I hear both of these terms often explained independently of one another but to me it seems that the are very related. I know the law of large numbers deals with the cumulative average of successive observations while regression to the mean is about the next observation.
But my thinking is as follows:
If the proportion of heads in a 100 coin flips is .75, regression to the mean says that it is more likely that the proportion of heads in the next 100 coin flips would be less extreme. Wether that is as extreme in the opposite direction(say .25) or less extreme in the same direction(say .6), both cases ultimately lower the total proportion of heads over the 200 flips. This, at least when repeated many times, leads the the result of the law of large numbers.
Or more generally each successive group of an arbitrary amount of flips is more likely to be less extreme then the previous so the cumulative average of all of the groups, as the number a groups approach’s infinity, approaches the theoretical average.
Is this a correct understanding of these two concepts?