Also a staff engineer. This is pretty much exactly what I do.

Often it is a result of suggesting an improvement to some PR for a program or system that someone is doing some work on, and discovering that for whatever reason it doesn't quite work. This tends to lead to a deep dive of really analyzing and understanding the problem and how the piece of the system fits into the overall picture. This analysis often leads to a more structured approach to a problem, placing it in the context of wider industry or CS theory, thus enabling us to leverage prior art and other people who have grappled with similar problems.