Did you ever have a teacher who was much keener on doling out criticism than encouragement? If so, it is possible that they were under the impression their pupils responded better to being admonished and might even slack off if they were praised in any way. And, if so, it is probable that they did not understand the principle of regression to the mean.
Say, for example, a pupil pulls off an above-average piece of sporting prowess – a killer backhand on the tennis court, perhaps, or a sublime cover drive in the cricket nets – they would typically not do so well the next time. If their teacher were unfamiliar with mean regression, they might attribute this lapse to any praise they had offered and so conclude, perversely, the pupil responds better to criticism.
Such an impression would only be enhanced if the pupil then plays a below-average shot as the chances are they would perform better the next time – regardless of whether their teacher had shouted at them. This idea was highlighted in a landmark 1973 paper by behavioural psychology pioneers Daniel Kahnemann and Amos Tversky, who noted military flight instructors’ tendency to criticise trainees.
Although the anecdote has since become a classic of behavioural psychology, Kahnemann and Tversky did not offer any actual data to support it and so, some years later, two US economists did precisely that. In Regression to the mean in flight tests, Reid Dorsey-Palmateer and Gary Smith used US Navy flight training data to demonstrate there is substantial regression to the mean in trainees’ performances.
One observation Kahnemann and Tversky made was that, while the trainee pilots’ skill levels could be expected to improve over time, this was obviously not apparent from one exercise to the next. As such, any noticeable divergences in performance – good or bad – from that slow, generally upward trend were mostly a matter of luck rather than skill.
For their part, Dorsey-Palmateer and Smith found that, while the pilots’ performances during training tended to be inconsistent in the short term, they did improve over time – and, as they did so, they reverted to the mean. One theory the pair advance here is that anything that is an imperfect measure of skill, such as athletic performances, does eventually regress to the mean.
They go on to suggest three reasons why people struggle to grasp the idea of regression. “First, they do not expect regression in many situations where it is bound to occur,” they write. “Second, as any teacher of statistics will attest, a proper notion of regression is extremely difficult to acquire. Third, when people observe regression, they typically invent spurious dynamic explanations for it.”
Although offered in the context of training and athletic performance, all three explanations apply very strongly to investment and markets. The trouble is, as Dorsey-Palmateer and Smith also found, even if you are aware of the phenomenon of mean regression, it is still extremely difficult to recognise. Even after the US Navy instructors were told about it, for example, they completely discounted the idea.
Here on The Value Perspective, we have touched on mean regression and athletic performance before – most recently in Rainbow worrier, in relation to professional cycling, but also in Netting returns, where we pointed out all games combine luck and skill. “A good way to work out the degree to which luck plays a part in a game is to consider how straightforward it would be to lose on purpose,” we added.
We suggested you could quite easily lose a tennis match, if you wanted to – before switching our focus to an activity that is a little closer to home for us. “Investment is a different matter entirely,” we continued. “There is a huge element of luck in investment and it would actually be quite hard to construct a portfolio you could guarantee would underperform over the next three years.”
Here on The Value Perspective, we are not setting ourselves up as ‘Maverick’, ‘Iceman’ and the rest of the Top Gun cast but, the fact is, the true ability of fighter pilots and, yes, investors cannot be appraised over the short term. Each are areas where skill will come to the fore – but only over extended periods of time.