My guess is that it depends a lot on the driver. There are a lot of really reckless drivers, or really bad drivers out there on the roads right now. I know people who've been in several (relatively minor) car crashes, driving the same-ish sort of route to/from college and work that I was during the same period. I think they're just a bad driver. I feel like they're driving recklessly when I'm a passenger in a car they're driving. So a self-driving car might be a better driver than them, while also being worse than the median driver, and much much worse than like the upper portion of the human driver spectrum, like the 1st quintile of the 20% of human drivers who are pretty good.

Given how reckless some drivers are, I'd imagine the distribution of crashes among drivers is very skewed. I don't know numbers, but I'd expect to see something like 80% of car crashes involving (or objectively caused by) 20% of the drivers, with most car crashes involving people who have been involved in numerous crashes, and a large minority of drivers having been involved in zero car crashes.