It's more complicated than this. They haven't just taken the rank ordering by the teachers and projected onto a curve.

Here is the 319 page document published on results day. This is the totality of the current description of the 'algorithm'. https://assets.publishing.service.gov.uk/government/uploads/...

There's some kind of predictive linear model (page 40) which is based on a student's prior attainment (i.e. GCSE and SATs 'data'), but then modelled at the level of the exam centre (i.e. school). These models are separately fitted for different bins (I think ten are shown at one point) of achievement.

The whole document is pretty incoherent. I suspect the 'algorithm' is a set of excel spreadsheets.