The Academy of Quantitative Billiards
Billiards Quarterly Review is privileged and honoured to be in receipt of a number of articles produced at the Academy by members of its professorial staff. We are proud to present the first of these articles together with profiles of the authors.
Ivan Stevenage has been playing for 35 years and is an established figure on the Mini-Prix circuit where he can often be found at the bar after round.1 of the plate has been played. Recently retired from British Telecom, he much appreciates the cheapness of the beer and the friendliness of the people in the clubs, but he finds the game remains fascinating and elusive wherever he goes.
Brendon Carroll works in the chemical industry and would like to find the time to play regularly on the billiards circuit as the last time he played - Widnes - he found the bar (After round. 1 of the plate) very much to his liking. He long ago realised that for him, quantitative billiards may exist in the realm of pencil and paper, but seldom in that of the cue and the green table cloth.
It is well known that the top pockets play an important part in the compilation of a break in both billiards and snooker. This has led us at the Laboratory of Quantitative Billiards to ask the question: 'How Big, in actual playing terms, is a corner pocket?' The official templates for the pocket shape do not specify a measurement, but a distance of 3 1/2" (undercut excluded) between the cushions at the 'fall' of the slate is standard. Now, the ball diameter is 2 1/16"(52.5mm). The margin for error is thus 23/32" on either side of a ball aimed for the pocket centre; that is, about 3/4".
In practice, the margin is rather bigger than the figure just given, since, as is well known, a ball can strike the cushion first and still fall: for practical purposes, the margin for error can be regarded as 1" on either side, making the effective pocket width (cushion to cushion at the fall of the slate) about two ball diameters. It can thus be stated that the ball will drop if the position of the centre of a ball aimed for the middle of the pocket varies by up to one half ball on either side. So, from the point of view of the centre of the ball, the effective width of the pocket is about one ball diameter (Figure 1).
The length BC is one ball diameter.
The line BC one ball diameter long drawn at the fall of the slate in Fig.2 is part of the solution to the following problem: If one is cueing a single ball towards the pocket, how accurately must one aim to ensure that the ball drops'? The complete solution has also to take into account the distance of the ball from the dotted line and whether the ball is aimed towards the full face of the pocket, or towards a more-or-less 'blind' pocket. If only the former case is considered (although 'blind' pockets are readily dealt with), the answer to the problem is best given in terms of the angle at the apex of the triangle having the base-line BC (one ball diameter), and by the cue ball centre A (the apex). For example, if this angle is 2 degree, one has a 1 degree latitude in aim either way. (this, incidentally, is roughly the accuracy needed just to pot a ball from the pyramid spot into a top pocket). A more realistic problem which we are not yet in a position to consider concerns the winning or losing hazard, and is: What is the margin of error allowed in one's aim for one still to get the desired hazard? This problem involves separate computations for each ball involved and is deferred to a later article. It is, however, already possible to compare the ease with which certain shots can be made when these shots differ only in the final phase, as is the case with an in-off and a cannon. If the distance from the object ball to the pocket in the in-off equals that of the second 'leg' of the cannon, the relative difficulty of the two shots is the same as the relative 'widths' of the pocket and the cannon to the second object ball. The calculation of the latter width is a little deceptive, to the extent that Charles Dawson ('Practical Billiards') and Joe Davis ("How I play Snooker") both got the wrong answer. These two champions were each of the opinion that the width in question is three ball diameters, as a quick look at Fig. 1 indeed suggests; however, consideration of the positions of the centre of the cue ball in the two extreme cannoning positions gives the result as two ball diameters only.
Thus, the cannon should be twice as easy to get as the corresponding losing hazard. So there is much less excuse for missing the drop cannon than for missing the long in-off, although, of course, the cannon is often set up so that the second contact is a thin one.
ANSWERS PLEASE Finally, a little problem for the diversion of those who have had the patience to get this far.
Our club table is a fast one and it is possible to place the cue ball on the baulk line and with a top strength shot to make it double the table lengthwise three times. If the top and bottom cushion noses are exactly 12ft. apart and if they yield 1/4"on average each time the ball impacts onto them, what is the total distance travelled by the ball if it stops exactly on the baulk line after one of these top speed shots?
(Our Editor has agreed to award his copy of Levi's 'Million' (3 vv) to the sender of the first correct solution opened. WOW!)