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    New improved damage formula (Warning if you hate math..)

    The old and well known formula of attack*.39*AP/100-defense*.19 was very very basic with a low accuracy rate but at least kept people in the right direction. With many many hours of tests after test, number crunching, and math left right up and down, I have created a much much much more accurate formula, that also includes procs. Here it is (second warning for math haters)

    AB((C+D-E)/100)*(1+(CritY|CritN))+(FGH)-IJ-K([1+L]*[1+M]*[1+NO+P]-1)= Final Damage

    Key
    A
    - Attack (If paladin using divine smash or Dual sword, this value is attack+defense/2)
    B- Attack scaling (Roughly .4)
    C- AP
    D- AP buffs (Includes attack stance, Joan, Banshee, test/heart procs beside fatal, etc)
    E- AP subtractions (Includes defense stance, and enemy damage down procs only, reflect does not go here)
    Crit Y- Yes it crit, .5
    Crit N- No it did not crit, 0
    F- Element multiplier (Roughly 5%)
    G- Element count
    H- AB((C+D-E)/100)
    I- Defense
    J- Defense scaling (Roughly .2)
    K- H*1+{CritY/CritN} +FGH-IJ
    L- Reflect % (Including reflect procs and abilities, they stack additive)
    M- Protection % (Includes barrier)
    N- Amount of constants (0, 1, or 2
    O- Constant scaling (Solid 6.5% per. Add 50% if guarding)
    P- Guard (.5 if yes, 0 if no)


    I'm really sorry it looks like cancer in written form, but the formula is indeed long (I shortened it using H and K as their own variables).
    There is (what I find to be) a 7.5% rng factor in the beginning of the formula (After C+D-E is divided by 100) that determines if your attack will do as low as 92.5% or as high as 107.5% of your true damage.

    note most of these variables only apply to either PvE, or PvP.

    Blue is elemental, and can be ignored in PvP or if you have no advantage.

    Red is only armor procs/constant reductions, and can be ignored in PvE.




    !-Here, I added a cleaned up version of the formula to make it a little easier to read through.


    Raw power, H= AB((C+D-E)/100)
    Modified power, K= H(1+{CritY/CritN})+FGH-IJ
    Final Formula= K-K([1+L][1+M][1+NO+P]-1


    Do that step by step, and it should be much much easier than translating my moon language!
    Last edited by vzReo; 04-24-2016, 04:38 PM.

    #2
    I'll bookmark that and try to decipher your moon language tomorrow or something


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    • Guest's Avatar
      Guest commented
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      Sounds promising

    #3
    Wow. I've never seen the damage formula so honestly I have no idea how close you are, but back when we did the AMAA the team said that the formula was very complex and spread across multiple cells in an Excel file. So, what you have here is probably closer to what they use.

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    • Guest's Avatar
      Guest commented
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      I actually had this in an excel file for 2 months before deciding to post it. I can probably give out the file so people only have to plug in their numbers... once I clean it up and figure out how

    #4
    Originally posted by Ateam Admin View Post
    Wow. I've never seen the damage formula so honestly I have no idea how close you are, but back when we did the AMAA the team said that the formula was very complex and spread across multiple cells in an Excel file. So, what you have here is probably closer to what they use.
    I've been talking with Reo the past few months as he was making this formula and have seen him go through the logic of deriving this.

    Whatever formula the team has should still be essentially, mathematically equivalent to the one Reo has shown, but perhaps in a different format and maybe with more precise numbers. Reo has done all the testing to ensure that each variable is being mathematically computed correctly. Some nuances that were surprising include the fact that reflect was stacked additively by % and that damage was calculated outside of damage reduction, so even if damage is reduced before reflect, the damage reflected back is still a % of the original damage before damage mitigation.

    I recall your mentioning back during the AMAA that the formula is really long. As you can see, the primary reason why it's so long is because it reuses the same factors over and over again. In order to ensure independence of factors like elemental boost and critical (so that they both don't influence each other!), the formula must separate each factor instead of multiplying everything together with the "AP multiplier" (the H variable). However, everything must still scale based off of this "AP multiplier", so the formula reuses the H variable again. In the defense subtraction, the damage mitigation must still scale off of the AP multiplier as well as defense and we see this in the form of the variable K, which is essentially the whole formula repeated again. Independence of damage factors but dependence on the same scalar require the formula to be extremely long.
    Last edited by Ace; 04-21-2016, 03:06 AM.
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      #5
      Even if this formula does seem like cancer at first, and extremely complex, it isn't too difficult to understand if you feed it a few times.

      vzReo, this is a great formula and I completely agree with it!
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      • xexvc0302
        xexvc0302 commented
        Editing a comment
        Let's be honest. You have no clue what the formula says.

      • MTT the Tank
        MTT the Tank commented
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        I do, took me half an hour to understand it, had to use make up stats, but I made it

      • Rngesus
        Rngesus commented
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        lol k

      #6

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        #7
        Originally posted by vzReo View Post
        AB((C+D-E)/100)*1{CritY/CritN}+(FGH)-IJ-K([1+L]*[1+M]*[1+NO+P]-1)= Final Damage

        Crit Y- Yes it crit, .5
        Crit N- No it did not crit, 0
        Did you just divide by 0...
        Too casual for signatures...

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        • Omega
          Omega commented
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          vzReo Or would be | for EBNF.

        • Guest's Avatar
          Guest commented
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          Ah, makes sense. Fixed.

        • dpaladin
          dpaladin commented
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          vzReo You already used: P- Guard (.5 if yes, 0 if no), why not make it: Crit (0.5 if yes, 0 if no)

        #8
        Looking good Reo! Looks so much nicer as text rather than chicken scratch. Maybe we should change your title to formula breaker. Huehuehue

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          #9
          sorry but ur 0 atk is still 0

          I could break things down to give a better understanding for readers if you want

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          • Guest's Avatar
            Guest commented
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            Gopher it

          #10
          I like math and this is still cancer D:

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            #11
            Cleaning it up right now

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              #12
              Okay... gimme like 8 hours and I'll maybe understand it 😂 appreciate the effort put into this though man! Must've been painstakingly difficult. Or maybe you're a mathematician and you like this stuff idk xD
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                #13
                Ah fk I didn't hit save edit..

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                  #14
                  My brother would like to share his with you too reo

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                  • Guest's Avatar
                    Guest commented
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                    Knock yourself out

                  • Rngesus
                    Rngesus commented
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                    lolol k

                  • Kuroi
                    Kuroi commented
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                    vzReo you don't like PX, right? xD

                  #15
                  There's a lot of questions about this formula. Did u just assume everything from scaling to their multiplier? how would u know their scaling was 0.2, 0.4, 0.5 and the elemental multiplier was 5%. And you cannot prove anything about this without taking consideration of enemy's exact armor even if you neglect how their elemental multiplier works.
                  English isnt my native language

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                  • 09zeronine
                    09zeronine commented
                    Editing a comment
                    Ace Lol you dont need to figure out constants, they are called constant simply because they are there and doesnt need to solve it from formulas to get their values. average magnitude of earth is 9.81 m/s^2 thats an example of constant. The only constants here is the 5% elemental multiplier, armor/weapon skills, skill % reductions, 0.4, 0.2.

                  • Guest's Avatar
                    Guest commented
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                    09zeronine maybe I'll show how I did it some day, but the reason jp got 39% and 19% because the guy who did it did a few amount of tests to get a less accurate result, and his luck was that the RNG in the formula scored low for him majorily. He threw in the 19% instead of 20% for just assuming (Score 1 for jp>global?)

                  • Ace
                    Ace commented
                    Editing a comment
                    That's what I was referring to: figuring out the values. Idk how defining what a constant serves in this but okay :P
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