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

[u/FateOfMuffins]

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

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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:

  • X * C = 2.1875 * C
  • X = 2.1875

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.

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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:

  • ED = X * (C1 + C2)
  • X = 2.1875

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.

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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,

  • X > 1.98

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

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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,

  • X > 2.1875

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

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• 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)

[u/[deleted]]

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.

[u/PatenteDeCorso → u/[deleted]]

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.

[u/[deleted] → u/PatenteDeCorso]

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.

[u/yorunomegami → u/[deleted]]

The thing with those somehow niche chars like TM WB is that while they might not be the holy grail in general whenever their niche (or conditions etc) is fulfilled the outshine any other unit. Personally i rate Mihawk the worst TM char so far (not including Kizaru here as i haven't done enough testing). Mainly due to the fact that he's a Mihawk and not char xyz (in which case he'd be way better than as Mihawk) and he only works for slashers which obviously each Mihawk is. Having said that, he might be the best TM char for beginner (and to a lesser part even f2p players as i think overall Ace is the best unit for f2p atm) but for players with a advanced box there's almost no need to rely on him while there are situations Ace, WB, Cavendish and Zanji shine.

Regarding Cavendish, there were people who said he's not good as he doesn't have that x2+ boost in raw numbers (basically the same thing OP complains. Also v2 Doffy wasn't available so the beneficial orb part was overlooked by most people etc.