A ball fraction describes projected overlap seen along the incoming line, not stroke power. For equal balls, familiar fractions provide useful reference cuts; positions between them still require intermediate aims.
Read ball thickness at the instant of contact
Set contact thickness first. Then evaluate speed, side spin, throw and table conditions separately.
Derive the angle instead of memorising a slogan
Let f be the overlap as a fraction of one ball diameter and r the ball radius. The lateral separation of the centres at contact is b = 2r(1 − f). For the ideal object-ball direction along the line of centres, sin θ = b/(2r), so θ = arcsin(1 − f).
This is collision geometry without ball-ball throw. The resulting angle describes the object ball relative to the incoming cue-ball line. It is not the cue ball’s outgoing angle.
Worked reference values
For a quarter-ball overlap, f = 0.25: θ = arcsin(0.75) ≈ 48.59°. For half-ball, θ = arcsin(0.5) = 30°. The angle steps are not evenly spaced. Values below are calculated references, rounded to two decimals.
| Overlap f | Ideal cut θ | Centre offset b/r |
|---|---|---|
| 1 | 0° | 0 |
| 3/4 | 14.48° | 0.5 |
| 1/2 | 30° | 1 |
| 1/4 | 48.59° | 1.5 |
| 1/8 | 61.04° | 1.75 |
Use the table as a diagnostic tool
Begin with no deliberate side spin and a fixed, unobstructed setup. Try full, half and quarter contacts with consistent speed. Record intended overlap, observed object-ball direction and actual cue-ball route separately. Judge the first collision before assessing a later cushion or point.
If adding side spin changes the result, check both actual thickness and throw. Squirt or swerve can alter the delivered line, while ball-ball friction can move the object ball away from the ideal centre line. A changed final route alone does not identify which effect caused it.
Use the half-ball centre-to-edge reference as one visual check. For an angle between table entries, adjust between the references rather than rounding every shot to the nearest familiar fraction.