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Part 1: Mathematics Behind the DPS classes of Maplesaga

Discussion in 'General Guides' started by AndyZ, Jul 15, 2020.

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  1. AndyZ

    AndyZ Legendary Mapler

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    AndyX
    This guide will look at the balance between DPS classes, but I will not include any personal comments on what I think the balance of classes should be. I'll delve into all the mathematics behind damage and I will assume level 200 (for max available weapon mastery) for all classes.

    In order to compare classes, I use the measure of a "Damage Coefficient" this number isn't perfect because it ignores the secondary stats of most DPS classes. However I choose to use it because in general, the secondary stat of a DPS class contributes to less than 5% of that classes DPS. Additionally, in my calculations I assumed all classes have the Sharp Eyes buff as currently every raid has SE.

    In order to create this guide, I had to talk to a lot of people to test damage numbers and mechanics. Each person I talked to is credited in the individual section.
    Huge credit goes to @Pepperspray@Pepperspray for helping me understand the basics of critical hits.
    Night Lords (NLs) Credit to @n.Kev@n.Kev for helping me with calculations here
    Night Lords are the primary single target DPS class on Saga. Oddly enough this is the only class where their damage dealt and does not scale with the range (in the stats screen). This because an NL's attack uses a different damage calculation than the info shown on the range screen.

    An NL's range(on the stats screen) is calculated with the following formula:
    Upper Bound = [(LUK * 3.6 + STR + DEX) / 100]* Weapon Attack
    Lower Bound = (LUK * 0.9 * 3.6 * .6 + STR + DEX) / 100 * Weapon Attack
    While this is kind of a measure of how strong an NL is, it doesn't show the entire picture. As stated before the real number is hidden and can only be calculated. The damage output of a character is determined by the average hit and attack rate.

    This damage is calculated by the following formula:
    Upper bound = [((5.0*LUK)/100)*(Weapon Attack)] * 1.5 (for Triple Throw)* 1.5 (for Shadow Partner)
    Lower bound = [((2.5*LUK)/100)*(Weapon Attack)]* 1.5 (for Triple Throw) * 1.5 (for Shadow Partner)

    Therefore:
    Average hit = [((3.75*LUK)/100)*(Weapon Attack)]* 1.5 (for Triple Throw) * 1.5 (for Shadow Partner)

    An's NL's DPS calculations don't just stop there, as NL's have the 2nd job skill Critical Blow. This, combined with Sharp Eyes from a Bowmaster/Marksman, means that they have a base crit rate of 65% and a crit bonus of +240% (They do an additional 240% damage on a crit).

    Using this formula and crit rate NL's have a damage coefficient of 17.21.​
    The attack rate of NLs is much simpler. With Triple Throw, and Claw Booster it is 3 stars every 600 ms. While these formulae and attack speeds shouldn't mean much yet, I will use them when comparing to other jobs.

    In addition to a really high attack speed and high average hit, NLs are the primary DPS classes because of their high avoid and the skill Shadow Shifter. The high "miss" rate on this class allows it to more easily tank seduces (w/o logging off) and not being interrupted when getting hit.

    Another minor advantage is the use of the skill Flash Jump. While its a minor advantage, it helps when moving around most raids as well as removing cancel weapon attack in Horntail.

    Corsair Credit to @Pepperspray@Pepperspray and @sjayl@sjayl for helping me with testing here
    Corsairs are niche single target DPS class the can struggle in certain scenarios while flourishing in others. Specifically, corsairs players do well when they can maintain their Battleship HP. In general the order of how "easy" it is to keep your ship alive is:

    1. The Boss
    2. Chaos Zakum
    3. Horntail
    4. Castellan Toad
    Corsairs must split their time between using Battleship Cannon (while their ship is alive) and Rapid Fire (while their ship is dead). For this guide I'll do both calculations and the damage output will be between the two numbers based on what % of the time the character is firing from the ship.

    When using Battleship Cannon the damage formula is:
    Upper bound = [(DEX * 3.6 + STR) / 100] * Weapon Attack * 3.8 (for Battleship Cannon) * 1.2 (for homing beacon)
    Lower bound = [(DEX * 0.9 * 3.6 * .6 + STR) / 100] * Weapon Attack * 3.8 (for Battleship Cannon)* 1.2 (for Homing Beacon)

    Therefore:
    Average hit = (DEX * 2.772 + STR) / 100 * Weapon Attack * 3.8 (for Battleship Cannon) * 1.2 (for Homing Beacon)

    Unfortunately Corsairs don't have a natural crit rate, and therefore with SE their crit rate is 15% w/ a crit bonus of +140%.

    Using the average hit formula and crit rate, you can see that damage coefficient for Corsairs on their Battleship is an 13.34.
    Corsairs' Battleship cannon has 4 attacks every 630ms (600ms w/ Speed Infusion). Only hitting a single target. This damage is complemented by the fact Corsairs have more weapon attack on their gun+bullet than an NL does on their claw+star (166 vs 145) as well as summons that can output DPS along with the Corsair. However, we must also look at the Rapid Fire damage numbers to get a whole idea of a Corsairs' DPS output.

    When using Rapid fire the damage formula is:
    Upper bound = [(DEX * 3.6 + STR) / 100] * Weapon Attack * 1.2 (for homing beacon) * 1.7 (for rapid fire)
    Lower bound = [(DEX * 0.9 * 3.6 * .6 + STR) / 100] * Weapon Attack * 1.2 (for homing beacon) * 1.7 (for rapid fire)


    Therefore:
    Average hit = (DEX * 2.772 + STR) / 100 * Weapon Attack * 1.2 (for homing beacon) * 1.7 (for rapid fire)


    Using this formula (again including SE), you can see that the damage coefficient for unmounted Corsairs is 6.35.
    Corsairs' Rapid Fire has 1 attack every 120 ms. Only hitting a single target. Notably, Corsairs derive incredible benefit from the Smokescreen ability of Shadowers as if the Corsair is safe to bombard away with Battleship Cannon, then they do not have to worry about losing their battleship buff.

    Heroes Credit to @eggosyum@eggosyum for helping me with testing here
    Heroes are the primary multi-target DPS class in Maplesaga. This is because while their damage numbers are relatively unimpressive compared to NL's on a single target, Heroes are able to hit 3 targets with Brandish (their main attack). Its important to note that while I have them here in the DPS section, warriors are needed as a support class in all raids due to raids needing the Monster Magnet or Rush skills.

    In Maplesaga Heroes have currently have two different viable builds: 1-handed with shield and 2-handed. Both seem viable so far as they get buffed differently from speed infusion. I could go on about the pros and cons of both, but that would turn this post into an essay. Therefore I will just go through the stats of both builds individually.


    For a 2-handed sword user, the range formula is as follows:
    Upper bound = [(STR * 4.6 + DEX) / 100] * Weapon Attack * 5.1 (for Brandish and ACA)
    Lower bound = (STR * 0.9 * 4.6 * 0.6 + DEX) / 100 * Weapon Attack * 5.1 (for Brandish and ACA)

    Therefore:
    Average hit = (STR * 0.77 * 4.6 + DEX) / 100 * Weapon Attack * 5.1 (for Brandish and ACA)

    Using this formula (and again including SE), the 2-handed Hero's damage coefficient comes out to roughly 18.80.
    2-handed sword users have 2 attacks every 750ms (630ms w/ Speed Infusion). This attack can hit up to 3 targets.

    For a 1-handed sword+shield user, the range formula is as follows:
    Upper bound = [(STR * 4.0 + DEX) / 100] * Weapon Attack * 5.1 (for Brandish and ACA)
    Lower bound = (STR * 0.9 * 4.0 * .6 + DEX) / 100 * Weapon Attack * 5.1 (for Brandish and ACA)

    Therefore:
    Average hit = (STR * 0.77 * 4.0 + DEX) / 100 * Weapon Attack * 5.1 (for Brandish and ACA)

    Using this formula and crit rate, the 1-handed Hero's damage coefficient comes out to roughly 16.35.
    1-handed sword + shield users have 2 attacks ever 690ms (630ms w/ Speed Infusion). This attack can hit up to 3 targets.

    When you compare the damage coefficients, Heroes and NLs seem comparable. However the attack speed and # of attacks is where they differ significantly. Heroes brandish hits 2 times while an NL's Triple throw will hit 3 times for a single target. Therefore all else being equal, an NL will likely out-DPS a Hero on a single target. However, this balance shifts when there are 2 targets as Brandish can hit multiple targets. This makes Heroes more DPS efficient for 2 or more targets.

    In addition to being able to hit multiple targets, Heroes have sever abilities that help them maintain their dps while in raids. The best of which is Power Stance. This allows all the character to not be knocked back when being hit 90% of the time, requiring they adjust their position less and attack more. Another skill Heroes have access to is Guardian. This skill is specific to 1-handed+shield Heroes and it allows them to ignore damage entirely 15% of the time.


    Paladin (Pallys) Credit to @Tawn@Tawn and @n.Kev@n.Kev for helping me with this section
    Pallys are the other DPS oriented warrior class as they are much less popular on Maplesaga than Heroes are, it is tough to do a head to head comparison of their DPS. However, Pallys tend to do better in scenarios w/ >3 targets as they have skills like Heavens Hammer and Charged Blow. Much like Heroes, Pallys are also able to use Rush and Monster Magnet as a "support" class in raids. Pallys have several viable skills to DPS with, but the main skill is Blast. There is some discussion about the perfect weapon for a Pally in the forum however, I will be doing my calculations with a 1-handed blunt weapon + shield as this seems to be the highest possible range obtainable by a Pally.
    The average hit of a Pally is calculated as follows:
    Upper Bound = [(STR * 4.4 + DEX) / 100] * Weapon Attack* 7.2 (damage ratio for Blast + Divine Charge)
    Lower Bound = = (STR * 0.9 * 3.2 * .6 + DEX) / 100 * Weapon Attack * 7.2 (damage ratio for Blast + Divine Charge)

    Therefore:
    Average hit = (STR * 3.064 + DEX) / 100 * Weapon Attack * 7.2 (damage ratio for Blast + Divine Charge)

    Using this formula and crit rate, the 1-handed Pally's damage coefficient comes out to roughly 22.70.
    1-handed blunt weapon + shield users have 1 attack ever 690ms (630ms w/ Speed Infusion). Blast can only hit one target. Because Blast only hits 1 target, Pallys use a different skill in a mobbing situation. When there are 2 or more targets, Pallys use Advanced Charge Blow. The damage formula is nearly the same so I'll just include the final calculation:

    Average hit = (STR * 3.064 + DEX) / 100 * Weapon Attack * 4.9 (damage ratio for Advanced Charged Blow + Divine Charge)

    Using this formula the 1-handed Pally's damage coefficient comes out to roughly 15.66.
    Charged Blow has a slightly faster attack speed than blast at 660ms (600ms w/ Speed Infusion). However, this attack can hit up to 6 targets.

    From the damage numbers, its pretty clear that Pallys do not have the same damage output as Heroes on 1-3 targets. However, they do have the ability Heavens Hammer. This is a 20 second cool down ability that hits up to 15 targets for "high" damage giving Pallys an edge in raids w/ large number of targets. It is also notable that Pallys also have access to the Power Stance skill.

    Edit: After talking more with @Pepperspray@Pepperspray and doing testing with @SML@SML I have found that Heaven's Hammer does upward of 1 million damage per target on Bosses. This is not reflected anywhere in the skill description or library and is not show in game. However, this greatly increase the DPS output of Paladins across any number of targets. Given the long cool-down and no distinct Damage %s to calculate DPS rates with, I've opt-ed not to include it
    mathematically.

    Edit 2: It's also been brought to my attention that there are bosses with elemental weaknesses. Specifically all three phases of The Boss and the second phase of Castellan Toad. This doesn't change much to my calculations as the amount of HP across these bosses is relatively small compared to the total health pool of all raids. Addionally, it's actually possible for Pallys to hit the damage cap of 200,000 damage with Blast on these bosses, meaning that their elemental amplification means less in terms of DPS output.


    Wrap Up
    Using the calculated Damage Coefficients, I created a table for all the DPS outputs w/ SI:

    upload_2020-7-18_3-6-49.png

    This table uses the calculated Damage Coefficients and known attack speeds to calculate the relative DPS output of each job on a single target. Additionally, I added a weapon attack modifier because the weapon attack of end game weapons varies pretty heavily between the jobs. In these columns I introduced the relative weapon attacks of each job and then showed them as a % of 300 weapon attack (which is roughly what most end game NLs have during raids).

    Overall, its pretty clear that NLs have a distinct advantage in raid scenarios unless the Corsair is allowed to stay on their battleship for a vast majority of the time. However once there is more than 1 target available, Heroes hold a distinct advantage as Brandish can hit up to 3 targets. Pallys sit lowest on the chart for a single target, but keep in mind the chart does not account for damage from Heaven's Hammer.

    Additionally, I did the same table but did not include SI:

    upload_2020-7-18_3-8-20.png

    The data in this table is expected as NL's aren't affected by SI, their damage is not affected. Every class is affected except Corsairs when using Rapid Fire. Notably, the damage output of 1-handed sword+shield Heroes and 2-handed sword Heroes switch places. This is because SI more significantly increases the attack speed of 2-handed sword Heroes.

    Part 2 of this guide will include all the Support Classes: Bowmaster/Marksman, Dark Knight, Shadower, and Buccaneer

    Huge credit to @eggosyum@eggosyum for checking over this post and being the best saga wifey
     

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    #1 AndyZ, Jul 15, 2020
    Last edited: Aug 3, 2020
    Seafood, Hauntr, darrelwg and 14 others like this.
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  3. eggosyum

    eggosyum Swords And Shields

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    THATS MY HUBBBBBBYYYYYYYY
     
  4. Exentus

    Exentus Ninja Castle Expert

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  5. AndyZ

    AndyZ Legendary Mapler

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    tbh i just didn't want to make a whole other section for DKs.
    I haven't done the math so its possible they should be in this post instead of the Support Classes one.
     
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  6. Spectre

    Spectre Moderator
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    *Utility class* because ain't no one need hb anymore......


    BUT GREAT JOB GODKING!!
     
  7. Mu L

    Mu L The Hotness

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    YAS GODKING @@@@@@@@@@@
     
  8. kevin lee

    kevin lee Superstar

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    Neat post. I liked that you remained transparent and objective.

    Using 3 stars per 600ms as your numbers, wouldn't that mean it's not quite as fast as hurricane?
    That's unless you include the 3 extra stars thrown at 50% damage with shadow partner...
     
  9. AndyZ

    AndyZ Legendary Mapler

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    You're right, left that in there before I changed up my calculation method for Shadow Partner.

    To be clear, NL's hit 6 times per TT. But only 3 of the attacks use the 150% damage numbers from Triple Throw. The other 3 attacks use 150% * (.5) = 75% damage number. I accounted for this in my equation forgot to re-word that section. I'll fix it now.
     
    kevin lee likes this.
  10. CrunchyEgg

    CrunchyEgg Joy To The World

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    Perfect guide! Thank you GodKingAndyX for inspiring me to continue playing Night Lord. You da MANS
     
  11. Caleus

    Caleus A Strong Pupil

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    For Pallies, it looks like you forgot to include divine charge in the calculation for blast, which would boost things up by around 1.4x

    Also, what multiplier did you use for ACA, and how did you come up with it? Ive seen a lot of conflicting information on what the number actually is.

    Lastly, on the topic of DKs being a support class or not, I'm almost certain their dps should be comparable to Heroes, possibly even higher with good enough gear. Spear Crusher is a bit slower than brandish, but spears make up for it with higher base W.att, and a higher strength modifier (5.0 instead of 4.6) so they scale better with your gear.
     
  12. AndyZ

    AndyZ Legendary Mapler

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    You're right. Based on the descriptions in the library, I was under the assumption that charged elemental buffs only worked with advanced charged blow blow. However damage % in maplesaga (and all of pre-bb maplestory) doesn't stack manipulatively. So instead of multiplying by 1.4x, you'd just add 140% to the existing 580% to get 720%. I'll add this to my next batch of edits.

    I had to do a bunch of testing + research for this. I did find a formula on another Maple Forum (which will remain unlinked). However in their post they themselves had uncertainties in the damage formula. Therefore I tested two potential formulae:
    1. 260%(brandish)+250%(ACA)
    2. 260%(brandish))*1.9(ACA) *This is the formula from the other forum
    I did this by using what I knew about how SE worked. Because I know that a crit w/ SE adds 140% damage to the base attack the two formulae will differ on the damage ratio between a crit and non-crit.

    If ACA worked like I found in formula 1, then the crit ratio would be:

    (260%(brandish)+250%(ACA))/(260%(brandish)+250%(ACA)+140%(Crit)) = .78​

    If ACA worked like I found in formula 2, then the crit ratio would be:

    (260%(brandish)*1.9)/((260%(brandish)+140%(Crit))*1.9) = .65
    After doing some testing w/ @eggosyum@eggosyum . The damage ratio between crits and non crits came out to be roughly .79. Therefore, I settled on formula 1 for my damage calculations.

    The distinction between "DPS" and "Support" here really isn't that clear. I really split the two categories by if the job contained a party buff. And since DK's have HB, they fell in the "Support" bucket. And since I haven't done the math yet, I don't know how their DPS compares to Heroes. Once I've done the calculations for all jobs, I'll edit the tables on both posts to reflect all the jobs.

    Also if you consider BM/MM to be one class, this neatly means I can do 4 classes per guide.
     
  13. Caleus

    Caleus A Strong Pupil

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    I get you on your reasoning for classifying DK as a support class. I mostly just wanted to point out that they're gonna have numbers similar to Hero.

    As for BM/MM you may want to make them separate since the use very different skills. MM in particular is kind of a weird case since a big part of their damage (Snipe) is not affected by stats.
     
  14. LifeSummer

    LifeSummer Captain Mapler

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    Looks like there is many works to edit for pally’s recent changes.
     
  15. AndyZ

    AndyZ Legendary Mapler

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    Fuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu*k. I still gotta work on part 2 (probably coming out in early August). Looks like the Pally section is gonna be wrong for a bit.
     
  16. Seafood

    Seafood Training Mapler

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    I cannot get this answer "17.21".

    This is my calculation,
    [((3.75*LUK)/100)*(Weapon Attack)]* 1.5 (for Triple Throw) * 1.5 (for Shadow Partner)*(0.65*340%+0.35*100%)
    = 3.75/100*1.5*1.5*(0.65*340%+0.35*100%)*LUK*WA
    = 0.216*LUK*WA

    I like this game and the mathematics. Where is my wrong?

    Thanks.
     
    #15 Seafood, Sep 12, 2020
    Last edited: Sep 13, 2020
  17. Pepperspray

    Pepperspray Keen Heart

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    @Seafood@Seafood Crits add to your skill multiplier; e.g. Triple Throw's skill multiplier is ((150 + 240) * 0.65 + 150 * 0.35), not ((100 + 240) * 0.65 + 100 * 0.35) * 150%.

    (3.75/100)*((150 + 240) * 0.65 + 150 * 0.35) * 1.5 (from SP) = 17.21
     
    Seafood likes this.

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