Fold one of the strips in half; it might already have a crease. Thread the needle and poke it through both layers of rubber near the fold. Slide the rubber strip down the thread, leaving about a four inch tail. Repeat with a few more strips; I used thirteen here.
Pull both ends of the string together so the strips form a tight circle. Pull tightly and tie, but don't snip the string. You'll notice that, due to the knot, some strips are closer together than other strips. Wrap the string tightly around the ball between strips that are close together to help space things out more evenly.