On transformation multipliers 10 and 50 for SSJ.

[Desassina]

Super Saiya-jin was a 10 fold increase from his regular state, which brought him to about 50 times the power that he had on Namek, due to him getting fresh with transformation. It's not a decreasing multiplier theory, but one that supports Goku getting replenished from an injured state, which could be 20% of his power due to Kaioken x20. It's one multiplier for a percentage, and the only thing left to justify is Goku's rising power, so that it could be 10 times short of his SSJ figure.

The idea comes from DB Super and the use of Kaioken x10, SSJ Blue being 10% short of its potential, and the possbility of a 10 fold increase towards full power. If Goku can use SSJ Blue without draining himself through SSJ God, then the percentage that Vegeta was brought to is actually the same increase over SSJ God, in case they are allowed to focus their energy. It could have been the same thing with Kaioken x20 back then: it brought Goku to about 20% of his power by using it.

In other words, or figures:

Goku (before KKx20) - 15'000 (full)
Goku (during KKx20) - 60'000 (20% off)
Goku (after KKx20) - 3'000 (20 times less)
Super Saiya-jin - 150'000 (10 times over full)

Goku was still 50 times stronger with SSJ after using KKx20, but it would be an increase of 10 fold elsewhere, so that it matches the current events and Akira Toriyama's wishes.

[Gog]

Goku was still 50 times stronger with SSJ after using KKx20, but it would be an increase of 10 fold elsewhere, so that it matches the current events and Akira Toriyama's wishes.

Well, I do have to ask then if Super Saiyan was a 10x multiplication in power why did Goku never use the Kaio Ken ever again? The form clearly offers the superior boost in power in comparison to Super Saiyan.

[Desassina]

I guess that it's because Kaioken was still the straining technique that didn't allow his power to be mastered like SSJ. Super Saiya-jin brings him to about 10 times the power without heavy strain, while Kaioken x20 can only enjoy a peak of 20 fold before going down, so we're talking about 2 times the difference without benefits. That difference is easily put out with the Grades and Full Power. I guess that it's the reason why it was abandoned in the Cell and Boo sagas as well.

[Gog]

I guess that it's because Kaioken was still the straining technique that didn't allow his power to be mastered like SSJ. Super Saiya-jin brings him to about 10 times the power without heavy strain, while Kaioken x20 can only enjoy a peak of 20 fold before going down, so we're talking about 2 times the difference without benefits. That difference is easily put out with the Grades and Full Power. I guess that it's the reason why it was abandoned in the Cell and Boo sagas as well.

You do have a point here, Kaio Ken is an incredibly dangerous and straining technique to use, but in the narrative its weird that it was never once acknowledged or even considered by Goku. There's also the fact that Super Saiyan being a smaller multiplier than Kaio Ken also completely breaks the Goku V Freeza fight on Namek, Kaio Ken was incapable of even harming Freeza at half power while Super Saiyan was slightly greater than his full power.

[Desassina]

The only problem would be Goku at 15'000 to increase his power by 10 without the heavy strain of a 20 fold Kaioken. He would arrive at the exact same number as SSJ over his full power, while Freeza didn't even use more than 50%, meaning that Goku had a peak of 300'000 with Kaioken x20 before going down. Man, this is a head scratcher... It's only much easier to consider the multiplier of 50 in this battle, but not elsewhere. I mean, how else are Piccolo and Vegeta going to stack up to Mecha Freeza, when they are without that kind of increase?

[Captain Strawberry]

I'll give a new theory

SSJ1 10x with rage boost.

SSJ provides ki control than Kaioken so Goku was able to tank Frieza's hits more and he would get stronger during the fight.

[emperior]

Toriyama said SSJ felt like a 10x increase over what Goku had at that moment, probably referring to Kaio-Ken x10 as Goku used it all throughout his fight with Freezer up until he started collecting energy for the Genkidama.
So, if anything, SSJ was more like 100x than 50x.

It's also obvious that SSJ had to be above Kaio-Ken x20, or it would have been underwhelming. It's classic Dragon Ball. And Goku never considered Kaio-Ken again which wouldn't make sense if it were superior to SSJ. Also makes no sense for the legendary SSJ to be just as strong as an Oozaru.

[Desassina]

Ok, I will accept SSJ being 50 times stronger than base, like it used to be all along. We have a perfectly fine system not to be messed with, so there's no point in trying to reinvent the logic, but we could try to improve it at least. I'm going to say that Goku was brought to 50 times the power that he had, as if it were a new state of suppression in his SSJ form, which requires him to shave 50% in order to accomplish full power. It's base times 50 divided by 0.5 to arrive at 100. I believe that it's better to speak in terms of suppression, because SSJ can be taken as low as their base, and become whatever multiplier over the latter. The idea is as follows:

Super Saiyan -> from x to 100
Full Power -> x divided by x/100

If x is equal to 10, then he needs to shave 10% of suppression, otherwise it's any percentage that is equal to the multiplier divided by 100.

The same thing could be said about the power ups and techniques. They don't unlock their power, but increase it past the state that they are in, so figuring out the full power of SSJ2 and 3 is the same process. You'll have to define their limits though.

[Supaman]

The effects of the Kaioken are simply degressive.
The more power is amplified the more it is heavy and hard to control.
For example,
Kaioken x2 => Goku base x2
Kaioken x3 => Goku base x2,8
Kaioken x10 => Goku base x4
Kaioken x20 => Goku base x5

Then for Toriyama, ´Goku SSJ = Goku base x10.

The folds with Kaioken, il just means that Goku is more powerful. When he use Kaioken x4, he's just more powerful than with Kaioken x3. Not really a multiplier.
Very simply for the kids.

[cheddarsword]

Ok, I will accept SSJ being 50 times stronger than base, like it used to be all along. We have a perfectly fine system not to be messed with, so there's no point in trying to reinvent the logic, but we could try to improve it at least. I'm going to say that Goku was brought to 50 times the power that he had, as if it were a new state of suppression in his SSJ form, which requires him to shave 50% in order to accomplish full power. It's base times 50 divided by 0.5 to arrive at 100. I believe that it's better to speak in terms of suppression, because SSJ can be taken as low as their base, and become whatever multiplier over the latter. The idea is as follows:

Super Saiyan -> from x to 100
Full Power -> x divided by x/100

If x is equal to 10, then he needs to shave 10% of suppression, otherwise it's any percentage that is equal to the multiplier divided by 100.

The same thing could be said about the power ups and techniques. They don't unlock their power, but increase it past the state that they are in, so figuring out the full power of SSJ2 and 3 is the same process. You'll have to define their limits though.

No where is it stated that SS can be dropped as low as base. Rather, it is heavily implied that it has a minimum output that is well above base due to what has become known as "Ki leakage". Even SSB isn't confirmed to be able to go that low and it has the best Ki control of all SS forms (barring SSG).

[Desassina]

No where is it stated that SS can be dropped as low as base. Rather, it is heavily implied that it has a minimum output that is well above base due to what has become known as "Ki leakage". Even SSB isn't confirmed to be able to go that low and it has the best Ki control of all SS forms (barring SSG).

What about Gohan hitting some thugs by transforming into SSJ to disguise himself without killing them? Not stated, but shown, and the idea is to let it be an increase over base. However, if Goku was powering up towards half of his full power in front of Korin, then he was lower than 0.5 times the same, but without detransforming, or starting at base. An increase of 50 times his battle power divided by 0.5 is the multiplier 100. He was lower than what would seem to be the threshold of transformation. In case you want some numbers to get the idea better:

1. Battle power times 10 as the starting level, works towards 50 just fine, which could have been Goku's against Freeza.
2. Goku's base times 50 could be half of his full power, since 0.5 times less than that is at the threshold to become a SSJ2.