Background Health inequalities in the European Union (EU) are usually reported as national and socioeconomic averages. Simple-Means MAIHDA (S-MAIHDA), a multilevel analysis of individual heterogeneity and discriminatory accuracy, reads the specific contextual effect (SCE), the general contextual effect (GCE) and the discriminatory accuracy (DA) from observed proportions, without a model. Methods We analysed 171,193 people aged 15 years or over in 24 EU countries from five rounds of the European Social Survey (2014-2023). Sex, age and household financial situation defined 16 sociodemographic strata and 384 country-sociodemographic (C-SD) strata. The primary outcome was poor or very poor self-rated health (poor health). Findings The prevalence of poor health was 7.7%, and national prevalences ranged from 3.8% in Greece to 15.0% in Latvia. The 16 sociodemographic strata differed more than twice as much as the countries, and the size of these differences varied between countries. The standardised variance partition coefficient (VPC*) was 10.4% for the C-SD strata and 0.9% for the country. The standardised contextual area under the receiver operating characteristic curve (coAUC*) showed that the GCE was very large for the C-SD strata (80.1%) and small or very small for the country (61.1%). Of the inequality between the C-SD strata, 9.0% lay between countries, 79.9% followed a sociodemographic pattern shared by all countries and 11.1% lay in country-specific departures from that pattern. The DA, measured by the coAUC, was 79.1% for the C-SD strata and 60.7% for the country. A strategy directed at the C-SD strata at or above the population prevalence would reach three quarters of the cases and leave one in four out. Interpretation National averages say little about individuals. Poor health follows one European sociodemographic pattern whose size varies between countries. We recommend S-MAIHDA for monitoring health inequalities in Europe.