You could put it in one of those lists of scientific puzzlers like “Do penguins have knees?’ or “Where do flies go in the winter?”. Certainly, by note and anecdote, it is ever more apparent that something about school headship causes a man (rarely a woman) to pull on nylon shorts and pound 26 miles across London, just when any normal teacher is stretched out on the sofa eating the children’s chocolate Easter eggs and watching re-runs of I’m A Celebrity Ballroom Dancer, Please Drench Me Iin Maggots.

Our children’s first head, at the village primary, alerted us to this symbiosis of school headship and sore feet when he suddenly announced that he was doing it. He was a fit chap, keen on PE and all that; but for those of us bred to a tradition of round-shouldered and bespectacled scholars, this sudden outbreak of physical bravado was a surprise. Especially when he finished.

Within a few years the children had moved on, and the boy’s next head revealed that he, too, was in strict training for the marathon. Knees bent, arms swinging, off he went in turn. Even faster. The school didn’t suit, though, so next there was another head to size up. He looked suspiciously fit: before I even dared ask, he was indeed off on a half-marathon, streaking past his sixth-formers. Now, newly retired, he is going for the full 26 miles.

It is a trend, almost a plague; a mania like the ergot-fuelled dancing crazes of the middle ages. Google the words “headmaster runs marathon” on the web, and herds of them thunder towards you, puffing and groaning towards the finishing-tape. Primary heads, secondary heads, old and young , deputies and veterans - they’re all at it.

Sometimes it is gung-ho CV stuff: “Dear boys, parents, and Old Bastardians, I would like to introduce myself as your new headmaster... my wife and I are looking forward to the move... blah, blah... something about me... Cambridge boxing blue... MAI PGCEI oh yes, and I have run the London Marathon twice in under 4 hours...”

Or: “Following teaching posts at Bogstandard Comprehensive, voted most improved school in its LEA, he headed the liberal studies department... a trained counsellor, Mr Fitball has completed the London Marathon six times...”.

You just look, if you don’t believe me. There are hundreds of them. As I write, I gather that Sir Dexter Hutt, executive head of the Ninestiles federation of secondary schools in Birmingham, is planning to run in his third (the last being seven years ago) and has set himself a target of doing it in under 3 hours 45 minutes.

So why this weird correlation of academic leadership and sweaty trainers? A brainstorming session with teacher-moles came up with several suggestions.

The first, obviously, is showing off. Your pupils, especially big frightening boys, will surely revere a head who runs a marathon. As for the girls, they will see you on TV and think, “Woooah! More than just an assembly pin-up!”.

They’ll admire you... won’t they? Well, yes. On the other hand, given the nature of running, students are just as likely to see their headmaster sitting on the pavement with his head in his hands like Paula Radcliffe, while he is insouciantly overtaken by men in flippers and girls in bunny-ears and comedy waitress outfits carrying trays of fake champagne. So perhaps it isn’t exhibitionism.

Another explanation is purely chemical: testosterone, endorphins, all that.

These are alpha males. Heads are statistically more likely to be tall than short; it may yet turn out that they are left-handed as well, since research now claims that left-handers survived by being better warriors. In the jungle that is modern education, a man must hone his abilities in both fight and flight. Hence the marathons?

No: still not convinced. We scratched our heads. And at last, we came to the likeliest explanation. A former deputy head put his finger on why headmasters run marathons. “It’s desperate hunger for achievement,” he said. “In education you’re always running to stand still, putting your heart into hopeless causes, or getting a job three-quarters done and then being foiled by bureaucracy or budget shortfalls”.

He sighed, wistfully. “In a marathon, all you have to do is keep putting one foot in front of the other and endure the pain, and you’ve achieved something. No LEA to trip you up.” We were silent, stunned by the brilliance of this insight. Then someone said: “Why don’t female headteachers do it much, then?”.

“Easy,” said the genius. “Women rather like failing. It makes them feel feminine.”

The conclave broke up in disarray.