ONCE IN the bluest of moons, someone in a business school does a piece of research that is sensible and useful. Last week a study was published in the journal PNAS telling us something very handy indeed: that we should stop worshipping the world’s top business leaders because they are not quite as good as everyone thinks they are.

The authors – Chengwei Liu from Warwick Business School and Jerker Denrell from Oxford’s Saïd Business School – argue that the super-successful are outliers who achieve extraordinary things partly through luck. And once lucky, they get more so. The rich get richer, as we all know.

Take Bill Gates. Had he not come from a well-off family – making it easy for him to indulge his young love affair with computers – and had his well-connected mother not opened doors with IBM, he probably wouldn’t have become the richest man in the world. That doesn’t mean that Mr Gates isn’t clever; it just means that we can study him all we like but we’re not going to end up where he is.

The academics suggest we should focus our attention on number twos who owe less to chance and more to skill. By looking at how they made it we might learn something.

All this comes as a massive relief. It means I can chuck out half of my business books.

Farewell Jack Welch. Farewell Sir Terry Leahy. Goodbye Lord Browne and Sir Richard Branson. I won’t miss you. I can’t think of a single thing I learnt from all you megastars, except a bit of shockingly poor counsel from Steve Jobs. One of his most trusty principles was “don’t settle” – possibly the worst tip ever.

Just now I popped out for an egg sandwich, only to find that the shop had run out, so I settled for ham and cheese instead. As a result, I didn’t starve, and the sandwich turned out to be rather tasty.

A similar point about the irrelevance of the mega-successful was made even more powerfully to me last week by a 14-year-old schoolboy. Salah Sirad was one of nine finalists in a competition I was judging backed by Bank of America Merrill Lynch.

Each of the children had to give a presentation (which they did considerably better than many successful adults I know). Salah talked with precision and wit about his role model and how he had rejected Sir Richard, Barack Obama and David Beckham for the role in favour of someone more obscure: his older brother.

In making this choice Salah is on to something bigger than the two academics. If they are right that we ought not to revere extreme success, then we should also regard number twos – and numbers threes, fours and fives – with suspicion. If you are Paul Allen or Joe Biden luck has surely played a huge role in your success too.

Even someone as far down the ladder as I am owes almost everything to luck.

I was born in just the right place at just the right time to just the right family. I was just the right sex and stumbled (by luck) into just the right industry in its glory days. So I would make a lousy role model: the layers of luck are so thick they obscure any skill or grit.

Salah got it right by picking instead his smart, hard-working brother whose (thin) layer of luck is the same as his own.

The trouble is that no one wants to hear the truth about the power of luck. The lucky don’t like talking about it, and even the unlucky have a fondness for stories of stars rising to the top. Luck isn’t a good story at all; it’s random and there is not much that’s funny to say about it.

Unless you’re Michael Lewis, that is. This month the writer gave a commencement speech at Princeton in which he described an experiment where Californian psychology professors gave groups of three students four cookies. One member of each group was chosen at random as a leader, and in each case it was this person who automatically laid claim to the extra cookie.

Mr Lewis told the Princeton students that they were the ones with two cookies and that they would soon be getting more still. They were lucky, and should not forget it.

Only they will, of course.

I have briefly remembered how lucky I am for the purposes of writing this column, but one of the laws of luck is that I fear I will have forgotten it by the time I get home.

Fortunately Mr Lewis has come up with a different version of you’re-so-lucky that may be harder to forget as it’s more uncomfortable.

We owe a debt not just to our own good luck but also to the bad luck of others.