Standard Reporting already shows a useful metric on the Search tab: Tickets Created. This allows you to see what search strings ultimately resulted in a ticket conversion.
However, with the inclusion of Chat in the Web Widget, some search strings may lead to a chat session via the Chat Widget instead of a ticket via the Contact Form. There is no way to see what searches are leading to chat sessions. If this metric were included, it would enable us to better optimize self-service to deflect chat sessions that could easily be solved with a knowledge article.