I noticed that Ha Na Jang don't watch the other players putt. Also some golfers when they hit a good drive right away pick up the tee.
I have always done what Hall of Famer Inbee Park does. She watches the other players putt to gather information. She also watch the flight of her drives until they land.
I watch the other player putt, to see what their putter head does when it make contact. Do they decelerate, open the head, close the head or just make a bad putt. I always watch my drive until it lands to see what kind of spin I put on the ball.