I was flicking though a book on Caravaggio and noticed that virtually none of his figures look out of the picture. They pretty much all look off to the side or at other figures. This gives you the feeling of voyeurism watching a real scene or story unfold rather than it be posed for the specifically for the viewer like a still life or conventional portrait. This creates a real sense of drama.
The exception seems to be when the figure is actually a self portrait, in character but Caravaggio himself.
Caravaggio is watching you watching the scene.