Throw: why cut shots need a touch of overcut

The ghost-ball method rests on one assumption: the object ball leaves along the line from the cue ball's centre through its own. For smooth balls that is exact. Real balls rub against each other for a few thousandths of a second, and that friction pushes the object ball slightly off the line. The push is called throw, and on a cut shot it always goes the same way. This post covers which way, how big it is, and what it does to a shot over a metre.

Where throw comes from

On a straight shot the balls touch face to face and there is nothing to rub. On a cut shot the cue ball is still moving forward along its own line while the push between the balls acts along the line of centres. At the contact point the two surfaces therefore slide past each other, and friction between them drags the object ball in the direction the cue ball's surface is moving.

That direction is sideways across the line of centres, the same way the cue ball's own motion carries it across that line: towards the tangent line the cue ball leaves along. The object ball does not go where the geometry says. It leaves at a smaller cut angle, turned a little towards the cue ball's path, so the shot is slightly undercut. To pot it, you have to cut it slightly more than the pure geometry says, which is the overcut in the title. The name for this is collision-induced throw, to tell it from the throw produced by sidespin, which cue-ball spin explained covers.

How big it is, and what changes it

The figures below are roughly what published measurements, such as Dr Dave Alciatore's work on pool physics, report. Treat them as ranges, not constants, because they depend on the balls, how clean they are, and the cloth.

• Size. Up to roughly 5 degrees for a stun shot at slow speed. Most shots throw less than that.
• Cut angle. None on a straight shot, because nothing slides. It grows as the cut opens up and is largest at around a half-ball hit, a 30-degree cut, then eases off on thinner cuts.
• Speed. Slow shots throw most, and a harder hit gives a smaller throw. A gentle cut is the shot to be careful with.
• Cue-ball spin. Stun, with no top or bottom spin, throws the most. Follow or draw reduces it.

The practical reading is that a slow, centre-ball half-ball cut is where you should expect to need an adjustment, and a firm rolling shot needs less.

What a few degrees does at distance

A throw of 2 degrees sounds too small to matter. The object ball then travels a long way, and the sideways error is the distance multiplied by the tangent of the angle. For 1 metre:

• 1 degree: 100 cm × tan 1° = 1.7 cm
• 2 degrees: 100 cm × tan 2° = 3.5 cm
• 3 degrees: 100 cm × tan 3° = 5.2 cm
• 5 degrees: 100 cm × tan 5° = 8.7 cm

A standard ball is 57.15 mm (2¼ in) across, so 3.5 cm is 0.61 of a ball. On a long cut that can be the difference between potting the ball and missing it. For comparison, the ghost-ball post shows a 1 mm slip in cue-ball aim costs about 1 degree on a straight shot and 2 degrees at a 60-degree cut. Throw adds to those errors, and it is broadly repeatable for the same shot, so you can learn it.

Compensating

You do not need a large shift. Moving the cut angle by t moves the ghost ball's position by 2R × t, with t in radians, where 2R is the 57.15 mm ball diameter:

• 2 degrees: 57.15 mm × 0.0349 = about 2 mm
• 5 degrees: 57.15 mm × 0.0873 = about 5 mm

So allowing for a few degrees of throw means aiming a couple of millimetres thinner at the ghost ball, which is a small movement of the cue. In practice:

1. Set up the ghost-ball line as normal, with the pot line from pocket through the object ball.
2. Move your aim a hair towards the thin side, so the cue ball cuts the object ball slightly more than the geometry asks for.
3. Hit it firmer if you can. More speed and some follow both reduce the throw you are compensating for, so the same aim is more reliable.
4. Remember the slow ones. A soft half-ball cut with a stun hit is the case that throws most. Keep a note of how far it drifts and use that next time.

What to check in the app

The Play listing for 8balls says you can adjust your aim, shot power and cue-ball spin, switch between overhead and aiming views, and practise at your own pace. It does not say whether the app models ball-to-ball friction, so do not assume it does. The way to find out is to set up a slow half-ball cut with a plain centre-ball hit, aim it with the ghost-ball method, and see whether the object ball goes where the pure geometry says. Then try the same cut harder and with follow. If the results match the geometry in every case, the app is not throwing the ball, and you learn the geometry. If they drift, you have found the effect described here.

Either way, the line of centres is the baseline. It decides where the object ball goes in the ideal case, and where the cue ball goes afterwards for a rolling hit. Throw is the correction on top.