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Establishing how Critical Rate works

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  • lolzfaillolzfail
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    Method for testing crit rate:
    Use the Personal Performance Meter to ensure accuracy. You can enable it under Options->Game->Interface
    Go to the guild hall (creating one costs 2k or something), on the right side there's a 3x3 square with 3 dummies. If you stand in the middle, Arrow Storm will hit all 3. I'm calling one "rotation" the combo of using Arrow Storm and then Arrow Stream until Arrow Storm is off cooldown. Arrow Stream fires approx 22 times in 13 seconds, so a conservative estimate for total hits from one rotation is 60 from Arrow Storm and 20*5 from Arrow Stream. Doing 20 rotations is at least 3200 hits and takes about 260 seconds.
    I'm sure there are ways to get more hits per second, something like the priority list being Arrow Storm > Eagle's Majesty > Rapid Shot > Arrow Stream where you use the first one in the list that's available, but that requires more effort so meh
    You can set up a macro with just Arrow Storm and Arrow Stream, that way you only have to hold down one button.

    When I say crit rate, I mean the rate that's shown on the Character page, not the Stat Sheet. Presumably that one is just bugged and doesn't display the value after adding in Luck >.>

    20 rotations, 27 luck, 73 crit rate: 8.41% crit
    20 rotations, 56 luck, 73 crit rate: 11.53% crit
    20 rotations, 27 luck, 160 crit rate: 14.73% crit
    20 rotations, 27 luck, 265 crit rate: 23% crit

    I think it's safe to say that crit chance increases linearly or close to linearly with crit rate. One MAJOR factor missing from this discussion is the enemy's Critical Evasion! Seems like the only proper way to test crit rate is to grab another player and go to a hostile zone. I would be up for this during the next beta (if there is one), but right now I'm more interested in figuring out the damage formula. IMO Crit Rate is sort of a dump stat until you can get gear that significantly increases critical damage, so there's still some time left before it becomes super important to know the formula :p

    According to my formula,

    27 luck 73 crit = 8.54%,
    56 luck 73 crit = 11.44%
    27 luck 160 crit = 15.5%
    27 luck 265 crit = 23.9%

    Your results are close to the theoretical values.
    DrYoshiyahu
  • lolzfaillolzfail
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    edited 11:18PM May 15, 2018
    What's making you sure they don't have crit evasion? I think there's a chance they might since players have it too.

    That thread is for Attack which doesn't seem to be a great indicator of how much damage you actually do. In the Attack formula physical attack is just added on but I'm fairly certain that physical attack is a multiplier in the actual damage formula.

    Physical damage isn't added on in the damage formula. The formula I derived is the formula for your attack score(the one shown on the character page). Naturally your damage is proportional to your attack. One thing I found out too was that your attack score reflects your magic attack, and may not be a good indicator of your actual damage, so the only thing of interest is the contribution of weapon attack and physical attack relative to each other.

    As for crit evasion on training dummies, they should generally have minimal defensive stats, for the purposes of damage testing, so it would be safe to say that the training dummies have no crit evasion. Also, even if they were to have crit evasion, we won't be able to get the exact number, and it does not affect the accuracy of the crit rate formula. However, @DrYoshiyahu's original post seemed to have much lower stats that predicted. I assume he did not test on training dummies, so there may have been crit evasion. From the increasing nature of the errors, I would hypothesize that crit evasion works multiplicatively to crit rate, that is

    (1 - crit evasion rate) * crit rate = actual crit rate

    As you mentioned, we would need testing from PvP scenarios where we know the crit evasion stat of our target. One other thing worth mentioning is, does the 40% cap work on the crit rate, or the actual crit rate? If it works on the crit rate, we would have a much lower cap on crit rate when high crit evasion enemies exist. However, if it works on actual crit rate, then that may explain why assassins have a 1000 crit set effect which equates to 80% bonus crit rate, as mentioned by @Olujiwan.
  • DrYoshiyahuDrYoshiyahu
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    edited 12:18AM May 16, 2018
    The issue is that the guild has level 50 boss training dummies, and not level 1 mob training dummies. That creates uncertainties, despite the fact that critical evade is not a common stat on enemies, because it's actually possible to miss shots against those boss dummies, even for a maxed-out Archer.

    It's not likely that even a boss dummy has critical evade, but I would rather wait until they give us one of the level 1 models before testing extensively. I'm still hoping we get them as meso-purchasable furnishings. In any case, I would imagine that whatever enemies I was attacking previously id have critical evade, which may account for the discrepancies. Against the training dummies, I was able to get 29% crit chance with 326 CRIT/27 LUK.

    It's actually interesting to note that an Archer with max Sharp Eyes and full Epic gear at level 50 may be capable of hitting the 40% crit chance max if they have the right bonus attributes on their gear. At a certain level of Bronze Eagle, it's probably better to move the APs from CRIT to DEX anyway, but post-level 50, when you can get 20+ CRIT on potentially every item of clothing, moving to a pure-DEX build may just be better to ensure you're not capping.

    As for Attack verses Physical Attack, there's two things that need to be considered:

    Firstly, Attack is what people are paying attention to. That's the forward-facing stat, and even if it's tainted with Magic Attack, it's still going to dominate the public discussion.

    Secondly, we don't actually know if the damage multipliers on the skills are taking their base damage from the Attack stat or the Physical Attack (for physical-based skills). It may actually turn out that Intelligence does boost an Archer's damage, however unlikely, and the difference may be too small to ever prove one way or the other.

    We may never actually be able to work out true DPS, but we don't need to, that's what the performance meter is for. What the meter can't tell us is whether it's better to upgrade DEX or CRIT with our AP points, or whether it's better to take the cape with 10 DEX or 30 STR. That's what we need to solve.
  • lolzfaillolzfail
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    326 crit 27 luk is 28.78% crit rate, so this would further support my guess that training dummies have no/minimal crit evasion. As for 40% crit chance, you would need 467 crit according to my formula, which is 362 without sharp eyes, so it is definitely possible if you stack crit on equips. However, if crit evasion exists, we may need to exceed this "cap" crit rate, in order to achieve true cap on enemies with crit evasion, but this all depends on how crit evasion works.

    For attack vs physical attack, I completely agree with you. Attack score will be used in most discussions, and in fact, it can be used to a certain extent. Assuming we don't randomly get int from equips or buffs, the amount of magic attack contribution will stay the same, so a higher attack score will equate to a higher physical attack and vice versa. However, this argument will fail if we were to compare percentages and flat increases. For example, crit affects your damage by a percentage, while dex affects it by a flat amount. Thus crit will also affect the magic attack portion of your attack score, which may or may not be what we want. This is not a huge problem for now as max crit rate only increases the attack score contribution of magic attack by less than 1. However, when higher percentage buffs exist, for example crit damage increase, the attack score will become less reliable assuming damage is not calculated on attack score.

    As for whether damage is calculated based on attack score or physical attack, it is possible to test, and I would strongly believe it is calculated based on physical attack. My reason is as follows:

    Based on the values I reverse engineered,

    physical attack = 0.63 * dex + 0.175 * str
    magic attack = 0.35 * int

    Both these formulae are accurate to around 0.1% error margin, with the exception of str at 0.7%. Also, I calculated that magic attack has at least 10% more contribution to attack score than physical attack. This puts int at around 0.385 ~ 0.4 physical attack(rough estimates, I did not do serious calcs). Now this is a big problem, as int contributes more than twice as much as str, and almost 2/3 of dex. If damage was calculated by attack score, int would be a legit stat on archers.

    As for testing, I do not know if you can attack without a weapon, but if you use a low lvl weapon like the tutorial weapon(16 attack if I'm not wrong) at lvl 50, then your attack clean is around 243 to 245, and adding 36 AP into int will raise it by around 14 to 15 attack score, which equates to around 6% increase in damage. This is definitely testable if we were to observe minimum and maximum damage over a large number of shots, or even via the performance meter.
  • SubglaciousSubglacious
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    edited 2:00AM May 16, 2018
    lolzfail wrote: »
    Physical damage isn't added on in the damage formula. The formula I derived is the formula for your attack score(the one shown on the character page). Naturally your damage is proportional to your attack. One thing I found out too was that your attack score reflects your magic attack, and may not be a good indicator of your actual damage, so the only thing of interest is the contribution of weapon attack and physical attack relative to each other.

    What I was getting is that the Attack on your character page isn't very useful because it has the (simplified) form of (WA + PA) * (crit modifier) while the actual damage is something like WA * PA * (other terms) * (crit modifier). Because of this difference (and because Attack doesn't take crit evasion into account I guess), the value of crit is strongly inflated if you just go by Attack. It's a poor metric.

    lolzfail wrote: »
    As for crit evasion on training dummies, they should generally have minimal defensive stats, for the purposes of damage testing, so it would be safe to say that the training dummies have no crit evasion.

    DrYoshi already answered this but they definitely have at least some defensive stats: damage done to training dummies matches damage done to level 50 mobs.

    lolzfail wrote: »
    One other thing worth mentioning is, does the 40% cap work on the crit rate, or the actual crit rate? If it works on the crit rate, we would have a much lower cap on crit rate when high crit evasion enemies exist. However, if it works on actual crit rate, then that may explain why assassins have a 1000 crit set effect which equates to 80% bonus crit rate, as mentioned by @Olujiwan.

    I'd assume the latter, both because of your point and because everyone would complain endlessly if they could never crit the endgame bosses :^)

  • SubglaciousSubglacious
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    edited 2:41AM May 16, 2018
    lolzfail wrote: »
    As for testing, I do not know if you can attack without a weapon, but if you use a low lvl weapon like the tutorial weapon(16 attack if I'm not wrong) at lvl 50, then your attack clean is around 243 to 245, and adding 36 AP into int will raise it by around 14 to 15 attack score, which equates to around 6% increase in damage. This is definitely testable if we were to observe minimum and maximum damage over a large number of shots, or even via the performance meter.

    IIRC you can attack without a bow but it's just a knife swipe and it only does 1 damage. I've previously tested adding points to intelligence/luck/crit rate and there's no difference on average damage for Arrow Stream after you account for crit % differences.
  • lolzfaillolzfail
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    edited 3:42AM May 16, 2018
    What I was getting is that the Attack on your character page isn't very useful because it has the (simplified) form of (WA + PA) * (crit modifier) while the actual damage is something like WA * PA * (other terms) * (crit modifier). Because of this difference (and because Attack doesn't take crit evasion into account I guess), the value of crit is strongly inflated if you just go by Attack. It's a poor metric.

    The reason why I used the formula on that page was because in order to calculate our actual damage, we would first need to find out how stats interact with our damage. As the attack score is meant to be an indicator(albeit flawed) of our damage, it would be useful in determining the general form of the damage formula, as instead of testing our damage, which is prone to large variances unless we hit many times (on the order of 100k to 1m hits for crit rate), we can pinpoint the contribution of stats by the attack score which basically calculates your "average damage". As for external factors like crit evasion and accuracy, we can incorporate them into our "actual damage" formula, but in order to do so we need a good understanding of how crit rate works before we can account in crit evasion, and the attack score which doesn't account for crit evasion is perfect for that as it ignores crit evasion. As such, I want to first determine the formula for attack score, so I know certain facts like 1 dex = 3.6 str, and 1 WA is around 0.99968 ~ 0.99971 attack score. Also, I am pretty sure it is (WA + PA) instead of (WA * PA) because I have data from 80 WA, 70+ PA and 1.2k WA 227+ PA, and it most definitely is not multiplied together.

    I have changed my post on the formula accordingly, do check it out and tell me if you want me to add anything.

    DrYoshi already answered this but they definitely have at least some defensive stats: damage done to training dummies matches damage done to level 50 mobs.

    As for this, he did test his crit rate on them and got 4% higher than when he tested on normal mobs, so I believe training dummies will have a minimal amount of crit evasion. Nevertheless, this is proof that normal mobs do have a non-negligible amount of crit evasion, and as you suggested, we would need PvP to accurately determine the effect of crit evasion. Currently I am looking at 2 possible models: crit evasion is subtracted from your crit stat, or crit evasion is calculated as a separate chance to change crits back into normal hits. I believe the latter is true, as the deviations in crit rates seem higher at higher crit rates. This also brings up another weakness of the attack score, which does not account for crit evasion.


    I'd assume the latter, both because of your point and because everyone would complain endlessly if they could never crit the endgame bosses :^)
    so true xD
  • lolzfaillolzfail
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    edited 4:00AM May 16, 2018
    lolzfail wrote: »
    As for testing, I do not know if you can attack without a weapon, but if you use a low lvl weapon like the tutorial weapon(16 attack if I'm not wrong) at lvl 50, then your attack clean is around 243 to 245, and adding 36 AP into int will raise it by around 14 to 15 attack score, which equates to around 6% increase in damage. This is definitely testable if we were to observe minimum and maximum damage over a large number of shots, or even via the performance meter.

    IIRC you can attack without a bow but it's just a knife swipe and it only does 1 damage. I've previously tested adding points to intelligence/luck/crit rate and there's no difference on average damage for Arrow Stream after you account for crit % differences.

    Nice, this means that magic attack has no effect on our damage whatsoever. I was starting to fear that int was going to be a good stat for archers. What this also means is that I have gathered enough information to stop focussing on attack score now, and we can move on to calculating the effects of external factors affecting dps, like crit evasion and accuracy.
  • OlujiwanOlujiwan
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    lolzfail wrote: »
    Olujiwan wrote: »
    If you're correct though, that means 1600 Critical Rate would be necessary to get 40% critical chance, which is so much higher than I think anyone was expecting (or wanting).

    Yes and no. While I'm an assassin, this makes sense.

    Assassins get a level 50 set bonus on their gear with 2 options;

    1. 20% increased attack speed when wearing the full set (proc chance on hit)
    2. 1000 crit rate when wearing full set (proc chance on hit)

    Last night, because of lack of data, I was thinking those were ridiculously high numbers. Now that I think about it, it makes sense. Why would developers add a set that is pretty much useless? On the other hand, I definitely feel like I crit way more than just 20% atm (my stats are similar to yours).

    Interesting... according to a linear model you would only need less than 500 crit to cap crit rate. Do you happen to have the set? If so, do you mind proccing the effect and seeing how much your attack score increases by? I would need to know your attack score, crit and luk before and after the effect.

    Did have the set, not anymore. Pretty stupid I know. I only had 3 pieces, so it was increased by 600 crit. It did not seem to do anything for my crit rate, but my crit damage went up by 100% exactly.
  • SubglaciousSubglacious
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    lolzfail wrote: »
    What I was getting is that the Attack on your character page isn't very useful because it has the (simplified) form of (WA + PA) * (crit modifier) while the actual damage is something like WA * PA * (other terms) * (crit modifier). Because of this difference (and because Attack doesn't take crit evasion into account I guess), the value of crit is strongly inflated if you just go by Attack. It's a poor metric.

    Also, I am pretty sure it is (WA + PA) instead of (WA * PA) because I have data from 80 WA, 70+ PA and 1.2k WA 227+ PA, and it most definitely is not multiplied together.

    Could you copy/paste that? I'm fairly sure that either the data or the interpretation is wrong.

    After a bit more testing, average damage is something like
    weapon attack * physical attack * 2 * (crit modifier) * (resistance modifier) * (defense modifer)
    where:
    weapon attack = average of min and max attacks on your weapon (so the weapon attack for a given hit is a roll from min to max and the average damage is the average weapon attack)
    physical attack = your formula
    crit modifier = 1 + (bonus crit damage)*(actual crit chance)
    resistance modifier = 1 - resistance/1500 (assuming 0 resistance piercing. Not yet sure how resistance piercing plays into this)
    defense modifier = 1 / (defense*(1-piercing))
  • lolzfaillolzfail
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    edited 11:08AM May 16, 2018
    lolzfail wrote: »
    What I was getting is that the Attack on your character page isn't very useful because it has the (simplified) form of (WA + PA) * (crit modifier) while the actual damage is something like WA * PA * (other terms) * (crit modifier). Because of this difference (and because Attack doesn't take crit evasion into account I guess), the value of crit is strongly inflated if you just go by Attack. It's a poor metric.

    Also, I am pretty sure it is (WA + PA) instead of (WA * PA) because I have data from 80 WA, 70+ PA and 1.2k WA 227+ PA, and it most definitely is not multiplied together.

    Could you copy/paste that? I'm fairly sure that either the data or the interpretation is wrong.

    After a bit more testing, average damage is something like
    weapon attack * physical attack * 2 * (crit modifier) * (resistance modifier) * (defense modifer)
    where:
    weapon attack = average of min and max attacks on your weapon (so the weapon attack for a given hit is a roll from min to max and the average damage is the average weapon attack)
    physical attack = your formula
    crit modifier = 1 + (bonus crit damage)*(actual crit chance)
    resistance modifier = 1 - resistance/1500 (assuming 0 resistance piercing. Not yet sure how resistance piercing plays into this)
    defense modifier = 1 / (defense*(1-piercing))

    I have just been informed that while displayed attack adds PA and WA, actual damage multiplies them.(I just realised you said that too, my bad I misread what you wrote) As I was calculating damage based on the assumption that displayed attack was suitably reliable, I assumed it was supposed to be added. Apparently displayed attack is completely useless now. But thanks for the additional information. I would assume resistance piercing works in the same way as defense piercing.
  • KillerkonnatKillerkonnat
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    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
  • GoeringGoering
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    edited 8:20AM October 11, 2018
    My assassin has 463 luck. Wouldn't that mean that I would hit the crit chance cap of 40%? I only get about 8.8-9% crit % with that much luck and 71 crit rate stat.

    Tested again (both tests were several minutes of holding down an attack macro consisting of all my skills, minus buffs. no skills have a modified crit chance) with 417 luck and 209 crit rate, got 21.4%
  • WAtheAnumWAtheAnum
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    gees i came here and wanted to know how the crit system works and ended up in a math system XD

    But srsly, to go on easy, why didnt they just add a state ingame which SHOWS actually your crit "rate"? I mean it really -is- confusing if you just put points in "critrate" but you dont see anywhere a "%" status you have as chance as crits, is that so hard to add that into the game? I mean it could be just add in the advanced status screen that you have a critchance rate from (as sample) 8,7% with XYZ points placed on critrate. it would make this a LOT more understandable...