# How does the law of large numbers relate to regression to the mean?

Intuitively, these two important statistical principles appear to describe two facets of the same phenomenon, namely that in the long run, any extreme occurrences get counter-balanced, and things tend to even out.

However, the law of large numbers and regression to the mean are formally differently specified, and I found no good writing that treated their similarities and differences in detail (if any is in fact warranted - see below).

In terms of the timeframe of analysis, regression to the mean appears to describe what changes at the sample-to-sample level, whereas the LLN describes what happens at the limit (n→∞). But is that the most important of the differences?

Perhaps this just betrays my superficial understanding of one or both of those principles, but insofar as others may have asked themselves the same question, maybe this thread is worth responding to, at least in the comments? Thanks!

• Related (though I don’t think a duplicate)
– Dave
Sep 23 at 9:57
• Indeed. Thank you! Sep 23 at 9:59
• There’s no close relationship between these two phenomena Sep 23 at 10:59