Drop a baseball on the floor and notice how high it bounces. It bounces a little, but not much. Now hold the baseball on top of the basketball. Drop the two balls together and notice what happens. The baseball will bounce off the basketball and fly off over your head. Try the same thing with the other balls you've gathered and see which one bounces best.
To get a feel for what's going on here, drop the basketball on its own and notice how high it bounces. Then drop the basketball and the baseball together and notice how high the basketball bounces. When you send the baseball flying, the basketball doesn't bounce as high. How high the basketball bounces is an indication of how much energy (in this case, kinetic energy, the energy of motion) the basketball has. When the basketball sends the baseball flying, the basketball doesn't bounce as high because it has transferred some of its energy to the baseball. This may look like a party trick, but it's really an important demonstration of one of nature's fundamental laws: Energy can't be created or destroyed. All you can do is move it around, change it from one form to another.
What does all this have to do with baseball -- or sports in general? When you bounce a baseball off a basketball, you are transferring energy from the deformation of the basketball to the baseball. When you bounce a baseball off a bat, you are transferring energy from the bat to the baseball. Even though tennis balls and Superballs ordinarily bounce much better than baseballs, we found that the baseball actually bounced better off the basketball. How well a ball bounces off the basketball has to do with timing. When the basketball hits the floor, it squashes a bit. When it springs back to its original shape, it pushes off the floor -- it bounces. The baseball (or tennis ball or Superball) does the same. To get the maximum bounce when you're bouncing a ball off a basketball, you want the basketball to spring back to its original shape at just the right time to give the other ball a push as it springs back to its original shape. If the second ball squashes and springs back too fast, it'll already be gone by the time the basketball tries to give it a push.