Median offset between the centre of the gravitational potential and the BCG (BCG wobble) as a function of source redshift for: the CL (black-dotted), CL+LoS (green-dashed), CL+σ_ϵ (blue-dot-dashed), CL+LoS+σ_ϵ (red-solid), Euclid+CL (purple-cross) and Euclid+CL+LoS (orange-cross) mocks. The error bars indicate the 1σ bootstrapped uncertainty. The red dashed line indicates the median wobble as expected from random sampling the posterior distribution for the centre on the CL+LoS+σ_ϵ mock. For upcoming Euclid data, measured median offsets of ∼14 kpc are expected for cold dark matter, with no significant contribution of LoS structure.