Incidence refers to the number of times something happens or develops—in other words, the rate at which something occurs.

// The neighborhood boasts excellent schools and a low incidence of crime.

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"Pickleball, which is played with a perforated plastic ball and wooden paddles on a badminton-sized court, is the fastest growing sport in the U.S., with the number of players rising from 4.8 million in 2021 to 8.9 million in 2023, according to USA Pickleball. … A study co-authored by [Dr. Eric] Bowman that has not yet been published finds that between 2017 and 2022, the incidence of pickleball-related injuries rose faster than the growth of the sport’s popularity." — Linda Carroll, NBC News, 12 Feb. 2024

The words incident, incidence, and instance may seem similar (and, in fact, incident and incidence are closely related), but they are applied in different ways. In current use, incidence usually means "rate of occurrence" and is often qualified in some way ("a high incidence of bear sightings"). Incident usually refers to a particular event, often something unusual or unpleasant ("many such incidents go unreported"). Instance suggests a particular occurrence that is offered as an example ("another instance of a simple change bringing real improvement"); it can also be synonymous with case ("many instances/cases in which the wrong form was submitted"). The plural incidences sometimes occurs in such contexts as "several recent incidences of bear sightings," but this use is often criticized as incorrect.