The theory behind magic was simple. Everyone had a 'Willpower' pool, which was used to impose the will of the Noble upon the world. By doing so, fundamental laws could be altered, truths could be denied, and basically, bullshit could happen. Be it in the form of 'I want a hurricane right here and right now' to 'I want a fire snake to burn my foes'. The Mage used his Willpower pool to 'buy off' the spell, and in order to select the spell, the Mage had to concentrate on it and chant.
The 'magic system' however, was ruthless. Karin was the king of hacks, and she promptly deserved her status as such. You needed a wand you grew accustomed to, and you needed to concentrate on it. Sure, you could grow accustomed to a pitchfork, or to a harp, or to a large war hammer, but you also needed to train throwing spells with them. Your pool regenerated after resting and sleeping, which meant that you couldn't just keep on training throughout the day, and the 'amount' you were born with didn't change.