While it is easy to lie with statistics, it is even easier to lie without them. And if you are going to accuse teachers from certain subjects of being worse school leaders than others, you probably ought to have some numbers to back you up.

Researchers Alex Hill and Ben Laker are no stranger to controversy. Their research into the actions of superheads, exclusively revealed in Schools Week earlier this year, drew a crowd of haters.

Hill and Laker’s view that school leaders’ penchant for excluding low-attaining pupils was not a great idea, actually, became lost when people vilified them for pointing out the fact that if you went ahead and excluded the kids, it would look like your school really had “improved” on the performance measures looked at by Ofsted and the education department.

Now, they are back with another rather awkward message.

After studying detailed information, gathered during Laker’s PhD study of more than 400 turnaround leaders, they have found that – shock, horror – secondary academy heads tend to behave stereotypically based on the academic subject they previously taught.

Mathematicians focus on numbers: increasing revenues and driving for growth. English teachers focus on the “craft” of teaching, engaging people with stories and debating ideas. The only problem? It tends to be a lot of words, and not a lot of action.

For someone who rolls her eyes about the pomposity of many historians, it gives me no joy to say that they came out of the research well. Seemingly, they are the ones most likely to gain gradual, sustainable exam improvements due to their focus on strong leadership, long-term trends and building a “strong nation”. Their pomposity is well-earned, it seems.

“It gives me no joy to say historians came out of the research well

On the one hand, this is hugely controversial. Telling teachers of RE, PE and English they are likely to be less good leaders in turnaround academies could put off thousands of people from doing crucial roles.

On the other hand, it sort of makes sense. It is only natural that any teacher, faced with the pressured situation of taking over a failing school, will fall back on what they know best. You can’t spend years succeeding at a subject at school, take it for a degree, spend eons teaching it – and then be expected to become a totally different person once in a leadership role.

It also shows that if the incentives push the wrong way then there is no reason to hold back from behaving in problematic ways.

Which is why the words uttered by Libby Nicholas, the chief executive of growing new academy trust Reach4, are so important. Nicholas is an English teacher, but has never forgotten what a pupil once wrote on a feedback form about her. It said: “Miss inspires us through words and emotions and stories. But it might also be useful for her to think about those one or two people in the class who are inspired more by facts and figures.”

Since the decline in the national qualification for headteachers, there has been a void in leadership training, especially for leaders going into the most challenging failing schools. Without broader managing experience they are finding themselves falling back into bad habits.

This can be resolved by better leadership training, which many trusts and universities are now developing, but also through simple awareness.

Laker and Hill’s statistics may be uncomfortable and they will rightly be scrutinised.

For a full look at their research, you would do well to take a look at Newsnight’s take on it, where policy editor Chris Cook has boiled down its main messages. Or the Harvard Business Review article, which is a peer-reviewed management journal.

But even if you dislike the study or findings, they are a useful chance for a thought-pause. Are we really sure that having teachers focus on one academic discipline for decades is the best training for running an organisation? Or, maybe, could that route be causing rather a lot of problems when mixed with a high-stakes accountability framework and incentives pointing in a wrong, short-termist direction?

The data may be uncomfortable, but its message is worth considering.