Burning Question

I thought sure that I would find the answer to this in either IMDb or Wikipedia, but to no avail.

I don't usually turn in to Letterman until Two and a Half Men is over, so I often miss his monologue and catch him just as he's about to do the top ten list. But every time I do see his show from the beginning, I see a curious thing:

Just before the announcer says, "Da-vid LETTERman!", Dave runs across the back of the stage, and then enters from stage left.

Why on earth doesn't he just enter from stage right?