A puck can pretty easily travel something like 30-40 m/s, and shots are regularly taken 4-5 meters from the net.
Goalies have, what, 1/10th of a second to track and evaluate the shot and make a qualified save. If that was pure evaluation and reaction we would be far too slow.
I also think most people who've played goalie in any sport know that you get a _sense_ for where the shot is going. High, low, left, right etc so it's not just guesswork and statistics either.