This report is published as a supplement to the main project research report, Hierarchy, Markets and Networks: Analysing the ‘self-improving school-led system’ agenda in England and the implications for schools. The main project report analyses how schools in England have interpreted and begun to respond to the government’s ‘self-improving school-led system’ (SISS) policy agenda, an overarching narrative for schools policy since 2010 that encompasses an ensemble of reforms including academies, multi-academy trusts (MATs) and teaching school alliances (TSAs). The statistical analysis of MAT impact on pupil attainment and progress set out in this supplementary report is the first published analysis to compare schools in MATs over a three-year period with standalone academies and maintained schools with similar characteristics and levels of prior pupil attainment. The analysis set out here uses 2013–15 attainment data and 2016 data on the composition of MATs. Our finding in this paper that there is no positive impact from MAT status overall is largely consistent with other recent studies (Hutchings and Francis, 2017; Andrews, 2019). Where this report provides significant new evidence is in terms of MAT size, as we show that pupils in small and mid-sized MATs tend to perform better, on average, than their peers in comparable maintained schools in both phases and, in the primary phase, than comparable standalone academies. Conversely, secondary school pupils in larger MATs (with 16+ schools) tend to do worse compared to those in both standalone academies and maintained schools. These findings suggest that the economic drive for MAT growth promoted in contemporary policy may well be in tension with an educational argument for smaller groupings of schools.