Snooker shot - does margin of error increase or decrease as the target angle increases? There is a perception (widely held) in snooker that a straight shot is more difficult than an angled shot. There are many forum discussion about this, and the reasons are usually accepted to be psychological. 
But I was wondering, is there a mathematical reason for it. Is the margin of error greater when the shot being taken is at an angle? 
Example - if the white ball was 1 degree off target on a straight shot, and one degree off target on an angled shot (same target for both shots), and each shot hit at the same speed, would the red ball travel off line to the same extent?

Let the ball be radius $r$ and distance between balls $d$. Let $\theta$ be angle white is struck from line between centre of balls and $\phi$ direction red moves from line between red ball and white before struck. Then get $2r sin(\theta + \phi) = d sin(\theta)$. Call $a=\frac{d}{2r}$. This gives $\frac{d\phi}{d\theta}=-1+ \frac{a cos(\theta)}{\sqrt{1-a^2 sin^2(\theta)}}$. This represents the ratio of the error in the direction of red to the error in hitting the white. It increases monotonically from straight shot to a fine cut.  If $d \approx r$ then this will not hold true as the target spot on the red is further away for a cut compared to a straight shot.
