A Bayesian procedure was used to estimate linear reaction norms (i.e. individual G × E plots) on 297 518 litter size records of 121 104 sows, daughters of 2040 sires, recorded on 144 farms in North and Latin America, Europe, Asia and Australia. The method allowed for simultaneous estimation of all parameters involved. The analysis was carried out on three subsets, comprising (i) parity 1 records of 33 641 sows of line B, (ii) all parity records of 52 120 sows of line B and (iii) all parity records of 121 104 sows of lines A, B and A × B. Estimated heritabilities ranged from 0.09 to 0.10 (smallest to largest subset) for the intercept of the reaction norms, and were 0.15, 0.08 and 0.02 (ditto) for the slope. Estimated genetic correlations between intercept and slope were −0.09, +0.26 and +0.69 (ditto). The three subsets therefore showed a progressively lower genetic component to environmental sensitivity, and progressively less re-ranking of genotypes across the environmental (herd–year–season) range. In a genetic evaluation that does not include reaction norms in the statistical model, part of the G × E effect remains confounded with the additive genetic effect, which may lead to errors in the estimates of the additive genetic effect; the reaction norms model removes this confounding. The intercept estimates from the largest data subset show correlations with litter size estimated breeding values (EBV) from routine genetic evaluation (without reaction norms included) of 0.78 to 0.85 for sows with one to seven litter records, and 0.75 for sires. Hence, including reaction norms in genetic evaluation would increase the reliability of the EBV of young selection candidates without own performance or progeny data by considerably more than 100 × (1/0.75−1) = 33%. Reaction norm slope estimates turn out to be very demanding statistics; environmental sensitivity must therefore be classified as a ‘hard-to-measure’ trait.