How unusual is it for a funny comedian to be completely unfunny in person?

It also depends on their comedy breeding ground. It seems like those that call New York’s Comedy Cellar home base have the ability to be better off the cuff than most. It has a lot to do with the infamous comic’s table at the place. If you weren’t on your game even when off stage someone like Bill Burr, Louis CK or god forbid Patrice O’Neal would destroy your soul. If you could think on your feet and give right back you were welcomed into the fold. I’ve heard that West Coast comics who come in are horrified.

If you write your own material (or have a good memory) you might have a big stock of jokes not good enough to use onstage. If you can use some of them in real life you can get the reputation as a great wit, since even a half-funny spur of the moment joke might go over well. Comedians also have schemas of jokes into which relevant material can be placed.
Comedians are famous for not laughing at other people’s jokes because they are too busy analyzing what makes the joke work to laugh.

Aziz Ansari had it even worse. Kanye West wanted him to perform at his house, on the spot.

I know an inlaw who’s a standup. Her mother is a character, you know, and the daughter is a clone. But it depends on her mood. If she’s down, she’s down. If she’s happy, then hold on for a stream of consciousness fun ride.

I do standup, of course.

In my experience comics are, in person, only marginally funnier than people usually are, on average. Many aren’t funny in person at all. I know people who are NOT comics who in person are funnier than most comics.

Standup comedy is a finely honed skill, not “just being funny.”