Precision is the share of a system's positive flags that turn out to be correct. If a moderation system flags 100 posts as violations and 90 really are, its precision is 90%. In medicine and statistics it's also called positive predictive value.
Why it matters
It answers a simple question: when the system says yes, how often is it right? That matters most when a false alarm has a cost, like wrongly penalizing a user. Precision alone can flatter a cautious system, though. One that only flags the most obvious cases can post very high precision while missing most of the real ones, which is why it's read alongside recall.
How it's calculated
Precision is true positives divided by the sum of true positives and false positives, so correct flags divided by all flags. A useful follow-up is to read a sample of the wrongly flagged items, since that often shows whether one rule or one category is causing most of the bad flags.
When precision matters most
Spam filters are the classic case, since a real email sent to spam usually costs more than a spam email reaching the inbox. Automated account suspensions work the same way, because a wrongly banned user is a real customer or community member lost. In both, teams are usually willing to miss some bad items to avoid punishing good ones.

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