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At some point in the battle with Freezer in Dragon Ball Z, it's revealed by King Kai that Goku is using Kaioken times ten (x10) when battling Freezer. In the same battle, in the moment Freezer is beating Goku badly, Freezer confesses he's using 1/4 (25%) of his power.

The Daizenshuu 7 states that 100% of Freezer power is 120 millions, meaning 25% of his power is 30 millions. And the Dainzenshuu 7 also states Goku's base form is 3 millions, meaning kaioken times 10 (x10) gives him a power level of 30 millions. So Goku and Freezer should be relatively even because they have exactly the same power level, but Freezer is beating Goku badly, overpowering and overspeeding him.

How was Freezer at 25% of his power capable of overpowering and overspeeding Goku, when they were supposed to have the same power level?

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Well what I realized is that DBZ was inconsistent before the internet started pointing things out. Also I don't think that a persons speed is equal to their power so Freeza could have very well been faster so Goku, although can see him, his reflexes couldn't respond in time kinda like Rock vs Sasuke when they first meet and Sasuke just couldn't physically keep up even if he could see through his hand to hand combat but still got whooped on pretty bad.

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Though @londn Link had pretty well answer, as manga reader and anime watcher I feel the need to expand little more on this matter:

  1. The Power Rate (PR for short), though to be accurate, is later in Cell arc being showed that have only one aspect on the battle - Power alone. Its pretty much saying that if person A who have 10,000 PR firing kamehameha against person B who have 9,000 PR, he will win. On the situation when both person A and B have the same PR, the kamehmeha will just blow away and no one will be harmed. But in the stats of other factors, such as speed and tactic, are irrelevant for the PR. So basically saying that Frieza have much more speed in his hand than Goku, or have better tactic, makes the trick even if their PR are the same.

  2. It's pretty well connected to first point, but all the same have it's own rule. Goku was as you said in kaioken state, in other words the more it's activate, the more it's burdening the body. Unlike in SS mode where power doesn't have whatsoever effect on the body. So assuming the burden on Goku body could make him not fighting well, it's not matter how PR he have.

  3. The above point 2 and this one are actually the same. But generally speaking, since Goku was in 100% state while Freeza hasn't, just saying that Goku did used lots more of energy than Freeza. As said in point 1, PR isn't everything. And if Goku had been fighting with 100% when Frieza hasn't, it's just saying that Feeeza hasn't used so much energy as Goku. Only when Freeza getting to 100% state he really begins to use his real power.

To summarise things up - Power Rate isn't everything. In Cell arc it's pretty well presented that even bigger PR cannot beat someone with less, due his speed being left for much more power. The same logic goes for here.

So though those 3 points are generally one, I think separating this idea this way is more expendable. If someone could edit this to be better phrased, it might be preferable.

I think this is pretty much summarise the answer that @London Link also wanted to say, but in more expended note.

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