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Currently we treat the Super Saiyan multiplier as being x50 for both, strength and speed.
The reason for this is because Freeza said that he was using 50% of his power and Kaioken x20 Goku was slightly weaker than him. Which means:
50% Freeza > Kaioken x20 Goku
So 100% Freeza should be stronger/faster than a hypothetical x40 Goku. And since SSJ Goku was slightly stronger/faster than 100% Freeza, it gives credence to the 50x multiplier for both, strength and speed.
Let's take a look again at the events and try to verify the validity of it.
(Note that the following excerpts come from Herms.)
Chapter: 312 (DBZ 118), P2.3-6
Freeza: “You’re quite confident. But I’ve noticed that though you told me you’d fight seriously, you still have a considerable amount of power remaining…”
Goku: “So the jig’s up, huh?”
Freeza: “Even taking that into consideration, in my estimation… If I put out about 50%, that is to say, half of my maximum power, I'll be able to turn you into space dust..."
Here Freeza is saying that he only needs to use half of his maximum power to turn Goku into space dust. Note that Freeza is referring to power/strength here and is confident that he can beat Goku even while pulling back his punches.
Chapter: 312 (DBZ 118), P5.5
Context: after Freeza's "I can beat you with 50% of my power" line
Goku: “H-he’s…not bluffing…!”
Chapter: 312 (DBZ 118), P13.2
Context: as Freeza beats up on Goku
Piccolo: “Th-this is bad…There’s too much of a gap between the power they were hiding…”
Chapter: 312 (DBZ 118), P13.4
Context: as Freeza beats up on Goku
Kaio: “It-it’s no use…He’s too strong…To think that he’d be this [strong]…”
Chapter: 313 (DBZ 119), P6.1-2
Kuririn: “A-anyway, what’s Goku thinking…He’s starting to get one-sidedly beaten up…”
Piccolo: “He’s not thinking anything…It’s simply that Freeza’s true ability was outrageously greater than we or Goku expected…”
Here Goku was using Kaioken x10 and was still getting one-sidedly stomped. The only option left was to use kaioken x20.
Chapter: 313 (DBZ 119), P14.1
Context: after the Kaio-Ken x20 Kamehameha doesn’t hurt Freeza much
Goku: “…! D-damn it all…!”
Chapter: 314 (DBZ 120), P3.1-2
Context: still following the Kaio-Ken x20 Kamehameha
Kuririn: “Un-unbelievable…Goku’s Kamehameha just now ought to have had outrageous power…So why did Freeza take hardly any damage…!?”
Gohan: “Fa-father’s ki has fallen a lot…”
Chapter: 314 (DBZ 120), P1.3-4
Context: still following the Kaio-Ken x20 Kamehameha
Goku: “Wh-what…! That didn’t effect him much…! S-so that wasn’t a bluff either…He really is only using half his power…”
Even Kaioken x20 Kamehameha was not able to do much damage to Freeza. But notice what Goku says at the end. "That didn’t effect him much…! S-so that wasn’t a bluff either…He really is only using half his power…”
This statement implies that Goku somewhat wanted to confirm whether Freeza was bluffing when he said he will only use half of his power/strength to beat up Goku. But when Freeza easily survived Kaioken x20 Kamehameha, he realized that Freeza wasn't lying and his real power far surpasses that. This realization would only come if Goku expected the Kamehameha to be strong enough to deal some considerable amount of damage, having first-hand experienced the beating from him.
Which means that Goku fired that Kamehameha, hoping that Freeza's half-power statement was only a bluff, and expecting his kamehameha to do some decent damage, making it somewhat stronger than the level of beating Freeza was giving him. But since Freeza easily survived it, it was confirmed that Freeza's real durability at that moment was greater than 50%, which made Goku realize that he wasn't bluffing and was just holding back his punches to beat up Goku before.
Long story short:
Kaioken x20 Goku's Kamehameha >= Half of Freeza's strength > Kaioken x10 Goku
Freeza was only pulling his punches back so as to use half of his strength. His actual power/durability at that moment was still above that, as indicated by him surviving something with almost no damage, and making Goku realize that he was really using only half of his strength.
The statement about using half of his power to turn Goku into space dust, only refers to strength. It doesn't say anything about using half of his speed/durability.
Full power Freeza should be 2x stronger than what he used to beat up Goku. And assuming Kaioken x20 Kamehameha was only a little stronger than half of Freeza's strength or roughly the same, SSJ Goku should also be a bit more than 2x stronger than his Kaioken x20 level. The 50x strength increase is plausible.
However, Freeza's max power being 2x greater than what he used to beat up Goku doesn't mean his speed also increases by a factor of 2. We don't treat statements like "I am using half of my power" as being valid for speed as well.
In conclusion, while SSJ being a 50x multiplier for strength makes sense, this has no reason to be applied to speed. Freeza's strength being twice at his max than what he used to beat up Goku doesn't mean he is twice as fast as well. All we can safely say is that SSJ at least provides a 20x speed boost as it is still faster than Kaioken x20.
The reason for this is because Freeza said that he was using 50% of his power and Kaioken x20 Goku was slightly weaker than him. Which means:
50% Freeza > Kaioken x20 Goku
So 100% Freeza should be stronger/faster than a hypothetical x40 Goku. And since SSJ Goku was slightly stronger/faster than 100% Freeza, it gives credence to the 50x multiplier for both, strength and speed.
Let's take a look again at the events and try to verify the validity of it.
(Note that the following excerpts come from Herms.)
Chapter: 312 (DBZ 118), P2.3-6
Freeza: “You’re quite confident. But I’ve noticed that though you told me you’d fight seriously, you still have a considerable amount of power remaining…”
Goku: “So the jig’s up, huh?”
Freeza: “Even taking that into consideration, in my estimation… If I put out about 50%, that is to say, half of my maximum power, I'll be able to turn you into space dust..."
Here Freeza is saying that he only needs to use half of his maximum power to turn Goku into space dust. Note that Freeza is referring to power/strength here and is confident that he can beat Goku even while pulling back his punches.
Chapter: 312 (DBZ 118), P5.5
Context: after Freeza's "I can beat you with 50% of my power" line
Goku: “H-he’s…not bluffing…!”
Chapter: 312 (DBZ 118), P13.2
Context: as Freeza beats up on Goku
Piccolo: “Th-this is bad…There’s too much of a gap between the power they were hiding…”
Chapter: 312 (DBZ 118), P13.4
Context: as Freeza beats up on Goku
Kaio: “It-it’s no use…He’s too strong…To think that he’d be this [strong]…”
Chapter: 313 (DBZ 119), P6.1-2
Kuririn: “A-anyway, what’s Goku thinking…He’s starting to get one-sidedly beaten up…”
Piccolo: “He’s not thinking anything…It’s simply that Freeza’s true ability was outrageously greater than we or Goku expected…”
Here Goku was using Kaioken x10 and was still getting one-sidedly stomped. The only option left was to use kaioken x20.
Chapter: 313 (DBZ 119), P14.1
Context: after the Kaio-Ken x20 Kamehameha doesn’t hurt Freeza much
Goku: “…! D-damn it all…!”
Chapter: 314 (DBZ 120), P3.1-2
Context: still following the Kaio-Ken x20 Kamehameha
Kuririn: “Un-unbelievable…Goku’s Kamehameha just now ought to have had outrageous power…So why did Freeza take hardly any damage…!?”
Gohan: “Fa-father’s ki has fallen a lot…”
Chapter: 314 (DBZ 120), P1.3-4
Context: still following the Kaio-Ken x20 Kamehameha
Goku: “Wh-what…! That didn’t effect him much…! S-so that wasn’t a bluff either…He really is only using half his power…”
Even Kaioken x20 Kamehameha was not able to do much damage to Freeza. But notice what Goku says at the end. "That didn’t effect him much…! S-so that wasn’t a bluff either…He really is only using half his power…”
This statement implies that Goku somewhat wanted to confirm whether Freeza was bluffing when he said he will only use half of his power/strength to beat up Goku. But when Freeza easily survived Kaioken x20 Kamehameha, he realized that Freeza wasn't lying and his real power far surpasses that. This realization would only come if Goku expected the Kamehameha to be strong enough to deal some considerable amount of damage, having first-hand experienced the beating from him.
Which means that Goku fired that Kamehameha, hoping that Freeza's half-power statement was only a bluff, and expecting his kamehameha to do some decent damage, making it somewhat stronger than the level of beating Freeza was giving him. But since Freeza easily survived it, it was confirmed that Freeza's real durability at that moment was greater than 50%, which made Goku realize that he wasn't bluffing and was just holding back his punches to beat up Goku before.
Long story short:
Kaioken x20 Goku's Kamehameha >= Half of Freeza's strength > Kaioken x10 Goku
Freeza was only pulling his punches back so as to use half of his strength. His actual power/durability at that moment was still above that, as indicated by him surviving something with almost no damage, and making Goku realize that he was really using only half of his strength.
The statement about using half of his power to turn Goku into space dust, only refers to strength. It doesn't say anything about using half of his speed/durability.
Full power Freeza should be 2x stronger than what he used to beat up Goku. And assuming Kaioken x20 Kamehameha was only a little stronger than half of Freeza's strength or roughly the same, SSJ Goku should also be a bit more than 2x stronger than his Kaioken x20 level. The 50x strength increase is plausible.
However, Freeza's max power being 2x greater than what he used to beat up Goku doesn't mean his speed also increases by a factor of 2. We don't treat statements like "I am using half of my power" as being valid for speed as well.
In conclusion, while SSJ being a 50x multiplier for strength makes sense, this has no reason to be applied to speed. Freeza's strength being twice at his max than what he used to beat up Goku doesn't mean he is twice as fast as well. All we can safely say is that SSJ at least provides a 20x speed boost as it is still faster than Kaioken x20.
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