Bolo bat

The Bolo bat was a child's toy popular in the 1930s through the 1960s. It consisted of a round wooden paddle-like bat with a handle, not unlike a ping-pong paddle, attached to the center of which was a piece of elastic band about three feet long. Attached to end of the elastic band was a rubber ball about an inch in diameter.[1]

The child would bat the ball as far as the elastic would allow it to travel. When it reached the furthest distance from the bat that the elastic would allow, it sprang back at the bat where it was hit again and again. The object of the game was to see how many times the child could hit the ball and have it return and be hit again. Children competed against themselves and others for the greatest number of successful hits.

This is possibly the same thing as a paddle ball.