Combination shots: potting one ball off another

A combination shot sends the cue ball into one ball, called here the first ball, and drives that into a second ball, which is the one you want to pot. It is legal in both main pool games and harder than it looks. The reason is what the gap between the two balls does to a small error in your aim.

What the rules allow

Legality depends on the first ball the cue ball touches, not on which ball ends up in the pocket.

• 9-ball: the first contact must be the lowest-numbered ball on the table. Pocketing a higher ball off it is fine, and the 9 wins the game when it is pocketed on a legal shot. That is the classic combination: hit the 1, drive it into the 9. The 9-ball rules post covers the fouls that cancel it.
• 8-ball: once groups are decided, the first contact must be a ball from your own group. A combination that starts on an opponent's ball is a foul, even if your own ball drops. Under WPA rules the shot should be called, because a combination is not an obvious shot. See 8-ball rules explained.

Venues vary on the finer points, so these are the standard WPA-style versions. The app's Play listing does not describe its rules in this detail.

Aim in two steps

The ghost-ball method works backwards from the pocket, and a combination just applies it twice.

1. Ghost for the second ball. Draw the pot line from the pocket through the second ball and continue behind it. The first ball must arrive with its centre one diameter behind the second ball's centre, on that line.
2. Ghost for the first ball. Draw a line from the first ball's resting place to that target position, and continue behind the first ball. The cue ball's centre must arrive one diameter behind the first ball's centre, on that line.

Most misses come from skipping the second step and aiming the cue ball at the first ball itself.

How the error grows

Suppose the cue ball's path is 1 mm to one side of where it should be. A standard ball is 57.15 mm across, and at the first contact the sideways slip of e mm turns the first ball's direction by an angle with sine e / 57.15. For 1 mm that is asin(1 / 57.15) = 1.0 degree. For a plain pot that is the end of it.

In a combination the first ball then travels a distance d before it meets the second. Its sideways error on arrival is d × tan(1.0°), and that slip is exactly the kind that the second contact converts into an angle, now with sine (d × tan 1.0°) / 57.15. For a straight-in shot at both contacts, the result is close to a simple rule: the angle error is multiplied by d divided by 57.15 mm, the gap measured in ball diameters.

The working for each bar: 1.0° at the first ball, a sideways slip of d × tan 1.0° on arrival, then asin of that slip over 57.15 mm.

• 150 mm: 150 × 0.0175 = 2.6 mm, and asin(2.6 / 57.15) = 2.6°.
• 300 mm: 300 × 0.0175 = 5.3 mm, and asin(5.3 / 57.15) = 5.3°.
• 600 mm: 600 × 0.0175 = 10.5 mm, and asin(10.5 / 57.15) = 10.6°.

On the cloth, the ball you are potting then travels on towards the pocket. After 1 m, a 1.0 degree error is 100 cm × tan 1.0° = 1.7 cm off line, the plain pot. A 5.3 degree error is 100 cm × tan 5.3° = 9.3 cm, about 1.6 ball widths. The slip of the cue is the same; the result is not.

Cuts make it worse

The figures above assume both contacts are straight-in. As the ghost-ball post shows, a sideways slip costs about 1 / cos(cut angle) more direction on a cut. In a combination that factor applies at each contact, so the total magnification is roughly:

(d / 57.15 mm) × 1 / (cos of first cut) × 1 / (cos of second cut)

With a 60-degree cut on the second ball and a straight first contact, cos 60° = 1/2, so the 5.3° at 300 mm becomes roughly 10°. Cut both contacts by 60° and it is four times the straight-in figure. This is a small-angle estimate, so use it for ordering shots rather than for exact numbers. Throw, covered in the overcut post, acts at both contacts too and is not included here.

Choosing a good one

The numbers above give a short checklist.

1. Keep the gap short. Two balls close together are far more forgiving than two balls a table apart. The error scales directly with d.
2. Keep the cuts small. The best combination has the first ball, the second ball and the pocket nearly in a line, so both cos terms are close to 1.
3. Count the cost of a miss. In 9-ball a failed combination costs only your turn, as long as the first contact was right. In 8-ball, check that the first ball is in your group before you consider anything else.

Trying it in the app

The listing says you can practise at your own pace and switch between overhead and aiming views. The overhead view is the natural place to draw the two ghost positions in your head. Set up two balls with a short gap, aim with both ghosts, then widen the gap a ball diameter at a time and see how your tolerance shrinks.