Deflecting is something very fun to do as a drill or for fun like flip or pepper.
Logically, deflecting is not faster than a quick transfer. The ball needs time to deflect from the glove to the hand. If you are merely stopping and covering the ball with your throwing hand, this is faster. Yes, it looks cool and looks fast, but it is difficult to keep your rhythm when you do this.
The best person I have ever seen at deflecting is "Rafi" down at the Bucky Dent Baseball School in Delray Beach, FL. He can go behind his back, through his legs, pretty much anything he wants. While this exhibits incredible glove control, I have never seen it happen in a game nor would I ever recommend doing this in a game.
In the relay throw mentioned above, I'd love to see video of that. I would bet he has his feet moving much faster than his hands, putting his body in a position to make the fast transfer and throw. I don't doubt that he was very fast, but I do doubt he deflected the ball as my previous video showed.
Lots of great info here! 