I'm interested in quantifying what level of precision a snooker player has to work with to comprehend the level of skill on display and I suspect at least there is a mathematical perspective to it. For the sake of simplicity, I would suggest ignoring physical factors such as any resistance created by the cloth, etc which I appreciate is unrealistic (and indeed adds more factors).
Assume a cue ball 1m from the object ball and the object ball 1m from the pocket. Pocket is 86mm wide and ball is 52.5mm diameter and balls lined up in a straight line.
Then same dimensons, but pocket is at varying degrees to the object ball.
What is the margin of error in striking the cue ball so that a the whole ball will fall into the pocket (assuming that any contact with the side of the pocket causes the pot to miss, or maybe allow that variable to be tweaked so that a target area > 86mm can be allowed for). Or put another way, how wide is the contact area between the two balls that will cause the ball to be potted / what is the precision of the angle at which the player sends the cue ball away with that will result in a successful pot?
How does this scale with distance?
My instinct is that the cue ball has to commence it's route to the object ball at a very high level of initial precision (perhaps best measured in angles)?
Clearly the answer is related to some of the work here Snooker shot - does margin of error increase or decrease as the target angle increases?
