There are striking similarities between Nick Offerman and his libertarian-leaning “Parks and Recreation” alter ego, Ron Swanson. Besides the obvious physical resemblance, each spends a good chunk of his downtime working in his wood shop. Both are musicians. Both have a history with Megan Mullally, although on the show she is Swanson’s evil ex-wife, Tammy, while in real life Offerman and Mullally are married, and he speaks of her with palpable affection.

There are other points where the two diverge. Swanson might agree with the meat of Offerman’s one-man show, “American Ham,” but he would never get onstage to present his advice to a crowd of strangers. He might admire Offerman’s skills as a onetime fight choreographer for the stage, but he’d never go to a theater, especially not in a big city like Chicago, where Offerman cut his teeth with Steppenwolf Theatre Company and other troupes.