The first thing that we're actually shown is Snape's modifications to the Draught of Living Death potion. Some of his modifications, like crushing the bean instead of cutting to release more juice, seem like reasonable things to try. Even adding juice from 1 extra bean seems like a reasonable thing to try.

However, the stirring directions (7 times clockwise, 1 time counterclockwise) seems absurdly specific. The directions say to stir twice clockwise. How do you get from "stir twice clockwise" to "stir 7 times clockwise and once counterclockwise"? How did he know to do 7 times rather than 6 or 8? Yeah, I know that 7 is a magically significant number, but 1 (the number of counterclockwise stirs) isn't, and neither is 2 (the number of stirs in the original directions), so really, I could ask how either of them came up with any of their numbers for stirs - it seems quite arbitrary.

Also, his Levicorups spell shows multiple attempts to get it right. How did he "figure it out" - guess at the incantation or something? What might his previous experiments have looked like, and what were the results likely to have been? Presumably, they had some effect given that he had written them down, but the fact that he crossed them out implies that successive attempts were better somehow. Better how, though?

TL;DR How did Snape figure out the stuff he had written in his book?


Probably because Snape was, like Dumbledore and Voldemort, incredibly smart and willing to tread off the beaten path. It's not that uncommon to invent new spells/magic things: Fred and George do it all the time for their magic shop. No offense to Fred and George, but if they can do it, Snape definitely can. Hermione doesn't do it because inventing new things/using untested spells is not approved by the ministry of magic (quote from HBP):

"So you just decided to try out an unknown, handwritten incantation and see what would happen?"

"Why does it matter if it's handwritten?" said Harry, preferring not to answer the rest of the question.

"Because it's probably not Ministry of Magic approved," said Hermione. "And also," she added, as Harry and Ron rolled their eyes, "because I'm starting to think this Prince character was a bit dodgy."

Inventing spells is also dangerous: Luna's mother died inventing a spell (from Order of the Phoenix: "'Yes,' said Luna simply, 'my mother. She was a quite extraordinary witch, you know, but she did like to experiment and one of her spells went rather badly wrong one day."). So you have to be willing to take risks and bend the rules, which isn't something that Hermione does often.

As for the specific process that is used to invent new spells/magic thingies: we never actually got a description of this process. This makes sense because the Harry Potter books focus on Harry Potter's perspective, and Harry never shows that much interest in the theory of magic. I'm sure if the books focused on Fred and George, we would get much more information about this.

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