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Damage formula

lolzfaillolzfail
Maplestory 2 Rep: 1,095
Posts: 36
Member
edited 2:49AM May 21, 2018 in Archer
Since there was already a critical rate thread, I was thinking, why not damage formula too. The damage formula is essential for strategies involving min-maxing, to avoid having to try things out one by one. However, there does not seem to be any information regarding the damage formula, so I would like the help of beta testers to provide data in order to reverse engineer the damage formula. As I do not have a beta key, most of my information was obtained from CMS2, which has its disadvantages, so it would be preferable to have data from the global servers.

IMPORTANT: The attack score in your character window is NOT an accurate representation of your actual damage. The formula for attack score and formula for actual damage are very different from each other.

First of all, I would like to introduce some terms, so I can use them without sounding confusing:

PA- Physical attack, the stat in the detailed stats part of character info
MA- Magic attack, also the stat in the detailed stats part, which I assume archers don't ever use
AP- attribute points, the points you can assign to your stats
str, dex, int, luk, crit - the 5 stats you can assign AP to
CR- the rate at which your hits are critical hits, not to be confused with crit
CD- crit dmg taken as a decimal number rather than a percentage, i.e. 1.25 is the base CD
CE- crit evasion
DM - defense modifier
RM - resistance modifier
WA- total attack gained from equips. In the case of equips like weapons giving a range a~b, WA will be determined by (a+b)/2

A formula for actual damage will be something like this:

damage = A * WA * PA * (1 + (CD - 1) * actual CR) * accuracy * DM * RM * skill damage

First of all, we need to calculate MA and PA. These are affected by dex/str/int and equips as follows:
MA = 0.35 * int
PA = 0.63 * dex + 0.175 * str

*These formulae are incredibly accurate, and can be used as the exact ones. It takes at least 1140 int to make a difference in 1 magic attack(and you should not be adding int anyway). For dex, it is at least 905 for 1 attack difference, and at least 142 str per attack difference in error(you shouldn't be adding str either anyway). One thing to note, however, is that this is only based on data from the archer class, so if you are not an archer change to a real class like archer this formula may not work for you, but do try to test and see if it does.

In the critical rate thread I have reverse engineered a formula of:

CR = luk/1000 + crit/1250
Crit damage as a stat from equips gives 0.1% CD per crit damage

Once again, this may not be correct, but the margin of error is very small(I believe somewhere along the lines of 100 luk to 1% crit rate, and 125 crit to 1% crit rate), so feel free to use it as if it were true. Do note that this is your BASE crit rate. There is crit evasion on enemies, which serve to reduce your actual crit rate.

Apparently there is a crit evasion stat. We do not yet know exactly how it works, but it should be one of the two models below:

actual CR =( luk/1000 + crit/1250 - (effect of CE)) and
actual CR =( luk/1000 + crit/1250) * (effect of CE)

As Crit evasion is not a stat we know for any monster, this can only be tested in PvP, where you know your opponent's crit evasion.

DM = 1/(defense * (1 - piercing))
RM = 1 - resistance(1 - resistance piercing) / 1500


How to collect data:

- If you create a new character, check your stats before equipping the weapon in the tutorial, as you will not be able to unequip it until lvl 5 or so.
- When gathering data, first unequip all stat boosting equips and make sure you have no buffs. Your PA should not have a (+x) beside it.
- It would be helpful to add your AP 1 by 1, in different combinations of str, dex and crit.
- Make use of stat boosting equips to further vary your stats.
- Make sure you are an archer, as i believe wizards and archers have different values, not sure about other classes. Data from other classes is welcome, but please indicate if you are not an archer.

Thank you for your time :D

Thanks to @DrYoshiyahu for providing some data, which helped greatly in finding the values.

Comments

  • DrYoshiyahuDrYoshiyahu
    Maplestory 2 Rep: 8,200
    Posts: 504
    Forum Moderator
    edited 10:45PM May 12, 2018
    I'll dump some screenshots in here for you. Hopefully these are somewhat helpful. I'd do some calculations myself, but I really should be doing essays and exam prep, right now.

    EDIT: I'll also mention that, according to the descriptions of the stats, Intelligence only increases magic attack and magic resistance, which is irrelevant for Archers since none of our skills are magical.

    Luck increases the physical attack of only Wizards, Thieves, Assassins, and Heavy Gunners. It does however, affect Critical Rate, which makes it relevant for Archers.

    So I made a new character at level 1. Here are the character stats with and without the tutorial bow:
    uvApQMz.jpg
    5Kv16he.jpg
    u1JiHXO.jpg

    Back on my main character (level 50), I took all my skills to 0, removed all my attribute points, and all my armour. Then I took all my points and put them into STR, DEX, and Crit Rate. Here are the results:

    Clean:
    1kjAkof.jpg
    STR:
    zfCHFoD.jpg
    DEX:
    9L9k4XP.jpg
    LUK:
    okjXWau.jpg
    Crit Rate:
    Jx3byau.jpg

    Then I took each of my items and re-equipped them one at a time, showing the stats as I went:

    Bow:
    KtPUvCU.jpg
    tUGb2aS.jpg

    Overalls:
    PDoxGIo.jpg
    Fr3Yxo6.jpg

    Hat:
    OlBWzSG.jpg
    Le7W5vX.jpg

    Gloves:
    KrZpZvb.jpg
    NmLGYXD.jpg

    Boots:
    34jRfDW.jpg
    Rz1PrbU.jpg

    Other (Inconsequential) items:
    kVCFUaJ.jpg
    86bKD98.jpg
    WL8HyHJ.jpg
    TKUpfJh.jpg
    b15tUmv.jpg

    Finally, with all my equipment back on, I put my points into STR, DEX, and Crit Rate once more:

    Clean:
    lmP6m8M.jpg
    STR:
    oM5mckp.jpg
    DEX:
    LEmq2Qw.jpg
    LUK:
    xr59pvM.jpg
    Crit Rate:
    tkE6LVd.jpg
    lolzfail
  • lolzfaillolzfail
    Maplestory 2 Rep: 1,095
    Posts: 36
    Member
    edited 12:05AM May 13, 2018
    Thanks for the data! It helps to have data from high level people where small errors are magnified. It also helped me realise the 2% buff in CMS had messed up one of my data points, which was why I failed miserably. Hopefully I can figure out everything else soon. I also have exams to study for, but this is technically related to my exams haha.
    It does however, affect Critical Rate, which makes it relevant for Archers.

    If luk invisibly affects crit rate, this would surely add complications in finding the crit formula.
  • lolzfaillolzfail
    Maplestory 2 Rep: 1,095
    Posts: 36
    Member
    @DrYoshiyahu If it's not too troublesome for you, is it possible for you to add str/dex 1 by 1 and tell me your physical attack(the one displayed in the stat sheet), just like what you did for crit and luk? Without equipping your weapon as it has bonus physical attack.
  • DrYoshiyahuDrYoshiyahu
    Maplestory 2 Rep: 8,200
    Posts: 504
    Forum Moderator
    edited 2:44AM May 15, 2018
    EDIT: Apparently I'm actually just terrible at reading, so below is the Attack Score (ATT) and the Physical/Magic Attack of STR, DEX, and INT without my weapon equipped. You should be aware that the numbers I previously gave you for CRIT and LUK were the Attack Score, and not the Physical Attack stat. I included INT, since I've only just realised that the Attack Score takes Magic Attack into consideration. This is actually unhelpful because Archers have no magical attacks.

    I don't know if you think I have the weapon I have, so here's a picture of my current weapon. You'll notice that, with it equipped, my Bonus Attack stat is 0. The same is true even with all my equips on. It does, however, set my Physical Attack to +17. 8 of which is coming directly from the weapon, and the other 9 is coming from the +14 DEX. I also made sure Attack Speed didn't affect any stats, and based on the 3% buff from Precision Shooter, I don't believe it does.

    Clean Stats:
    20180515_185733_92.jpg

    STR:
    55-57 STR: 247 Physical Attack, 1492 ATT
    58-63 STR: 248 Physical Attack, 1492 ATT
    64-68 STR: 249 Physical Attack, 1493 ATT
    69-74 STR: 250 Physical Attack, 1494 ATT
    75-80 STR: 251 Physical Attack, 1495 ATT
    81-85 STR: 252 Physical Attack, 1496 ATT
    86-?? STR: 253 Physical Attack, 1497 ATT
    

    DEX:
    365     DEX: 247 Physical Attack, 1492 ATT
    366-367 DEX: 248 Physical Attack, 1492 ATT
    368     DEX: 249 Physical Attack, 1493 ATT
    369-370 DEX: 250 Physical Attack, 1494 ATT
    371-372 DEX: 251 Physical Attack, 1495 ATT
    373     DEX: 252 Physical Attack, 1496 ATT
    374-375 DEX: 253 Physical Attack, 1497 ATT
    376     DEX: 254 Physical Attack, 1498 ATT
    377-378 DEX: 255 Physical Attack, 1499 ATT
    379     DEX: 256 Physical Attack, 1500 ATT
    380-381 DEX: 257 Physical Attack, 1501 ATT
    382-383 DEX: 258 Physical Attack, 1502 ATT
    384     DEX: 259 Physical Attack, 1503 ATT
    385-386 DEX: 260 Physical Attack, 1504 ATT
    387     DEX: 261 Physical Attack, 1505 ATT
    388-389 DEX: 262 Physical Attack, 1506 ATT
    390-391 DEX: 263 Physical Attack, 1507 ATT
    392     DEX: 264 Physical Attack, 1508 ATT
    393-394 DEX: 265 Physical Attack, 1509 ATT
    395     DEX: 266 Physical Attack, 1510 ATT
    396-397 DEX: 267 Physical Attack, 1511 ATT
    398-399 DEX: 268 Physical Attack, 1512 ATT
    400     DEX: 269 Physical Attack, 1513 ATT
    401-??? DEX: 270 Physical Attack, 1513 ATT
    
    

    Without a weapon (because apparently I can't read simple instructions):

    Clean Stats:
    20180515_180133_91.jpg

    STR:
    55-56 STR: 230 Physical Attack, 227 ATT
    57-62 STR: 231 Physical Attack, 228 ATT
    63-67 STR: 232 Physical Attack, 229 ATT
    68-73 STR: 233 Physical Attack, 230 ATT
    74-79 STR: 234 Physical Attack, 231 ATT
    80-84 STR: 235 Physical Attack, 232 ATT
    85-90 STR: 236 Physical Attack, 232 ATT
    91-?? STR: 237 Physical Attack, 233 ATT
    

    DEX:
    351     DEX: 230 Physical Attack, 227 ATT
    352     DEX: 231 Physical Attack, 228 ATT
    353-354 DEX: 232 Physical Attack, 229 ATT
    355-356 DEX: 233 Physical Attack, 230 ATT
    357     DEX: 234 Physical Attack, 231 ATT
    358-359 DEX: 235 Physical Attack, 232 ATT
    360     DEX: 236 Physical Attack, 232 ATT
    361-362 DEX: 237 Physical Attack, 233 ATT
    363-364 DEX: 238 Physical Attack, 234 ATT
    365     DEX: 239 Physical Attack, 235 ATT
    366-367 DEX: 240 Physical Attack, 236 ATT
    368     DEX: 241 Physical Attack, 237 ATT
    369-370 DEX: 242 Physical Attack, 238 ATT
    371-372 DEX: 243 Physical Attack, 239 ATT
    373     DEX: 244 Physical Attack, 240 ATT
    374-375 DEX: 245 Physical Attack, 241 ATT
    376     DEX: 246 Physical Attack, 242 ATT
    377-378 DEX: 247 Physical Attack, 243 ATT
    379     DEX: 248 Physical Attack, 244 ATT
    380-381 DEX: 249 Physical Attack, 245 ATT
    382-383 DEX: 250 Physical Attack, 246 ATT
    384     DEX: 251 Physical Attack, 247 ATT
    385-386 DEX: 252 Physical Attack, 248 ATT
    387-??? DEX: 253 Physical Attack, 249 ATT
    

    INT:
    25    INT:  8 Magic Attack, 227 ATT
    26-28 INT:  9 Magic Attack, 228 ATT
    29-31 INT: 10 Magic Attack, 229 ATT
    32-34 INT: 11 Magic Attack, 230 ATT
    35-37 INT: 12 Magic Attack, 231 ATT
    38-39 INT: 13 Magic Attack, 232 ATT
    40-42 INT: 14 Magic Attack, 233 ATT
    43-45 INT: 15 Magic Attack, 234 ATT
    46-48 INT: 16 Magic Attack, 235 ATT
    49-51 INT: 17 Magic Attack, 236 ATT
    52-54 INT: 18 Magic Attack, 237 ATT
    55-57 INT: 19 Magic Attack, 239 ATT (not a typo, I triple-checked)
    58-59 INT: 20 Magic Attack, 240 ATT
    60-?? INT: 21 Magic Attack, 241 ATT
    
    lolzfail
  • lolzfaillolzfail
    Maplestory 2 Rep: 1,095
    Posts: 36
    Member
    edited 10:53AM May 15, 2018
    EDIT: Apparently I'm actually just terrible at reading, so below is the Attack Score (ATT) and the Physical/Magic Attack of STR, DEX, and INT without my weapon equipped. You should be aware that the numbers I previously gave you for CRIT and LUK were the Attack Score, and not the Physical Attack stat. I included INT, since I've only just realised that the Attack Score takes Magic Attack into consideration. This is actually unhelpful because Archers have no magical attacks.

    I don't know if you think I have the weapon I have, so here's a picture of my current weapon. You'll notice that, with it equipped, my Bonus Attack stat is 0. The same is true even with all my equips on. It does, however, set my Physical Attack to +17. 8 of which is coming directly from the weapon, and the other 9 is coming from the +14 DEX. I also made sure Attack Speed didn't affect any stats, and based on the 3% buff from Precision Shooter, I don't believe it does.

    Clean Stats:
    20180515_185733_92.jpg

    STR:
    55-57 STR: 247 Physical Attack, 1492 ATT
    58-63 STR: 248 Physical Attack, 1492 ATT
    64-68 STR: 249 Physical Attack, 1493 ATT
    69-74 STR: 250 Physical Attack, 1494 ATT
    75-80 STR: 251 Physical Attack, 1495 ATT
    81-85 STR: 252 Physical Attack, 1496 ATT
    86-?? STR: 253 Physical Attack, 1497 ATT
    

    DEX:
    365     DEX: 247 Physical Attack, 1492 ATT
    366-367 DEX: 248 Physical Attack, 1492 ATT
    368     DEX: 249 Physical Attack, 1493 ATT
    369-370 DEX: 250 Physical Attack, 1494 ATT
    371-372 DEX: 251 Physical Attack, 1495 ATT
    373     DEX: 252 Physical Attack, 1496 ATT
    374-375 DEX: 253 Physical Attack, 1497 ATT
    376     DEX: 254 Physical Attack, 1498 ATT
    377-378 DEX: 255 Physical Attack, 1499 ATT
    379     DEX: 256 Physical Attack, 1500 ATT
    380-381 DEX: 257 Physical Attack, 1501 ATT
    382-383 DEX: 258 Physical Attack, 1502 ATT
    384     DEX: 259 Physical Attack, 1503 ATT
    385-386 DEX: 260 Physical Attack, 1504 ATT
    387     DEX: 261 Physical Attack, 1505 ATT
    388-389 DEX: 262 Physical Attack, 1506 ATT
    390-391 DEX: 263 Physical Attack, 1507 ATT
    392     DEX: 264 Physical Attack, 1508 ATT
    393-394 DEX: 265 Physical Attack, 1509 ATT
    395     DEX: 266 Physical Attack, 1510 ATT
    396-397 DEX: 267 Physical Attack, 1511 ATT
    398-399 DEX: 268 Physical Attack, 1512 ATT
    400     DEX: 269 Physical Attack, 1513 ATT
    401-??? DEX: 270 Physical Attack, 1513 ATT
    
    

    Without a weapon (because apparently I can't read simple instructions):

    Clean Stats:
    20180515_180133_91.jpg

    STR:
    55-56 STR: 230 Physical Attack, 227 ATT
    57-62 STR: 231 Physical Attack, 228 ATT
    63-67 STR: 232 Physical Attack, 229 ATT
    68-73 STR: 233 Physical Attack, 230 ATT
    74-79 STR: 234 Physical Attack, 231 ATT
    80-84 STR: 235 Physical Attack, 232 ATT
    85-90 STR: 236 Physical Attack, 232 ATT
    91-?? STR: 237 Physical Attack, 233 ATT
    

    DEX:
    351     DEX: 230 Physical Attack, 227 ATT
    352     DEX: 231 Physical Attack, 228 ATT
    353-354 DEX: 232 Physical Attack, 229 ATT
    355-356 DEX: 233 Physical Attack, 230 ATT
    357     DEX: 234 Physical Attack, 231 ATT
    358-359 DEX: 235 Physical Attack, 232 ATT
    360     DEX: 236 Physical Attack, 232 ATT
    361-362 DEX: 237 Physical Attack, 233 ATT
    363-364 DEX: 238 Physical Attack, 234 ATT
    365     DEX: 239 Physical Attack, 235 ATT
    366-367 DEX: 240 Physical Attack, 236 ATT
    368     DEX: 241 Physical Attack, 237 ATT
    369-370 DEX: 242 Physical Attack, 238 ATT
    371-372 DEX: 243 Physical Attack, 239 ATT
    373     DEX: 244 Physical Attack, 240 ATT
    374-375 DEX: 245 Physical Attack, 241 ATT
    376     DEX: 246 Physical Attack, 242 ATT
    377-378 DEX: 247 Physical Attack, 243 ATT
    379     DEX: 248 Physical Attack, 244 ATT
    380-381 DEX: 249 Physical Attack, 245 ATT
    382-383 DEX: 250 Physical Attack, 246 ATT
    384     DEX: 251 Physical Attack, 247 ATT
    385-386 DEX: 252 Physical Attack, 248 ATT
    387-??? DEX: 253 Physical Attack, 249 ATT
    

    INT:
    25    INT:  8 Magic Attack, 227 ATT
    26-28 INT:  9 Magic Attack, 228 ATT
    29-31 INT: 10 Magic Attack, 229 ATT
    32-34 INT: 11 Magic Attack, 230 ATT
    35-37 INT: 12 Magic Attack, 231 ATT
    38-39 INT: 13 Magic Attack, 232 ATT
    40-42 INT: 14 Magic Attack, 233 ATT
    43-45 INT: 15 Magic Attack, 234 ATT
    46-48 INT: 16 Magic Attack, 235 ATT
    49-51 INT: 17 Magic Attack, 236 ATT
    52-54 INT: 18 Magic Attack, 237 ATT
    55-57 INT: 19 Magic Attack, 239 ATT (not a typo, I triple-checked)
    58-59 INT: 20 Magic Attack, 240 ATT
    60-?? INT: 21 Magic Attack, 241 ATT
    

    Thanks alot for these data, will look into them when I'm free. The jump in attack is interesting though, it's probably caused by rounding somewhere. Just to be sure, are your physical attack and magic attack both increased at the same time as your attack score? (that means that you didn't get, say 8 magic attack and 228 ATT at 27 int). As for crit and luk, no worries, I was looking at attack score. I also wasn't very clear, next time I will say attack score, physical and magic attack to refer to them.

    EDIT: 1 str = 0.174 ~ 0.182 physical attack, this would mean 1 dex = 0.628895 ~ 0.630977 physical attack. Their numbers have more decimal places than I expected.

    EDIT 2: My hypothesis of PA = 0.63 * dex + 0.175 * str agrees completely with your data! Since the margin of error is 905 dex to 1 physical attack(and 142 str to 1 physical attack, but seriously who even adds that much str), I believe we can treat this formula as the real formula, so I have updated my original post accordingly.

    EDIT 3: int = 0.35 MA, with an error margin of 1140 int per MA. Also, MA is useless for archers lol.
  • KillerkonnatKillerkonnat
    Maplestory 2 Rep: 550
    Posts: 14
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    A formula for actual damage will be something like this:

    damage = A * (1.07 * WA + PA)

    It's not. It's WA * PA and not WA + PA. Confirmed by my own testing and a bunch of Korean server researchers. Displayed attack <IS> WA + PA though which makes it really inaccurate for gauging damage. (For example early lvl 50 you could easily have something like 700 WA and 300 PA. Which means +1 PA would give more than twice the damage of +1 WA even though they both show up as +1 attack on your character sheet.)

    Also, if "A" happens to be the hidden class-specific damage multiplier I've got some of the Korean numbers but I don't know how useful that is because we might have completely different numbers on our patch than Korean server. It's an easy way to balance the classes' dps numbers a bit. (Though I heard we'll release on the same patch as CMS so if we found some chinese numbers it could be more useful) Also note that there could be multiple factors instead of just 1 (A*B*C instead of A) so the class multiplier might be just one part of it. At least knowing you've got a class-specific component might make it easier to test. I have NO IDEA whether the multiplier is displayed in VA or only actual damage numbers.

    The multipliers I remember:
    Berserker 1.05
    Knight 0.85
    Thief 0.9
    Archer 0.89 (80% confidence in this number)

    I don't remember the other classes but I know nobody has as high as the berserker. I think Heavy Gunner might be the second highest at something like 1.00 but I have no confidence about that.
  • lolzfaillolzfail
    Maplestory 2 Rep: 1,095
    Posts: 36
    Member
    A formula for actual damage will be something like this:

    damage = A * (1.07 * WA + PA)

    It's not. It's WA * PA and not WA + PA. Confirmed by my own testing and a bunch of Korean server researchers. Displayed attack <IS> WA + PA though which makes it really inaccurate for gauging damage. (For example early lvl 50 you could easily have something like 700 WA and 300 PA. Which means +1 PA would give more than twice the damage of +1 WA even though they both show up as +1 attack on your character sheet.)

    Also, if "A" happens to be the hidden class-specific damage multiplier I've got some of the Korean numbers but I don't know how useful that is because we might have completely different numbers on our patch than Korean server. It's an easy way to balance the classes' dps numbers a bit. (Though I heard we'll release on the same patch as CMS so if we found some chinese numbers it could be more useful) Also note that there could be multiple factors instead of just 1 (A*B*C instead of A) so the class multiplier might be just one part of it. At least knowing you've got a class-specific component might make it easier to test. I have NO IDEA whether the multiplier is displayed in VA or only actual damage numbers.

    The multipliers I remember:
    Berserker 1.05
    Knight 0.85
    Thief 0.9
    Archer 0.89 (80% confidence in this number)

    I don't remember the other classes but I know nobody has as high as the berserker. I think Heavy Gunner might be the second highest at something like 1.00 but I have no confidence about that.

    I see, time to delete everything about the displayed attack then. As for A, I just meant to say that it is proportional to all the stats I have listed. A could depend on multiple factors, but I put it there just to say that your damage increases proportionately if you increase those other stats in the formula.
  • KillerkonnatKillerkonnat
    Maplestory 2 Rep: 550
    Posts: 14
    Member
    edited 1:05PM May 16, 2018
    I was actually a little bit wrong about the class damage multipliers. Berserker wasn't the highest like I remembered. I found the full list:

    Knight 0,85
    Berserker 1,05
    Ranger 0,89
    Heavy Gunner 1,06
    Wizard 1,10
    Priest 0,76
    Assassin 0,86
    Thief 0,90

    It's useful to mention in the post though that displayed attack is misleading and why it's wrong. So people avoid just staring at it when they start min-maxing.