The air pressure in a ball will determine how quickly is responds to being bounced or kicked. Higher pressure would make the ball too fast and difficult to control, while lower pressure would make it too slow and erratic.
The physics behind this is expressed in the following formula: pressure equals force divided by area. Air inside a ball is pushing outward in the same way that atmospheric pressure in the world around us is pressing in on everything.
The more air there is in a ball, the greater the number of molecules that strike its inner wall and the greater the frequency with which they will do so. The action of the molecules intensifies as the air pressure is pumped up and decreases if air is allowed to escape through the valve. As the air pressure in a ball is increased, it becomes harder to press it in with your hands. Eventually it becomes almost impossible. The air pressure being exerted inside the ball is getting closer to the atmospheric pressure outside it.
A simple experiment can be carried out with three basketballs. Use a pressure gauge to measure the air pressure in each. Keep one at the pressure required by the NBA. Overinflate one of the others by 25 percent and underinflate the third by 25 percent. Drop each of them from a three-foot height. Under laboratory conditions, the bounce differentials can be measured exactly, but it will be plain to see that the under-inflated ball does not bounce as high as the NBA standard pressure ball, while the over-inflated ball bounces higher.
When a basketball player bounces the ball, he transfers energy from his body, arm and hand to the ball. The greater the pressure in the ball, the less of that energy will be dissipated when it hits the floor and the greater will be its ability to bounce higher.