whens it time to move from polling to WebSockets?

Lately, I've been building a few apps where I need to update client-side data a lot. I usually just poll, maybe with some exponential backoff if things get crazy. But honestly, for some stuff, like when updates need to be super fast, or when the client is sending tons of little updates to the server, polling just feels clunky and inefficient. I'm wondering when other people started using WebSockets instead. What made you finally say polling wasn't good enough, and how did it go when you switched?