Reformed GCSEs in English and mathematics will be introduced in 2017. Noticeboards in staff rooms across the country are adorned in postcards from Ofqual summarising the changes. But although the grading structure will change, we are led to believe that broadly similar proportions of pupils will achieve grade 4 and above as currently achieve grade C and above.

However, DfE has decided at the same time to raise the bar of its “basics” measure, henceforth reporting the percentage of pupils achieving grade 5 or above in both English & mathematics. If the new grading structure existed in 2015, how many pupils who achieved A*-C would have achieved 5 or above?

58% of pupils achieved A*-C grades in both English and maths in 2015. But…

So we start with the 2015 data and tabulate pupils’ GCSE English and maths grades (Table 1). 58% of pupils achieved A*-C in both English and maths. Sounds simple.

However, there is a lot of detail we’re going to gloss over. For a start there are different examining boards with different specifications in different subjects.

Then there are some pupils, particularly those attending independent schools, who were apparently not entered for GCSE English or maths but on closer inspection are found to have entered unapproved international GCSEs.

And finally there are pupils entering GCSEs early (e.g. in year 10) and some pupils entering multiple times although this has reduced substantially since pupils’ first, rather than best, results were counted in Performance Tables.

So for illustrative purposes we just use the results attending state-funded schools including alternative provision. We also use pupils’ first entries in line with Performance Tables rules.

Table 1: Grades achieved in GCSE English and maths, 2015

So how many would have achieved grade 5 and above?

We can safely count the 27% of pupils who achieved A*-B in English and maths (the blue cells in Table 1) in our grade 5 group.

We now think about pupils who achieved grade C. According to Ofqual’s postcard, only the top third of the grade C range will be awarded grade 5. In Table 1, 29% of pupils achieved grade C in each of English and maths so we might expect around 9-10% to be awarded a grade 5 in each.

The best case scenario for schools would be if pupils awarded a grade C only needed to achieve a grade 5 in one subject because they already have a B grade or above in the other subject. For both English and Maths, around one-third of pupils awarded a C grade have a B grade or above in the other subject, so, in theory, up to 45% of pupils could achieve grade 5 in both English and maths based on the distribution shown in Table 1.

The worst case scenario is that there is minimal overlap, in other words pupils achieve 5 or above in English but 4 in maths (and vice versa). So the lowest possible percentage of pupils who could achieve grade 5 in both is around 30%.

How does 35% sound?

Both these scenarios are frankly unlikely and the actual percentage will be somewhere between the two. So we try to model the group of pupils in the top third of the grade C range in English in 2015 in terms of prior attainment, pupil backgrounds, type of school and grade in GCSE maths. We then repeat the process for GCSE maths.

As a result, and based on the assumptions we’ve made, we think around 35% of pupils would have achieved Grade 5 or above in both English and maths in 2015 had GCSEs been graded on the 1-9 scale. As Figure 1 shows, raising the bar to Grade 5 is likely to have a greater impact for some schools more than others. It will also introduce more variation between schools.

Figure 1: Percentage of pupils achieving A*-C in GCSE English and maths and modelled percentage achieving Grade 5 and above by school, 2015

NB: State-funded mainstream schools only