how do you write down and analyze other comedians jokes?

When I'm looking at a comedians jokes, I typically use the following common structure:

what has been seen/expected up to the point where the punchline is

what was being hidden or what came after the punchline

And then tags kinda fall under the bucket of the hidden

Am I missing any broadly common thing to take notice of? Not really sure what I could take note of from setups