Spacial awareness, or at least table tennis specific spacial awareness, can be improved with practice, and hours spent playing, in my opinion.
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Good players also have excellent peripheral vision or awareness so they have a sense of where their opponent is while at the same time getting ready to hit the ball.
I believe that the pros, who typically practice about about 6 hours a day, subconsciousness learn to read cues from the opponents, rather than watching the ball all of the time. It is like a professional cricketer, baseball or tennis player knowing where the ball is going, as they know where to look on the opponents body, and through the power of practice, their brains learn how to process the information to create this illusion of players seemingly knowing where the ball is going before it is hit. Practice and repletion help a player play shots and intuitively knowing where the next ball is going to be hit.
As an example, there is Desmond Douglas, regarded as the player with the greatest reactions. When faced with a basic reactions test at a University, which involved touching pads when they lighted up, he finished bottom in his team, even below the manager. His innate reactions were very slow, however his table tennis specific reactions were super fast because during his formative years as a player, he played in a cramped classroom, which forced him to play very close to the table, sharpening his reactions. He played in these conditions for about the first 4 years of his table tennis career. That is how a man with slow innate reactions gained the quickest table tennis specific reactions.*
Nowadays, multiball training is used to coach the next generations of players. The real advantage with multiball is the feeder can always push the player to the outer limits of his reaction time. Over time, this leads to increadible reaction times and spacial awareness the top players have (players often extend the table by half a table width), because players reactions and footwork patterns are always pushed to deal with what the feeder is giving the player.
That is, in my opinion, why top players have the Superior reaction times and spacial awareness that they have.
* Source - Bounce, Matthew Syed