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[Harry Potter/General Fantasy]What makes one wizard more powerful than another?

If magic just involves saying the right words and making the right gestures, how is anyone more "powerful" than anyone else? I vaguely remember Moody (well, the fake Moody) saying none of the students were powerful enough to kill him with avada kedavra, but... why not?
gpt
Much of magic is based on skill - saying the right words and making the right gestures are harder than they sound. There's unquestionably an element of skill, as Neville Longbottom demonstrated when he went from trash to a very skilled fighter from fierce dedication and intensive practice.

Some spells have emotional or intentional components; the Killing Curse and Patronus Charm both have *very* different mindsets that are required to use effectively.Voldemort, one of the otherwise most powerful wizards to ever live, couldn't cast the meanest Patronus because he'd never been happy, while Harry (a fairly talented teenager) cast an extremely powerful one because he spent his whole (thoroughly non-magical childhood) clinging fiercely to joy. The Imperious Curse seems to be remarkably easy to cast, but is experienced as a sheer battle of will.

More generally, though, there's enough variety and types of magic that "more powerful" isn't a very meaningful phrase. Natural inclination plays a part here; there's a reason a wand that's good for charms picked Lily Potter, who was known for charms.

Blasting off killing curses with raw force of hatred is one type of power.

Brewing finicky potions that confer extraordinary luck is another. 

Clever and well-executed utility of Charms was a huge component of Britain's First Wizarding War - the clandestine, ever-shifting battlefields of the conflict needed powerful Charms to conceal, uncover, communicate secretly, hide objects, and otherwise fight a war in the shadows.

Gilderoy Lockhart secured fame and fortune by having the charisma to get stories out of better wizards and the skill with memory charms to steal them, which is a type of power. 

Even Neville (before he got good), renowned for being fucking terrible at magic, was so gifted with magical plants that he was quietly assisting a decades-long expert in the background. There was so much crazy shit in those greenhouses. Dark Herbologist Neville could have easily maimed or killed Malfoy by putting on a pair of earmuffs and lobbing a mandrake into the bathroom just in case the Devil's Snare Neville left in the toilet didn't choke the life out of him first. And that's just from what *first and second years* studied. That's fucking *power* without even touching a wand.