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

---

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.

---

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.

---

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

---

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

---

• 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]]

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.

[u/FateOfMuffins → u/[deleted]]

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.

[u/[deleted] → u/FateOfMuffins]

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?

[u/FateOfMuffins → u/[deleted]]

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).

[u/[deleted] → u/FateOfMuffins]

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.

[u/FateOfMuffins → u/[deleted]]

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.

[u/[deleted] → u/FateOfMuffins]

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.

[u/FateOfMuffins → u/[deleted]]

Eh university habits die hard. I can assure you that I could have made this a lot more "elongated" than what was presented.

Right before I make my definitions and dive into the nitty gritty details, I specifically stated the simplified calculations, which are but a few lines long in total. The remaining calculations are "elongated" because they were supposed to be in order to show the details.

I'll keep that in mind to highlight this part more clearly and possibly put it in the TLDR.

Yes I agree realistic applications are more important than hypotheticals, but there's a reason why hypothetical theories and mathematical models exist in every aspect of our world in the first place. (You may not see them, but I assure you, they're there in the background). Compared to "realistic" scenarios, theoretical models are much simpler, yet provide a reasonable approximation to "reality".

If you want realistic calculations, I could easily extend the calculations beyond a few lines of equations each. Why did I not do so? Because it will become incredibly complicated and require significantly more effort and more "elongated" equations.

Search up the 80/20 rule, otherwise known as the Pareto principle. 20% of effort will produce an 80% result (which is theoretical model and good enough). If you want the 100% result (realistic), you'll need to put in maybe 5x the effort.

Lastly, doesn't it seem ironic that you want realistic and practical results from the unit instead of fake hypotheticals that everyone has been stating ever since TM Kizaru was announced?

In which case, why not wait till you actually use him in practice before shitting on him based on theory craft?

[u/[deleted] → u/FateOfMuffins]

You botched the Pareto principle.

80% of (x) is the result of 20% of (y). You reversed that.

Lastly, doesn't it seem ironic that you want realistic and practical results from the unit instead of fake hypotheticals that everyone has been stating ever since TM Kizaru was announced?

He is nothing new. We know exactly how he will perform.

You keep theory testing him in imaginary content specifically structured to make him look good. How is that helpful or even semi-realistic as you claim?

[u/FateOfMuffins → u/[deleted]]

That's exactly what I said for Pareto.

The only "imaginary" content that Kizaru needs is one without barriers. That's commonplace. How is that "unrealistic"?

Without barriers he is a 2.1875x attack booster. With barriers, he is simply a 1.75x attack booster. No other math needed.

It's like my example with WB - 2x orb with delay protection, jack shit without.

[u/[deleted] → u/FateOfMuffins]

You're assumptions all enemies have enough HP to make HP cuts better than ATK boosts.

How many QCK enemies have HP that high?

[u/FateOfMuffins → u/[deleted]]

?

I've mentioned this countless times - HP does NOT affect % HP Cut multipliers! That's why I used a variable for how much damage is dealt and NEVER stated how much damage was dealt. The variable HP could be 10 or 10M - it does NOT change the effective multiplier.

This isn't a difficult concept - it's basic elementary school multiplication and middle school/early high school algebra.

There's no further point in this discussion if you can't understand this concept after this many explanations.

[u/fangowango → u/[deleted]]

HP cuts are % cuts, which means a 20% cut will do 20% of the enemy's healthy regardless if that health is 1M, 2M, 10M, 100000M.

I think the point you're missing is that Kizaru provides BOTH a HP cut and a damage boost. So he's effectively weakening an opponent first and then boosting damage, which in turn makes him an effectively higher booster.

IF Kizaru was just a HP cut and nothing else, then yes the amount of HP the enemy has will matter big time. A 20% cut with no boost on a 3M enemy (so a 600K cut) is not gonna compare to an attack/orb boost of any kind on a half decent team. But that's not the point OP is trying to make.

[u/[deleted] → u/fangowango]

An HP cut is not always more valuable.

An ATK boost is always useful. Always. An HP cut can be countered, or simply blocked by a barrier. Or simply obsoleted by a higher attack value, hence why I keep questioning why he's testing Kizaru in his theorycraft against 10m+ HP enemies.

He keeps testing Kizaru against HP sponges designed to let him reign supreme then wondering why people don't like him as much in reality when in practice he's totally OP.

The exception for an ATK boost being more useful is a zombie team, which... won't use Kizaru anyway likely.

2x ATK > 1.75x + 20% HP cut, unless the enemy has 10m+ HP, in which case, a DEX boost isn't any good, because enemies with health that high are either STR or DEX... and the latter (Stage 20 BB in his forest) will remove your buff because of the HP cut anyway.

...and if the captain isn't DEX, you have better options guaranteed.