One thing I wonder in all of this, do the BBC run focus groups/polling/whatever you want to call it. Is the AI just a single rating or is it broken down? I'd just be interested to see whether the BBC have data on what particular elements the viewers do/don't like. i.e. "I really like Capaldi but the episode sucked." or "The episode was really clever, shame about Peter Capaldi" that kind of thing.
They do detailed audience research that goes beyond I liked this / I didn't like this but obviously it's not made public.
There have been claims that it was this research that was behind the radical change in Capaldi's Doctor between this series and last, but there's nothing to back them up. (It's certainly believable, however.)