Ball-batting tasks requires tight integration of high-speed visual tracking of the flying ball, immediate decision making on when and how to hit the ball, and precise and agile motion control. The so-called 'precision ball-batting' in this paper means not only to hit the ball, but also to send the rebounding ball to a specified target location. It is challenging for robots, but professional human players can do it very well. Therefore, precision ball-batting can serve as a testbed for modern eye-hand coordinate techniques of robots. This paper extends the authors' previous work on the precision ball-batting robot by upgrading the vision system and proposing a novel decision making procedure that combines the advantages of the physical rebounding model and the neural network model. Experimental results show that the successful rate of precision ball-batting increases from 13.75% in the previous work to more than 60% in this paper, while the rate of swing and miss decreases from 11.25% in the previous work to 0% in this paper.