Son Goku's True Boost in Strength When Becoming Super Saiyan

[beast mode]

• (Freeza) (BP)
  Normal Goku (3,000,000)
  Normal Goku (Kaio-ken x10) (30,000,000)
  Normal Goku (Kaio-ken x20) (60,000,000)
  Super Saiyan Goku (150,000,000) (50x increase)
  
  (Majin Buu) (Kiri)
  Yakon (800)
  Normal (higher than 800, probably 1,000 or 1,500)
  Super Saiyan (3,000) (2x/3x increase)
  
  I believe in one of the more recent data books Toriyama states that he originally imagined the Super Saiyan transformation as multiplying Goku's base power by 10x

OK, now we have 3 different conflicting (or are they?) statements on just how much stronger Goku becomes by transforming. I think I figured out a way to reconcile these.

During Goku's first transformation he indeed becomes 50x stronger than his base... or his old base. The transformation didn't just multiply his power by 50, but increased his natural power 5-fold then multiplies by 10-fold (temporarily) on top of that. So now he'd look like this:

• Normal Goku (15,000,000)
  Super Saiyan Goku (150,000,000) (10x increase)

Ah, but what about Kaio-ken? Why wouldn't Goku just use it x20! Then he'd be twice as strong as a Super Saiyan! Well, I think we need to look to another big strength increase, Gohan's in the Majin Buu arc where his Super Saiyan forms don't do anything! I think this is because those forms are actually still multiplying off his original base, even after the boost in power.

• Gohan (A)
  Gohan (B) (Way stronger than x10 Gohan (A))
  Super Saiyan Gohan (Gohan Ax10)

Even if he uses Super Saiyan, it's still weaker than his 'new base', effectively giving him no strength bonus, just a waste of ki.

So Goku's Kaio-ken multiplications are still multiplying off his 'old base' while his Super Saiyan transformation is multiplying off his 'new base'

• Normal Goku (15,000,000)
  Normal Goku (Kaio-ken x10) (30,000,000)
  Normal Goku (Kaio-ken x20) (60,000,000)
  Super Saiyan Goku (150,000,000) (10x increase)

Even if Goku used Kaio-ken x40, he'd still be weaker than his Super Saiyan form, so I assume he just gave up on that technique.

Now there's the problem of his Super Saiyan transformation going from a 10x increase to a 2x or 3x increase in the Buu arc. However, since I've established Goku's power as rising 5-fold after transforming into a Super Saiyan then his new form being a 10x increase on top of that, we can assume that this is true for Super Saiyan 2 and Super Saiyan 3, but if these new forms are a 10x increase, then the original Super Saiyan (or Super Saiyan 2 circa Super Saiyan 3) must now become a lower multiplier (and guess what, halving the Super Saiyan increase with each successive transformation ends up with a 2.5x increase on Goku's base form, the perfect number between the probable 2x or 3x I established earlier):

• (note: these battle powers are all assuming that Goku didn't gain any strength other than what he got from the Super Saiyan transformations to make everything super simple)
  
  Normal Goku (3,000,000 BP/10 Kiri)
  
  Normal Goku (15,000,000/48 Kiri)
  Super Saiyan Goku (150,000,000/480 Kiri) (10x)
  
  Normal Goku (75,000,000/240 Kiri)
  Super Saiyan Goku (375,000,000/1,200 Kiri) (5x)
  Super Saiyan 2 Goku (750,000,000/2,400 Kiri) (10x)
  
  Normal Goku (375,000,000/1,200 Kiri)
  Super Saiyan Goku (937,500,000 BP/3,000 Kiri) (2.5x)
  Super Saiyan 2 Goku (1,875,000,000 BP/6,000 Kiri) (5x)
  Super Saiyan 3 Goku (3,750,000,000 BP/12,000 Kiri) (10x)

Bonus:

• Super Kaio Ken (x2 on top of whatever the original Super Saiyan's multiplier is or equivelant to Super Saiyan 2, although massively less efficient I suppose)

If you guys see any holes in this (or ways to improve) please do tell!


I know Toriyama never cared about any of this. It's still fun to see if you can make sense out of it all, though.