Warning: this is a nerdy post for a pool forum:grin:. I hope some folks will wade through and comment.
I think the difficulty of potting a ball from the spot is directly related to corner pocket width (the distance between the points), starting at pocket size = ball size, the smallest pocket size for which it is possible to pot a ball.
In the same way, we can look at a shot along the rail. In this case the difficulty is based on how far the back point of the pocket stands out from the rail compared to three-quarters the size of a ball, since that is what needs to fit in for the ball to enter the pocket from the rail.
We can figure out what the pocket size is for a given point distance from the rail, since the ratio is based on a right isosceles (45:45:90) triangle, where the proportions of the sides are 1:1:sqrt(2). For a 1.7" corner point, the pocket size is about 2.4". So with very tight pockets, the difference in difficulty between spot and rail shots is not very large.
Working towards larger pockets, spot shots should get increasingly relatively easier than rail shots, since every 1" increase in pocket width only buys 0.7" increase in point distance from the rail. Does that make sense?
It would be interesting to play on a table where shots from any direction were of closer to the same difficulty; that would seem to be with pockets much smaller than typically used in the US.
I would like to hear from people who could confirm or deny from practice that rail shots get *relatively* easier as pocket size gets smaller.
I think the difficulty of potting a ball from the spot is directly related to corner pocket width (the distance between the points), starting at pocket size = ball size, the smallest pocket size for which it is possible to pot a ball.
In the same way, we can look at a shot along the rail. In this case the difficulty is based on how far the back point of the pocket stands out from the rail compared to three-quarters the size of a ball, since that is what needs to fit in for the ball to enter the pocket from the rail.
We can figure out what the pocket size is for a given point distance from the rail, since the ratio is based on a right isosceles (45:45:90) triangle, where the proportions of the sides are 1:1:sqrt(2). For a 1.7" corner point, the pocket size is about 2.4". So with very tight pockets, the difference in difficulty between spot and rail shots is not very large.
Working towards larger pockets, spot shots should get increasingly relatively easier than rail shots, since every 1" increase in pocket width only buys 0.7" increase in point distance from the rail. Does that make sense?
It would be interesting to play on a table where shots from any direction were of closer to the same difficulty; that would seem to be with pockets much smaller than typically used in the US.
I would like to hear from people who could confirm or deny from practice that rail shots get *relatively* easier as pocket size gets smaller.
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