Counting is easy when you don’t have to count anything with it: 1, 2, 3 . . . it could go on for ever, precise, regular and blissfully abstract.

This is how children learn to count in the nursery, at teacher’s knee.

But for grown-ups putting counting to use in the wider world, it has to lose that innocence. The difference is between counting, which is easy, and counting something, which is anything but.

Some find this confusing and struggle to put the childhood ideal behind them.

But life is more complicated than a number. The first is multi-dimensional and shape-shifting, the other flat and precise. That is why, when counting something, we risk torturing reality until it fits the numbers, when the process should be the other way round. And then, worst of all, the fact that all this was a struggle is forgotten. To master counting in real life, follow a better guide: mushy peas.

“Yob Britain! 1 in 4 teen boys is a criminal!” said headlines in January 2005. “1 in 4 teen boys claims they have done a robbery, burglary, assault or sold drugs.” As another newspaper put it: “Welcome to Yob UK!”

A survey of teenage boys suggested Britain had nurtured a breed of thugs, thieves and pushers. Newspapers mourned parenting or civilisation, politicians held their heads in their hands and the survey itself really did say that 1 in 4 teenage boys was a “prolific or serious offender”.

A competent survey, which this was, asking boys what they’d been up to and then counting the answers, ought to be straightforward (assuming the boys told the truth).

But when counting anything that matters in our social or political world, although we act as if the simple rules apply, they do not, they cannot and to behave otherwise is to indulge a childish fantasy of orderliness in a world of windblown, adult jumble.

It is, for a start, a fundamental of almost any statistic that, to produce it, something, somewhere has been defined and identified. Never underestimate how much nuisance that small practical detail can cause.

First, it has to be agreed what to count. In maths numbers seem hard, pristine and bright, neatly defined around the edges. In life, we do better to think of something murkier and softer. It is the difference, in one sense, between diamonds and mushy peas; hard to believe, it is a difference we forget or neglect.

In that real world of soft edges, what was the definition used to identify those teenage boys as serious or prolific offenders? The largest category of offence by far was assault, and judged serious if it caused injury. Here is how it was defined by a survey question: “Have you ever used force or violence on someone on purpose, for example by scratching, hitting, kicking or throwing things, which you think injured them in some way?”

And then, deliciously: “Please include your family and people you know as well as strangers.”

Fifty-eight per cent of assaults turn out to have been “pushing” or “grabbing”. Thirty-six per cent were against siblings. So anyone who pushes a brother or sister six times leaving them no worse for wear is counted a “prolific offender”. Push little brother or sister even once and bruise an arm and you are a “serious offender”, since the offence led to injury. Or, as the press put it, you are a yob, bracketed with drug dealers, burglars, murderers and every other extremity of juvenile psychopath.

Some of the crime identified by the survey was certainly brutal, but, given the definitions, what were the headline numbers from the survey really counting? Was there clear statistical evidence of Yob UK? Or did the survey rather reveal a remarkably bovine placidity in Britain’s sons and brothers?

After all, 75 per cent of all teenage boys claimed not to have pushed, grabbed, scratched or kicked as many as six times in the past year (what, not even in the school dinner queue?), nor to have done any of these things once in a way that caused even the mildest scrape.

According to these definitions, the authors of this book must make their confession: both were serious or prolific offenders in their youth. Reader, your writers were yobs. But perhaps you too were one of us?

We make no argument about whether the behaviour of Britain’s youth is better or worse than it used to be. We do argue that the 1 in 4 statistic – reported in a way that implied things were getting worse – was no evidence for it, being no evidence of anything very much.

It wouldn’t sell, but a more accurate tabloid headline might have read: “One in four boys, depending how they interpret our question, admits getting up to something or other that isn’t nice, a bit thoughtless maybe, and is sometimes truly vicious and nasty; more than that, we can’t really say on the evidence available to us.”

The fault here is not with numbers and the inevitable way that they must bully reality into some semblance of orderliness. It is with people, and their tendency to ignore that this compromise took place, while leaping to big conclusions.

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