The Clock Face
Where to address the cue ball?
Although there are many points at which you can address the cue ball, it is easy to consider the cue ball as a clock in order to describe the aim points.
It is best to address along the vertical bisecting line of the cue ball if the shot permits, as this means that you do not have to allow for any side that you are imparting.
By addressing below centre the tip stays in contact with the cue ball for a fraction of a second longer - in effect the cue ball does not move away from the tip quite so easily as the tip follows through. This means more 'action' is put on the cue ball.
It is a common myth that to get maximum side on the cue ball you must address at 3 or 9 o'clock. This is not true! By addressing below centre at around 4.30 or 7.30 you will get just as much side on and you will get less swerve (and squirt) on the cue ball.
Newton's 3rd law
This states that "to every action there is an equal and opposite reaction" and in Billiard terms this means that the further to the side you address the cue ball the more it will push off line (squirt) and the more difficult it will be to judge the line of the shot.
When you impart side it is the inner edge of the tip that is in contact with the object ball, not the centre of the tip.
Getting the most 'action' on the cue ball
To get the most combined screw and spin on the cue ball it should be addressed at either 4.30 or 7.30 and this is simply a matter of trigonometry. At 4.30 and 7.30 the tip strikes a point that is 45° from either the horizontal or vertical bisecting line on the cue ball. Cosine (or Sine) 45 = 0.71 so the cue ball gets 0.71 of the maximum screw and 0.71 of the maximum side, giving a total of 1.42 of combined screw and side. This is not totally accurate as striking below centre allows you to get more side on, but nevertheless will suffice for this explanation. At 5 or 7 o'clock the tip strikes a point that is approximately 60° from the horizontal bisecting line and 30° from the vertical bisecting line on the cue ball. As Cosine 60 = 0.87 and Cosine 30 = 0.5 (you could use Sine if you wished) the total amount of combined screw and side would be 1.37, which is obviously less than 1.42.