Progress 8 scores ard calculated in the same way for all mainstream state schools, regardless of any internal testing carried out by the school itself; the latter will inform how the individual school assesses its individual pupils' likely outcome at GCSE, given how they are actually doing academicslly, regardless of what they 'should' get.
Progress 8 aims to capture the progress that pupils in a school make from the end of primary school to the end of KS4. It is a type of value-added measure, which means that pupils’ results are compared to other pupils nationally with similar prior attainment. Every increase in grade a pupil achieves in their Attainment 8 subjects counts towards a school’s Progress 8 score. Progress 8 is calculated for individual pupils solely in order to calculate average Progress 8 scores including school Progress 8 scores. Schools should not share individual pupil progress scores with pupils or parents.
A Progress 8 score is calculated for each pupil by comparing their Attainment 8 score with the average Attainment 8 scores of all pupils nationally who had a similar starting point, using assessment results from the end of primary school. In 2016, changes were introduced to KS2 outcomes in English reading and maths. They are now reported as scaled scores instead of national curriculum levels (more information is available in the measurement of prior attainment section). The greater the Progress 8 score, the greater the progress made by the pupil compared to the average for pupils with similar prior attainment. A school’s Progress 8 score is calculated as the average of its pupils’ Progress 8 scores. It gives an indication of whether, as a group, pupils in the school made above or below average progress compared to similar pupils in other schools. • a score of zero means pupils in this school on average did as well at KS4 as other pupils across England who got similar results at the end of KS2 • a score above zero means pupils made more progress, on average, than pupils across England who got similar results at the end of KS2 • a score below zero means pupils made less progress, on average, than pupils across England who got similar results at the end of KS2
A negative progress score does not mean pupils made no progress, or the school has failed, rather it means pupils in the school made less progress than other pupils across England with similar results at the end of KS2.
https://assets.publishing.service.gov.uk/media/6620e69b651136bd0b757d4f/Secondary_accountability_measures_-2023-2024_guidance-_April_24.pdf
SATs don't 'count' for grammar schools only as much as in, no grammar school uses the applicant's SATs scores as an entrance test. But they will be used in the calculation of P8, same as for a non-selective school, and on an individual level, may be taken into account for initial setting in e.g. Maths.