More detail on the algorithm:

https://www.theguardian.com/education/2 ... -is-unfair

https://www.theguardian.com/education/2 ... -is-unfair

...suppose a class of 27 pupils is predicted to achieve 2.3% A* grades and 2.3% U grades; how many pupils should be given each grade? Show your working.

There are a few ways you could solve the problem. Each of the 27 pupils is 3.7% of the class, so maybe you give no one an A* or a U at all. After all, your class was effectively predicted to get less than one of each of those grades, and the only number of pupils less than one is zero.

Or you go the other way: 2.3% is more than “half” a pupil in that class, after all, and everyone knows you should round up in that case. So perhaps you should give one A* and one U.

Or you could pick the system that the exam regulator applied to calculate results on Thursday – now decried as shockingly unfair – and declare that no one should get the A* but someone should still get the U.

The unfairness was exactly flipped at the other end of the scale: no matter how good a pupil you were, you could only achieve an A* if the Ofqual algorithm had predicted that at least one pupil would get that grade.

A class predicted just less than one A* and just more than zero U grades would be given zero A*s and one U.

From there, the rounding process wrecks things further. That school, with its class of 27, was given one A* and one U – 3.7% for each. “This seems rather harsh,” Thomson writes, “given that the model prediction is for fewer than one pupil (2.30%, when each pupil counts as 3.70%) to achieve this grade.

Beyond the rounding, though, it is the adjustment process that “is absolutely fundamental to understanding how this year’s grades have been calculated”.

“Unfortunately, it raises more questions than it answers,” he says.

And that U, which was only ever predicted for just half a pupil, must be given to one pupil – whoever is ranked bottom of class by teachers –no matter how well that individual performed.

Mene, mene tekel upharsin, Johnson.