A bounce has two parts. The court returns a fraction e of the vertical speed (the coefficient of restitution) and takes horizontal speed through friction μ. If the ball slides through the whole contact:
If friction is high enough it starts rolling before it leaves, and the exit is set by angular momentum alone: v_x' = (3 v_x + 2 R ω)/5 for a thin shell.
Pace rating
The ITF's court pace rating is CPR = 100(1 − μ) + 150(0.81 − e): low friction and a dead bounce mean fast. Grass (CPR ≈ 48) keeps 90% of a 200 km/h serve's speed and stays low; clay (≈ 24) keeps 85% and lifts. The receiver's budget differs by about a hundredth of a second, which is the return.
The same serve on five surfaces. Grass hands the receiver 153 km/h and a low ball; clay takes eight km/h off it and sits up half a metre higher.