Well, I am currently taking martial arts, and really, there are skills I learned in non-combat sports that do help.
For example, in tennis, I liked to rush the net. You learn really quick to either block the ball back into the other side of the court...or dodge. The body motions are different, but you still learn timing and how to avoid getting hit.
Then there's the footwork. Stances change between 'normal' sports and martial arts, but you still need good balance and to be able to move any direction almost instantly.