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    The RISE Update

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    ac355deny
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    Re: The RISE Update

    Post by ac355deny on Sun Aug 13, 2017 3:16 pm

    I'd done some experiments. 

    google spreadsheets: spreadsheets/d/19Arc7ogKlfMlFSrngRpn4TbHuT0lGJ_GA5jwpmGpYRE

    damage formula = (Effective ATT * BAL + Additional damage multiplier * Additional damage * BAL) * skill multiplier


    Effective ATT: A function of ATT, DEF and ALR. (ATT-DEF) is capped at 10,000 if there is no ALR.
    BAL: (balance/100 ~ 1.00) with step 0.005
    Additional damage multiplier: vary by ATT, DEF and ALR. When ATT is over ATT cap and no ALR, this value ~ 6.25.

    Effective ATT:
    When there's no additional damage, the precise Effective ATT can obtain by raw_damage_calculator because the possible value of damage is limited. 




    3rd order polynomial can fit the data quite nicely with error < 0.01%.
    The formula by Ainama in 2013 can fit too with error < 3%.
    There's a newer formula in 2015, but I don't fully understand...


    Additional damage multiplier:
    The effect of additional damage can be obtain by subtracting effective ATT from raw ATT. Sadly, the raw ATT is no longer obtain by raw_damage_calculator. My guess is that there's a separated balance roll in additional damage part, so that the damage value is spread. So I have to use more data to get a more reliable value.   



    The multiplier is quite linear to (ATT-DEF) when (ATT-DEF)>3000.
    The statement "Effectiveness of additional DMG will vary by your ATTand monster's DEF" seems correct.

    Attack Limit Release:
    This is the part that I'm not sure about. The data point is few and error is larger compare to the above 2 experiments. But a least it shows that ALR affects Additional damage multiplier as well.



    Shippuu
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    Re: The RISE Update

    Post by Shippuu on Sun Aug 13, 2017 5:50 pm

    Wow, that's a lot of data, thanks for the initiative.

    Which ATT formula are you using? There was a change to the formula a few years ago to make really weak chars do more damage. I don't have the original as Ainama posted it, but I do have the JavaScript version I converted it into:

    Code:

    var flag = (att - def + 900) / (def + 900);
    if (flag < 1) {
     var x = Math.sqrt(1 - flag);
     var funcX = (0.58012277 * x) + (-0.75477080 * Math.pow(x,2)) + (-0.50902587 * Math.pow(x,3)) + (2.51785703 * Math.pow(x,4)) + (-1.81621180 * Math.pow(x,5)) + (0.41384712 * Math.pow(x,6));
     var effATT = (def + 900) * (Math.pow(funcX,2) + flag); // Capped 10,900
    }
    else {
    (Using the old formula if flag >= 1)
    }

    Some notes on calculation:

    The flag value there does exist in Ainama's version. In it, he uses it to kinda indicate where the formula is losing accuracy (once its below -0.3). I clipped off the JS checks related to that, to keep it to just the formula.

    Regarding Balance - are you suggesting a Balance roll is happening for Additional Damage? This might be something KR got recently (or is going to get soon), but I wasn't aware NA was doing anything like that.
    ac355deny
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    Re: The RISE Update

    Post by ac355deny on Mon Aug 14, 2017 6:54 pm

    The formula I used is obtain by running regression on 2 separate cases, so it's not a general form.

    Code:
    Define x = (att-def)/10000 where (att-def) is capped at 10,000

    Def 18500:
    eff.att = 4114.249 + 5929.665*x + 1771.191*x^2 - 207.647*x^3

    Def 13000:
    eff.att = 3171.844 + 5699.765*x + 3089.088*x^2 - 797.401*x^3


    The forumula by Ainama in 2013 (the older version) I refer to is this:
    284-anyone-seen-the-changes-to-the-damage-equation (vsonbs in webarchive)
    Segment 1 : For DEF <= ATT < 2 * DEF

    Define ξ ≡ 1 - (ATT - DEF) / DEF. (Note this is 1 when ATT = DEF, and decreases down to 0 when ATT = 2 * DEF.)
    New Effective ATT = (ATT - DEF) + 900 + (DEF / 6) ξ sqrt( 2 (ξ - 0.39)^2 + 0.26 ) + 6.25 * (Add Dmg).

    Segment 2 : For ATT >= 2 * DEF

    New Effective ATT = (ATT - DEF) + 900 + 6.25 * (Add Dmg). (same as before)


    Code:
    var flag = (att - def + 900) / (def + 900);
    if (flag < 1) {
     var x = Math.sqrt(1 - flag);
     var funcX = (0.58012277 * x) + (-0.75477080 * Math.pow(x,2)) + (-0.50902587 * Math.pow(x,3)) + (2.51785703 * Math.pow(x,4)) + (-1.81621180 * Math.pow(x,5)) + (0.41384712 * Math.pow(x,6));[size=12][/size]
     var effATT = (def + 900) * (Math.pow(funcX,2) + flag); // Capped 10,900
    }
    else {
    (Using the old formula if flag >= 1)
    }
    Thanks, I can understand the newer formula more now.

    I studied a bit the detailed experiment report by Ainama:
    w_w_w.inven.co.kr/board/powerbbs.php?come_idx=2028&l=34224
    The correlation of (ATT-DEF+900)/(DEF+900) and (effATT)/(DEF+900) still exist in new data, but the precise curve is still hard to find.

    Adjust the formula a bit, make that effATT is no longer capped at 10,900, instead make (att-def) capped at 10,000. Then it still fit data pretty well, with error < 0.2% in higher end.

    Regarding Balance - are you suggesting a Balance roll is happening for Additional Damage? This might be something KR got recently (or is going to get soon), but I wasn't aware NA was doing anything like that.

    It was changed in Dullahan at 95 update.

    • Fixed an issue where Additional Damage was not affected by balance

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    Re: The RISE Update

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