Why a made ball does not tell the whole story — and how PerformStars measures the margin for error in a billiards position.

Two shots can end with exactly the same result: the object ball drops into the pocket. But one may allow a generous aiming error while the other requires an exceptionally precise contact.

At PerformStars , we wanted a measure of that difference which did not depend on a player's reputation or historical potting percentage. Instead, we asked a geometric question: how many initial cue-ball directions would still allow a direct pot?

That question leads to a reproducible shot-difficulty score. Here is the intuition, a few examples, and the limitations of what the number actually means.

A shot has a window, not just a line

A pocket is not a single point. It has an entrance of finite width, and the object ball itself has a nonzero radius. Consequently, several nearby outgoing object-ball directions can still lead to the pocket.

But the player does not aim the object ball directly.…