The Art of Statistics: Learning from Data

by David Spiegelhalter

We have a strong psychological tendency to attribute change to intervention, and this makes before-and-after comparisons treacherous. A classic example concerns speed cameras, which tend to get put in places that have recently experienced accidents. When the accident rate subsequently goes down, this change is then attributed to the presence of the cameras. But would the accident rates have gone down anyway? Strings of good (or bad) luck do not go on for ever, and eventually things settle back down – this can also be considered as regression-to-the-mean, just like tall fathers tending to have shorter sons. But if we believe these runs of good or bad fortune represent a constant state of affairs, then we will wrongly attribute the reversion to normal as the consequence of any intervention we have made. Perhaps this all seems rather obvious, but this simple idea has remarkable ramifications, such as: Football managers who get sacked after a string of losses, only to find their successors getting credit for the return to normal. Active fund managers dropping in performance, after being tipped (and perhaps getting large bonuses) after a couple of good years. The ‘Curse of Sports Illustrated’, in which athletes get featured on the cover of a prominent magazine following a series of achievements, only to subsequently have their performance plummet. Luck plays a considerable part

Regression to mean examples