Crime-solving as theater is a comparison that appears in nearly every story in this collection. Watson notes that their house in Baker Street is like a stage (Priory School.1). In fact, Sherlock Holmes stories read a lot like TV show episodes, complete with new cases, guest stars, recurring cast members, and a handy sum-up at the end of every episode. Though to be more accurate, modern TV shows play out like a Sherlock Holmes story. At any rate, there's a lot of theatrics and performance themes in the Sherlock Holmes stories. Holmes himself is often likened to a budding thespian, or actor; he has a definite flair for the dramatic.
Lestrade and I sat silent for a moment, and then, with a spontaneous impulse, we both broke out clapping, as at the well-wrought crisis of a play. A flush of colour sprang to Holmes's pale cheeks, and he bowed to us like the master dramatist who receives the homage of his audience. (Six Napoleons.43)
Holmes's penchant for acting contrasts with his extreme scientific detachment and helps to make him a more complex character. He may be a bit like a robot, but he's a robot with an acting-bug. Which is scary actually – he might be a Cylon.
Theater comparisons are also important in terms of narrative. The plots of Sherlock Holmes stories are often structured a lot like a play: they have a clear beginning, middle, and end; everything is resolved at the end; characters often go off on lengthy monologues to explain things; and Holmes often makes dramatic reveals to his audience.