Any idea how many times the camera cuts in the average Spielberg film, say?
No idea. You can extrapolate, though - here's a nice representative clip from Jurassic Park. I count 8 shots in the first minute. It's 127 minutes long, of which probably 8 minutes or so are credits'n'shit. Spitballing, we're talking around a thousand shots. Compare and contrast, though - here's Tony Scott's *Domino.* there's a dozen shots in 30 seconds. If you had to storyboard that shit (all 127 minutes - what a coinkidink!) you'd be looking at around three thousand shots. Fortunately, Tony Scott didn't storyboard shit. He brought three or four cameras, pointed them all over the place, shot the fuck out of everything and then gave it in a bucket to his editors and said "turn this into a movie." Crimson Tide was shot with four cameras simultaneously and the editor had to turn over 240 hours of footage into a 2-hour movie. Michael Mann did nine cameras on some shots of Miami Vice. So you don't exactly get a one-to-one.
Hitchcock made a movie, Rope, with exactly 9 cuts, each one only because the film he was using came in 10 minute reels. If you watch it, you will count 4 cuts, the other 5 are disguised with close ups on dark objects such as a man's suit. Edit: I guess technically it's 10 cuts, since the end of the movie is a cut. But maybe I'm just splitting hairs.
Funny that you mention that movie, because I just recently heard of it the other day. They are screening it soon at the Detroit Film Theater, which is the theater associated with the Detroit Institute of Art. I read about it in their flyer, and I plan to see it. Funny the way you avoid something in your consciousness for years then come across it multiple times in a short span. That seems to happen a lot. Maybe it's a matter of just paying attention.