The batter has to estimate the necessary position by doing an impressive amount of computation. All a batter has to go on is a view of the unfolding pitch, which you can think of as a series of pictures giving the position of the ball. From the change in position between successive pictures, the batter can estimate the speed and direction of the ball’s motion. That estimate gets refined and updated over the third of a second or so in which the batter gets to track the ball before the swing needs to start.

It’s nearly impossible to overstate how difficult a problem this is– just being able to reliably pick the baseball out of a complicated visual field is an impressive achievement. Human brains are highly optimized for this sort of task, though, which is why so many “citizen science” projects revolve around identifying patterns in images. We’re also programmed to make the necessary on-the-fly calculations to estimate the current velocity and future position of the approaching ball. While professional baseball players have honed this skill to just about the highest level possible, the basic ability seems to be wired into our brains at a pretty deep level– my three-year-old son can catch a gently tossed ball more often than not, and his failures are more a matter of imperfect coordination of his motion than a failure to correctly predict where the ball will be.