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Easy H2H Mathematics For Monks V1.0 by HumbleMNK

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  • Easy H2H Mathematics For Monks V1.0 by HumbleMNK

    This is a post made by HumbleMNK over on the allakhazam monk forum. I did not see this over here so I thought I would move it over for you all to look at. No one over there has been able to find any errors in it. If you want to easily do the math grab my spreadsheet in my sig. Sorry if I missed a post with this stuff in it already.

    Easy H2H Mathematics For Monks V1.0


    Well, here it is. This is my (Humble) attempt at making as clear and concise an outline of H2H damage mechanics as possible. I hope you find it useful and informative, and that these stripped-down formulae are not only comprehensive, but more easily comprehensible than previous attempts at this task.

    Inx. (Easter '06)



    1. Overview

    When we hit an enemy, a calculation is made that stripped down to its most basic form looks like this:

    Unit_Damage x Damage_Multiplier = Per_Fist_Damage

    That’s it.


    The value Unit_Damage is the sum of 3 smaller values drawn from current H2H skill, Weapon Damage rating, and the amount of STR you have compared to the VIT of whatever you are hitting.

    I’ll explain exactly how this is calculated later, but for now just assume that Unit_Damage can only vary between 3 and 63 dependant upon level and gearing.

    The Damage_Multiplier is calculated by comparing player ATK vs mob DEF, and is a fractional value that normally calcs out between 0.0, and 3.0. Under certain circumstances this can rise to up to 5.0, but I’ll get to criticals and other adjustments later on.

    It seems very probable that the normal random “dice-roll” variance that causes our shot damage to fluctuate is applied purely to the Damage_Multiplier, as the Unit_Damage sits in a very small range of integers (whole numbers), whereas the multiplier goes to at least one decimal point.

    It’s extremely likely that all weapon attacks in the game work this way, radically different results can be achieved by simply tweaking the way the Unit_Damage is composed in conjunction with other combat properties like attack delay and accuracy.




    2. Calculating Unit_Damage

    Unit_Damage has 3 basic components:

    H2H Skill based Damage (iH2H). This is defined as floor(h2h_skill/10). So basically take your current H2H skill rating, divide it by 10 and lose the decimal points.

    iH2H sits in a range between 0 and 29.

    Weapon Property Damage (iWPD). This is even easier, just take the +Damage value on your weapon and add 3 to it. Barefist is equivalent to a +0 damage weapon.

    iWPD sits in a range between 3 and 26.

    STR bonus (iSTRB). Unlike the preceding values, iSTRB is calculated on a per-fist basis by subtracting the target’s VIT from the player’s STR. As this is a bonus, should the STR-VIT result in a negative value, iSTRB will be 0.

    iSTRB sits in a range between 1 and 13, regardless of how much STR you have because there is a cap on this bonus.

    The iSTRB Cap is defined as follows: 8+ floor(iH2H/9) + floor(iWPD/9). I’ll return to this later.

    So to get our Unit_Damage we simply add all these things up:

    Unit Damage (iUD) = iH2H + iWPD + iSTRB.

    So, currently our maximum possible iUD is 68. Assuming you had h2h skill >290, were toting a pair of Spharai, and got maximum iSTRB bonus.

    More likely, wearing Destroyers you’ll end up with a highly respectable iUD 63 at endgame.



    3. The Damage Multiplier

    Previous articles defining H2H damage mechanics normally refer the variable that is used to multiply out the unit damage by a factor that is the ratio of PLYR ATK to MOB DEF, pDif for some reason. This seems a pretty meaningless label to me, so I’m going to bin it in favor of the more sensible (imho) fADM!

    This is because it’s a floating-point Attack Damage Multiplier.

    Before going any further its worth pointing out that while the basic workings of this half of the damage calculations are well understood, the precise detail is not. Much of what is stated from this point onward is highly speculative beyond defining the overall principle of what is believed to happen. Anyway, I’ll try and deal with the various gray areas in the following section.

    fADM as noted previously is a floating point value that is used to multiply up the iUD. It’s basic formulation is rooted in the ratio of PLAYER ATK vs MOB DEF; therefore you’d expect a situation where a player with 500 ATK hitting a mob with 250 DEF to resolve a fADM of 2.0.

    There are 3 further factors that modify the fADM value:

    1. Dice Roll: The random variance that is applied to this value in order to create a more naturalistic sequence of actions.

    2. Critical Hits: A critical hit adds a straight +1.0 to fADM.

    3. Weapon Type to Mob Type Affinity: Using blunt weapons versus bones and slimes results in extremely different results.

    Once these are factored in, a final cap is applied to fADM. Under normal circumstances the limit for fADM is 3.0, however Weapon Affinities can raise this value up to a maximum of 5.0, although this peak can only reach that high under very specific circumstances.

    Once fADM is finally calculated, we are ready to define our final hit damage:

    iFinal_Damage = floor(iUD*fADM);

    And there we are.



    4. The Gray Areas: A discussion

    We’re going to get into some murky stuff here, be warned tech heavy detail ahead!

    While the series of operations described to this point is generally agreed upon, the exact calculation behind of fADM is unknown. A key problem is that much of the work on this has been done by working backwards from analyzing the size of maximum critical-hit damage for various weapons. In short, we have observed the hard-limits, but know less about how damage is dispersed in the low-to-mid range.

    Historically SE have always been vague about the workings of this system, merely describing STR as setting the range of a damage “curve” while ATK sets the point along the “curve”. The foregoing agrees with this, but disregards the spread of damage as having any sort of curvature whatsoever.

    Simply assigning fADM as PLYR_STR/MOB_DEF resolves a linear ratio, which begs the question that there is more to this conversion than we currently understand, but what could it be?

    This may seem like a minor point but it in fact is crucial to the conclusions we should draw: in a linear conversion loading up on ATK will never suffer diminishing returns until the cap limit is hit at which point only a more favorable weapon affinity can increase damage. In a curved system the benefit of ATK will vary according to the bigger picture, with the improvement “flattening” towards the high-end of fADM (2.0-3.0).

    In this respect a good question to ask is whether the “dice-roll” is of a consistent magnitude, or is scaled it according to the fADM result? In simple terms does the randomizer multiply the fADM or does it just add/subtract a certain amount to/from the total?

    Another question is the order in which the fADM modifiers are applied. My suspicion is that the 3.0 cap is applied before the Weapon Affinity modifier, but after Crit Hit is factored in. Anecdotal evidence for this was drawn from scoring consistent 0’s against ultra high def mobs, but an exact +1.0 fADM from a critical hit. Similarly in SW Appolyon (the special weapon-type affinity Limbus area) I’ve experienced 0 crits on super resistant slimes, while getting 5.0 fADM super-crits on susceptible mobs (315 max crit with Destroyers).

    To recap, I believe the order looks something like this:

    fADM= ((ratio(P_ATK,M-DEF, RANDOM)+CRIT)&3.0)+WPN_AFFINITY_MOD

    This analysis would suggest that WPN affinities are physically added to the fADM value, rather than being secondary multipliers as I initially thought.



    5. Conclusions

    ATK is more effective than STR at raising damage.

    The most you can ever gain from STR is a iUD bonus of 13, or +39 from an unadjusted max crit.

    If you are using a low damage weapon (< +8 DMG) STR is very important however as iSTRB is a proportionately larger component of your iUD than your weapon.

    For damage improvement only H2H ratings in multiples of 10 counts. Also, iUD improves only at 2 and 7 merit levels respectively).

    Crit Rate is king. If you’re serious about damage, merit this first.

    To increase beyond its current max of 63, iUD H2H skill >300, or a +24 dmg weapon will need to be made available.




    6. Credits

    This text is the result of many people’s hard work, the overall knowledge-base on the h2h calc has been built up over a long time and many hours of mental effort and investigation. There truly are too many people to name. That said, I’d particularly like to thank BastokFL for his work in unraveling the “magic 13” (iSTRB), which was for me anyway, the last piece of the puzzle.

    Appendices and corrections/additions will be added in due course.

    To be continued...

    Attached Files
    Last edited by Freyr; 05-04-2006, 03:53 PM.
    Freyr - Not Started

    Websites: FFXI Atlas | FFXI Wiki
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  • #2
    Re: Easy H2H Mathematics For Monks V1.0 by HumbleMNK

    Thanks for bringing this over. I read this post the other day, and was really impressed with the data in it.^^

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    • #3
      Re: Easy H2H Mathematics For Monks V1.0 by HumbleMNK

      Sticky-icky ^^~

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      • #4
        Re: Easy H2H Mathematics For Monks V1.0 by HumbleMNK

        Originally posted by TBoTB
        Sticky-icky ^^~
        LOL only made my account like 6 hours ago and I got a sticky already. ^.^

        Hey TBoTB how about a super post with links to tons of posts instead of having dozens of sticks at the top? If you like the idea i'll put something together.

        p.s. I like this forum a lot, mods going around and doing stuff. On alla you never see any mods what so ever on the class boards.
        Freyr - Not Started

        Websites: FFXI Atlas | FFXI Wiki
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        • #5
          Re: Easy H2H Mathematics For Monks V1.0 by HumbleMNK

          Ouch...in my opinion it's so much easier to read as (D + fSTR) * PDIF, but to each his own.
          STR bonus (iSTRB). Unlike the preceding values, iSTRB is calculated on a per-fist basis by subtracting the target’s VIT from the player’s STR. As this is a bonus, should the STR-VIT result in a negative value, iSTRB will be 0.
          It's not straight subtraction. It's a function that takes into account your DMG, STR, and the mob's VIT. It generally takes 4 STR or so to increase fSTR or iSTRB, however you want to call it, by 1. fSTR starts to increase sooner (even to the point that you can have an fSTR of 1 with negative STR compared to the mob's VIT,) with weapons of higher DMG. There's no easy way to calculate fSTR, but Apple Pie (a.k.a. Grendal) left us with this general formula for *estimating* it: (Player's STR - Enemy's VIT + 4)/4.
          3. Weapon Type to Mob Type Affinity: Using blunt weapons versus bones and slimes results in extremely different results.

          Once these are factored in, a final cap is applied to fADM. Under normal circumstances the limit for fADM is 3.0, however Weapon Affinities can raise this value up to a maximum of 5.0, although this peak can only reach that high under very specific circumstances.
          Weapon vs Mob modifiers are not part of PDIF or fADM. They're a percentage applied at the end. Attack/Defense caps out at 2.0, at which point the random variance can be from -0.4 to +0.4, giving PDIF a max value of 2.4 under normal circumstances. Criticals add +1.0 to it, but PDIF cannot exceed 3.0. I.e. having ATK/DEF capped at 2.0, and getting a critical on a hit where the random number was +0.2 will result in a PDIF of 3.0, not 3.2.
          While the series of operations described to this point is generally agreed upon, the exact calculation behind of fADM is unknown.
          PDIF/fADM is simply (Attack/Defense + Random). There is no diminishing returns; however, PDIF (note that I'm making a distinction here by specifying PDIF and not Attack/Defense) isn't linear, because the range of the Random value isn't always even. At some points you may have a range of, say, -0.3 to +5.0, or you may have a range of -0.5 to +0.3. Its range depends on your Attack/Defense ratio. See this graph to see how that range varies. It's pretty old and a bit inaccurate, but it's accurate enough.
          ATK is more effective than STR at raising damage.
          STR is better than Attack point-per-point, it's just that Attack is easier to get in larger ammounts.

          Regarding the credits: I believe the formula was developed by Studio Gobli.

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          • #6
            Re: Easy H2H Mathematics For Monks V1.0 by HumbleMNK

            Nice to see this post has made its way over here... ah the magic of the internet :D

            FWIW My version is a variant on the Studio Gobli calculation, that is deliberately stripped down as much as possible. My background is in games design/programming and based on that experience this type of system would be very deliberately kept only as complex as is neccessary to produce the desired effect. And besides, the random factor that varies our shots makes more complex calculations pointless imho, as much of that subtlety will be lost in the margin-of-error it creates.

            My version was hacked out over time, without making any direct reference to the Gobli data (although it casts a long, long, shadow!), hence the reason I dont credit their work directly.

            Honestly I advise anyone seriously interested in this to work it out for themselves also, you may or may not come out with something different/better than I have, but whichever way you'll probably be a better monk for looking into it.

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            • #7
              Re: Easy H2H Mathematics For Monks V1.0 by HumbleMNK

              Hey Humble, glad you don't mind me posting this over here. I got it from your original Alla post when I jumped ship and I did not want this to be lost. If you get a chance man, can you take a look at my spreadsheet I made and see if I made any errors in understanding your math. Glad to see your over here.
              Freyr - Not Started

              Websites: FFXI Atlas | FFXI Wiki
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