I was assuming that Goku's Power Level while fighting Piccolo Jr was in the mid-300s because he probably got a Zenkai from that fight and trained a bit in those five years. I got 108x by multiplying Goku's 1.333...x increase by 27 to represent the Human's rough 9x increase, than multiplying by 3 to account for the time difference.
Yes, these numbers are rough, make a lot of estimations, and are flawed, but; they do their job of showing that, if the Humans make similar radical gains under Kaio than they did under Kami, they could VERY easily be in the hundreds of thousands or even the ones of millions once they're done training.
edited 13th Dec '15 6:19:30 AM by PushoverMediaCritic
Welp. My numbers were off. I blame it on lack of sleep. The Humans actually grew about 24x faster than Goku did under Kami's training (and don't forget that Goku even spent a month in the HTC and didn't grow nearly as much as they did). Though applying that to Kaio's training still results in approximately a 480x boost for the Humans. Tenshinhan still goes from 1,830 to 878,400 in a year.
edited 13th Dec '15 6:32:39 AM by PushoverMediaCritic
the math I quickly did with your figures was like this -
The humans 1 year increase is multiplied by 3 to get a 27x increase
they increase by 27x in 3 years, Goku by 1.333...x in 3 years
Divide 27x by 1.333...x to see how much more effective the human's increase was (not multiply!)
End result = 20.25x
In a year of Kaio's training, they'd get 405x stronger. 1830 x 405 = 741,150
In 6 days, they'd get about 6.6x stronger - 1830 x 6.6 = 12,078
Even with this most generous and flawed math, Ten doesn't even come close to beating Cui.
Also, Goku being in the 300s for the 23rd doesn't gel with the fact that Piccolo was meant to be much stronger than Daimao, and even if you assume the 900 readings were for Kamehamehas-only then Goku's Kamehameha strength barely changed between the years which should be indicative of his overall improvement.
Round two with more accurate figures, assuming 900 readings are Kamehameha-only:
Goku gets 1.5x stronger in 3 years, Ten gets (7.3 x 3 = 21.9) times stronger in 3 years.
14.6x effectiveness.
In one year at Kaio's, he increases his battle power by 277.4x = 507,642. In six days, about 4.5x increase = 8,235.
Now if we go by Goku's BP = 910
In 3 years he increases his BP by 3.5, Ten 21.9x
6.25x as effective
Goku increases his battle power by 8000 / 924 = 8.65x on Kaio's in one year. Tenshinhan increases his battle power by 54x in one year = 98,820.
In six days, he barely moves it.
Now you've got the fact that the amount their training was more effective by wasn't accurate in the first place, diminishing returns, and any other influences in the training.
The Ginyu Force filler really doesn't hold up. Like I've said, I don't have a problem with them reaching that strength at the end of their training.
edited 13th Dec '15 6:47:40 AM by Saiga
Maybe your right, but I think there's always gonna be a part of me that wishes more was done with them. And it's obviously the same for others.
I can see where you're coming from here Saiga (the humans were never really important, and it was always Goku's story), but for some, it's a bitter pill to swallow because they like these guys and wish the plot hadn't left them in the dust.
One Strip! One Strip!
Oh man. Don't even bother. People would rather make jokes about how much Yamcha sucks, so I've never bothered to bring up his inclusion.
The jokes just never stop.
One Strip! One Strip!Ah, so the reason this film is so low on the list is because Lani and Takahata are spoilsports
In the film, the Native Americans live on a region claimed by an Expy of Imperial China. Also, Yamcha loses a fight with Bora, poor guy just can't catch a break.
I thought it was going to be Episode 51?
But I think Kaiser has also been working on Hellsing. Somewhere I heard it was coming out in January.
The *Legendary* Super Saiyan is motivated by a crying infant! He is a literal giant f***ing baby!I think 51's still got a bit longer to go. It could be another movie or special.
I guess we'll find out wen it's released.
"It's liberating, realizing you never need to be competent." — Ultimatepheer

That is extremely flawed math and ignores several things about the training official battle powers. To say nothing of the fact that you even suggest it can be reduced to mathematical formulas like that.
First of all, Goku didn't train with God. It was mentioned that God let Popo handle most of the training, whereas he chose to oversee the humans' training personally for the best result. The fact that the humans had each other to spar with also contributed to better gains. They still have partners at Kaios, so I would still expect better gains, but they're now doing the same training instead of superior training and there are less sparring partners available.
Secondly, you've really rounded those figure in the humans favor. Even assuming Saiyan arc Goku's full power was 418 and not the 924 of his Kamehameha reading, that still means he improved by more than 1.6x from the Daimao arc to the Saiyan arc, and he was said to have not done much training from the 23rd Budokai (this is backed up by Shonen Jump giving his 23rd battle power as 910 in comparison to his Saiyan arc max reading of 924). So that's at least a 1.5x increase, not 1.3x - and again, that's only assuming 418 was his full power in the Saiyan arc.
But given that Piccolo said they amplify their energy whenever they attack, and Goku is outright listed as having a battle power of 910, I say it's more reasonable to use that number as a basis. Especially when there is no other official battle power for Goku at the 23rd Budokai, and the source for his 910 was published with chapter 231 of the manga. So I know that in order for you to make that calculation, you made up your own number for Goku which REALLY throws off the accuracy of your work.
Anyway, by using Goku's official battle power of 910, he improved by 3.5x from Popo's training. Kuririn and Yamcha improved by roughly 8.5x, and Ten by 7.3x (all lower than the figure you gave, the rounding makes a big difference when you start multiplying it by very long periods of time). Then Goku would go on to increase his battle power by about 8.6x at Kaio's, making the difference in quality of training there much smaller.
Yes, they made more progress in 1/3rd of the time with better training and access to sparring partners. We don't know how they'd fare in identical conditions because they've rarely been in identical conditions - Goku and Kuririn training under Master Roshi is the only example, and Kuririn doesn't outperform Goku here.
Now I can't figure out how, even with your own figures, you reached an answer of 108x effectiveness. Can you please list the actual steps you took?
On the other hand, there are numerous factors you did not mention at all that hurt the ability to calculate the results of their training - even loosely. For starters, the characters' most effective training sessions come when they're in most need of it, which I doubt is a coincidence. The better the motivator, the better the results. The Saiyans approach is treated as one of the most dire training arcs in the series, it doesn't surprise me to see that everyone here has better gains than in most other timeskips.
Secondly, there is the factor of diminishing returns. This is not only a real life concept, but clearly applies to Dragon Ball as they need to move on to bigger and better training methods as they grow stronger. Mentors have said their training won't suffice after a certain point. Characters outright hit their limits until they improve their training and grow stronger once more.
Someone in the thousands likely wouldn't be getting as much a benefit as someone in the hundreds. Definitely not for the tens of thousands, hundreds of thousands, and millions. They have made it perfectly clear that the characters don't just escalate in power without any limits or obstacles at all.
edited 13th Dec '15 6:02:13 AM by Saiga