Sir Francis Galton tends to be remembered for founding a field of research, eugenics, that makes no meaningful contribution to modern medicine. The Victorian polymath’s enthusiasm for breeding a super-race has thankfully had its day, and his theories of heredity are now recognised as pseudoscience.

Not all of Galton’s work, however, deserves to be dismissed. For all his misguided posturing about genetics, he also delivered insights into statistics that can still help us to take care of our health. The foremost of these is the principle of regression. Galton noticed that exceptionally tall people tend to have children who are somewhat shorter than their parents. Among the very small, the trend is reversed. From this he proposed a general rule: that extreme, outlying measurements do not usually repeat themselves. Over time, they will move back towards the average — or regress to the mean.

This insight can explain all manner of apparent statistical oddities. Take football’s “manager of the month” jinx. Popular wisdom has it that when a coach wins this award, his team becomes more likely to lose the next game and statistical analysis by my colleague Daniel Finkelstein has shown that this is indeed the case. The prize is not to blame but the principle of regression. After a golden run that brings an award, normal service is soon resumed.

I was reminded of the principle this week when dietitians and toxicologists attacked the detox industry, pointing out that the liver and kidneys will restore the body after festive excess without any help from £20 potions. The scientists are right, but why do so many people part with their money regardless? An ignorance of regression is part of the answer.

After a period of overconsumption and lack of sleep, most people feel ropey. But unless you’ve got food poisoning from undercooked poultry, there will be nothing in your system that won’t be put right by rehydrating and a few early nights.

The liver takes just 36 hours to clear even a near-lethal dose of alcohol. With time, you will feel better.

If you happened to indulge in a few “24-hour detox” tablets when at your lowest on New Year’ s Day, though, it will be tempting to attribute your improved condition to the pills. The liver does the hard work, regressing the body to its healthy norm, while a dubious detox plan gets the credit.

There is a wider lesson here for understanding medicine. The placebo effect is not the only confounding factor that can make treatments appear to work when they have no direct physiological impact. Common colds generally last a week or so, regardless of treatment, with the heaviest symptoms coming a couple of days in. Load yourself up with vitamin C and cough mixture at this point and you’ll probably link your clearer head to what you’ve taken. Regression, though, remains a much more likely cause. You were going to get better anyway.

The pull of the regressive fallacy is greater still for more chronic conditions such as back pain and migraine, which are episodic and difficult to treat. Flashes of intense discomfort are interspersed with periods of calm. It is when symptoms are worst that patients will grasp at anything for help, often trying unproven or extreme remedies out of desperation. This, though, is also when the pain is most likely to dissipate of its own accord. It is all too easy to make an erroneous connection.

The problem can apply to conventional as well as alternative medicine, though the former is at least tested with proper controls that miminise its influence. It is a prime cause of unnecessary treatment. Before you reach for the pills that seemed to work last time, give some thought to Galton’s principle. An understanding of regression can protect against risking needless side-effects, as well as the contents of your wallet.

Mark Henderson is the Times science correspondent