The cerebellum is the part of the brain that controls procedural memory for motor skills, as well as muscle control. Part of becoming a skilled athlete involves constant practice. Not only does this develop muscle strength and conditioning, but it also ingrains sequences of motions into muscle memory so the competitor doesn't have to think consciously.
With every successive repetition of a motion or sequence of motions, the synapses of the muscles become more strongly linked, requiring less conscious thought to perform the action until it seems like a spinal reflex. It can never become a true reflex, because a neuronal connection goes to the cerebellum. Reflex actions such as blocks in martial arts are trained as a response to a stimulus. For example: the martial artist being punched or kicked at.
In tense situations, such as a buzzer-beating basketball shot or a free throw, it's tempting to think about the actions required to follow through. This, however, takes brainpower that would normally be used to automatically perform and makes the muscles work less fluidly. The cerebellum, specifically the prefrontal cortex, contains working/procedural memory and controls the ability to perform a majority of everyday actions such as walking or driving a car.