CROQUET COACHING: Croquet Angles

17 August 2008
by Leo Nikora

This graph by Ian Brown shows the theoretical* relationship between the stroke angle and the split angle of a croquet stroke for different split ratios.

• The stroke angle is the angle between the line joining the centers of the two balls, and the line along which the mallet is swung. See small diagram inside the graph.
• The split angle is the angle between the lines along which the two balls travel.
• The split ratio is the ratio of the distances the two balls travel.

Remember, the croqueted ball always travels along the line joining the centers of the two balls, and the striker ball never travels along the line in which the mallet is swung. It is hard for beginners to overcome the tempation to swing the mallet in the desired direction for the striker ball; they just cannot trust in the physics shown in the graph.

Curves for three ideal split ratios are shown: stop, drive, and push.

• In an ideal stop shot, the mallet completely stops after hitting the striker ball, and the split ratio is very high. The croqueted ball travels much further than the striker ball.
• In an ideal drive shot, the mallet slows down after hitting the striker ball, and the split ratio is about 4:1. The croqueted ball travels four times as far as the striker ball.
• In an ideal push shot, the mallet does not even slow down after hitting the striker ball, the split ratio is very low. The croqueted ball travels about as far as the striker ball. An ideal push is, of course, a fault.

Split ratios between an ideal stop and an ideal drive would be somewhere in the red shaded area, and between an ideal drive and an ideal push in the green area. A 2:1 shot would be in the green area.

So, if a drive shot was made with a stroke angle of 20 degrees, the graph shows that the split angle would be about 50 degrees.

The graph shows two interesting properties of a croquet stroke that most players do not account for.

The Half-Angle Method is Incorrect

Most players use the half-angle method when making a croquet stroke. They swing their mallet along a line that bisects the split angle.

The graph shows (in blue) the stroke angle as a percentage of the split angle. If the half-angle method were correct, then the curves would lie on the (purple) 50% line. They mostly lie to the left of the 50% line; the stroke angle should normally be less than half the split angle.

A better approximation to the curves shown in the graph is the half-distance method. Players should swing their mallet along a line that runs to the midpoint between the final resting places of the two balls.

The diagram on the right shows that the half-distance method results in a stroke angle that is less than half the split angle.

So the half-distance method is more accurate than the half-angle method.

Note, when the split ratio is 1:1, then the half-angle method yields the same stroke angle as the half-distance method. So the half-angle method is accurate when the split ratio is near 1:1.

Pass Rolls Don't Split as Much

Most players are surprised when their pass rolls don't split as much as they expected. Their striker ball travels almost in the direction that they swung their mallet.

The graph does not show a pass roll, but it does show that the curve moves to the right with increasing split ratio. Looking at the stroke angle as a percentage of the split angle, a drive shot lies mostly at 40%, while a push is mostly at 50%.

If the graph did show a pass roll, it would be to the right of a push, and lie mostly at around 70%.

* The theory behind this graph can be found on the Mechanics of the Game by C.R. Calladine and Jaques Heyman in
Engineering (29 June 1962, pp 861-863), and republished at the Oxford Croquet website.