Damage, Defense and Criticals - The Damage Formula

Discussion in 'Guides & Game Mechanics' started by Rhaeven, May 23, 2014.

  1. Xnosider

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    Okay that make sense now. Thank you for help. It was not clear that fixed skills scaled off of gear.
     
  2. Rhaeven

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    To be honest, a good chunk of the work was done by other people and I just compiled it together. For example, the base damage formula (the one used at the time) was probably taken from some korean or japanese site that had the formula. The damage reduction formula was done by Spore ages ago (and to this day, I think his work is brilliant). That was all the hard stuff. After I saw those concepts, it wasn't hard at all to figure out the other stuff (criticals, elementals and other damage modifications).

    My major contribution is the aforementioned compilation as well as cleaning up the way the formula is expressed. Before percent and independent damage were calculated separately. At the time, this caused incorrect damage calculations because of how the damage formula was (There was a small amount of bonus damage that str/int tacked on to the end of the damage formula. The damage formula changed a little bit during Second Impact and that little discrepancy no longer matters. Anyways, I figured that str/int was only applied once during the calculation (really obvious in retrospect) and I came up with the formula and term for "Mixed damage".

    There are still some elements we don't understand though. Ever since nxdfo, we've been looking at something we call "pierce dampening". As the name suggests, there is something that mitigates the amount of damage your piercing/upgraded weapons do. The amount of mitigation is much smaller than armor reduction, but it does exist and it's noticeable (albeit barely). Even now, we haven't figured out how exactly it works. Boba (@Necrofancy) has taken a quick look at it in this incarnation of DFO and it definitely still exists. He hasn't been able to make an accurate model so far, but we at least know it's there.

    Unfortunately, I don't really keep the data I use once I reach a stable conclusion. But others, like Boba keep their spreadsheets and share them in their topics. As mentioned before, the process of making a model for a certain mechanic (elemental damage modification for instance) is very easy for the most part. You simply have to know how to manipulate a single stat (elemental damage in this case) without disturbing your other stats. Most of these modifiers are linear in nature making them very easy to deal with. I believe the most complicated mechanic being used by DFO is the reduction formula, who again, was done by Spore. The reduction mechanic isn't straightforward at all as it approaches an asymptote (I guess the devs don't want you to achieve absolute invincibility).
     
  3. Necrofancy Blame Blobâ„¢

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    Piercing reduction is actually pretty straightforward from my testing. What I'm trying to model right now is base defense, which is all kinds of fun. :9:

    Since the change to independent damage I've started viewing what we call "Base Damage" as the mix between percent and fixed that isn't piercing. They're basically the same in how they work now.

    As for like a really simplified model for damage, I think this makes it simplest (given that you have mixed damage):
    Total Damage = Piercing Damage + Base Damage
    Where:
    Piercing Damage = Piercing Attack * Attack Percent * (100% - Piercing Reduction)
    Base Damage = BASE MODIFIER * (WeaponAttack*WeaponPercent + IndependentAttack*IndependentPercent)

    Where BASE MODIFIER is the combination of STR/INT stacking, element stacking, and enemy reduction (and all similarly-applied bonuses). It's a nice way of showing the relative power of your base damage at a glance, and makes it a bit intuitive/heuristic to compare piercing to non-piercing damage on percent classes. On hard mode, piercing damage is going to be 80% of the attack*percent, so, if your BASE MODIFIER is 1.6, then basically one extra weapon attack would be worth twice as much as one piercing attack.
     
    Last edited: Apr 20, 2015
  4. Dubin carried by fmage

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    THIS SO MUCH
     
  5. shot040

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    OK, but what is "base attack"
     
  6. Dubin carried by fmage

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    If you're referring to the "Base Attack +352" etc in the weapon description, that's how much the weapon adds to your Independent Attack Power on your character sheet.
     
  7. Everspace I will murder your family

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    Speaking of base attack/independant attack power, it now shows up in some(?) skill tooltips and modifies the number displayed. This is kinda awful for the wiki.

    In the case of frosty head:
    Code:
    IAP    SLv +DMG     Ratio
    496 -> (1) 540      1.0887 
           (22)2023     4.0786
    497 -> (1) 541      1.0885
           (22)2027     4.0784
    747 -> (1) 814      1.0969
           (22)3047     4.0789
    Should we list these skills by their ratio now?

    On Furious Grab on my Avenger, there was no change. Why neople?!
     
  8. Dubin carried by fmage

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    Hweh? I'm psure that's just the standard issue "mixed" damage f.mage t1s have had since 70cap '3' already adjusted and accounted for in the wikis.
     
  9. Rhaeven

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    I don't know how to deal with that issue. I think the best way to handle it is to list the ratio (mind the significant digits). Listing any value outside of the ratio would lead to confusion because everyone will have different Independent Attack values. This means that people who want to understand their fixed damage will have to perform an extra step of actually multiplying out the value. This isn't a problem for me, but like... I have such little faith in people and their ability to understand / do work.
     
  10. Everspace I will murder your family

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    No, because my M.Brawlers Needle Spin's damage (completely flat) changed from 15610 (1173 Independant) to 10047 when I unequipped my claws (755), and then down to 9595 with my subequip (721). Most of the tooltips exhibit this behaviour now (with few exceptions).

    This means that the the number shown on your tooltip can change, and using a range of values isn't correct either because the upper bounds are "unlimited" depending on how much independent attack power you have. So as a skill levels, there is a hidden ratio now that we have to dig out.

    This will be so gross for any skill with a flat damage number now. I wonder if INT/STR is included in the rigmarole too.
     
  11. Rhaeven

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    I think when you make the table, you simply have to clarify whether the column describes

    Percent
    Base Fixed Ratio
    Cooldown
    Duration
    Proc Chance
    etc

    Also, it doesn't include str/int in its calculation. If you want, I referred to a post earlier in the thread that shows how to calculate for it.

    edit: http://www.dfonexus.com/posts/96875/

    edit 2: again, the biggest problem here is that a new standard has to be adopted. People have to learn how to use Independent Attack with Base Fixed Ratio instead of just looking at a static Fixed value because there is no such thing as a static Fixed value.
     
  12. Everspace I will murder your family

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    Element damage is still (stat/42)
     
  13. Rhaeven

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    42? I'm pretty sure Boba's done testing and has data that suggests it is now (1 + element/222)
     
  14. Everspace I will murder your family

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    It is the answer, to life, the universe, and the denominator to the coefficient of elemental damage.

    Dark damage, Shadow Render, 5 skill uses with no weapon on the reinforcement machine in the training room. Enchanted a terrible white ring with +4 shadow damage.

    Here is the road I followed:
    Code:
    +0 Shadow -> 42164 damage
    +4 Shadow -> 46267 damage
    
    46267/42164 = 1.097310501849919
    
    4 damage / (That - 1) = 41.11
    
    Since the result was close to the previously thought number of 42, I thought it was "close enough" for the RNG to fudge it.

    I find the idea of having it be (Element/222) really odd because that means a point of INT would be valued close to a point of element. Currently, it is not weighted like that internally by neople (I'm getting 542INT compared to 15 Shadow from Painful Rapture for example). We would have gobs of it like INT or STR which they tend to hand out like candy.

    Another pointer to this weighting is the the stats from suffixes in magic seal items. +24 from an [Intellect B] vs +5 from a [Element Boost B] in level 60 purples for example means that these should be similarly weighted, or at least in a similar class of an upgrade. This would be 0.10 vs 0.12 if we assume that they are (INT/250) and (Element/42), which I think is an apt comparison since one is more than likely slightly more rare.

    This is however from a design standpoint, and how I would personally engineer the numbers.
     
  15. Dubin carried by fmage

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    Boba also seemed to find that the reinforcement machine has -11 shadow resistance '3' which would throw the ratios off for your equation since yours is assuming resistance = 0. But idek, I need to take a closer look at it with in game and pencil + paper to be sure.
     
  16. Everspace I will murder your family

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    I don't think it would make a difference, since the comparison is in the same stat. So I have 11 and 15 effect shadow damage instead of 0 and 4. It's about the difference between the two values since the -11 is the same between the two and so can be removed from the comparison.
     
  17. Dubin carried by fmage

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    But it does make a difference whether the denominator is a 0 or an 11 factor.

    But if anything it should have made the difference smaller, so again like I said I need to take a closer look in game etc.
     
  18. Necrofancy Blame Blobâ„¢

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    Just taking a quick recording and working with it:
    Using DMG ticks because it's simple to do, recording noncrits because why not:
    [​IMG]

    [​IMG]

    With [​IMG]

    If the elemental coefficient was really that low, I would expect a much larger improvement than that.
    There are two possible explanations:
    • The resistance on the reinforcement machine is SO negative that the damage improvement is only ~12%.
      • If this was the case, I would expect going from neutral to shadow damage would improve damage by a very large factor (I get -190 shadow resist, so even with 0 element it'd be a 4.5x multiplier to damage just by having shadow element instead of neutral element).
      • Very simply poking the reinforcement machine with an enchanted weapon shows that, no, damage doesn't improve by a large factor for simply adding shadow damage.
    • It's not a linear improvement
      • I've been able to do a linear fit with this, so that's probably not the case.
    • Different coefficient.
      • Admittedly, since I didn't care to try to account for variance at all, I don't get exactly -11 shadow resist at 222 (-9.69 shadow resist instead 'w' )
    It wouldn't make sense.... if you were looking at it with 0 INT as well as 0 Element. With buffs, it's easy to break 2k INT on more than a couple classes. With that in mind, even small amounts of element have relatively huge amounts of equivalent INT for the same percent boost in damage.
     
    Last edited: May 5, 2015
  19. Dice Dragon Top Kekrator

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    So im gonna post even though bobas gonna post cause I did the work so I might as well.

    So my base damage on stat before peircing is 2290, my shadow rendor does 524% per hit. Echos of nothing makes this a 670%, this means before shadow damage or shadow resistance my raw damage on the machine should be 15343.

    I hit the machine and found my number to be 16.2kish. So I solved for the missing variable (bobas data claims it has negative -11 shadow. Elemental damage final = elemental damage - elemental reisistance.) Meaning I have 11 shadow damage essentially. 1.0495 * 15342 = 16103, I have 113 peirce that isnt effected by the shadow damage. so there we get my 16.2k.

    So I used a scythe (same grade and stats, only diffrence is this one has +4 shadow.) So I hit the machine and found that I did 16.5k

    15/222 = 1.067
    15343 * 1.067 = 16379 + 113 = 16492, this fell within 1% of my observered damage.

    So using bobas formula of Element/222 was observed to be correct.
     
  20. Dubin carried by fmage

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    That's all well and good but
    WHAT ABOUT THIS

    I mean I expect to find 222 when I log in tomorrow but this leap is still got me stuck
     

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