system
Given the following post, respond as if you're commenting on Reddit:
human
[Harry Potter] What determines a wizards 'power level'?

Hermione Granger is a good argument for it just being about the effort you put in. However, it does seem like some wizards have a innate or genetic advantage, which doesn't see to correlate with the power of said person's wizard ancestors, if they have any.

Why did half-blood Tom Riddle (hobo witch mother and muggle father, raised in a muddle orphanage)  have exceptional control over his powers even as a child, while pure blood Neville Longbottom (noted aurors as parents, raised by a witch) barely showed any magic at all?
gpt
Magical power is not genetic. 

When it comes to magic, you have it or you don't. That much is determined by genetics, true. However, the "magic gene" does not behave simply. It is unclear quite how it is inherited - it could be that it follows a Mendelian pattern and Muggleborns are actually born from Squibs (who would be the result of illicit affairs with Muggles). However, it could also be supernatural or extremely complicated - it could be that a magician mating with a Muggle will almost always produce a magician (since Squibs are apparently ridiculously rare), which implies magical influence on meiosis. Muggleborns and Squibs would be the result of mutations, which might be made more likely due to the presence of magic. 

Magical power is simply a result of knowledge, practice and intelligence. Intelligent and dedicated individuals like Hermione become powerful through understanding; Harry became fairly powerful by being forced into combat situations, giving him a lot of practice; Ron was raised in a family of wizards and is fairly talented (though lazy).

The *truly* powerful wizards and witches like Dumbledore are slightly different. These are individuals who have spent their lives delving into magic, who have read crumbling scrolls in the ruins of shattered libraries, bought endless drinks for half-mad adventurers in a shady tavern for some fragment of lore, who have studied relentlessly the secrets of magic. They are rare not for any unusual genetic trait, but for their combination of intellect, curiosity, dedication and longevity. It is a sad truth that most don't bother to make themselves into powerful magicians for the same reason that few Muggles dedicate themselves to becoming superb athletes, mnemonists, musicians etc. 


WARNING: fanfic, but well-supported by canon evidence e.g. Hermione and others being exceptionally powerful despite being Muggleborn, Voldemort being one of the most powerful wizards despite being half-blood, etc.