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Numerical analysis of HT dpm between hero and paladin

Discussion in 'General Discussion' started by wanpi12456, Jul 21, 2021.

  1. wanpi12456
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    Last update: 2021-7-23
    ---
    Special thanks to Isac (ign=Shear).
    ---
    Warning
    Before you read, you should know that the whole thing is just my assumption.
    Cannot equal apply to the real HT.
    ---
    Contents
    Part 1: Basic knowledge - 1 target dpm
    Part 2: Hero's and Pally's standing spot in HT
    Part 3: Cancel mechanism - Boss skill casting
    Part 4: How does the 2 heads' Cancel mechanism affect hero and pally
    Part 5: How does the 1 head's Cancel mechanism affect hero and pally
    Part 6: The situation of HT heads and the formula of total damage output
    Part 7: Results
    Part 8: Discussion
    Part 9: Suggestion

    ---
    Part 1: Basic knowledge - 1 target dpm
    For end-game lv200 hero and lv200 paladin, I assume that they have perfect +7 weapon and OP 14wa cape/21wa glove/10wa MoN.
    Here is the ideal dpm.
    投影片3.PNG
    hero (claymore) dpm = 9,582,106
    pally (claymore) dpm = 10,487,906
    pally (claymore) dpm = x1.095 hero (claymore) dpm
    → pally does 9.5% more dmg than hero.
    ---
    Part 2: Hero's and Pally's standing spot in HT
    When we talk about dpm in HT, we are saying the total damage on 3 HT heads. Ignore the damage on wing, arms, summons.

    To be fair,
    (2-1) both hero and paladin stand at the top left platform.
    (2-2) hero and paladin stand at different spot under different situation.
    (2-3) focus on mid head + left head only.
    (2-4) ignore hit box issue for pally.
    (2-5) ignore edge issue for hero.

    投影片2.PNG
    ---
    Part 3: Cancel mechanism - Boss skill casting
    The latest change on Boss skill casting is in 2021 Anniversary Event.

    (3-1) Anniversary Event 2021 Balance Changes [Explained]
    With this boss skill casting system, the HT heads spend most of the time doing Weapon cancel (wc) and Magic cancel (mc).
    → I assume that extreme case is 50%wc + 50%mc.

    (3-2) Balance Road Map: Post-Anniversary 2021
    With this future change, it just randomize Weapon cancel or Magic cancel.
    GM said: "we were sure this was how it was meant to work"
    → In my cognition, the total time of wc+mc will not change.
    In other words, it will not change the average situation for Cancel mechanism which we're talking about.
    ---
    Part 4: How does the 2 heads' Cancel mechanism affect hero and paladin
    So, if there is a Cancel mechanism for 2 targets, what is the difference for hero and paladin?
    We can simply divide it into:
    (4-1) no cancel - e.g. 2 dummies
    (4-2) 100% cancel (50%wc+50%mc) - e.g. HT left head + mid head

    (4-1) no cancel - e.g. 2 dummies
    The hitting target, Pally : Hero = 1 : 2
    投影片5.PNG
    (4-2) 100% cancel (50%wc+50%mc) - e.g. HT left head + mid head
    Don't forget to multiply by 1/4 chance of each case.
    The hitting target, Pally : Hero = 3/4 : 1
    投影片6.PNG
    Myth - People may ask that the time point of HT casting cancel is different.
    However, if we discuss it in average, it is the same.
    (4-2-1) double wc = 1/4
    (4-2-2) double mc = 1/4
    (4-2-3) 1 mc 1 wc = 1/2
    Becareful that it only applies to total time of wc+mc = 100%.
    投影片1.PNG

    → As the total time of wc+mc increases (0%~100%), a single-target attacker get (0~50%) benefits.

    → As the total time of wc+mc increases (0%→100%), both range and cleave lose dpm (but range favorable):
    range dpm decrease (1→0.75)
    cleave dpm decrease (2→1)

    → As the total time of wc+mc decreases (100%→0%), both range and cleave gain dpm (but cleave favorable):
    range dpm increase (0.75→1)
    cleave dpm increase (1→2)

    ---
    Part 5: How does the 1 head's Cancel mechanism affect hero and pally
    The cancel mechanism of 1 head is easier than 2 heads'.
    Don't forget to multiply by 1/2 chance.
    The hitting target, Pally : Hero = 1/2 : 1/2 (= 1 : 1 )
    投影片7.PNG
    ---
    Part 6: The situation of HT heads and the formula of total damage output
    Define time:
    t1 = time you can only hit 1 head (mostly mid head)
    t2 = time when you can hit 2 heads
    The HP of the mid head, left head, and right head is different.
    mid head = 490m HP
    left head = 330m HP
    right head = 330m HP

    In the following 3 situations:
    (6-1) start from left side
    (6-2) start from right side
    (6-3) melee stand at left side and range stand at right side
    Usually, they get the same numbers for t1 and t2 because we are talking in general.
    → t2 >> t1
    → a
    ssume t2 = 5x t1

    Define 1 target dpm:
    hero dpm = 1, pally dpm = 1.1
    (Use the data from Part1)

    total dmg output = (1 target dpm) x [ (targets) x (time) ]
    ---
    Part 7: Results

    hero total dmg of HT heads = (1) x [ (1) x t2 + (1/2) x t1 ] = t2 + 0.5 t1 = 5.5 t1
    pally total dmg of HT heads = (1.1) x [ (3/4) x t2 + (1/2) x t1 ] = 0.825 t2 + 0.55 t1 = 4.675 t1

    hero dpm : pally dpm = 5.5 : 4.675
    → hero does 17.6% more dmg than pally.
    ---
    Part 8: Discussion
    (8-1) HT head's duck animation
    We assume that duck animation has same effect for hero and pally.
    However, it is different in the real HT.
    If left head in wc + mid head in mc, when mid head duck,
    (8-1-1) pally will hit air
    (8-1-2) hero can still hit mid head
    It leads to the actual output of pally is lower than the number we calculated.

    (8-2) The guardian buff to One-handed warrior is same to pally and hero, both limited
    Christmas 2020 Balance Changes
    People say: "Pally's guardian is a good passive skill in HT. BM wish to have it."
    Well, as a real end-game pally, who use crushed skull?
    Guardian does 0 advantage when you equip claymore, which is Two-handed weapon.
    If pally choose to use crushed skull or other One-handed weapon, they already lose dpm.
    So, the guardian is like an equality of life for One-handed warrior.

    (8-3) Class identity
    People say: "HT team only want range attacker to clear heads faster."
    Seems incorrect.
    The Part7: Results show us that hero does 17.6% more dmg than pally on HT heads.
    Errrrrrr, so the HT heads are now actually more friendly to hero than to pally.
    Also, hero can cleave wing/arms... which pally can't.
    It is ridiculous after you learned that the game defined Pally as a single target DPS.

    (8-4) Boss skill casting
    People say: "The state of HT depends on how the cancels work and what changes staff decide to make to the cancels. Last patch cleave were great, this patch not so much."
    Seems correct.
    But, how many impact is it?
    From Part4, we can say:
    → As the total time of wc+mc increases (0%→100%), both range and cleave lose dpm (but range favorable):
    range dpm decrease (1→0.75)
    cleave dpm decrease (2→1)

    Last patch has less total time of wc+mc than this patch.
    Estimate, last patch total time ~66%, this patch total time ~90%.
    As total time increase (66%→90%), b
    oth range and cleave lose dpm (but range favorable):
    range dpm decrease (0.833→0.775)
    cleave dpm decrease (1.333→1.100)

    ---
    Part 9: Suggestion
    In this post, I am not going to give any new suggestion.
    I just want to show how is the hero's and pally's dpm on HT heads.
    Even if GM buff mid head hit box, the hero still does 17.6% more dmg than pally.
    (In other words, it is >17.6% for now.)
    But there is also edge issue for hero if we talk the real HT.

    TL;DR - Hero does 17.6% more dmg on head only than paladin if we follow by every assumption which is hard to achieve.

    View more about... suggestion for pally:
    (9-1) The buff Paladins need
    (9-2) Increase vertical hitbox for mid head in Horntail
    (9-3) Making parts of Horntail elementally-weak

    View more about... shield issue for crushed skull pally:
    (9-4) Anniversary 2021 Event Feedback Thread

    View more about... the nerf history for pally:
    (9-5) Skill Changes: 21/12/2019
    (9-6) Summer 2020 Balance Changes [Explained]

    View more about... other bosses for pally:
    (9-7) Analyze end-game WARRIOR bossing dpm of current meta

    View more about... weapon choice for pally:
    (9-8) Paladin damage comparison 20wa shield

    View more about... meme for pally:
    (9-9) Destitute Paladins Support Group

    View more about... guide for pally:
    (9-10) Hammer Bro's Guide to the Modern Paladin
    (9-11) [Guide] Nisse's Hybrid Paladin Guide! (Updated)
    (9-12) Paladin Guide
    ---
     
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  2. Huiae
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    Huiae Headless Horseman

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    Great analysis. but huge gap with actual situation.

    1. Cleaving from leftside, requires 1 extra rush, to get 'exact pixel point for cleaving', which is also DPM-loss while pally just jump over the platform easily and spam blast, also, always sometimes fail and fall.
    2. Cleaving from rightside, I won't tell furthermore. If RH stays alive till LH downs, I blame intlords.
    3. If your squad hero cleaves arm+wings, fire him as quickly as possible. he's threating and dragging your run down. I'm serious.
    4. for most of times in HT when cleavers can't cleave (from 2 preheads, till end of run, except 'opened 2 heads' and 'leg+tail only if you're pro'. Don't mention about wings+arm cleaving please, that's griefing, ngl.), pally outputs higher DPM than cleavers.

    your 17.6% number assumed 'perfect stepping w/o any mistake for cleavers' which is actually impossible. while pally just easily jump over platforms on situations for cancel, hero/DK try hard to get pixelpoint cleaving position (and falls a lot lmao, especially when it's from rightside). so actual gap IS FAR LESS than 17.6% for sure even in ideal perfect condition and stepping which isn't possible unless we're micro bot.

    Trust me. cleaving 2 heads is possible but you'll know it's really shitty to focus on it and impossible to pull out maximum potential if you try it. If you aren't good with it, sometimes it's far better to just focus on 1 head than trying grabbing 2 heads and falling over and over.

    I feel your salt for continual pally nerf, but I can surely tell that actual DPM gap in action isn't vast like 17.6%. you missed many factors. I'm totally agree on pally buff for PB because 1/2*1/2=1/4 is literally bullshit while others gets 1/2 or not at all, but for HT, sorry, I can't agree on.

    now, let's talk about scarga/NT. I didn't do exact math but pretty sure gap between cleavers and pally is over at least 30%. um......alright. i'll stop it. my pally friend will kill me if I continue.
     
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  3. OP
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    Thanks for providing the difference between ideal and real.

    1. I did ignore the hit box issues for pally. But in real, it cannot be ignored.
    Please check (9-2)

    2. If your squad hero cannot cleave left + mid head, they are not defined as end-game hero in my post.
    Also, pally have edge platform issue too.
    If not close enough to edge, HH can't reach right head.
    I do agree hero need more effort to reach that spot.

    3. I said focus on left side, because that's the spot for pally and bucc.
    When it comes to right side, warriors are suffer from stance.
    The edge player skill can be improved.
    (BM also need this player skill I believe)

    4. Scarga or NT?
    Why not take a look at cwkpq/krexel/HT also? :)
    Please check (9-7) to see how is the real scarga.
     
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  4. JDPJHC
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    JDPJHC Mixed Golem

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    so are Heros just supposed to be worse than Pallys at everything? You guys have us beat by MILES at Scar/Targa/NT/Area Bosses. I was whiting my own lvl 200 hero with perfect gear on a lvl 170 pally with very mediocre gear (might as well have been naked)
     
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  5. OP
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    Please check (9-1) and (9-7) and class identity.
     
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  6. Huiae
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    Huiae Headless Horseman

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    I agree depends on classes, we have shit situations, and we need to understand each others. I just hoped to criticize that you exaggerated pally's shit situations only while shining other classes ideal situations and put such biased situations on scale to compare about.

    This "A vs B" comparision can be fall into trap like "A is superior than B" which is so dumb and myopic. I wish to say, let's just get with each classes characteristics, rather than comparing too much nerdy and laying down asking buff/nerf.

    I'm not talking 'pally>hero, you're wrong!'. there's obviously situations like pally>hero and vice versa. again, you're putting weights on scale in wrong way.
     
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  7. OP
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    Share my idea of writing this post.

    Before the hit box change, pally can hit 100% on mid head.
    After the hit box change, pally
    (1) hit air because mid head duck
    (2) distribute dmg : most dmg on left head + little dmg on mid head

    (1) cause to the direct nerf to pally
    Average hitting 2/8 of blast into the air.
    (2) cause to indirect nerf to pally because we should consider Cancel mechanism, which I explained in the post. People didn't notice it. So I explain it here.

    I agreed need the buff to cleave attacker in HT.
    But saying class identity of pally in HT. It's really bad actually.
     
  8. xiaoyaoz
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    xiaoyaoz Balance Team Staff Member Balance Team

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    I wonder how pally is when compared to other single target attackers since that is the supposed class identity.
    Feel like it's still sort of unfair to include head cleave damage as part of the dpm comparison since you still have the case when 1 head is left, remaining arms and prehead which solely depends on single dpm, and not to mentioned HT is (supposed to be) cleave advantageous.
    Is there a possibility to provide a dpm comparison for pally against other single target?
     
  9. OP
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    wanpi12456 Timer

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    Please check Part5 and Part6.
    The situation of 1 head has been included.
    Sorry I can't give the data of other single target.
     
  10. Huiae
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    Yes, I hoped to hear pallys pain because i didn't train pally actually, needed to get idea about it.
    and I totally agree on it's shit case for pally to see midhead ducking and cleavers do hit fully while pally can't.

    now it's cleavers side. it's shit case to fall when rush 'fails' and slips down so climb over and over tryharding to get 'pixelpoint ideal position' while pally doesn't care about such micro jumping over and over between platforms and blast on head which they want easily.

    and above stuffs are hard to be numberized.

    So now, time to summarize. you mathed 17.4% DPM advantage on period when cleavers grab 2 heads while pally hits only 1. This requires literally 0-mistake perfect stepping which isn't realistic. and during HT, I think such 'cleaving time' is less than 30%. now, for over 70% of runtime, pally outdpm cleaves because they're specialized for single target.

    you're telling 'when they cleave, they outdpm us, pally is shit'. and 'when they can't cleave, we outdpm them, this is deserved class characteristics'. maybe this is real reason why my mind can't get your idea. In your logic, when they cleave after tryharding to get such narrow pixel position, they 'deserves' to outdpm single-target melee class. I'd say it's characteristic also.

    Again, pally's situation in HT isn't terrible like you think. of course, it's not perfectly balanced like 100%, but it's pointless to math who is better for ? %. I'd say, if pally and hero use exactly same gear so have exactly same range in clean status, pally isn't subpar of hero thanks for their heavily focused on single target DPM. remember, more than 70% of HT run is singletargetting, and pally is overcoming for it. you said it's characteristics. this means, you can't say pally is terrible comparing 'you're doing single while they're doing perfect cleave (which is actually impossible indeed)'. but you did. with this flow, only conclusion I can get is - pally MUST BE stronger than any other warriors in EVERY situations - which blows my mind.

    If you want to respect your characteristics - single-target focused melee warrior so overcomes others when do 1vs1 - respect others aswell - cleave focused melee warrior so overcomes 1vs1 when they cleave-.

    + and this is why I'm totally agree on pally buff in PB. they has 1vs1 specialist characterist and being subpar of hero, which is nonsense. but for HT, sorry, disagreed.
     
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  11. xiaoyaoz
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    xiaoyaoz Balance Team Staff Member Balance Team

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    What I mean is when only 1 head is remained instead of 1 head is cancelled and the other is not.
    I actually don't even get how you assume the timing for part 7, which is the essential part where hero dpm > pally dpm.

    Ok, let me just put some words into these assumption, t2=5x t1 means that in 60minute, only 10minute you can hit 1 head, while the other 50min u can hit 2 heads, which seems quite... unrealistic?
    Next, why is there a (1) x t2 for hero vs (3/4) x t2 for pally? does this mean pally somehow have an increase in damage when u can hit both head? o.o

    Anyhow, I feel like comparing cleave dmg vs single damage is still kinda apple vs orange. If there is a possibility to show single attackers comparison, it will seem more convincing.

    p.s.: I'm not in any way against your post, just trying to make sense some of the numbers and set up a good comparison for pally.
     
  12. OP
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    The hit box issues and the cancel mechanism do the significant impact for pally.
    Before that patch, it didnt exist.
    I would say it is same important as hero's edge issue.
    Please check (9-7) for a rough look.
    They suit well in other bosses.

    I write these is to provide data and the feelings from it.
    It might be not close enough to real.
    Everyone can agree or disagree of what I write.
    It is just one of the method we can take a closer look at it.
     
  13. OP
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    I'm not 100% sure about it so I said "assume".
    Because the hp is different between mid head and left/right head, "5" is just a rough estimate.
    Pally should use blast when the 2 heads are live, with Cancel mechanism in Part4, it goes to "3/4".
     
  14. akashsky
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    Numbers should also include heavens hammer dpm, as its not insignificant. In my experience playing paladin, it added a few hundred k dpm.

    I still claim that paladin is probably equal to hero at current HT if you factor in HH damage, along with the fact that preheads take up ~1/3 of the total fight (which paladins have a big advantage in).
     
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  15. xiaoyaoz
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    xiaoyaoz Balance Team Staff Member Balance Team

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    Oh, let me get this clear, does t2 means the time when at least 2 head exists and they are allowed to do all the different cancels while t1 is the time when only 1 head exists?
    I think your definition of time might be confusing since I thought t1 means the time you can only hit 1 head despite having 2/3 heads still alive. o.o

    Lets just redefine properly:
    t1 = time when only 1 head exists
    t2 = time when >1 heads exist
     
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  16. OP
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    Yes, it is t1, the time when only 1 head exists.
    Language gap XD

    You can adjust t1 and t2 multiplier, no need to be "5".
     
  17. Lin
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    This is some big brain juice, thanks for making this comparison thread PrEP!
     
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  18. OP
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    Update :
    1. The warning words is added at the top of post.
    2. (2-5) is added. Thanks Huiae to provide this issue for hero.
    3. Fix the tl;dr to not mislead people.
    4. Quote xiaoyaoz's redefine to Part6. Thanks!
     
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  19. -ovv
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    I'm inclined to say that Paladins are currently in a better spot than Heroes/DKs due to the run preference of having desync'd heads on one side for single-target attackers to alternate between cancels. This allows single target attackers to output closer to 100% of their damage without having to travel across body/switch sides or hit wings during cancels. A few strategies have emerged regarding how to better maintain the strict cancel rotations, albeit finicky and not 100% consistent.
     
  20. OP
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    Seriously reply to the message I quoted.

    Any kind of strategy for controlling wc / mc will NOT give you a better cancel situation for cleave or range. I'm saying in average. It is a myth.

    We take a look at (4-2) further explanation pic.
    We cannot choose the wc or mc for 2nd head after we trigger 1st head cancel.

    Look at that pic.
    It shows us after trigger 1st head cancel.
    (Mid head wc)
    There is still 50% chance for second head to do mc and 50% chance wc.
    If you are lucky and get a (Left head mc), but this chance is only 50%.
    There is another 50% chance (Left head wc), when you are unlucky.
    IMG_20210722_032511.jpg
    The average Cancel situation of 2 green circle is still same as
    1/4 double mc
    1/4 double wc
    1/2 1mc 1wc

    Even if you decide to trigger 2nd head cancel at different time point, it is still the same results.

    -> It is a myth.
     

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