Why does a bouncing ball rise to a lower height with each bounce? What energy conversion is taking place?

So we want to know why the does a bouncing ball rise to a lower height with each bounce. So lets say the ball is first on some height h. There it has potential energy Ep=m*g*h. Then as the ball starts falling to the ground the energy converts to kinetic energy Ek = (1/2) * m*v^2. When the ball falls to the ground, the kinetic energy transforms to elastic energy because the ball deforms as it hits the ground and some small quantity of heat. The heat goes to the air and to the ground so it gets removed from the system. So there is less energy in the system to be converted back to kinetic energy as the ball starts to rise in height again. Thats why the ball is not able to get bact to the same height as it started from.