Schools much prefer the new system that allows them to present their own assessment of progress to the inspectors and in which the inspector calls at short notice. But there is little doubt that the arrangement puts more pressure on heads. They are responsible for the paperwork that plays such an important part in the outcome and for getting the self-evaluation right.

They are also vulnerable if the statistics on which the process relies suggest they are underperforming. More than a quarter of schools said they were unhappy with Ofsted’s use and interpretation of data.

Ofsted has a vital part to play in solving the recruitment difficulties of the many schools that will search for heads in the next couple of years as the number of retirements increases. Some heads are retiring early with one good inspection report under their belt because they cannot face another.

Already, the average primary of 100 pupils attracts only a couple of candidates. Three-quarters of primary heads say teachers who would make good heads are not interested in the job.

If heads are to be damned by statistics, the latter must be right. A change in Ofsted’s role would be even better. The organisation is already very different from the one that appeared to confront rather than monitor teachers in the days of Chris Woodhead.

It needs to change again. A longer view of a school’s leadership and whether it is capable of bringing about improvement would help. So would a further move in the direction of self-evaluation.

Two-thirds of schools already report that there is no difference between grades they awarded themselves and those of the inspectors. The next step should be towards even lighter-touch inspections for most schools.