The owner of the once-exalted Leeds United Football Club recently confessed that he had no real idea whether his new manager would prove to be of any use. He said that football managers were “like watermelons - you only find out when you open them”. The really encouraging sign, he added, was that his new man was good-looking.

This innovative selection process prompted derision from the media, but is attractiveness really so irrelevant? I would challenge any football-following readers out there to name a single successful ugly football coach at the highest level of the game. The harder-featured figures on the managerial merry-go-round seem to get sacked on a fairly regular basis, whereas handsome fellows such as Jos Mourinho and Pep Guardiola have a proud record of success. Even the rugged Sir Alex Ferguson had a smile to melt hearts.

So I wondered whether the same kind of correlation might be found among another set of high-profile, results-driven managers - headteachers. Do the most successful schools tend to be run by the better-looking and the least successful by the less physically attractive?

Education should, of course, challenge shallowness, prejudice and superficiality, but those who work in it are only human. If a George Clooney or Scarlett Johansson lookalike is at the helm, it’s conceivable that a school might feel a little more motivated and inspired each day, other things being equal.

My own research into this area might politely be described as in its preliminary stages, although the early findings are interesting. After choosing a local authority region at random, I looked up its top and bottom five performing schools. I then found smiling mugshots of each of the 10 headteachers, cut them out and stuck them randomly on to a sheet of A4.

Next, I asked people to rank them in terms of attractiveness. My sample had no idea who these people were. The methodology is borrowed from scientists who similarly reported this year that the highest-placed Tour de France cyclists were also considered the most attractive in a gallery of 80 competitors, according to a survey of hundreds of women selected for their ignorance of bicycle racing.

My results are strikingly similar. The five most successful heads are all significantly ahead of the others on the looks front, too. That said, a few of my respondents struggled to find anyone in the gallery they could call “good-looking”. Let’s face it, we’re talking headteachers here. In one instance, I was accused of distorting someone’s face to fit it on to the page. Sadly I had not.

My research is limited and mathematically flawed, I know. We need a much larger sample size before I can safely recommend that TES headship advertisements request a photo alongside a CV. However, it could be that the owner of Leeds United is partly right: if you want a headteacher or a melon, make sure you pick a decent-looking one. Maybe it’s all about the survival of the “fittest” these days - and perhaps it always has been.

Stephen Petty is head of humanities at Lord Williams’s School in Thame, Oxfordshire, England