The camera will continue to adjust focus almost until the instant of exposure. One reason is that a moving subject may escape the focus target at the moment you press the shutter release. Another reason is that although autofocus lenses respond in fractions of a second, the subject may be moving faster than the focusing motor can adjust focus. Finally, there is a lag between the time you press the shutter and the time it takes for the camera to move the mirror out of the way and expose the film. At least one camera is programmed to take this time lag into consideration along with the speed and direction of the subject-and adjust focus so that it is correct at the very instant of exposure.
Sports are a natural for action photography.
The main concern is to watch for the most opportune moment to snap the shutter as the action takes place. This is where an autowinder or motor drive comes in handy because you can take pictures rapidly.