In episode 2 of the anime, Saya crashes her broom into Elaina and then steals her witch badge. Ostensibly, this is because Saya is lonely and she's trying to trap Elaina in the Land of Mages with her as her magic teacher. But under close scrutiny, this plan doesn't really make sense. It's quite hard to believe Saya planned out the entirety of the events of the episode. It would make sense if she improvised a lot after failing to do whatever it was she was originally trying, but I don't see how she could have guessed everything would happen the way it did, given she didn't even know Elaina. For that matter, who was her intended target? The first witch she saw? Or Elaina specifically?
One thing I recall when watching the episode, is that when Elaina first shows up at the inn Saya is working at, Saya apologizes profusely and begs Elaina not to hurt her. Given the sudden burst of anxiety after their mostly cordial farewell, I wondered if perhaps Saya thought Elaina had figured out she'd stolen her witch badge at this point. It's not possible to tell if that's the case, but to me it points to the possibility that Saya didn't have some kind of master plan that went perfectly. I would also suspect she didn't want Elaina to fly away during their first encounter before she'd even asked her to stay at the inn.
I don't think the show had much time to explain the plan, as all Saya really says when Elaina confronts her about it is that she was really lonely. Do the books elaborate on what she was trying to accomplish by crashing into Elaina, what her whole plan was, and whether everything went exactly as planned?
Basically, I want to know what Saya was thinking, and whether the books have more information on that than the show.