Numerical analysis of HT dpm between hero and paladin

Last update: 2021-7-23
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Special thanks to Isac (ign=Shear).
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Warning
Before you read, you should know that the whole thing is just my assumption.
Cannot equal apply to the real HT.
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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
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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.

Spoiler: Data

https://docs.google.com/spreadsheets/d/14rvch4SbrG1AxvbZ5pz3UryxeDQkAYYpxhJJjzC2ZKw/edit?usp=sharing
(1-1) include enrage for hero.
(1-2) ignore HH for pally.

Here is the ideal dpm.

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.
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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.

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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.
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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

(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

Spoiler: Further explanation

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%.

→ 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)
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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 )

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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
→ assume 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) ]
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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.
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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%), both range and cleave lose dpm (but range favorable):
range dpm decrease (0.833→0.775)
cleave dpm decrease (1.333→1.100)
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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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