How Do Baseball Outfielders Know Where to Run to Make a Catch?

With the crack of the bat, the ball sails deep into the outfield. The center-fielder starts his run, moving back and to the right, trying to keep his eyes on the ball. His pace quickens initially, then slows down as the ball approaches. He arrives just in time to make the catch.

How did he know where to run and at what speed so that he and the ball intersected at the same exact spot on the field? Why didn't he sprint to the landing spot and then wait for the ball to drop, instead of running at a controlled speed to arrive just when the ball did?

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