By combining various factors related to social background, this study uses a more comprehensive concept to assess relative educational mobility. The inequality of educational opportunity (IEOp) approach estimates the share of inequality in educational performance that can only be attributed to students' characteristics beyond their control (circumstances). One-fifth of students' educational achievement in Switzerland can be attributed to circumstances. Canton level analysis reveals significant variations, with the German-speaking region exhibiting higher levels of unfair educational inequalities. The IEOp estimates are decomposed to identify the contributions of different circumstances and better understand the observed inequality. Socioeconomic status, parental education, and occupation emerge as the predominant factors in most cantons. The institutional structure of cantonal education systems, including the level of stratification in secondary schools and educational inputs in primary schools, is linked to the inequality of educational opportunity. A higher level of stratification in compulsory school leads to greater inequality of opportunity without improving efficiency. Increasing instructional time at primary school is related to higher student achievement, particularly for those from lower socioeconomic backgrounds. The findings support the theory that early-age schooling has the potential to address inequalities, improve student achievement, and demonstrate that equity and efficiency are not exclusive dimensions.