FCR measures whether the customer's problem was actually put to bed the first time they raised it — no callback, no reopened ticket, no second email. It is one of the strongest predictors of satisfaction, which is exactly why it gets gamed.
The formula is resolved-on-first-contact divided by total contacts. The catch is that "resolved" is a definition you choose, and every generous definition inflates the number.
What it hides: reopen windows, channel-hopping (a chat that becomes an email counts as two "first" contacts), and the quiet incentive to close fast. Measure it alongside reopen rate or it quietly rots.