Sport ball with energy absorbing foam at varying locations

An inflatable sport ball, such as a soccer ball, a volleyball, a basketball, a football or a playground ball, is provided with a self-contained inflation mechanism for inflating or more likely adding pressure to the ball. The mechanism is a pump which is inside the ball and which is operable to pump ambient air into the ball. Energy absorbing foam panels are used at varying locations to maximize rebound performance by minimizing the rebound height differential. The foam panels may be of different types and/or thicknesses.