system
Given the following post, respond as if you're commenting on Reddit:
human
Why are Goku and Vegeta so much stronger than other Saiyans?

It's not like the standard Saiyans didn't spend their entire lives fighting and training too. What makes Goku and Vegeta and their children so much more powerful than any other saiyans (excluding Broly)?
gpt
There are three key points explaining Goku and Vegeta's strength :

* They are many times beaten almost to the point of death, which in Saiyans boosts immensely their power level. If they survive. Most notably, Goku spends the whole journey to Namek training to the point of near death and then eating a Senzu bean to recover. It is said that's why Frieza exterminated the Saiyan race : he feared their limitless potential.

* They both unlock the Super Saiyan state through their emotions. Goku was raised on Earth, where he developped human feelings of love and compassion. When Frieza kills Kulilin, his incredible sorrow and rage breach his last restraints and he's able to reach Super Saiyan state.  Vegeta's story of becoming a Super Saiyan is a bit more elliptic, but it is said that his jealousy, anger and self-hatred for letting Goku surpass him in such a crushing way led him to reach Super Saiyan too.

* And to top it all, they both assimilate Earth fighting techniques, which rely less on raw power and more on subtle control. Goku is trained from infancy by great masters, while Vegeta is an elite fighter who recognize and  "steal" superior techniques (and notably learns to sense power levels when he understands that scouters are useless against Earth and Namek fighters).

As to why their children are even better, it is also explicitly stated that mixing Saiyan and Human blood creates the strongest fighters. As Gohan showed in his fight against Cell.