Using a cue stick, I strike a pool ball on a pool table vertically downwards, slightly off centre. What is the motion of the ball? I was playing a game of pool when I struck a ball directly from the top albeit not directly on its centre. It was a bit like .
The ball moved left and rotated anticlockwise. I know that the net force on the ball was radial in direction and had equal horizontal and vertical components. Directly following this, ball experienced a leftward translational force and a downward translational force which is cancelled out by the contact force. I don't know why the ball rotates anticlockwise, the effect of friction (between the table and the ball) on the ball, and from what axis I could regard the ball to rotate from. I also understand that there are both clockwise and anticlockwise torques on the ball, but I don't understand why the anticlockwise torque prevails.
How and why does the ball rotate?
 A: The cue imparts a force to the left and also a clockwise spin.  There is also a down force on the ball, but that is cancelled by an upward force from the table.
So initially the ball will move quickly to the left, also spinning clockwise.
As it slides along the table, there is a friction force on the ball acting at the bottom to the right - this is an anti-clockwise torque.  This force then reduces the clockwise spin and also slows the ball.  This part of the motion lasts for just a short time, for example half a second.
When the clockwise spin is reduced to zero, the ball is sliding along the table to the left, but again there is the anticlockwise torque and that makes the ball start to spin anticlockwise.  The anticlockwise spin is increased until the ball can roll without sliding to the left.
The friction force is almost zero during the roll, but the ball is left with an anticlockwise spin and a translational motion to the left. This part of the motion is presumably what you've seen and can last longer, until gradually resistive forces, some friction and air resistance bring the ball to rest.
You might find this video interesting, https://www.youtube.com/watch?v=RwjZAjjrG_k  9mins 40s has a similar shot, the spots on the cue ball help the viewers to see the spin.
...and couldn't resist adding this:  a similar shot where the clockwise spin prevails (which prevails depends on the exact angle of the shot), Jimmy White, 2 mins 10s, trying to get to the brown
https://www.youtube.com/watch?v=PGmGBiftpC4
