Stiffness and mobility are often looked as isolated modalities but they are a complex interaction when trained. It would be convenient that one can just do some mobility drills or bridges to become a great athlete but that is far from the truth. Reducing muscle slack at key times and allowing controlled motion requires very good coaching abilities, hence why interns at various performance centers produce robots instead of cats. In horror, I observed an overly simplified deadlift without teaching or cuing back stiffness. We are back to the dark ages again. Pretension is building up enough force to resist the bully of gravity for a short period of time, therefore creating temporary force bridges along joints. An obvious example is skipping rope with those that are skilled. The small joint angles of the knee and little range of motion in the ankle complex allows people to bounce effortlessly, while those that are not skilled leak the forces out by allowing joints to melt into larger than optimal angles or apply less force over longer time periods. Some athletes are natural with stiffness and some are not, but it can be trained and that is our job. To get the best better and those that are not the best better.
Mobility is about keeping the internal resistance reduced so that the joint can flow without any restrictions besides the natural decelerators of the body. The speeds of mobility range from slow eccentrics to ballistic actions. The motions are natural but with over a hundred joints in the body, one must look at program design to cover the huge demands. Mobility is not a few PT exercises but integrated coordination. An example of this is a physioball walk-out (stomach on the ball in a push-up on the ground and crawling out hand by hand) with pointing of the toes and allowing internal rotation of the femur. A simple exercise will prepare for pushing actions and bridge the spine.
Training athletes to do movements that are athletic and intelligent will improve mobility and stiffness naturally and better. Teaching athletes to have a stiff back during a clean or having athletes do speed hops do reduce muscle slack is nothing new.