Controversial Cantabrigian Francis Galton, who balanced out his contributions to statistics by also pioneering eugenics, observed that extreme characteristics in parents such as height are not entirely inherited by their children, who tend to be closer to, what he termed, mediocrity. This phenomena, thankfully redubbed regression to the mean, has subsequently been widely observed.
Everything from sports performances to medical conditions seem to display a cyclical nature, where highs and lows tend to be followed by a return to the baseline. The high points and low points are, however, also the points at which we tend to take interventional action, and the post hoc attribution of the intervention for the subsequent return to the baseline is known as a regression fallacy.
Common situations for possible misattribution include a drop in the frequency of accidents at a blackspot after the instillation of speed cameras there, a rise in a failing student’s test scores after punishment is administered and the sophomore slump of an exciting new sports star. Without proper controls in place it is impossible to know the correct attribution.
Examples from the world of scepticism include an end to a slump in your golf scores after donning of a holographic wrist band, the end of a particularly bad bought of back pain after the consumption of sugar pills and the end of a long drought after intercessory prayer. In such cases it seems warranted to provisionally accept regression to the mean as the most reasonable explanation.
We must, of course, be careful not to misapply this fallacy; Galton’s failure to achieve the lasting greatness his work in statistics and other fields should have brought is more likely due to his championing of eugenics than regression to the mean. In science and medicine control groups are used to counter this phenomena, but for the rest of us long term records are needed to benchmark these patterns.