Where is that figure coming from? I'm curious what kinds of failures they have.

https://news.ycombinator.com/item?id=11492569 <- I detailed it a bit more in this comment, including linking the source report from Google.

I think when you say they "fail", I think you are referring to the disengagements, right? The report you link to there says:

“Immediate manual control” disengage thresholds are set conservatively. Our objective is not to minimize disengages; rather, it is to gather as much data as possible to enable us to improve our self-driving system.

Also, table 4 reports the number of disengagements (for any reason) each month, as well as the miles driven each month. In the most recent month in that table, it's actually 16 disengagements over 43275.9 miles. That's approximately one disengagement every 2705 miles; about the distance from Sacramento, CA to Washington, DC. At the start of 2015 it was only 343 miles per disengagement; 53 disengagements over 18192.1 miles. The pace of improvement is incredible, especially considering disengagements are set conservatively.

Can a human drive from Sacramento CA to Washington DC without a single close call or mistake along the way? I really doubt it. This technology will be saving lives soon.

do you have a comparison for the number of miles between human errors?

It's hard to get an exact figure, particularly because of unreported accidents, and various sources. But I believe insurance companies have previously stated it's about one in every 250,000 miles. For the sake of giving a wide berth for unreported accidents, and to not give humans the benefit of the doubt, I've been using the rough figure of 150,000 miles between accidents.

I don't have a great source for it though, and if anyone finds a good source, it'd be fantastic.