I'm not gonna do that here. This blog will take as given that a good magic system is internally consistent and has rules that both the characters and the audience can figure out. I'm going to take a step further and break down the different types of internally consistent magic system in a way that might help some of my writer friends with their worldbuilding.
Dungeons and Dragons has, broadly speaking, three types of magic that are representative of the vast majority of fictional magic systems. They are:
- Innate magic, used by sorcerers
- Learned magic, used by wizards
- Granted magic, used by clerics and druids
The Abhorsen trilogy has learned magic. Anyone can learn it if they study hard enough, and it is taught alongside other subjects as part of a normal school curriculum. Some people are better at it than others, but only to the degree that some people are better at math or writing than others. There are no chosen ones, only choosing ones (and those whose parents chose it for them).
Lord of the Rings has granted magic. Magical abilities come from gods or godlike nature spirits. Most granted-magic settings come with their own gods, or a variation on classical European pantheons; but some, including the Alpennia series, integrate magic into the mythology of Christian saints and miracles.
Many magic systems that look like a combination of these types are actually primarily one or the other. For example, not all magic systems that require training or active study are learned systems. In fact, most "school of magic" settings, such as Harry Potter, Akata Witch, and X-Men, are innate, and the purpose of the school is to teach magical children to gain some basic control over their power so that it doesn't kill them before they have a chance to learn to use it properly.
Likewise, not all systems that involve making contracts with extradimensional beings are granted systems. Young Wizards is, because becoming a wizard requires that you be sought out by the One Power and agree to accept its faith in you; but Bartimaeus is not, because even though its wizarding society is built on the backs of enslaved demons, the wizards themselves must study for years to even get to the point where they can bind the least powerful demon. It's a learned system.
Here are some settings that either have real hybrid systems or multiple coexisting systems:
- Terry Pratchett's Discworld series begins with rigorously academic learned magic and then introduces an innate system in which the eighth son of an eighth son is always a powerful wizard, and his eighth son is so powerful that there's a good reason for wizards to be celibate. These systems interact in interesting ways, especially in the early installments Equal Rites and Sourcery.
- Star Wars has gone back and forth between innate (anybody up for a blood test?) and granted sources of Force-wielding ability. The Last Jedi makes it officially a granted system with a large helping of Conservation of Ninjutsu: the more users of one side of the Force there are, the weaker each individual's power is. This explains a lot about the prequels: the Jedi were ineffectual because there were so many of them, while the Rule of Two allowed individual Sith lords access to much more power at any given time.
- Michelle West's House War series and its spinoffs have both gods granting magical ability and schools teaching it. This one might actually be a real hybrid, since the university faculty includes demigods who can call on their divine parents for help with their research.
- Avatar: the Last Airbender appears to be all three at once: there are four ethnic groups, each with a different innate elemental power, but those powers can be extended into new domains through training (think metalbending and bloodbending), but some of these powers are also believed to be divinely granted, and gods and spirits occasionally show up and interfere with the workings of the world.