In the UK, USA and elsewhere, school accountability systems increasingly compare schools using value-added measures of school performance derived from pupil scores in high-stakes standardised tests. Rather than naïvely comparing school average scores, which largely reflect school intake differences in prior attainment, these measures attempt to compare the average progress or improvement pupils make during a year or phase of schooling. Schools, however, also differ in terms of their pupil demographic and socioeconomic characteristics and these factors also predict why some schools subsequently score higher than others. Many therefore argue that value-added measures unadjusted for pupil background are biased in favour of schools with more 'educationally advantaged' intakes. But others worry that adjusting for pupil background entrenches socioeconomic inequities and excuses low-performing schools. In this article we explore these theoretical arguments and their practical importance in the context of the 'Progress 8' secondary school accountability system in England, which has chosen to ignore pupil background. We reveal how the reported low or high performance of many schools changes dramatically once adjustments are made for pupil background, and these changes also affect the reported differential performances of regions and of different school types. We conclude that accountability systems which choose to ignore pupil background are likely to reward and punish the wrong schools and this will likely have detrimental effects on pupil learning. These findings, especially when coupled with more general concerns surrounding high-stakes testing and school value-added models, raise serious doubts about their use in school accountability systems.