Where I work our core rendering algorithm which runs several times on every page load used naïve string concatenation. When I initially wrote it I knew string concatenation was inefficient but never got back to it and for 99.9% percent of cases it didn't matter! We finally hit that 0.1% case and after optimizing the algorithm, it didn't make a dent on our overall performance numbers at all.

The biggest impact to our performance has been switching one JSON serialization library for another, no algorithmic knowledge needed, just basic benchmarking skills.