The Saiyans are the Dragon Ball universe's powerful race of space warriors, equipped with adaptive physiology and a warrior's drive to propel them to unbelievable heights of combat strength, despite their limited remaining number. The Saiyans have survived extinction by having kids, but common wisdom would assume that a person with half the amount of Saiyan blood would have half the amount of Saiyan power. But is that actually true? In Dragon Ball, half-Saiyans might actually be naturally stronger than their full-blood parents but, if that's so, then how come the pure-blood Saiyans are typically shown to be more powerful?
A mighty race of warriors, the Saiyans are naturally driven to become stronger fighters and to pursue greater challenges. They're capable of increasing their power in various ways, including intense training and even healing from near-fatal wounds, adapting their bodies to weather the attacks that nearly took them out. Saiyans can even achieve forms like Super Saiyan through rigorous training, allowing them to surpass any previous limits. Saiyans like Goku and Vegeta have over the years become among the most powerful Saiyans in the universe -- simply through training harder and harder.
However, there's a notable difference between full-blood Saiyans and the children of Saiyans and humans. Half-blooded heroes like Goku's son Gohan or Vegeta's son Trunks are powerful in their own right, and aren't hindered by their human sides at all. In fact, their half-blood status actually increases the overall power of the half-Saiyans. It's something that even the Saiyans are aware of, as Vegeta and Nappa noted any children they had on Earth could prove too powerful for them to contend with during the "Saiyan Saga" in Dragon Ball Z.
This is proven repeatedly throughout Dragon Ball Z, especially with Gohan, Goten and Trunks. Gohan is quickly established as a prodigious in terms of raw power despite his young age. By the time he's eight, he's keeping up with far more mature and deadly foes. He even was able to achieve Super Saiyan 2 before anyone else, tapping into his potential to overtake even his father during the "Cell Saga." Likewise, Future Trunks was quietly able to surpass his father's power during the same story arc, and both Goten and Kid Trunks proved capable of going Super Saiyan despite their lack of experience in fighting over the course of the "Buu Saga."
Naturally, half-Saiyans have more raw potential than pure-blood Saiyans, starting with their parent's last strongest form as the baseline of their power. However, their half-blood status comes with an additional wrinkle, as they lack the fighting drive of their full-blooded counterparts. This is why Gohan eventually becomes more interested in studying and education than he does with fighting, developing a more pacifistic attitude and only fighting when he needs to. This means that while Gohan could become stronger than Goku if he trained more, he isn't as driven to train as Goku. By contrast, Goku and Vegeta are almost pathologically driven to become more powerful. This means Goku and Vegeta will often train far more than their sons, and will as a result typically be far more powerful, to the point of achieving advanced forms like Super Saiyan Blue.
While half-Saiyans could be more powerful in theory, it's an interesting behavioral difference between the full-blood Saiyans and their children that helps truly define the limits of each party. Half-blooded Saiyans lack the drive to become stronger -- and that means they'll often be playing catch-up to their fathers despite their own impressive power.
