This is a great use of search analytics. At Swiftype, we're using the feature to improve our own developer documentation.
Can you give us more details on how you are using this feature to improve your developer documentation? I'm working on yet-unreleased developer docs and I'm trying to figure out the analytics that will be useful for growing our developer base and for improving our docs once they are released. Analytics for products is familiar territory for me, but not analytics for documentation since it doesn't follow a predictable flow/funnel to optimize.
It's pretty simple really. The search analytics show us queries that had no results, which lets us know what we aren't covering in our documentation.