"Regression to the mean" was the bane of my undergraduate statistics class. We knew that it was out there, and that the final exam would have a question about it, but no-one understood it or had ever seen it. A bit like unicorns or fairies.
The lecture notes were unhelpful. They told us what it did - make things wrongly appear to change over time when actually stuff stayed the same - but not what it was. Some people claimed to get it, but they couldn't explain it to others.
I now see that our mistake was in thinking that there's some thing called "regression to the mean". There isn't. It's just a rather unhelpful term for what happens in a certain kind of situation, and once you understand those situations, there's nothing more to learn.
Suppose there's a number, which varies over time, and at least some of this ...
