What do we call a form of inductive reasoning where a student believes that her softball team's recent winning streak is due to the fact that she has been wearing her good luck jersey?

I believe the answer is: causal reasoning.

causal reasoning refers to the thought process that believe a certain pre-determined idea would lead to a certain effect.
From the scenario above, the player is already believe that her shirt would bring her victory, so she would see every outcome of her game as a result of her superstition rather than seeing objectively.