A groove is a furrow or channel, a long narrow indentation. The batter is feeling the way his bat disturbs the air as he swings. He is imagining or feeling the track of his bat as it moves through the resistance of the air.
From the perspective of a batter, a baseball traveling from the hand of the pitcher (at very high speeds), appears as a white streak. Most pitchers cause the ball to travel with some kind of added movement. In this case the ball is sinking, creating the flashing slant of your quote.
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