‘Regression to the mean’ or why it probably wasn’t David Moyes’ fault

Robert Matthews

Usually the month of May gives Manchester United fans something to celebrate – winning the English Premier League, say, or even a European Champions League title. This year, most will be glad to see the club make the humble Europa League.

It’s a year since their legendary manager Sir Alex Ferguson stepped down, and almost two decades since they last failed to make the Champions League.

The question now is – how does the club get back to its winning ways?

Every fan will have an answer. Some may think it takes the form of caretaker manager Ryan Giggs, but most know there is little sense in getting excited by a handful of results against ho-hum teams.

Fewer may realise that the club has experienced a phenomenon which commonly afflicts the most successful in any endeavour.

It is called “regression to the mean”, and it is notorious for fooling those convinced they know the reasons for success or failure.

The Nobel prize-winning Israeli-American psychologist Daniel Kahneman is famed for witnessing a classic example of its effects while working with fighter-pilot instructors in the 1960s.

Kahneman tried to convince the instructors that praising trainee pilots worked better than punishment. One of the veteran instructors was having none of this, however. He insisted that whenever he praised cadet pilots for doing well, they did worse on the next outing. In contrast, whenever he screamed at them for blunders, they usually did better.

“So please do not tell us that reward works and punishment does not,” intoned the instructor, “because the opposite is the case”.

Kahneman realised that this apparent refutation of his beliefs was an example of regression to the mean.

The training generally led to the pilots building on their innate talent, with their “mean performance” generally improving. But their performance on any specific outing was strongly influenced by random factors.

A sub-standard performance might be the result of a poor night’s sleep, say, while a good one might be due to having had a few days’ break. And sometimes a pilot would have a run of bad nights, producing a whole spate of poor flights.

Being random, these effects would cancel each other out in the long run, and the pilots’ performance would “regress to the mean”, which steadily improved.

But instructors who ignored the role of randomness could easily come to a different conclusion.

They would pounce on the bad performances – and believe that the resulting improvements were down to their criticisms. They would also find that praise after a good performance appeared pointless, as it typically led to pilots doing worse.

They would even have the hard evidence to back up their belief that their tough approach worked – unaware that the real cause was the random influences cancelling out over time, causing regression to the mean.

Kahneman realised the veteran instructor who had dismissed the “soft” approach had made the mistake of believing the performance of his pilots was dictated by just two factors – their innate skill, and his training.

In reality, the pilots were subject to something else every time they flew – the effect of random chance.

Exactly the same trap awaits anyone who thinks success or failure cannot involve a large element of chance.

And that makes an understanding of regression to the mean crucial to making sense of results in a host of fields.

For example, it helps explain the success of many implausible “alternative” medical therapies. Patients may well have tried conventional remedies for, say, aches and pains, and failed to get better. In desperation, they try something different, and sure enough they start to recover.

Cynics often attribute this to the placebo effect, where the patients think themselves better. But regression to the mean often plays a key role.

By definition, minor medical conditions usually cure themselves over time, but their precise duration is controlled by random factors. By using alternative therapies only after all else has failed, patients risk fooling themselves into believing the therapy has worked, when the real explanation is that the random effects that delayed their recovery have finally faded.

And as in medicine, so in football. If a club succeeds for a long time, it seems obvious that the explanation lies with the style of management. Indeed, as with that pilot instructor, Sir Alex Ferguson was renowned for the verbal blasting of underperforming players known as “the Hairdryer Treatment”.

Yet the success of Sir Alex and Manchester United should be seen through the prism of regression to the mean.

When he took over as manager in 1986, Manchester United had been in the doldrums for years, having once carried all before it.

The club had been relegated in the mid-1970s, and by the mid-1980s looked set for the drop again after a series of unhappy managerial appointments.

In short, the time was ripe for regression to the mean to trigger a resurgence in the club’s fortunes – with good management turbo-charged by good fortune.

Yet even Ferguson struggled at first, and reportedly came close to dismissal after several mediocre seasons.

Fortunately for both him and the club, Ferguson was given more time and by 1990, the effects of random chance had started to work for him, and the club’s fortunes began to change.

The following 23 years were the stuff of legend. By the time he retired, Sir Alex had become the most successful manager of the most successful club in English football history.

There is no doubt that the club benefited from his managerial skill. But it’s also the case that he benefited from the availability of such rare talents as Eric Cantona, Ryan Giggs, Peter Schmeichel and Wayne Rooney among many others.

The simultaneous decline of once-potent rival clubs, notably Liverpool and Arsenal, also helped.

Such a confluence of events is rare indeed. Even those unaware of regression to the mean could see Sir Alex would be a hard act to follow. Failure was all but guaranteed, and such proved to be the fate of his successor, David Moyes.

Over recent months, Moyes has been criticised for everything from sacking Ferguson’s back-room team to lacking tactical vision. He got one thing spot-on, though: securing a six-year contract.

As Sir Alex’s tenure showed, the best defence against the depredations of regression to the mean is time.

And if that’s not made available, a big pay-off is as good as it gets.

Robert Matthews is visiting reader in science at Aston University, Birmingham