There are two possible explanations for what's going on in this incredible video, which will change the way you watch David Letterman watching drummers forever:
1. Letterman is just crazy about drums. "Are these yours? Are these rentals? They're beautiful!" He must know if you're pounding your own set or if these are skins-for-hire. It's a crucial distinction to drum aficionados.
2. Every drummer who appears on Late Night is being unwittingly drafted into the secret recurring sketch "Are These Your Drums?" After the show, Letterman and his producers watch the tape to laugh at the drum questions.
We can't explain his obsession with trying to buy all the instruments. Maybe his basement is full of Ludwig sets, cellos, and vibraphones he's cadged from various musical guests, and occasionally he'll wander through the basement, quietly asking himself, "Are these your drums? Yes, yes they are. And they are beautiful."