People can hit rapidly moving balls with amazing precision. To determine how they manage to do so, we explored how various factors that we could manipulate influenced people's precision when intercepting virtual targets. We found that temporal precision was highest for fast targets that subjects were free to intercept wherever they wished. Temporal precision was much poorer when the point of interception was specified in advance. Examining responses to abrupt perturbations of the target's motion revealed that people adjusted where rather than when they would hit the target if given the choice. A model that combines judging how long it will take to reach the target's path with estimating the target's position at that time from its visually perceived position and velocity could account for the observed precision with reasonable values for all the parameters. The model considers all relevant sources of errors, together with the delays with which the various aspects can be adjusted. Our analysis provides a biologically plausible explanation for how light falling on the eye can guide the hand to intercept a moving ball with such high precision.