CROQUET COACHING: Critical Gap of a Double Target CROQUET COACHING: Critical Gap of a Double Target 11 June 2010
by Leo Nikora
Your opponent has broken down, and left you with a double target. You know you have a better chance of hitting a double target, than hitting a single target. But, should you aim halfway in between the two balls, or should you aim at one of the balls?
If the two balls are close enough together, then you should aim in the middle. If they are far enough apart, then aim at one of them. But how close together, or how far apart? Certainly, if a ball cannot go between them, then shooting at the middle is best. Certainly, you would not shoot at the middle of two balls ten feet apart.
There is a critical gap where aiming at one of the balls, or aiming halfway between both balls, results in the same chance of hitting either of the two balls. You should aim at the middle of any gap smaller than the critical gap, and aim at one ball of any gap larger than the critical gap.
How big is the critical gap? It depends on how accurately you shoot. The better shooter you are, the smaller your critical gap is, and the more you should aim at one ball. The poorer shooter you are, the larger your critical gap is, and the more you should aim between the two balls.
The following analysis assumes your shooting error follows a bell shaped curve (a Normal Distribution).
Your accuracy is reflected by your chance of roqueting one of the balls, if it were a single target.
For example, you might have a 40% chance of hitting just one ball; either because even though you're a good shooter, the ball is far away; or because even though the ball is close by, you're a poor shooter. You must assess your chance of hitting-in at that distance.
The critical gap between the two balls is measured in ball widths. The graph above shows the critical gap for a range of accuracy.
In the example above (with a 40% chance of hitting just one ball), the critical gap is 3.5 balls wide. So if a double target had a gap 4 balls wide, you should aim at one of the two balls. If it had a gap 3 balls wide, you should aim at the middle.
This chart is hard to memorize, so you might want to remember these approximations:
| Gap | Aim in the Middle if your chance of hitting is less than |
| 1 ball | all of the time |
| 2 balls | two thirds of the time |
| 3 balls | one half of the time |
| 4 balls | one third of the time |
| 6 balls | one quarter of the time |
| 8 balls | one fifth of the time |
If you only want to remember just one number, remember 2.5.
If a double target has a gap smaller than 2.5 balls, then aim in the middle, unless you have a very good chance of hitting one ball.
With a gap larger than 2.5 balls, then aim at one ball, unless you have a very poor chance of hitting it.