Log Power Scaling - A Different Approach

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shadowfox87
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Log Power Scaling - A Different Approach

Post by shadowfox87 » Tue Dec 12, 2017 4:28 pm

Alright guys, I know you have seen several attempts at power scaling, but I promise you this one is different. We all know that official power levels stopped at the end of the Freeza saga in DBZ. Since then, there have been a lot of rumors and speculation circulating all over the internet mixed with opinions. Most people have given up on power scaling and say that the series is too inconsistent and in a mess. Today, I will attempt to see if we can use logic and mathematics to derive a scaling method that satisfies all information and feats from official sources, primarily from the manga. Other sources will include the Daizenshuus, Databooks, and interviews or statements made by official writers. We will also use the anime and movies where needed but manga will always take precedence. There may also be some head canon. I don’t claim this to be the most accurate power scale, but just a different approach to power scaling that you may have not seen before that uses math to satisfy information we know from official sources. Hence, please keep an open mind!

Now, without further ado, let us begin!

After 17 years, in August 2014, the first DB movie was announced – Battle of the Gods (BoG), by Akira Toriyama himself! During that time, there was an interview with Toriyama:
Source: http://www.kanzenshuu.com/translations/ ... -toriyama/

Wait! In this interview, Toriyama gave us the first real indication of power scaling for Dragon Ball Super, stating that Goku is a 6, Beerus is a 10, and Whis is a 15. Now of course, this scaling is quite outdated and only represents where Goku was at during BoG. A lot of things have changed with new power creep from DBS Broly. He’s definitely not a 6 in SSG anymore. Beerus and Whis being only 10 and 15 don't make sense anymore either. Most of you might be skeptic, but stick with me here till the end before you make up your mind.

If you treat these numbers as a linear scale, it will never work. For example if Goku used Kaioken, then 6 x 2 = 12 > Beerus (10). Thus, I will show you the logarithmic scale approach. Logarithms are used when the numbers become too big (like power levels). They are used today to measure earthquakes, pH, sound loudness (decibels), and light intensity.

As an example, the pH of water is 8 while the pH of vinegar is 2. This doesn't mean that vinegar is 8/2 = 4x more acidic than water. Actually, it is 10^8/10^2 = 10^6 or 1 million x more acidic!
Power scaling communities commonly use percentage differences based on official power levels. During the Freeza saga, SSJ Goku was 150 million while Freeza was 120 million. The percentage gap here is 25% i.e. SSJ Goku is 1.25 times stronger than Freeza during the Freeza Saga. Similarly, a difference of 0.1 on the log scale is 25%.

Just to be clear, a 1-point difference in a log scale means 10x stronger, a 0.1 difference is 1.26x stronger, 0.2 difference is 1.58x stronger, 0.3 difference is 2x stronger, a 0.4 difference is 2.5x stronger, a 0.5 difference is 3.16x ~ 3x stronger, a 0.6 difference is 3.98x ~4x stronger, a a 0.7 difference is 5x stronger, 0.8 increase is 6.3x ~6x stronger, 0.9 increase is 7.94x ~ 8x stronger.

Ok, we shall take the inverse log of each scale value:
Goku (SSG) = 10^6 --> 1,000,000 or 1 million
Beerus = 10^10 --> 10,000,000,000 or 10 billion
Whis = 10^15 --> 1 quadrillion


Remember these aren’t power levels. These are numbers converted using the inverse log scale. It is these numbers that we can use our multipliers before converting back to log scale. Note also that taking the log of a number less than 1 results in a negative number. This will happen for weaker characters or forms.

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Super Saiyan God multiplier

Goku could not even touch Beerus as an SSJ3. As an SSG, he still lost against Beerus who was only using a fraction of his strength. The statement made by Goku in the BoG movie that even fusion would not be enough is not present in the DBS manga and hence, I will not include it. In the most recent DBS Broly movie, we see that the base fusion exceeds the maximum of an individual fusee.

In addition, the Daizenshuu 7, Base Vegito > SSJ3 Goku (Buu Saga)

Base Vegito > SSJ3 Goku (Daizenshuu 7)
Base Vegito > Buutenks > Ultimate Gohan > SSJ3 Gotenks > SSJ Gotenks > SSJ3 Goku
Base Vegito > 1.15x Buutenks > 1.1x Ultimate Gohan > 1.2x SSJ3 Gotenks > 8x SSJ Gotenks ~ SSJ3 Goku
Base Vegito > 1.15x 1.1x 1.2x 8x SSJ3 Goku
Base Vegito > 12.1x SSJ3 Goku
Base Vegito ~ 12.5x SSJ3 Goku

For A and B, the strongest versions of Goku and Vegeta were used. This allows for Base Vegito to exceed SSJ3 Goku by more than 10x and also still keep the "tens" of times multiplier. In the DBS Broly movie, we find that Gogeta = Vegito except for their time limit, so the formula has to be the same. Therefore, Base Gogeta > SSB Goku as seen from the feats in the movie.

In the BoG movie and anime, Goku states that he cannot defeat Beerus even with fusion. That would hypothetically mean the max potential of Vegito which is SSJ3 Vegito. It also means that SSG would have to be a greater multiplier than that!

SSG > SSJ3 Vegito (Hypothetical)
SSG > (A+B) x10 x400
SSG > (SSJ3 Goku + SSJ2 Vegeta) x10 x400
SSG > (400xBase + 100xBase) x10x400
SSG > (500x10x400)xBase
SSG > 2 million x Base

if we take SSG > 2.5x SSJ3 Vegito, then

SSG = 5 million x Base

Using this, we can now reverse engineer the log scale for the other forms of Goku (BoG):

Base Goku = SSG / 5 million = Log (10^6/5E6) = -0.7
SSJ Goku = 50 x Base Goku = Log (50 x 10^(-0.7)) = 1
SSJ2 Goku = 2 x SSJ Goku = Log (2 x 10^1) = 1.3
SSJ3 Goku = 4 x SSJ2 Goku = Log (4 x 10^1.3) = 1.9


Remember that space scene where SSJ Goku fought Beerus and was actually doing better even without SSG? How can that be if he wasn't in SSG anymore? Piccolo sensed his ki so he couldn't have been using god ki right? Wait! I thought Goku absorbed the power of a SSG into his base. Shouldn’t his new base=SSG Goku (BoG)?

Toriyama stated in his interview that Goku absorbed the power of SSG. In the anime and movie, we see that SSJ Goku in space was able to spar with Beerus even without SSG. To prevent Earth's destruction, he dug deep into his body and added a fraction of the god ki he had as SSG into his SSJ form. Goku has only transformed into SSG for the first time but he has "felt" it but has no idea how to use it yet. Goku has to dig deep to utilize fractions of his god ki because he is desperate now to defeat Beerus or Earth will be destroyed. It is not until after he trains with Whis that he learns to control this god ki and utilize 100% of that god ki into his SSJ form. This then creates SSB. Hence, the temporary SSJ form that Goku uses against Beerus in space is essentially an SSJ with some god ki or an incomplete SSB. This is my own headcannon to explain the anime scene. It's not needed for manga. Note that later in the ToP, Goku uses SSG as a separate form that is greater in power than Base, so that debunks Base=SSG.

Note also that I'm using the manga not the anime. The anime has inconsistencies like Beerus stating he was forced to use 1/10th of his strength against an Enraged SSJ2 Vegeta after Bulma got slapped. The manga also doesn't have that SSJ Goku vs Beerus space scene or things like Base Goku vs Beerus in Monaka costume or Base Vegeta vs SSJ3 Gotenks in Potafu arc.

To prove this theory, let's add 10% god ki to SSJ:

SSJ Goku (BoG + 10% God Ki) = Log (SSJ Goku (BoG) x10% SSG Goku (BoG) ) = Log (10^1 x 10% x 5E6) = 6.7 > SSG Goku (6)

We get slightly higher than SSG which makes sense since it's SSJ on top of SSG.
Super Saiyan Blue Multiplier

SSB is the power of SSJ with SSG. So by logic, we'd multiply SSG by 50x to get SSB. These multipliers are official and were released in the Super Exciting Guide (SEG).
Here, Whis explains that because Vegeta used SSB against Cabba, he wasn't able to exert even 10% of the full power of SSB against Hit due to loss of stamina. It's due to this that Goku in SSG was even stronger than Vegeta was when in SSB when facing Hit. Note very carefully though that Whis says Vegeta is not even 10% his full strength. If we are to say that SSB = 50x SSG, then SSG > 2% SSB or > .002x SSB. Since 2% is smaller than 10%, this is possible and doesn't contradict what Whis says.

Let's say that from BoG to RoF, Goku got 25% (1.25x) stronger after training with Whis.

So, SSB Goku (RoF) = 50 x SSG x 1.25 = Log [50 x 10^6 x 1.25 ]= 7.8
Golden Freeza >= 1.25x SSB Goku (RoF) = 7.9

Now back again to the "Saiyan Beyond God", both in the DBS anime and the RoF manga spin-off, Base Goku fought Final Form Freeza. In RoF, prior to meeting Freeza, Goku and Vegeta were both training in a dimension created by Whis's staff. Here, it was difficult for them to move unless they controlled their ki. It's here for the first time Vegeta felt god ki and utilized it without having to undergo the SSG ritual. Goku also learned to master his god ki and it was shortly after this, that he fought Freeza immediately. Thus, he already has using god ki in his base. It was thought again that this is a "new" Base Goku with the power of an SSG but really it's just god ki. Whether or not you want to buy into the "two base theory", I shall use the exact same headcanon above and add 10% god ki into Base, but since this time it's from Base and not SSJ, we multiply instead of add:

Base Goku (Base (RoF) x10% god ki) = Log (Base Goku (BoG) x 1.25 x 10% x 1000) = Log (10^-0.7 x 1.25 x 10% x 1000) = 5.1

Again, to validate, the 10% god ki can be changed to 100% and it should be SSG, which it is (6.1).

After RoF, Goku trained in the ROSAT for 3 years! Then, he fought Hit, Black, and Jiren. Did he get zenkais for all? The truth is that Goku has become too strong and after a point, you reach saturation point for zenkais. This means it becomes more difficult to get a zenkai the stronger one gets, which makes sense (see graph below). For example, in Namek, Goku went from 90,000 to 3 million in his base alone due to zenkai boost. He can still get stronger through traditional training.

In Chapter 20 of Dragon Ball Super, Trunks states that Goku and Vegeta have both pushed their bodies to their limits, so it’s not that easy to get zenkai boosts anymore.
Yet Black was able to still receive zenkai boosts while in Goku’s body. Why? Black himself stated in Chapter 20 that when he took Goku’s body, he was not able to access all of its power. He wasn’t even able to go SSJ. This is nothing new. Ginyu had the same problem back in the Freeza saga. Apparently, Black was able to discover a shortcut to quickly gaining access to the full power of Goku’s body – zenkai boosts. Each time Black healed himself from the brink of death, the healing regenerated new cells that used Zamasu’s own ki. This allowed Zamasu to make Goku’s body more his own. It’s actually the reason why he changed into Super Saiyan Rosé instead of Blue. In the anime, Black got stronger after taking damage but zenkai doesn’t work like that.
Source: Chapter 20, DBS Manga

Now that we understand how difficult it is to get stronger, let's say Goku got 15% stronger each year for 3 years so 1.10^3=1.33x. Then after fighting Hit, he got 1.25x stronger. Then after fighting Zamasu / Black, he got 1.33x stronger and finally, after the Tournament of Power, he got 1.33x stronger. This is 1.25x from BoG to RoF, 1.33x from RoF to U6 arc, 1.25x from U6 arc to Zamasu arc, 1.33x from Zamasu to ToP, and 1.33x Post-ToP. So total is 1.25x 1.33x 1.25x 1.33x 1.33x = 3.68x ~4x from BoG to Post-ToP. Doesn't seem like a lot does it? Again, remember that there aren't any free zenkais anymore.

-----------------------------------------Zamasu arc------------------------------------
Base Goku = Base Goku (BoG) x 1.25x 1.33x 1.25 = 3.3
SSB Goku = Base Goku x 50 x 5E6 = 8.0

The Completed SSB (CSSB) is a manga exclusive transformation that doesn't appear in the anime. Rather, in the anime, we see Goku used Kaioken x20 and Vegeta uses the SSBE. However, neither the Kaioken nor SSBE are shown in the DBS Broly movie which is the closest to Toriyama's original draft. However, the manga does have an SSBE equivalent version that Vegeta uses against Toppo and Jiren in ToP; and against Moro. This form has small blue flames and a darker blue aura surrounding a lighter blue, very similar to what we see in the DBS Broly movie.

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Fusion

Ok, let’s do Potara Fusion now. We have all heard what Vados said in Episode 114,
the fusion creates a new body and personality greater than the sum of the two individuals and increases their power by tens of times.
Here are the GT Perfect Files:
The above is from GT Perfect Files Volume 2. The green box above translates to:
This is the fusion of Super Saiyan 4 Goku and Super Saiyan 4 Vegeta. The strongest warrior in the entire Universe, and probably in every dimension!! It's Fusion of unprecedented power that lasts 30 minutes, however, it's only weakness is that lasts 10 minutes due to the Super Saiyan 4 state. His power is perhaps many tens of times stronger than a single Super Saiyan 4.

Again, in GT Perfect Files Volume 2:
Now since there are two sources that have stated that the fusion is "tens" of times stronger than the sum of their parts:

(A+B)x10 = Base Vegito (Buu Saga)
(SSJ3 Goku + SSJ2 Vegeta) x10 =
(400xA + 100xB)x10 =
(500xA)x10 =
5000xGoku = 12.5x SSJ3 Goku = Base Vegito
Furthermore, before I forget, in the SEG, it stated that the Fusion formula was AxB which also does not make sense. Multiplying together is essentially squaring Goku’s base power level which would give an enormous power rivaling even Whis. In statistics, the cross doesn't have to mean multiplication but can also mean "by" which relates two variables. https://en.wikipedia.org/wiki/Multiplication_sign

Base Vegito (Zamasu arc) = (SSB Goku + SSB Vegeta) x 10 = Log [(10^8 + 10^8) x 10] = 9.3
SSB Vegito = Base Vegito x 5E6 x 50 = Log [10^9.3 x 5E6 x 50] = 17.7

In the manga, Chapter 23, page 43, Shin states that SSB Vegito surpassed Beerus. We also know that Goku states that Broly was stronger than Beerus in the movie and that SSB Gogeta beat Broly, so SSB Vegito / Gogeta > Broly > Beerus.
However, Beerus=10 will not work with this scaling. Rather, I will put:

Beerus=15
Whis=25

Vegito in the manga, unlike in the anime, completely thrashed Merged Zamasu effortlessly not letting Zamasu hit him even once.

SSJ Vegito = 50 x Base Vegito = Log [50 x 10^9.3] = 11
SSJ2 Vegito = 2 x SSJ Vegito = Log [ 2 x 10^11] = 11.3
SSJ3 Vegito = 4 x SSJ2 Vegito = Log [ 4 x 10^11.3] = 11.9
SSG Vegito = 5E6 x Base Vegito = 16.0
SSB Vegito = 50x SSG Vegito = 17.7


Another fusion we can calculate really easy now is Zamasu! If we take SSR Black = 1.5x SSB Goku (Zamasu), then SSR Black = 8.2. Then, if we take Zamasu = SSJ2 Goku (Zamasu arc) / 1.5 then Zamasu = 1.7

The fusion multiplier is dynamic - it's different for different people. We know that the closer the physical characteristics and battle power between the fusees, the stronger the fusion. Toriyama himself confirmed that similar size and power is all that is needed. Factors like "personality" and "rival boost" were made-up things by fans who misinterpreted Elder Kai's words in the original DBZ manga. In fact, what the Elder Kai meant was that Goku and Vegeta live to outdo each other which helps them sustain similar battle powers.
Zamasu and Black (Goku's body) are completely different. Zamasu is a Shinjin and Black is a Saiyan. They have drastically different battle powers too. The difference between Zamasu and Black is the difference between a SSJ2 and SS Rose. Therefore, both battle powers and physical characteristics are different. They also fused together with Black already in SS Rose. Elder Kaioshin stated not to fuse as Super Saiyans as that shortens the lifespan:


In the DBZ Manga, Goku himself thought that fusing with someone significantly weaker like Mr. Satan or Dende would make the resulting fusion weaker:
Hence, it wasn't a perfect fusion. Yes, technically Zamasu and Black are the same person soul wise, but that doesn't matter. The power gap is immense and hence, the multiplier will be significantly lower. In addition, in the manga, MSSB Goku fought Merged Zamasu evenly.

Merged Zamasu = (Zamasu+SSR Black) x10
Merged Zamasu = log [(10^1.7 + 10^8.2) x10] = 9.2

Completed SSB (CSSB) Goku fought Merged Zamasu evenly and was winning. We also find out that CSSB in the manga is basically the equivalent of the Kaioken x20 in the anime which is also equivalent to the SSBE. Of course, this doesn't mean they are exactly the same, but the scenes in which SSBE Vegeta and SSB + Kaioken x20 Goku fight Jiren is the same exact scene in the manga where CSSB Goku and Vegeta fight Jiren. Therefore, to calculate CSSB:

CSSB Goku = SSB Goku x20 = log[ (10^8 x 20)] = 9.3 > Merged Zamasu (9.2)

Since we are on the subject of Zamasu, might as well do Future Trunks! We have clearly seen SSJ2 Future Trunks in Chapter 15 of the manga, spar equally with SSJ3 Goku. The SS Rage form of Trunks will not be used as it is anime exclusive.
SSJ2 Future Trunks (Post-Zamasu) ~ SSJ3 Goku (Post-Zamsu) = 2.5

-----------------------------------------Tournament of Power------------------------------------------------------------------------------

-------Post-ToP arc-----------
Base Goku (Post-ToP) = Base Goku (Zamasu arc) x1.33 x1.5 = Log (10^-0.7 x1.33 x1.5) = -0.1
SSJ Goku = Base Goku x 50 = 1.6
SSJ2 Goku = SSJ Goku x 2 = 1.9
SSJ3 Goku = SSJ2 Goku x 4 = 2.5
SSG Goku = Base Goku x 5E6 = 6.6
SSB Goku = SSG Goku x 50 = 8.3
CSSB Goku = SSB Goku x20 = 9.6

As for Jiren, Whis said that he is the mortal that surpasses a Hakaishin out of all 12 universes, even the four that were excluded. I will hence assume: Jiren > Beerus. You can argue about this but it's clear that the mortal is Jiren.

To simplify, Jiren (ToP) = 19 > Beerus (17)

MUI Goku (ToP) = 20.4 (100 trillion x Base)

Next up, Android 17. In Chapter 31 of the DBS manga, Android 17 was shown to be sparring with SSJ3 Goku evenly. Much different than the anime that portrayed SSB Goku vs 17. The scaling makes much more sense in the manga. Hence, we shall assign Android 17 the same log scale as SSJ3 Goku.



Android 17 = 2.5 =~ SSJ3 Goku (Post-Zamasu)

Furthermore, Toshio commented on his twitter that Gohan = 17>Frost>Piccolo.

Frost=1.4 (1.5x weaker than SSJ Goku (ToP))
Piccolo=1.2 (1.5x weaker than Frost)

Kefla is next, but to get her, we have to calculate Kale. According to Chapter 37-38 DBS Manga, Golden Freeza said that her strikes hurt more than SSJ Caulifla's, confirming that Base Kale > SSJ Caulifla. When she went BSSJ, she easily overpowered Golden Freeza and SSB Goku.

Base Caulifla = Base Goku (ToP) /1.5 = -0.3
SSJ Caulifla = Base Caulifla x 50 = 1.4

Hence, if we take Base Kale >= 2x SSJ Caulifla:

Then Base Kale (Post-ToP) = log ( 10^1.4 x2) = 1.7 ~ SSJ2 Goku (Post-ToP)
SSJ Kale = log (10^1.7 x 50) = 3.4
BSSJ Kale = SSJ Kale x1E6 = 9.4 > SSB Goku (8.3)

The multiplier used for BSSJ is the same one that has to be used for Broly by logic. Similar to Merged Zamasu, Kale and Caulifla made the same mistake by fusing while already transformed. Hence, there is no Base Kefla as incorrectly shown in the anime.

Then BSSJ Kefla = (SSJ Caulifla + BSSJ Kale) x 10 = Log [ (10^4.6 + 10^8.3) x10] = 10.4 < Beerus (15)

Note that there's no Base Kefla because if the fusees are already Super Saiyan, then the resulting fusion is also Super Saiyan.

Since Gohan and Kefla fought equally and did a double K.O.:

Ultimate Gohan (Post-ToP) = 10.4 (Those hybrid Saiyan genes)



Hakaishin Toppo = 9.4 < MSSB Vegeta (ToP) > CSSB Vegeta (9.6)

-------------------------------------------------BROLY-----------------------------------------------------------------------

Kale and Broly are both similar to each other, both being the legendary Saiyans from their respective universes. In the trailer, we see that Base Broly overpowers SSJ Vegeta, already stating that Base Broly > SSJ Vegeta. Kale in her base is also stronger than SSJ Caulifla and SSJ Cabba in the manga. Later, Broly still not even a regular SSJ is thrashing both SSG Goku and SSG Vegeta. Then, Ikari Broly Broly, which is the power of Oozaru in base, fights with SSB Goku equally but is slightly weaker This implies that Ikari Broly <= SSB Goku > SSG Goku. Then Broly transforms further into Super Saiyan Full Power and Gogeta is needed.



Base Broly (without collar) >= 3x SSG Goku (Post-ToP) = 7.1 > SSG Goku (6.6)
Ikari Broly = Base Broly x10 = 8.1 < SSB Goku (8.3)
SSJ Broly = log(10^8.3 x 50) = 9.8 > CSSB Goku (9.6)
SS Full Power Broly = log(10^10 x 1E6) = 15.8 > Beerus (15)




--------------------------------------------------DRAGON BALL GT---------------------------------------------------------------------------------------
Since we are on the subject of GT, let's do SSJ4. The SSJ4 is a transformation from Golden Oozaru not from SSJ3. The Golden Oozaru is implied to be an Oozaru that has just turned Super Saiyan, and hence the fur has become yellow. Thus,

Super Oozaru = 50x Oozaru = 500x Base
Super Oozaru 2 = 2x Super Oozaru = 1000x Base
Super Oozaru 3 = 4x Super Oozaru 2 = 4000x Base


So "Golden Oozaru" is not a fixed multiplier and is based on what state of SSJ is being used while in Golden Oozaru. The only way to determine this is by the hair but since the hair doesn't change much between SSJ1 and SSJ2, it can't be distinguished that easily.

According to the GT Perfect Files, Golden Oozaru Baby Vegeta > SSJ4 Goku. It is not until Goku absorbs the energies of Gohan, Goten, Trunks, and Pan that he is able to overpower Super Oozaru Baby Vegeta. Since Oozaru is a 10x multiplier, it means that the gap between SSJ4 Goku and Super Baby cannot have been more than 10x. The question is then how strong was Golden Oozaru Goku? Was he a regular SSJ, SSJ2, or SSJ3 in Golden Oozaru? Several people have theorized that Goku was a SSJ3, which would make the multiplier 400x10=4000x. However, based on the recent design of Golden Oozaru Cumber and previous designs of Golden Oozaru including Baby, Broly, and Gogeta, one thing that is consistent is the hair. The hair remains the same even in Oozaru. Hence, Goku could not be in SSJ3 because he doesn't have the long hair while in Oozaru. However, as the fight between Golden Oozaru Goku and Super Baby progressed, Goku's ki continues to rise. The only way to make sense of this is that, Goku did surpass SSJ2 while in Golden Oozaru and approached but did not reach SSJ3 as he could not control his power.

Adult Goku (53 years old) ~ Kid Goku (12 years old) - GT Perfect Files state that they are equal in power except stamina issues.
Adult Goku ~ 2x Vegeta

Baby Vegeta = 16x Vegeta ~ 8x Kid Goku
SSJ Baby Vegeta = 50x Baby Vegeta ~ 800x Vegeta ~ SSJ3 Kid Goku ~ 400x Kid Goku

Super Baby (Strongest Form 1) ~ 2x SSJ Baby Vegeta (After absorbing energies of Gohan, Goten, Trunks, and Bulla)

Super Baby (Strongest Form 2) ~ 4x Strongest Form 1 (After absorbing the energies of all people on Earth) ~ 3200x Kid Goku < Golden Oozaru Goku < SSJ4 Goku = 4000x Kid Goku


Golden Oozaru Goku = 500x to 4000x Kid Goku

Golden Oozaru Baby Vegeta = 10x Strongest Form 2 ~ 4000x Baby Vegeta ~ 32,000x Kid Goku > SSJ4 Goku ~ 4000x Kid Goku
Golden Oozaru Baby Vegeta ~ 8000x Vegeta ~ 32,000x Kid Goku < Full-Powered SSJ4 Goku ~ 40,000x Kid Goku

Hence, to make sense of this, I will say that:

SSJ4 = Condensed Golden Oozaru = 8x Super Oozaru = 4000x Base (Implied that Goku added the power of SSJ3 into Oozaru.)
Full-Powered SSJ4 Goku = 10x SSJ4 = 40,000x Kid Goku (After absorbing energies of Gohan, Goten, Trunks, and Pan)

The reason that Goku got a 10x multiplier when absorbing Gohan, Goten, Trunks, and Pan's energies versus Baby Vegeta who only got a 2x multiplier when absorbing the energies of Gohan, Goten, Trunks, and Bulla's energies is because when Baby Vegeta received their energies, none of them were Super Saiyan. This may be due to the fact that Gohan, Goten, and Trunks were already depleted of their energies after fighting with Goku and Uub and/or that their full power could not be drawn out without Baby inside their bodies. The egg inside their minds was not enough.

By the way, according to herms98 translation of the DBGT anime comics, a scan revealed that Base Vegito > SSJ4. This source is not stating that Base Vegito (Buu Saga) > SSJ4 Goku (GT) but rather a general statement that the current fusion of Goku and Vegeta still would perhaps surpass the SSJ4 form. (Source: https://twitter.com/Herms98/status/675785758473490432) This is consistent with what we calculated since Base Vegito ~ 20x SSJ3 Goku which is 2x SSJ4.

Once GT starts, Kid Goku was shown to fight Rilldo who was stated to be stronger than Kid Buu. Since SSJ3 Goku (Buu Saga) ~ Kid Buu, then Base Kid Goku > Rilldo > SSJ3 Goku (Buu Saga). Four years pass after the defeat of Buu to the start of BoG. Six years later is the 28th Tenkaichi Budokai where Goku meets Uub. Then Goku trains 5 more years with Uub in the ROSAT.

Since Goku (GT) > Rilldo > Kid Buu ~ SSJ3 Goku (Buu Saga)
Then Goku (GT) > 1.3x Rilldo > 1.25x Kid Buu ~ SSJ3 Goku (Buu Saga)
Goku (GT) > 1.3x 1.25x 400x Goku (Buu Saga)
Goku (GT) > 650x Goku (Buu Saga)

If Goku got 10% stronger for 4 years from Age 774 to Age 778, then 70% stronger for 6 years from Age 778 to Age 784, and finally 80% stronger for 5 years training with Uub from Age 784 to Age 789, then 1.1^4 x 1.7^6 x 1.8^5 =~ 667x > 650x.

Now let's say that after Goku's battle with Baby Vegeta, Super 17, and Evil Shenrons, he received a 10% (1.1x) boost from each one, so 1.1^3. Note that not a lot of time passed between these villains and Goku's zenkai by the same logic is also saturated. He can only get stronger through good old training. Goku: Xeno is a Goku summoned by Chronoa in Age 850 after she looks through Future Trunks memories. DBGT ends in Age 790 with Kid Goku leaving with Shenron. We don't see him until a 100 years later. However, since 850-790 = 60 years. Let's say Goku's peak is when he's in his 30s, so that's 20 years later. Thus, Chronoa may have summoned Goku 20 years after Age 790 to the Time Nest. That puts Goku at 12+20=32 years of age. Then, we can give him a 25% increase each year for the remaining 20 years, so 1.25^20 to get Goku: Xeno.

Kid Goku (GT) = Log [1.1^4 x 1.7^6 x 1.8^5 x 1.1^3 x Base Goku (Buu Saga) = Log (1.1^4 x 1.7^6 x 1.8^5 x 1.1^3 x 10^(-0.9) ) = 2.1
Goku: Xeno (60 years after GT) = Log (Kid Goku (GT) x 1.25^20) = 4.4
SSJ4 Goku: Xeno = 4000x Goku: Xeno = Log (4000x 10^4.4) = 8.0 < SSB Goku Post-ToP (8.3)

-------------------------------------------------------------------------------------------------------------

Well, that's it!



My raw data and calculations: https://www.dropbox.com/s/1wr2ll16h4rss ... .xlsx?dl=0

This is a graph of characters we know and have been revealed in Dragon Ball Super. I didn’t put characters like Gogeta since it’s not canon, even though Gogeta can be scaled. The anime does a lot of fan service and hence, until the manga catches up to the anime, characters like Kefla and Kale are based on educated guesses. Characters like Android 18 who hasn’t gotten any stronger since the Cell saga are too weak based on this log scale and would be below 1 and may even be negative.

Lastly, the point of this was to use math to see if there was a solution that meets all conditions. Sometimes there is no solution and that's when you have a plot hole.
----------------------------------PART 2 BEGINS---------------------------------------------------------

Super Saiyan Grades, Multipliers and Completed SSB


Since Super Saiyan was first achieved, we have seen different grades of Super Saiyan during the Cell saga. This includes grade 2 or Ascended SSJ (ASSJ) by Vegeta after he first came out of the Room of Spirit and Time with Trunks to fight Cell. Next was grade 3 or Ultra SSJ (USSJ), the form Trunks used which greatly increased his power at the expense of speed. In the DBS anime, Trunks even learned to trick Vegeta by using this form to bait him and then switch back to SSJ2. The Super Saiyan Rage form he used against Zamasu seemed to be a combination of grade 3 and SSJ2. Last was grade 4 or Fully powered SSJ (FPSSJ) when Goku and Gohan were able to maintain a SSJ for an entire day doing normal activities like taking a bath. Goku released his full power against Perfect Cell, showing to everyone how much stronger he has gotten. These grades are not fan-made but were written in an official source for the Trunks anime comics translated by Herms: http://www.kanzenshuu.com/forum/viewtopic.php?t=22411

-----------------DB----------------------
Oozaru = 10x Base

-----------------DBZ---------------------
Kaioken x N = Nx Base where N=2-20 (N>20 is possible but never shown)
SSJ Grade 1 = 50x Base (power, speed, stamina balanced but slight agitated state and stamina drain for all newly transformed SSJs)
SSJ Grade 2 (ASSJ) = 60x Base (Slight increase in power and speed, abandoned due to high energy consumption and stamina drain)
SSJ Grade 3 (USSJ) = 10x SSJ (Lots of power, Increased muscle mass lowers speed by a lot, very high energy consumption and stamina drain)
SSJ Grade 4 (FPSSJ) = 50x Base (power, speed, and stamina perfectly balanced)

Alternatively, some people have scaled SSJ Grade 3 = 75x Base if you don't agree with "Dragon Ball Legend of Manga" released in 2007 by Shueisha with original language Japanese which states 10x SSJ. It was translated to Spanish and French.
Source: http://www.kanzenshuu.com/forum/viewtopic.php?t=38328 https://lh3.googleusercontent.com/liNSB ... h768-rw-no

SSJ2 (SSJ Grade 5) = 2x SSJ
SSJ2 Grade 2 = 4x SSJ
SSJ2 Grade 3 = 8x SSJ ~ SSJ3 (Future Trunks and Vegeta have both shown to surpass SSJ3)
SSJ2 Grade 4 (SS Rage) = 10x SSJ2 (anime only, higher grade of SSJ2, exclusive to Future Trunks.)

SSJ3 = 4x SSJ2 (Lots of power but lots of stamina drain)

Base Fusion = (A+B) x C where C=10 usually when the fusees have similar size and power. If the Fusion is performed incorrectly, then the fusion can be weaker with C=0 to 1. Fusion Dance and Potara yield the same power. A and B are the maximum power of the individual fusees.

-----------------DBS---------------------
SSG (Base + 100% God ki) = 1000x Base (Derived above)
SSB (SSJ + 100% God ki) = 50x SSG (Derived above)
MSSB = 10x SSB (AKA. The SSB forms used in the DBS Broly movie and also the same form used by Vegeta in the ToP)

SSJ (+10% God Ki) = SSG (What Goku used against Beerus in space. Anime only.)
Base (+10% God Ki) = SSG/10 (AKA Saiyan Beyond God. What Goku uses against Freeza in RoF.)

Ultra Instinct = 100 million x Base (A technique that allows one to move instinctively and land critical blows. However, the "heat" accumulated is the result of gathering the kinetic energy around oneself from moving instinctively. It is also a transformation given that there is a change in physical appearance manifested by Goku.)

Ikari = 10x Base (Utilizing the power of Oozaru in humanoid form)
SSFP (Super Saiyan Full Power) = 10x SSJ (Combining the Ikari with SSJ)

-----------------GT---------------------
Super Oozaru = 50x Oozaru = 500x Base
SSJ4 = 8x Super Oozaru = 4000x Base (Condensed Golden Oozaru, 10x SSJ3)
Full-Powered SSJ4 = 10x SSJ4 (After absorbing energies of SSJ Goten, SSJ Trunks, Pan, and SSJ Gohan)


We've seen different grades of SSJ2 as well. We saw that Future Trunks in SSJ2 was able to fight on par with SSJ3 Goku and saw that Vegeta in SSJ2 after Bulma got slapped by Beerus was greater than SSJ3 Goku. This means that it is possible for characters to gain mastery over a transformation to reach higher grades. Characters like Vegeta and Trunks who never achieved SSJ3, trained more in their SSJ2 form and hence, is at a higher grade. The goal of any form is to have maximal power output without stamina drain.

In addition, in Super, we did not see ASSJ or FPSSJ from Caulifla or Cabba with Caulifa skipping directly to SSJ2. USSJ still exists as a distinct transformation however since we have seen both Future Trunks and Caulifla perform it. In addition, FPSSJ is a combination of good ki control and maintaining the SSJ state longer to consume less stamina. It is akin to the Completed SSB state or CSSB.

Ultra Instinct

UI=100 trillion (1E14) x Base
Read here for the theory on ultra instinct: http://www.kanzenshuu.com/forum/viewtop ... =8&t=40707

-----------------------------------------------Destructive Capacity-----------------------------------------------

Let me just get this out of the way - I don't believe in using real world physics to scale a fantasy show. Dragon Ball doesn't follow real world physics so even we try to use the feats by characters in the show with destructive capacity, it won't work. However, we'll do it just for fun any ways. This term has been used by Marvel, DC, and other fictional verses to gauge power of characters. The primary issue with this form of measurement has always been that our own universe is vastly different from the fictional verses. Thus, we can't easily use the same number of stars, galaxies, solar systems in our universe to equate that of another. In Dragon Ball, things like the Earth, Moon, and Sun however are consistent so the mass of each can be used.

In Dragon Ball, Jackie Chun aka Master Roshi, in the 21st Tenkaichi Budokai (Chapter 52), was able to destroy the moon with a Super Kamehameha. According to the V-Jump and the Daizenshuu, Master Roshi’s battle power at that time was 139. If you're having difficulty accepting these as sources, remember that V-Jump is the very magazine that the Dragon Ball manga was published in each week. The Earth has a mass (5.972 x 10^24 kg) approximately 81 times larger than the moon’s mass (7.347 x 10^22 kg). Therefore, 81x139 = 11,259 ~ 11,000. This would be the minimum battle power necessary to destroy the Earth. Why am I using mass instead of volume or density? Because mass is directly proportional to energy via E=mc^2 where c=speed of light. If I had used density, the Earth's density (5.51 g/cm^3) is only 1.65 times the Moon's density (3.34 g/cm^3). Obviously if Roshi is only 1.65 times stronger, he can't destroy the Earth. If I used volume, 50 Moons can make up Earth. Fifty is not a bad number to work with but as I said earlier, mass has a better relationship with energy than volume. During the Saiyan Saga, Vegeta with a battle power of 18,000 claimed he could destroy the Earth with his Galick Gun. In addition, we saw Freeza in his first form with a battle power of 530,000 easily destroy Planet Vegeta which is assumed to be the same size of the Earth.

The Sun has a mass of 1.989 x 10^30 kg which is approximately 333,054.243 times larger than the mass of the Earth. If 11,000 BP is the minimum needed to destroy Earth, then 333,000 x 11,000 =~ 3.67 billion BP is necessary to destroy a star the size of the Sun. Freeza’s first form (530,000 BP) thus would have a destructive capacity of 530,000/11,000 =~ 48 Earth-sized planets while Vegeta (18,000 BP) would have a destructive capacity of 18,000/11,000 =~ 1.6 Earth-sized planets. Freeza’s fourth form (120 million BP) is 120 million / 11,000 =~ 10,909 Earth-sized planets which is still lower than the destructive capacity of the Sun. Freeza final form would have to be at least 33x stronger to destroy the Sun.

Super Perfect Cell claimed that he is capable of destroying the solar system with his Kamehameha. A solar system comprises of the star with the orbiting planets. In the case for our solar system, that’s the Sun plus 8 planets. However, just the sheer destructive force of the Sun exploding would also destroy the orbiting planets. We can conclude that Cell's Kamehameha would have simply hit the Sun, destroying it and the solar system. Therefore, the destructive capacity for a solar system will still be equivalent to a single star and it would require Perfect Cell to be at least 333,054/10,909 =~ 33 times stronger than Freeza’s final form to be able to do this. This seems reasonable given that Super Perfect Cell > Perfect Cell > Semi-Perfect Cell > Imperfect Cell ~ Android 16 > Android 17 > Android 18 > SSJ Vegeta > Freeza. To put some numbers on this, Super Perfect Cell > 2x Perfect Cell, Perfect Cell > 2x Semi-Perfect Cell, Semi-Perfect Cell > 2x Imperfect Cell, Imperfect Cell > 1.5x Android 17, Android 17 > 1.25x Andriod 18, Android 18 > 1.5x SSJ Vegeta, SSJ Vegeta > 1.5x Freeza. Thus, 2x 2x 2x 1.5x 1.25x 1.5x 1.5x = 33.75x which is what we calculated earlier!

Many fans put Kid Buu as a galaxy buster (I used to as well), but nowhere in the DBZ manga or any guidebook has it been stated that he has accomplished this feat in the past. The anime always puts extra information or scenes not found in the manga. The manga is by the original author and it should take precedence. There's a lot of misinformation on the net, so go to the original source always and use Viz translations.

In Episode 9 of Dragon Ball Z Kai and Chapter 446 of the DBZ Manga, it is stated by Shin that Kid Buu destroyed "hundreds of planets" in a few years. In the anime however, we see a blue galaxy in the background disappear. This is the source of the confusion.



That blue galaxy in the background was added into the anime being erased because gradually, more planets were being wiped out in that galaxy. The less space debris and things orbiting the center black hole of a galaxy, the more it's going to look like it fades away over time. The entire galaxy wasn't wiped out by a single attack.

The final fight between SSJ3 Goku and Kid Buu took place on the Kaioshin realm. Here, in Chapter 510 of the DBZ manga, the Elder Kaioshin tells Goku to do what he wants and that “this world won’t break so easily!”.



The Kaioshin realm is 1/10th the size of Universe 7 and orbits the universe as stated in the Daizenshuu 4.


As far as what occurred, the Kaioshin realm withstood their fight and did not get destroyed. In Dragon Ball Super episode 31, Jaco explains that the universe contains a tremendous number of galaxies, and that his Galactic Patrol unit only covers the Milky Way Galaxy. This is the first time this term is ever used within the Dragon Ball franchise. If we use our own Milky Way galaxy as a standard, it comprises of approximately 250 billion stars or 2.5*10^11 stars (from NASA observation). Out of these stars, astronomers have found at least 2,500 stars that have orbiting planets so 2,500 solar systems. Again as we pointed out earlier, simply destroying a star would destroy neighboring planets and thus, the entire solar system as well. Hence, 2500 is really a lowball and 2.5*10^11 is the highball. Even taking the lowball, to destroy a galaxy, Kid Buu would have to be at least 2500 times more powerful than Super Perfect Cell. This does not seem logical. A Super Saiyan 3 Goku (Buu Saga) who is equal to Kid Goku is only 400x more powerful than a Base Goku that is WEAKER than Freeza’s fourth form. We know that Base Goku (BoG) < Freeza’s final form (120 million BP) because Beerus said so both in the Dragon Ball Super anime and manga. In the anime, it was directly stated when Goku powers up on King Kai's planet. In the DBS Manga, Beerus asks Whis why Goku has blonde hair and Whis responds that this is a Super Saiyan. Then, Beerus says he understands now how Goku defeated Freeza, which implies he did not understand before Goku turned into a Super Saiyan.



We know that SSJ2 Goku (Buu Saga) > SSJ2 Teen Gohan (Cell Saga). If SSJ2 Goku (Buu Saga) >= 1.25x SSJ2 Teen Gohan (Cell Saga), then SSJ3 Goku (Buu Saga) = 1.25x 4x SSJ2 Teen Gohan = 5x ~ 5x SSJ2 Teen Gohan. Then, if Kid Buu ~ SSJ3 Goku (Buu Saga) and SSJ2 Teen Gohan ~ Super Perfect Cell, Kid Buu >= 5x Super Perfect Cell. That would place Kid Buu only capable of destroying 5 solar systems (i.e. multi-solar system), not entire galaxies. One can even pick a higher multiplier than 1.25 between SSJ2 Goku > SSJ2 Teen Gohan, but it will get you nowhere near 2500 which is the needed number for Kid Buu to be a galaxy buster.

In DBS, the Elder Kaioshin states that the universe will be destroyed from the shockwaves generated from Beerus and SSG Goku's clashes is in danger from Beerus. This is the largest evidence in support that Beerus is a universe buster.



In addition, it is stated in an interview of Toriyama that when Beerus sealed the Elder Kaioshin in the Z-sword, he could have destroyed the Kaioshin realm but it wasn’t appropriate. Since the Kaioshin realm is 1/10th of Universe 7, it means he is at minimum a 1/10th universe buster. The DB verse is different from the real world. The manga and guidebooks all imply that there are only four galaxies per universe - one for each Kaio to look after. There are about 100 billion galaxies in our own universe and 250 billion (2.5*10^11) stars approximately in each one. Since there are so few galaxies in the DB verse, I'll have to increase the number of stars in each one and assume that they are very large galaxies. So for this calculation, I will use 4 galaxies with 0.5 x 10^13 stars in each one which is about 100x bigger. This gives 2 x 10^13 stars in the DB universe approximately. If Super Perfect Cell is 1 solar system and Buu is 5 solar systems and Beerus in the log scale is a 10, which is 10^10, then Kid Buu is log (10^5 x 10^10) / (2 x 10^13) =~ 1.7 ~ SS3 Goku (Buu Saga). By the way, the entire log scale incorporates all this and is consistent with it. Note that this is only the destructive capacity to destroy 4 galaxies but not necessarily an infinitely expanding universe, but the shockwave from the resulting explosion of 4 galaxies will probably take out the rest just like SSG Goku vs Beerus's shockwaves almost did.

Oh, and I didn't use 1 Kili = 50,000 BP or Dabura's statement that 200-300 Kili is equivalent to a multi-planet buster because it is inconsistent. It puts Vegeta (18,000 BP) = 0.36 kili and Freeza (530,000 BP) = 10.6 kili.


References:
1. Akira Toriyama
2. Kanzenshuu & Herms98 (translations for interviews, Daizenshuu, and gathering of information): http://www.kanzenshuu.com/forum/viewtop ... f=8&t=9633
3. Manga (DB, DBZ, DBS) - http://mangahasu.com/dragon-ball
4. GT Perfect Files
5. Daizenshuu
6. Anime (DB, DBZ, DBGT, DBS)
7. Hyourinjutsu and ygoofficial for sprites for transformation chart
Last edited by shadowfox87 on Tue Apr 16, 2019 11:15 am, edited 325 times in total.
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling

Post by Polyphase Avatron » Tue Dec 12, 2017 5:05 pm

You know they dropped the whole 6/10/15 thing after Super started, right?
Cool stuff that I upload here because Youtube will copyright claim it: https://vimeo.com/user60967147

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Re: Log Power Scaling

Post by shadowfox87 » Tue Dec 12, 2017 5:09 pm

Polyphase Avatron wrote:You know they dropped the whole 6/10/15 thing after Super started, right?
Read the first paragraph where I said I already acknowledged the 6-10-15 is outdated.
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling

Post by Polyphase Avatron » Tue Dec 12, 2017 5:11 pm

shadowfox87 wrote:
Polyphase Avatron wrote:You know they dropped the whole 6/10/15 thing after Super started, right?
Read the first paragraph where I said I already acknowledged the 6-10-15 is outdated.
But aren't you using it as a basis for your power levels?
Cool stuff that I upload here because Youtube will copyright claim it: https://vimeo.com/user60967147

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Re: Log Power Scaling

Post by shadowfox87 » Tue Dec 12, 2017 5:28 pm

Polyphase Avatron wrote: But aren't you using it as a basis for your power levels?
The first paragraph points out the major flaw in the 6-10-15 scale which is that it is outdated. Then it goes on to use logic and information on how to update it, mainly the 6. There is no official statement saying it was "dropped", only that this scale applied in Battle of Gods (BoG). Super is way beyond BoG, so this scale was abandoned. Also, none of the above numbers are power levels. Please read the whole thing.
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling

Post by Black Hawk » Tue Dec 12, 2017 8:08 pm

While I respectfully disagree with certain aspects of your scaling (and yet agree with certain other aspects), I can appreciate how much thought went into your calculation process, and I like how much detail you went into, both in your explanations and in your analyses! This was a pleasure to read, my friend, and I look forward to seeing an updated version once the manga catches up with the Tournament of Power! :thumbup:
"Reign supreme? In your dreams; you'll never make me bow.
Kick my ass? I'm world-class and Super Saiyan now."

I BURN - Jeff Williams feat. Casey Lee Williams, RWBY Volume 1 Soundtrack

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Re: Log Power Scaling

Post by shadowfox87 » Tue Dec 12, 2017 8:27 pm

Black Hawk wrote:While I respectfully disagree with certain aspects of your scaling (and yet agree with certain other aspects), I can appreciate how much thought went into your calculation process, and I like how much detail you went into, both in your explanations and in your analyses! This was a pleasure to read, my friend, and I look forward to seeing an updated version once the manga catches up with the Tournament of Power! :thumbup:
Thanks for reading all of it. I welcome any criticism. It's all to help improve the scaling. Can you tell me what aspects you disagree with?
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling

Post by Black Hawk » Tue Dec 12, 2017 9:20 pm

shadowfox87 wrote:Thanks for reading all of it. I welcome any criticism. It's all to help improve the scaling. Can you tell me what aspects you disagree with?
Oh, the only disagreements I have are my own methods of calculation and the final results I came up with. For example, my linear calculations produced a result of 7.5, whereas your logarithmic calculations produced a result of 7.3, surprisingly close, actually.

Essentially, I just took a simpler approach to my calculations, given Toriyama's lax feelings toward his franchise; I'm in no way trying to disparage your methods or results. Contrarily, as a math nerd, I like your method of calculation better than my own, really. If I had to make a suggestion (though I'm not particularly qualified to do so), I would base my calculations entirely on the films and manga, disregarding the anime adaptation entirely; that's just me, however, and if factoring in the anime helps your calculation method, then I encourage continuing to do so!

Edit: Haven't read part two yet, but I'll do so now!
"Reign supreme? In your dreams; you'll never make me bow.
Kick my ass? I'm world-class and Super Saiyan now."

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Re: Log Power Scaling

Post by shadowfox87 » Tue Dec 12, 2017 9:26 pm

Black Hawk wrote: Contrarily, as a math nerd, I like your method of calculation better than my own, really. If I had to make a suggestion (though I'm not particularly qualified to do so), I would base my calculations entirely on the films and manga, disregarding the anime adaptation entirely; that's just me, however, and if factoring in the anime helps your calculation method, then I encourage continuing to do so!

Edit: Haven't read part two yet, but I'll do so now!
Thanks, it's nice to have a math nerd read this. I really appreciate it. I did try the linear approach initially but was inspired by the video by V&J Reviews who used a cubic approach, so I thought of using logarithms since that's what is actually used in most of the world. Yea, I know that Toriyama's pretty lax about it. Most authors are, but it's still fun to analyze and make sense of everything. I would love to throw out the anime completely and just consider the manga but the manga has not caught up to the anime yet. Also, there are now distinct transformations in the anime that I have to take into consideration like the Kaioken. Though, if you read my Completed Super Saiyan Blue, I consider that to be equivalent to a SSB Kaioken x 20.
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling

Post by Black Hawk » Tue Dec 12, 2017 10:03 pm

shadowfox87 wrote:Thanks, it's nice to have a math nerd read this. I really appreciate it. I did try the linear approach initially but was inspired by the video by V&J Reviews who used a cubic approach, so I thought of using logarithms since that's what is actually used in most of the world. Yea, I know that Toriyama's pretty lax about it. Most authors are, but it's still fun to analyze and make sense of everything. I would love to throw out the anime completely and just consider the manga but the manga has not caught up to the anime yet. Also, there are now distinct transformations in the anime that I have to take into consideration like the Kaioken. Though, if you read my Completed Super Saiyan Blue, I consider that to be equivalent to a SSB Kaioken x 20.
You're very welcome! I just finished reading part two, and, though my numbers are quite a bit different, I still greatly enjoyed seeing your thought process and the rationale behind your numbers!

I'll admit that I do use the anime adaptation for one thing with regard to power scaling: as neither the film nor the manga make any mention of how Enraged Super Saiyajin 2 Vegeta compares to Beerus, I use the anime's "10%" line, for which 10% of Beerus would be a 1 and Enraged SSJ2 Vegeta would be a bit lesser.

Given how much you seem to have enjoyed the logarithmic approach to calculating Dragon Ball, I may just have to give it a go for myself!
"Reign supreme? In your dreams; you'll never make me bow.
Kick my ass? I'm world-class and Super Saiyan now."

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Re: Log Power Scaling

Post by shadowfox87 » Tue Dec 12, 2017 10:20 pm

Black Hawk wrote:I'll admit that I do use the anime adaptation for one thing with regard to power scaling: as neither the film nor the manga make any mention of how Enraged Super Saiyajin 2 Vegeta compares to Beerus, I use the anime's "10%" line, for which 10% of Beerus would be a 1 and Enraged SSJ2 Vegeta would be a bit lesser.

Given how much you seem to have enjoyed the logarithmic approach to calculating Dragon Ball, I may just have to give it a go for myself!
I wouldn't use the 10% line as it messes up the scaling a lot. It implies that 10 x SSJ2 Vegeta would be equivalent to Beerus and we both know that's not true. I would only say that Enraged SSJ2 Vegeta > SSJ3 Goku and that it is a higher grade of SSJ2, more powerful than SSJ2 Future Trunks who was equal to SSJ3 Goku.

Also, I noticed you're a martial arts instructor. That's really cool! I do mixed martial arts myself, mostly Brazilian Jiujitsu but with some kickboxing. I'm out of shape though haha. hopefully, will catch up next year.
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling

Post by Black Hawk » Wed Dec 13, 2017 12:44 am

shadowfox87 wrote:I wouldn't use the 10% line as it messes up the scaling a lot. It implies that 10 x SSJ2 Vegeta would be equivalent to Beerus and we both know that's not true. I would only say that Enraged SSJ2 Vegeta > SSJ3 Goku and that it is a higher grade of SSJ2, more powerful than SSJ2 Future Trunks who was equal to SSJ3 Goku.

Also, I noticed you're a martial arts instructor. That's really cool! I do mixed martial arts myself, mostly Brazilian Jiujitsu but with some kickboxing. I'm out of shape though haha. hopefully, will catch up next year.
It's still something I'm processing at the moment, so I haven't quite decided whether I'll stick with a 40000x multiplier for Enraged Super Saiyajin 2.

Indeed! My dad got trained me in shōrin-ryū from a very early age, and I've been hooked on training ever since! Maybe that's part of what I love Dragon Ball so much...
"Reign supreme? In your dreams; you'll never make me bow.
Kick my ass? I'm world-class and Super Saiyan now."

I BURN - Jeff Williams feat. Casey Lee Williams, RWBY Volume 1 Soundtrack

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Re: Log Power Scaling

Post by shadowfox87 » Wed Dec 13, 2017 12:46 am

Black Hawk wrote:It's still something I'm processing at the moment, so I haven't quite decided whether I'll stick with a 40000x multiplier for Enraged Super Saiyajin 2.

Indeed! My dad got trained me in shōrin-ryū from a very early age, and I've been hooked on training ever since! Maybe that's part of what I love Dragon Ball so much...
40,000 seems a lot for a SSJ2 multiplier. We've seen Vegeta enraged before but it has never jumped that much. I just think the 10% is wrong. That's very cool. In fact, it was the other way around for me. Dragon Ball got me into martial arts.
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling - A Different Approach

Post by shadowfox87 » Wed Dec 13, 2017 10:14 am

It seems some pages of the manga got leaked. This confirms that Android 17 is at SSJ3 level not SSB level like the anime had portrayed which makes a whole LOT more sense! The anime made SSB Goku fight with everyone for fan service. Hell, Goku was almost about to use SSB Kaioken for a second. Now we need to wait for Goku vs Gohan scene to confirm what level Gohan is at. This makes Android 17 = 3.6 on the log scale.
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling - A Different Approach

Post by Black Hawk » Wed Dec 13, 2017 2:12 pm

shadowfox87 wrote:It seems some pages of the manga got leaked. This confirms that Android 17 is at SSJ3 level not SSB level like the anime had portrayed which makes a whole LOT more sense! The anime made SSB Goku fight with everyone for fan service. Hell, Goku was almost about to use SSB Kaioken for a second. Now we need to wait for Goku vs Gohan scene to confirm what level Gohan is at. This makes Android 17 = 3.6 on the log scale.
I'm REALLY thankful for that; don't get me wrong, it wouldn't be impossible for No. 17 to reach that level of power, given that Freeza, who was initially weaker than him, did, but it just doesn't sit right with me for him to have been that strong for a while now and yet did nothing about Boo and Golden Freeza when all of that was going on.

I'm hoping that, given what Vegeta's been saying about Gohan-kun's potential, we'll find out that Vegeta has been training him in the Room of Spirit and Time, and that Gohan-kun's sparring match with his father will push him to his absolute limits. ... Not holding my breath, though.
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Re: Log Power Scaling - A Different Approach

Post by shadowfox87 » Wed Dec 13, 2017 2:41 pm

Black Hawk wrote:I'm REALLY thankful for that; don't get me wrong, it wouldn't be impossible for No. 17 to reach that level of power, given that Freeza, who was initially weaker than him, did, but it just doesn't sit right with me for him to have been that strong for a while now and yet did nothing about Boo and Golden Freeza when all of that was going on.

I'm hoping that, given what Vegeta's been saying about Gohan-kun's potential, we'll find out that Vegeta has been training him in the Room of Spirit and Time, and that Gohan-kun's sparring match with his father will push him to his absolute limits. ... Not holding my breath, though.
Toshio stated on his twitter that Gohan = 17 > Frost > Piccolo:
Image

Freeza was a prodigy and he never trained in his entire life. The databooks said that he was stronger than Cold and was the strongest ever in his entire species. Also, I've updated my graph above to add Gohan, Piccolo, Frost, 17, and SSR Black.
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling - A Different Approach

Post by dragonball0900 » Wed Dec 13, 2017 9:07 pm

Just want to point out that Dabura being just above 4,000 kilis shouldn't be trusted. Is that line from the Japanese dub or the English dub? Dabura is around Cell's strenght at his Perfect form, not Imperfect, meaning he is much stronger than that.

Also, the Androids, Piccolo (post Kami) and Kaioshin are too low. Remember that Future Trunks was stronger or around Goku from Namek (150 million), then SSJ Vegeta was much stronger than that, and got stomped by Android 18, who is weaker than Piccolo (post Kami), who is much weaker than his Buu arc self, who in turn is weaker than Kaioshin.

Kibito is also stated to be weaker Gohan in his base form in the Daizenshuu. He couldn't lift the Z sword while Gohan could in his base, Goku can also lift it in base too.

Goten and Trunks were also said to be above Android 18 in the Buu arc too.

However, this is just for part 2, which is your own headcanon. Your part 1 was excellent though, and I agree with most of your points. Though I wonder how the ROF characters (such as Gohan, Tagoma, Frieza and the base Goku and Vegeta states) can work.

I also think that Gohan's Ultimate form multiplier is higher since he was stronger than SSJ3 Gotenks and he and Super Buu (who were equal) were way above SSJ3 Goku. The latter in comparison to SSJ Gotenks aren't really that far apart. Maybe SSJ2 Gotenks is equal to SSJ3 Goku? Though that's just my opinion.

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Re: Log Power Scaling - A Different Approach

Post by shadowfox87 » Wed Dec 13, 2017 10:47 pm

dragonball0900 wrote:Just want to point out that Dabura being just above 4,000 kilis shouldn't be trusted. Is that line from the Japanese dub or the English dub? Dabura is around Cell's strenght at his Perfect form, not Imperfect, meaning he is much stronger than that.
Hey there. It's from the manga actually so it's official. I did gave him around the same power level as Perfect Cell, just a couple million lower. The 4000 kili (200 million) was just to show that he's above that number. I picked a number much higher.
dragonball0900 wrote:Also, the Androids, Piccolo (post Kami) and Kaioshin are too low. Remember that Future Trunks was stronger or around Goku from Namek (150 million), then SSJ Vegeta was much stronger than that, and got stomped by Android 18, who is weaker than Piccolo (post Kami), who is much weaker than his Buu arc self, who in turn is weaker than Kaioshin.
I would say that Future Trunks would be around the same or weaker than SSJ Goku, not stronger. As stated in the manga, Dabura said that even a guy with 4000 kili could not beat him. The Daizenshuu 7 already states that the East Kaioshin is stronger than Piccolo with Kami absorbed. We know that Piccolo = Android 17 > Android 18 > SSJ Vegeta. Hence, the power levels were decided based on that. I can't go above 200 million otherwise that would be higher than 4000 kili which the East Kaioshin is not.
dragonball0900 wrote:Kibito is also stated to be weaker Gohan in his base form in the Daizenshuu. He couldn't lift the Z sword while Gohan could in his base, Goku can also lift it in base too.
You're right about this! I'll fix it asap. I thought he was as strong as a SSJ1 Gohan, but I just read the Daizenshuu again and it was without SSJ.
dragonball0900 wrote:Goten and Trunks were also said to be above Android 18 in the Buu arc too.
Huh? Where is your basis for that? Goten and Trunks together in the masked man costume lost to 18. Goten and Trunks individually are still young SSJs, their base is still small. If you have another reference or source or feat, let me know though.
dragonball0900 wrote:However, this is just for part 2, which is your own headcanon. Your part 1 was excellent though, and I agree with most of your points. Though I wonder how the ROF characters (such as Gohan, Tagoma, Frieza and the base Goku and Vegeta states) can work.
I don't plan to scale the RoF. Part 1 was based on math and logic, so I will only scale characters that I can scale accurately. Tagoma is also a minor character that I don't care too much about. Vegeta is usually almost always around Goku level which is why I didn't keep stating Vegeta's level. Goku (RoF) and Freeza (RoF) can be calculated though. I gave Golden Freeza 0.1 above Goku via the log scale.
dragonball0900 wrote:I also think that Gohan's Ultimate form multiplier is higher since he was stronger than SSJ3 Gotenks and he and Super Buu (who were equal) were way above SSJ3 Goku. The latter in comparison to SSJ Gotenks aren't really that far apart. Maybe SSJ2 Gotenks is equal to SSJ3 Goku? Though that's just my opinion.
SSJ3's mutliplier is 400. I gave Gohan is 500, so I think that's pretty good. If I go any higher, then it ends up being close to the multiplier for Potara Fusion which is 600. If you read everything above, I gave a lot of evidence to show that Ultimate Gohan > Super Buu > SSJ3 Gotenks. Super Buu never acknowledged Gotenks as someone who was stronger than he was, only Gohan. Yes, initially SSJ3 Gotenks had the upper hand against Super Buu, but that fight never really finished.

I would not ever say that SSJ2 Gotenks is equal to SSJ3 Goku. Goku himself stated that he could've finished Fat Buu if he wanted but wanted to give the kids a shot. Based on all the multipliers and logic above, the SSJ2 multiplier will not yield results that will exceed SSJ3 Goku.
DBS Manga vs Anime Differences: viewtopic.php?f=25&t=42062
Timelines Explanation: viewtopic.php?f=8&t=42105
Log Power Scaling: viewtopic.php?f=8&t=40610
Science of Ultra Instinct: viewtopic.php?f=8&t=40707

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Re: Log Power Scaling - A Different Approach

Post by dragonball0900 » Thu Dec 14, 2017 8:27 am

shadowfox87 wrote:Hey there. It's from the manga actually so it's official. I did gave him around the same power level as Perfect Cell, just a couple million lower. The 4000 kili (200 million) was just to show that he's above that number. I picked a number much higher.
It's not from the manga really. I looked at it and it was never stated anywhere. It's just from the anime, and I don't know if it's from the japanese dub or the english one.
dragonball0900 wrote:I would say that Future Trunks would be around the same or weaker than SSJ Goku, not stronger. As stated in the manga, Dabura said that even a guy with 4000 kili could not beat him. The Daizenshuu 7 already states that the East Kaioshin is stronger than Piccolo with Kami absorbed. We know that Piccolo = Android 17 > Android 18 > SSJ Vegeta. Hence, the power levels were decided based on that. I can't go above 200 million otherwise that would be higher than 4000 kili which the East Kaioshin is not.
Where was it said that Future Trunks is not stronger than Namek Goku? He could be equal or stronger since he was stronger than Future Gohan, who never surpassed at least Yardrat Goku. You also have to remember that Piccolo trained in the ROSAT for a year, and managed to hold his own against a Cell Jr. Then trained 7 years which puts him at least on a level comparable to a Cell Jr. Kaioshin should be stronger than that, and stronger than him are the Buu arc SSJ's and Dabura.
dragonball0900 wrote:Huh? Where is your basis for that? Goten and Trunks together in the masked man costume lost to 18. Goten and Trunks individually are still young SSJs, their base is still small. If you have another reference or source or feat, let me know though.
This one is actually one of the most controversials between the fanbase. If you read the manga carefully, SSJ Kid Trunks threw a single suppressed (very suppressed) ki blast to Android 18, and the latter got freaked out by it, and had to dodge it. They were only weaker than her in base, and the reason they lost is because Android 18 separated both kids from the costume without even fighting.
Also, Gohan was struggling against Goten during a training match, and Trunks managed to threw a punch to Vegeta, something Android 18 would never do at this point.
And when Super Buu went Buuccolo for the first time, he didn't have Piccolo's full clothing (just the weighted ones). Meaning that the kids are not that far away behind Piccolo.
dragonball0900 wrote:SSJ3's mutliplier is 400. I gave Gohan is 500, so I think that's pretty good. If I go any higher, then it ends up being close to the multiplier for Potara Fusion which is 600. If you read everything above, I gave a lot of evidence to show that Ultimate Gohan > Super Buu > SSJ3 Gotenks. Super Buu never acknowledged Gotenks as someone who was stronger than he was, only Gohan. Yes, initially SSJ3 Gotenks had the upper hand against Super Buu, but that fight never really finished.

I would not ever say that SSJ2 Gotenks is equal to SSJ3 Goku. Goku himself stated that he could've finished Fat Buu if he wanted but wanted to give the kids a shot. Based on all the multipliers and logic above, the SSJ2 multiplier will not yield results that will exceed SSJ3 Goku.
Yeah, maybe SSJ3 Gotenks is weaker than Super Buu, and yeah, SSJ2 Gotenks might not be above SSJ3 Goku, but that doesn't mean SSJ3 Gotenks (or Ultimate Gohan for that matter) is too close to SSJ3 Goku. Goku was scared of fighting Super Buu even with Vegeta together with him. Their powers were too far away from each other. It will all depend on where you have Goten and Trunks though, and I think we are talking about that above.
Also, why can't the fusion multiplier be weaker than Ultimate Gohan? The guide only says it's far stronger than SSJ3, but not stronger than Ultimate.

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Re: Log Power Scaling - A Different Approach

Post by GreatSaiyaman123 » Thu Dec 14, 2017 6:18 pm

shadowfox87 wrote:So 1.2 for ASSJ, 1.3 for FPSSJ, and 1.5 for USSJ (only power) is reasonable.
So Vegeta went from equals with initial Semi Cell to completely ragdolling FP Semi Cell with a 1.2x boost? Trunks also was much stronger than a Cell who barely budged with Vegeta's kick. I doubt even a 2x boost can fit into that.
Piccolo (Kami absorbed) = 175 million
Android 17 = 175 million
Android 18 = 170 million
Imperfect Cell = 180 million
Android 16 = 185 million
So... Where can the three SSJs fit in here? Future Gohan was a bit above >50% Future 17 as he wasn't sure if he could take both Cyborgs down aand wasn't much weaker than Debut Trunks, who could clown Cyborg Freeza, . There's sure a gap bigger than 2x between the twins and Freeza.
And Cell tanked Piccolo's best blast withot a scratch while being almost equals with him? Recoome was 36~40k to Vegeta's >30k and was all bruised by Vegeta's proto Final Flash.
Bojack also appeared right after the Cell saga. He was a formidable opponent that required SSJ2 Gohan to defeat. He was punched straight through the stomach by Gohan, was still standing and was able to do a ki blast. In comparison, Perfect Cell was on his knees after 1 punch from SSJ2 Gohan, so I would say that Bojack > Perfect Cell but below Super Perfect Cell.
Bojack had a whole on his chest. Cell was hit twice and had no wholes on him. I'd say Cell is the stronger of the duo.
Legendary SSJ Broly = 1.4 billion > SSJ2 Teen Gohan
Er... V-Jump classified Gogeta less than twice stronger than Broly... I doubt the numbers from Broly, Gogeta and Cooler can be taken seriously.
Note that Perfect Cell > SSJ Gohan at the start. However, what doesn’t make sense is that if Perfect Cell is > SSJ Gohan, then when Perfect Cell regenerated himself into Super Perfect Cell, he had the aura of an SSJ2. Super Perfect Cell also reached a new transformation and a zenkai. Therefore, his power level should have also doubled, making Super Perfect Cell > SSJ2 Gohan. Not only that, but Gohan himself stated that he lost half his ki protecting Vegeta, losing 1 arm. We all know that Super Perfect Cell lost to a 1-handed SSJ2 Gohan. So how? Yes, Vegeta did distract him for that small window of opportunity for Gohan to go all out, but was that really it?
Gohan said he would kill Cell if he wasn't injured, and Gohan being constantly used as a measure stick on the Boo Arc when Cell was completely forgotten tells us who's the stronger of the duo.
SSJ Teen Gohan = 500 million < SSJ Goku and SSJ Vegeta from Buu saga :)
SSJ Goku = 490 million > Kooler (470 million) :)
SSJ Vegeta = 480 million
SSJ Future Trunks = 475 million
SSJ2 Teen Gohan = 500 million x 2 = 1 billion
Super Perfect Cell = 525 million x 2 > 1.05 billion > SSJ2 Gohan!?
Vegeta and Trunks shat themselves when Goku powered up at the Cell Games. Teen Gohan also was at least Dabra's equal, who was compared to the Cell who was blitzing Goku almost as good as Vegeta was blitizing Zarbon. CG Goku sure isn't almost Gohan's equal.
(A+B) = 2.6 million --> Trunks=1.35 million and Goten=1.25 million
(Each weaker than Goku base from Namek who was 3 million. Makes sense!)
So Teen Gohan < Goku in Namek? Goten was pretty much fighting evenly with Gohan as SSJs before the Budokai.

Also, according to you the kids are 2nd form Freeza level. If two Freeza's sat on each others' shoulders and put a clown suit, could they hold their own against #18? Because that's what the kids did.
SSJ3 Gotenks>SSJ3 Goku --> SSJ3 Gotenks = 5.2 billion (0.2 billion above SSJ3 Goku)
Unless all of Gotenks's forms (Including base and Pre Rosat SSJ) fit between 5 and 5.2 billions, Gotenks is much, much, much above Goku.
Dabura said that he is above 4000 kili
3000 kili*

Chapter: 451 (DBZ 257), P2.5-6
Babidi: "Thr... 3,000 kiri...!! H-how does an Earthling have 3,000 kiri of energy...?!!
Dabra: “3,000 kiri…That’s strange…There shouldn’t be any human race like that.”


Chapter: 452 (DBZ 258), P2.4
Context: as he confronts Goku and co.
Dabra: “...It’s quite impressive that you humans managed to defeat Yakon and come as far as Stage 3. I could even call it miraculous…However, this will be as far as you go. You’ve got me as an opponent now…”


He shit talks the three saiyans even after seeing Goku's 3000 kili.
1 kili=50,000 BP
50% Freeza >> Yakon?
Shin = 180 million (between 150 million and 200 million)
Piccolo = 175 million (more than 150 million, SSJ Goku’s initial power, but weaker than Shin.)
Kibito = 10 million (weaker than Base Gohan as he can't even pick up the Z-sword)
Chapter: 392 (DBZ 198), P13.1-3
Goku: “Hey… Piccolo! Did you go into the Room of Spirit and Time?”
Piccolo: “Indeed.”
Goku: “I can tell! You’ve risen to an entirely different level.”


Goku said Piccolo powered up a lot from the Rosat. He should be far stronger than 17 by now. A 180 isn't far stronger than a 175 either. Damn, a fight between 180 and a 175 would be close as hell and the 175 even might win.
Ultimate Gohan > Super Buu (5.3 billion) --> Ultimate Gohan (Buu saga) = 5.5 billion.
A 5.5 sure can't smack around a 5.3 like Gohan did.
Kid Buu = 5 billion < Super Buu but more evil and not inhibited by the kindness of Fat Buu
Super Buu = 5.3 billion > SSJ3 Gotenks (5.2 billion) but < Ultimate Gohan (5.5 billion)
Goku thought he had no shot against Boo. If he was 94% of Boo, he sure would give it a shot, even more with Vegeta there to back him up.
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