One of the things that intermediate players do all the time is try to move the cue ball around the table using high english with the object ball near the rail. In the diagram the black line shows what they are trying to do, and the red cue ball line shows what really happens. Using that little bit of high right with the object ball near the rail is just asking for trouble.

The next time this shot comes up, they hit the cue ball harder to get more power, and the result is the same or worse. What is going on here?

The cue ball has two forces in it, the forward force and the rotational force. This rotational force is what happens when a ball is rolling and is not english or spin, which comes from hitting the cue ball off the vertical axis.  What happens when the cue ball hits an object ball fairly full is that the most of the forward force is transferred to the object ball, but the rotational force stays in the cue ball. 

When the cue ball goes forward and hits the rail, the rotational force keeps pushing the cue ball towards the rail, bending its path more toward the rail and causing the cue ball to come up short of its target. 

The secret to moving the cue ball when the object ball is near a rail and the hit is full on the object ball is to use just side or low spin. This gets the cue ball off the rail smoothly and up the table on the track you want.

This effect of high near the rail is not necessarily bad because we can use it to play position as well. Here is an example of using this effect to get a good position from a difficult spot.

Using high near a rail we can hit the one ball full and bend the cue ball forward after it hits the rail to go down table and fall on the 2 ball for position.

Here is one more example that you can use in an 8 ball game.

I suppose you could slow roll the cue ball, but that shot has all sorts of problems. The cue ball could roll off, or bounce a little off the rail and not leave a shot. Likewise a draw or stun shot could turn the cue ball loose or hit the 8 and not leave you a shot. 

I like using the high near a rail effect to hit the 2 ball full in the face with a high ball. The full hit takes most of the forward force out of the cue ball and just leaves the rotational force, which bends the cue ball around the 8 ball, leaving a good shot on the 8.

Remember to chalk your tip, use a level cue and stay down on the shot when you are shooting this type of shot.