Thresholds: Why Does Continuous Change Become a Discrete Decision?

A threshold is a boundary that converts continuous change into a discrete response. An email filter may assign every message a continuous spam score, but the system must still decide at some point whether to block or deliver it. Two scores can differ only slightly while producing completely different actions.

A threshold is not necessarily a break that exists independently in nature. Many thresholds are rules chosen for action. Lowering a spam threshold catches more unwanted mail but also blocks more legitimate messages; raising it tends to do the reverse. A threshold is therefore more than a technical setting. It builds the costs of error, the purpose of the system and its attitude to risk into a decision.

It also differs from a critical point. A critical point describes a condition at which a system itself changes state. A threshold may simply mark when an observer chooses to classify or act. This distinction matters: a sudden change in the result does not prove that the object itself changed suddenly. Continuous evidence can appear as a simple “yes” or “no” after it crosses a decision boundary. We should test not only whether the score is sound, but why the boundary was placed there.

https://developers.google.com/machine-learning/crash-course/classification/accuracy-precision-recall