r/OnePieceTC • u/FateOfMuffins Doktah Carrot Muffins • May 03 '18

JPN Analysis TM Kizaru - The Misconception of Multi-Component Specials (PART 1)

Introduction

WARNING - LOTS OF TEXT BELOW

SEE TLDR IF YOU DON'T WANT TO READ THE MATH OR EXPLANATIONS

Ever since TM Kizaru's CA and special were introduced, players have been shitting on him, complaining that he is the worst TM unit and not worth farming (although Bandai decided to spice things up this time with the free Legend pulls).

Originally, I wanted to discuss his special and compare TM Kizaru with other TM units overall in this post. However, it's getting quite lengthy so I'm going to split it into 2 posts.

In this post, I want to begin with his special and how multi-component specials (especially health cuts) are seemingly misunderstood by most players. In particular, players seem to read specials such as 1.75x boost as being automatically weaker than specials with 2x boosts - this is NOT the case.

My next post will compare TM Kizaru with other TM units.

 

Part 1 - Multi-Component Specials

Most units these days have multiple components in their specials, including utility components such as reducing attack down, defense up, damage reduction, healing, etc., in addition to damage components such as attack boosts, orb boosts, HP cuts, nukes, etc.

I will not be spending any time analyzing utility components, as they are incredibly difficult to compare across units, as it is completely situational. It's practically impossible to theoretically say whether a special that reduces despair by 3 turns is better or worse than a special that reduces paralysis. Events may need an orb locker, or multi-turn attack booster, or perhaps a paralysis reducer, but these specials could be completely useless in other events. However, it is still important to note that TM Kizaru has other utility components, namely a 3 turn boost that extends across multiple boss stages, as well as an orb lock which synergizes well over multiple turn burst.

Therefore I will be only focusing on the damage components of specials, specifically excluding nukes (which although may be necessary in certain situations and definitely contributes to how much damage a unit deals, is situational and much more difficult to compare between different units).

 

Damage-Components of Specials & Health Cuts

Different boosts can stack with each other multiplicatively, but not with boosts of the same nature. However, health cuts are essentially damage boosts that can endlessly stack, both with other health cuts and with other attack boosts, provided the stage does not have a barrier and can be HP Cut.

How do HP cuts work as damage multipliers? A very simplified answer would be to divide the other damage multiplier by the percentage health remaining (or 100% - HP Cut). So a 20% health cut would be equivalent to a 1 / 0.8 = 1.25x damage multiplier.

While that's true for a single turn burst without other assumptions, let's get into the nitty gritty details and assumptions for some specific scenarios. For all the calculations below, we'll assume that each unit in the team has the same attack stat for simplifying purposes.

 

Definition: Effective Damage (ED) - If an enemy unit has X HP and the team deals Y > X total damage (which includes all damage components of specials, including HP cuts and nukes), the team's effective damage is equal to X.

Note: This excludes the effect of IntHawk and V2 Doffy specials from the remainder of the calculations as their specials are extremely unique and situational.

Example: Enemy unit has 5M HP. Your team after using all specials deal a total of 5.5M, including 1M from a 20% HP cut and other damage of 4.5M. Your effective damage is 5M. The principle is - it does not matter how much overkill damage you deal if you are still able to defeat the enemy unit.

 

Definition: Equivalent Multiplier (EM) - Suppose with unit A, the team is able to deal an effective damage of Y. The Equivalent Multiplier is the minimum flat damage multiplier X that a replacement unit B provides such that the team with unit B instead of unit A deals exactly Y effective damage.

Example: Enemy has 1M HP. Unit A does a 20% HP cut, after which the team one shots the enemy. ED is 1M. Without any other information, the team with A will deal at minimum 800k in damage after the HP cut. The minimum flat damage multiplier that a replacement unit B needs is then a 1.25x damage boost. Higher damage boosts, like 2x, will result in the same ED of 1M, but it is not the minimum damage boost. The EM is 1.25x.

 

Equivalent Multiplier for TM Kizaru

Suppose we have TM Kizaru's special, which has a 20% health cut in conjunction with a 3 turn 1.75x adaptable attack boost. Both components contribute to damage, but how much damage does TM Kizaru deal in total?

 

1) Single turn burst, mono-DEX team

To keep comparisons simple, assume that TM Kizaru is boosted in the team. Further assume that after the health cut, we are now able to 1-turn the enemy. Let X be the EM of a replacement unit. Let C be the damage multipliers from the remainder of the team, including the captain ability and chain multipliers and excluding TM Kizaru and the replacement unit.

  • Then for TM Kizaru:

    • 0.8 * ED = 1.75 * C
    • ED = 1.75 / 0.8 * C

  • For the replacement unit:

    • ED = X * C

  • Equating the two gives:

Conclusion

For a single turn mono-DEX team, TM Kizaru provides the highest attack boost @ 2.1875x in the game except for V2 Shanks.

 

2) 2 turn burst, constant attack boost, mono-DEX team.

Let's suppose that instead of a 1-turn situation, we now need 2 turns to completely burst the enemy, with the ED over 2 turns being the entire enemy's health bar. In this calculation, since TM Kizaru is a 1.75x boost for 3 turns, let's assume that the replacement unit provides a constant EM of X for at least 2 turns.

Let C1 being the remaining damage multiplier for the first turn and C2 being the remaining damage multiplier for the second turn.

  • Then for TM Kizaru:

    • 0.8 * ED = 1.75 * C1 + 1.75 * C2
    • ED = 1.75 / 0.8 * (C1 + C2)

  • For the replacement unit:

    • ED = X * C1 + X * C2

  • Equating the two gives:

Conclusion

In order to replace TM Kizaru for up to 3 turns of damage, you need a unit that provides an EM of 2.1875x for up to 3 turns.

 

3) Single turn burst, non mono-DEX team.

One unique feature of TM Kizaru's special is that the damage boost is adaptable, similar to V2 Shanks. What if you replace any other type booster (who is boosted in the team) with TM Kizaru? For example, if you decide to replace Colo Sicilian with TM Kizaru in a V2 Akainu team.

In which case TM Kizaru himself is not boosted by the CA and will be the first one attacking. To be simple, let's exclude chain lock or chain boost.

Let C1 be the damage multiplier for the units that are boosted by the team, excluding chain. Let C2 be the damage multiplier for the units that are not boosted by the team (TM Kizaru).

  • Then for TM Kizaru:

    • 0.8 * ED = C2 + 1.75 * C1 * (1.3 + 1.6 + 1.9 + 2.2 + 2.5)
    • ED = 1.25 * C2 + 2.1875 * 9.5 * C1

  • For the replacement unit:

    • ED = X * C1 * (1 + 1.3 + 1.6 + 1.9 + 2.2 + 2.5)
    • ED = 10.5 * X * C1

  • Equating the two gives:

    • 10.5 * X * C1 = 1.25 * C2 + 2.1875 * 9.5 * C1
    • X = 1.25 / 10.5 * C2 / C1 + 2.1875 * 9.5 / 10.5 * C1 / C1
    • X = 0.12 * C2 / C1 + 1.98

  • Since C1 and C2 > 0,

So even if he is not boosted, TM Kizaru provides almost as much damage as a 2x type booster. You can replace literally every other single turn 2x type booster in the game with TM Kizaru.

In fact, the result from 2) follows through as well. TM Kizaru is equivalent to a 3-turn 1.98x type booster FOR ANY TYPE.

In fact, if we compute 3) using chain lock of between 2.5x-3x OR a chain boost of between 0.5x-0.9x, we'd get that TM Kizaru is equivalent to a 3-turn 2.02x-2.05x type booster FOR ANY TYPE.

 

4) 2 turn burst - Other Units

Similar to example 2. This calculation works for other units with single turn boosts such as Colo Lucy or 6+ Croc. This differs from the TM Kizaru situation above since you are free to use a second unit for the 2nd turn of burst (for example, using Colo Lucy for turn 1 and V1 Doffy for turn 2).

For example, suppose we're looking at Lucy, who contributes a 1.75x orb boost for 1 turn and 20% HP cut. He is the only unit being changed and does not impact the 2nd turn's damage.

Assume C is the remaining damage multiplier for the first turn. Assume D is the total damage multiplier for the second turn. Assume that in the replacement team, the total damage multiplier for the 2nd turn is also equal to D (in the above example, suppose we switch out Lucy for turn 1 but keep Doffy for turn 2).

  • Then:

    • 0.8 * ED = 1.75 * C + D
    • ED = 2.1875 * C + 1.25 * D

  • For the replacement unit:

    • ED = X * C + D

  • Equating the two gives:

    • X * C + D = 2.1875 * C + 1.25 * D
    • (X - 2.1875) * C = 0.25 * D
    • X = 0.25 D / C + 2.1875

  • Since both C and D must be positive,

Conclusion

So a unit like Colo Lucy actually provides an orb boost with a minimum EM of 2.1875x for a single turn, which actually deals more damage than 2x orb boosters like Doffy, especially since his 20% HP cut is unblockable.

Furthermore, Lucy's EM is actually higher than 2.1875x if you are in situations where you need a multi-turn burst.

 

Common HP cut & damage boost units

The above math can be extended towards a number of different units, summarized below.

1.75x + 7% HP Cut 1.75x + 10% HP Cut 1.75x + 15% HP Cut 1.75x + 20% HP Cut 2x + 10% HP Cut 2x + 20% HP Cut
What Players See 1.75x 1.75x 1.75x 2x 2x
Effective Multiplier >= 1.88x 1.94x 2.06x 2.1875x 2.22x 2.5x
Examples Colo Jesus Valentine Nami 20 Anni Sanji TM Kizaru Franky 6+ Croc
Marguerite Lucci Colo Lucy
Oars
Daruma
Bellamy

Comments

  • 6+ Croc provides the strongest single turn burst in the game, despite Nami having a 2.25x attack boost.
    • For a 2 turn burst (on the same enemy), 6+ Croc will only need a 1.56x attack booster to match Nami's damage.
    • Nami has an advantange of both crew efficiency (only need 1 unit vs 2 for 6+ Croc and keeping the buff in between stages
  • Oars is actually the strongest conditional booster in the game, at an Effective Multiplier of 1.88x!

 

Thanks for reading! If anything doesn't make sense with my calculations or assumptions, or if you have any other questions, feel free to ask!

I'll be doing a Part 2 that compares TM Kizaru with other TM Units sometime soon.

 

TLDR

  • Units with 1.75x multipliers are NOT necessarily weaker than units with 2x multipliers

  • Colo Lucy is one of the strongest universal orb boosters in the game, equivalent to (at minimum) a 2.1875x orb booster

  • Versus all content that can be HP Cut, TM Kizaru is equivalent to a 3-turn 2.1875x DEX attack booster (+ orb lock)

  • Versus all content that can be HP Cut, TM Kizaru is equivalent to a 3-turn 1.98x (occasionally 2.02x-2.05x) ADAPTABLE attack booster (+ orb lock)

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7

u/[deleted] May 03 '18

He only boosts one type.

No one's misunderstanding anything, he's just not that good. His special is mediocre and rarely useful, and entirely useless when a captain.

I appreciate your effort of trying to use Steiner Math to uh, make this more needlessly complicated than it had to be, but it didn't help.

3

u/PatenteDeCorso May 03 '18

Time will tell. I've seen people complaining of how useless were TM Whitebeard, TM Cavendish, etc only to see them farming 3M points at their return to get them.

6

u/[deleted] May 03 '18

Well, no. There's no circumstance that needs to happen to make Kizaru useful.

His special is legitimately awful if you want to use him as a captain, and as a sub... he boosts one whole class (DEX, probably) for more turns than you'll actually need.

If he isn't boosting DEX, then he's excluded and his inclusion in the team is baffling, to say the least.

TM Cavendish? Who on god's green earth was saying he's "not useful"? General consensus was that he was incredible when he came out.

TM Whitebeard is conditional, and certainly there's periods where he's not as useful for recent content (when he came out, things were countering delays rather than having delay blocks for the most part), but is a good unit to have, both as a sub and captain.

3

u/FateOfMuffins Doktah Carrot Muffins May 03 '18

1) Kizaru on a team in which he is not boosted actually provides a type boost of between 1.98x-2.05x (depending on chain modifiers), which is good enough to outdamage every single other mono-type booster except for V2 Shanks and V2 Aokiji. I made this a whole point in the original post.

Some content may need the orb lock and/or the 3 turns carryforward between stages.

2) WB can be used against most content, so he's generally not bad to have as a sub. In fact, sometimes I use him for his AOE rather than his orb boost.

However, as a captain? Aside from the fact that WB is tanky (until burst turn) and 100% rainbow, Kizaru is mountains better as a captain. 3.1x all the time and only gets stronger with disparities in stats between units (and orbs), likely averages around 3.3x+.

4

u/xyzqsrbo May 03 '18

Mountains better as a captain? You know specials are included in there ability to be a good captain right? As a captain kizaru literally boosts only 4 of the units on the team unless you want to go mono Dex in which case you would only have a 2.5x and not the chain boost. Whitebeard is better as a captain.

Not to mention content that locks your chain making him more useless than others under those conditions.

0

u/[deleted] May 03 '18

You're also dealing with one unit who contributes no attacking damage, which with how hard fodders hit now, is not a good idea. Also, I'm not sure how you reached that conclusion of "1.98x-2.05x". What HP are you assuming enemies have here? 10m+ or something?

Kizaru is better as a captain? Yeah, sure. Until you have to boost ATK, and realize his special is cripplingly useless. He requires PSY and INT units that won't be boosted.

TM Whitebeard is very similar to 6*+ WB and Crocodile. He's a very good captain.

Also, chain boosts aren't the best. Aside from how easily they're thwarted, it's harder to boost their damage, as chain locks are counterproductive and chain boosts do nothing useful.

6

u/FateOfMuffins Doktah Carrot Muffins May 03 '18 edited May 03 '18

Vs. fodder, you're not using any attack boosting special.

PSY and INT units are equally boosted by Kizaru's CA - they all start at 2.5x which is not low at all (TM Mihawk for example is a flat 2.5x until burst turns).

In fact, TM Kizaru handles fodder stages better than most other TM units and is arguably as good as TM Ace and TM Zanji, who offer 2.75x attack boosts and TM Cavendish, who also starts at 2.5x. Btw here's a comparison between TM Cavendish (2.5 -> 2.5 -> 2.5 -> 3.5 -> 3.5 ->3.5) and Kizaru (2.5 -> 2.84 -> 3.03 -> 3.15 -> 3.24 -> 3.31).

TM WB on the other hand comes nowhere close. You need to be at 33% HP to even match the first unit of Kizaru's team and need to be near 1 HP to even consider matching overall damage.

Not to mention, his CA is a chain boosting CA, which puts most of the damage on the final few hitters. First 2 units not boosted by 1.75x attack boost? Good thing that they're still boosted by literally every other boost including CA, Orb, Conditional, etc. They also literally don't matter much in terms of Kizaru's damage.

2 Kizaru specials equivalently give the 4 DEX units on the team a whopping 2.7344x attack boost (and 1.5625x to the PSY and INT). Useless? Not really.

2

u/xyzqsrbo May 03 '18

TM cavendish is 3.75 not 3.5 after the 3 hits.

3

u/[deleted] May 03 '18

We keep ping-ponging here.

You keep talking about TM Kizaru as a sub and captain without telling me when you're doing so.

I began my comment in response to the beginning of yours which mentioned using Kizaru to boost non-DEX units, which means he is a sub for a non-DEX captain, meaning he is not likely to be boosted.

PSY and INT units are equally boosted by Kizaru's CA - they all start at 2.5x which is not low at all (TM Mihawk for example is a flat 2.5x until burst turns).

In fact, TM Kizaru handles fodder stages better than most other TM units and is arguably as good as TM Ace and TM Zanji, who offer 2.75x attack boosts and TM Cavendish, who also starts at 2.5x. TM WB on the other hand comes nowhere close. You need to be at 33% HP to even match the first unit of Kizaru's team and need to be near 1 HP to even consider matching overall damage.

This is the prime example. Absolutely nowhere did I say TM Kizaru as a captain won't handle fodder stages.

Not to mention, his CA is a chain boosting CA, which puts most of the damage on the final few hitters. First 2 units not boosted by 1.75x attack boost? Good thing that they're still boosted by literally every other boost including CA, Orb, Conditional, etc. They also literally don't matter much in terms of Kizaru's damage.

Ah the old "final hitters" meme. Conveniently, you ignore chain lockers to push the meme.

But we'll take it further.

http://optc-db.github.io/damage/#/transfer/D1314:99,1314:99,836:99,249:99,1924:99,1846:99C34,10B0D0E1365Q0L0G0R24S100H

8.6m advantage / 4.3m neutral / 2.1m resisted

http://optc-db.github.io/damage/#/transfer/D1314:99,1314:99,1518:99:67:0:0,249:99,1518:99:7:0:0,1846:99C34,10B0D0E5Q0L0G0R24S100H

7m advantage / ~3.7m neutral / 1.9m resisted

We sure lose a lot of damage not having the first two hitters be good.

Chain boosting isn't a good thing.

It's infinitely worse than just having the raw ATK and it's harder to supplement for more damage. Does this make it bad? No, not necessarily, but it's not something I'd wish for a unit to have.

2 Kizaru specials equivalently give the 4 DEX units on the team a whopping 2.7344x attack boost (and 1.5625x to the PSY and INT). Useless? Not really.

What on earth are you talking about??? His special does 1.75x ATK and it's probably to DEX.

6

u/FateOfMuffins Doktah Carrot Muffins May 03 '18

1) So Kizaru is an unboosted sub.

Great, you have 5 boosted units and 1 unboosted. I have not encountered any situation which this will prevent you from clearing fodder stages. Speed running 6 mob CC islands? Might want to use 6 boosted units. Clearing it? Heck no, 6 boosted units are unnecessary.

2) Final hitters and ignoring chain lock is absolutely relevant for Kizaru, who's a chain boosting Captain. You're not going to use a chain lock for a chain boosting captain - he defaults to being identical to a 2.5x captain since he literally loses a chunk of his Captain. You don't use chain locks with V1 Rayleigh do you? (However feel free to use chain boosts with Kizaru).

Also, since he's a chain boosting captain, his captain ability naturally favours the "final hitters" - it's not a meme, it's a mathematical reality (look at V1 Ray for the extreme example). Flat boosters like Akainu are different, where the early hitters make up a larger portion of damage.

3) Read the post. The entire post is dedicated to how Kizaru also has a 20% HP cut, which for content without barriers, is a stackable 25% attack buff at minimum. Then do the math with two Kizaru HP cuts: 1.75 * 1.25 * 1.25 = 2.7344x.

-1

u/[deleted] May 03 '18

3) Read the post. The entire post is dedicated to how Kizaru also has a 20% HP cut, which for content without barriers, is a stackable 25% attack buff at minimum. Then do the math with two Kizaru HP cuts: 1.75 * 1.25 * 1.25 = 2.7344x.

How about you try and make it readable? You made this needlessly complicated just to make Kizaru sound better than he is.

Furthermore, this is now my... third time asking? What HP are you assuming the enemy has to even factor in the HP cut?

5

u/madgoblin92 All legends May 03 '18

He is using multipliers in his calculations. Multipliers ignores initial HP.

4

u/JohnnyDgiov May 03 '18

needlessly complicated

I don't think it's that complicated, it's just basic math following a reasoning, the hp cut is factored in as a multiplier, so it ignores initial hp.

he's explaining how the maths of a game about bigger numbers works and he did so very well, you just need to put in effort to read it

1

u/[deleted] May 03 '18

You're instantly doing things really wrong if you're factoring in an HP cut as something it isn't, though.

It also assumes far too many things, like enemy HP, barriers, etc.

His math is poorly formatted (it is not because of Reddit) and elongated to make the situations look better for Kizaru, as if he's some "brainy" unit or something.

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u/FateOfMuffins Doktah Carrot Muffins May 03 '18 edited May 03 '18

Is my post long? Yes. I warned you at the start. Why? Because I made sure to explain each of my steps. And I doubt 4 minutes since my reply to you is enough for you to actually read it before commenting.

Secondly, % HP Cuts are a multiplicative factor. It does not matter how much HP the enemy has for % HP Cuts (it does however matter for nukes, which are a additive factor.

For example, suppose the team without Kizaru/replacement special deals 5M damage. Include Kizaru's 1.75x attack boost and you deal 8.75M instead. For this to one-turn the boss after a single Kizaru's 20% HP cut, the boss can at most have 8.75M / 0.8 = 8.75M * 1.25 = 10.9375M HP.

Suppose instead of Kizaru, we have some generic X attack booster. For this team to one turn the 10.9375M HP boss, you'd need 10.9375M / 5M = 2.1875x attack boost. Which, is equal to 1.75 * 1.25.

What if the boss has less than 10.9375M HP? What if it has 10M?

Well then, Kizaru team can one-turn the boss. The alternative team can also one-turn the boss. It does not matter if Kizaru team does (2M + 8.75M = 10.75M) and the alternative team does 10.9375M - in both situations the boss is dead and the Effective Damage dealt is still the same - 10M.

Refer to about 1/4 of the way into my post (or just control f "Effective Damage").

Edit: What if the boss has more than 10.9375M HP? Then refer to my calculations requiring multiple turns of burst - in which Kizaru remains at 2.1875x and other units like Colo Lucy actually reaches greater than 2.1875x effective multiplier.

What if the boss has a different HP? 5M? 1M? 100M?

What if the base damage that the team does is not 5M? 1M? 10M? 100M?

The end result is the same whatever HP bar the enemy has with % HP cuts - the effective attack buff is multiplicative.

Edit2: Ah I realize you were talking about the 1.98x-2.05x. Refer to 3) in my post talking about Single turn burst, non mono-DEX teams.

1.98x is the minimum effective multiplier calculated assuming no chain boost or lock. 2.05x is the minimum effective multiplier using the highest chain lock in the game with V2 Ray. You get about 2.03x using assuming the highest chain boost in the game with V2 Shanks (although kind of moot but future units may get a similar boost). The boost is slightly lower (still > 1.98x) assuming a lower chain boost (such as +0.5 or +0.7).

3

u/[deleted] May 03 '18

I'd prefer a long post with legible math and based on realistic situations than... well, the OP.

You did theory crafting, which isn't bad, but you mislabeled it, which is bad.

1

u/FateOfMuffins Doktah Carrot Muffins May 03 '18

Aside from Reddit formatting rather than LaTeX, what would you like me to do instead to make the math more readable?

Fewer explanations tend to make calculations more confusing.

And in no circumstance did I state this was anything other than theorycrafting - I mentioned assumptions and to simplify multiple times throughout the post if you've read it.

Practical situations usually come after theorycrafting after all (especially considering the damage calculator had not updated with Kizaru until recently, and is still broken atm). We also need to wait to see what kind of content Bandai throws at us later.

3

u/[deleted] May 03 '18

You applying unnecessary and elongated "equations" are not necessary.

Sure, you can say you had a ghoti sub for lunch, but "fish sub" is less pretentious?

Realistic scenarios and calculations are far more important than fake hypotheticals.

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u/optclinkbot link-decoder May 03 '18

Link #01

Link #02

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u/madgoblin92 All legends May 03 '18

The whole post is explaining it to you how he came to the conclusion of 1.98x-2.05x. It was simple algebra if you actually read it.

1

u/[deleted] May 03 '18

I live in the real world, though. Not a fantasy land where HP cuts are attack boosts and all enemies are specifically designed to make my units look good.