Calculated metrics are a great addition to Google Analytics (GA), enabling web analysts and marketing professionals to perform basic, yet very powerful, calculations directly in the GA interface.
One calculated metric I have found very useful is (AdWords) clicks vs. (AdWords) sessions. Given the tight integration between AdWords and GA (when using auto-tagging), one can generally expect there to be a very stable relationship between clicks and sessions. If this is not the case, there is a good chance there are issues with either your landing page URLs or website. By using the clicks vs. sessions calculated metric you can identify, at the campaign, ad group & keyword level, which links/landing pages are causing issues.
As an example (above image), a client we recently worked with made a new release of their website. After the release, all campaign parameters were being dropped due to some back-end routing logic, an issue we were able to identify immediately thanks to the clicks vs. sessions metric.
Head of Google Ads & Partner