"Actually I meant mean reversion in the boring pedantic mathematical sense."

Several years ago I plotted return versus PE of the S&P 500, but rather than plotting all the data together and fitting a linear regression to the data, I segmented the data into two buckets, one for long periods of rising PE, such as '81-'99 and 2010-2020, and one for long periods of declining PE, such as '64-'81 and 2000-2010, and then fitted polynomials to each of the two curves. The two curves converged at the ends, at PEs of 23 and 8, but diverged in the middle PEs. The data for periods of rising PE was fit well by a 2nd order polynomial with downward curvature, and the data for periods of declining PE was fit well by a 2nd order polynomial with upward curvature. In the middle, at a PE of 15 or so, the two curves diverged considerably. Together the two curves looked like a narrow football tilted on its end. (Sorry, I don't have the graphs at hand, but I hope that you can picture it.) This is what I refer to as cycling about the mean rather than reverting to the mean.

One consequence of these data, if you believe the analysis, is that if you're at a PE of 15 haven risen from 8, you're more likely to get a forward return that is somewhat higher than if you're at a PE of 15 having fallen from 23. It's like a heater with the thermostat set to turn on at a PE 8 and off at a PE of 23. The PE appears to be reverting to the mean of 15, but it's actually cycling between 8 and 23 and overshooting 15.