damage).
          If you now gain 50% magic res, your effective hp against magical damage is doubled to 200%, since you now need to take twice as much magical damage to die as before. (if you have 1000 hp, you die to 2000 magical damage)
          If you now gaint another 50%, your magic res is 75%. Your effective HP gets doubled again, to 400%. (1000 hp dies to 4000 magical damage)
          A 3rd 50% source increases to 87.5%, your effective hp increases to 800% (1000 hp dies to 8000 magical damage)
          A 4th 50% source increases to 93.75%, effective hp increases to 1600%. (1000 hp dies to 16000 magical damage)
          If your magic resistance is 100%, your effective hp vs magical damage is infinite

          Now lets apply this to your test:

          0 cloaks, 0% magic res, 2468 hp dies to 2468 magical damage, 5 dagon hits
          1 cloak, 20% magic res, 2468 hp dies to 3085 magical damage, 7 dagon hits
          2 cloaks, 36% magic res, 2468 hp dies to 3856.25 magical damage, 8 dagon hits
          3 cloaks, 48.8% magic res, 2468 hp dies to 4820.31 magical damage, 10 dagon hits
          4 cloaks, 59.04% magic res, 2468 hp dies to 6025.39 magical damage, 13 dagon hits
          5 cloaks, 67.232% magic res, 2468 hp dies to 7531.74 magical damage, 16 dagon hits
          6 cloaks, 73.7856% magic res, 2468 hp dies to 9414.67 magical damage, 19 dagon hits


          There are 3 reasons why you needed 20 hits in your test. Natural Order does not completely negate 25% magic resistance. It still leaves 0.25% magic resistance. Another reason is Doom's hp regen. 4 regen doesnt seem much, but it is enough. And the last reason, you were simply too slow. These 3 factors combined made you need 1 more cast. I just copied your test, and used Chronosphere as help. Put Elder and Doom in chronosphere, and then shift-queue dagon on Doom many times and then check console. This eliminates regen and speed as problems.
          1. [05:46.50] Elder Titan hits Doom with Dagon for 130 damage (2467->2337).
          2. [05:46.53] Elder Titan hits Doom with Dagon for 130 damage (2336->2206).
          3. [05:46.57] Elder Titan hits Doom with Dagon for 130 damage (2206->2076).
          4. [05:46.60] Elder Titan hits Doom with Dagon for 130 damage (2075->1945).
          5. [05:46.63] Elder Titan hits Doom with Dagon for 130 damage (1945->1815).
          6. [05:46.67] Elder Titan hits Doom with Dagon for 130 damage (1814->1684).
          7. [05:46.70] Elder Titan hits Doom with Dagon for 130 damage (1684->1554).
          8. [05:46.73] Elder Titan hits Doom with Dagon for 130 damage (1553->1423).
          9. [05:46.77] Elder Titan hits Doom with Dagon for 130 damage (1422->1292).
          10. [05:46.80] Elder Titan hits Doom with Dagon for 130 damage (1291->1161).
          11. [05:46.83] Elder Titan hits Doom with Dagon for 130 damage (1162->1032).
          12. [05:46.87] Elder Titan hits Doom with Dagon for 130 damage (1031->901).
          13. [05:46.90] Elder Titan hits Doom with Dagon for 130 damage (900->770).
          14. [05:46.93] Elder Titan hits Doom with Dagon for 130 damage (769->639).
          15. [05:46.97] Elder Titan hits Doom with Dagon for 130 damage (639->509).
          16. [05:47.00] Elder Titan hits Doom with Dagon for 130 damage (508->378).
          17. [05:47.03] Elder Titan hits Doom with Dagon for 130 damage (377->247).
          18. [05:47.07] Elder Titan hits Doom with Dagon for 130 damage (246->116).
          19. [05:47.10] Elder Titan hits Doom with Dagon for 130 damage.


          I'ma add this stuff about effective hp to the magic res article.
          Please, just call me buny.

          Comment


          • #6
            Golly gee willikers, Mathman!

            That is some impressive computing work.

            Thank you both for replying and explaining

            Comment

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