Distributions of the ratio of the line-of-sight velocity to the group velocity dispersion for BGG (left) and satellite (right) (v_prop/σ_v, VT), for the S-I (dotted lines) and combined S-II to S-IV samples (solid lines) in COSMOS (black) and HORIZON-AGN (orange). We find no significant redshift evolution of the distribution in both observations and simulation, thus the sub-samples S-II to S-IV are combined here. The distribution for BGGs in low mass groups at z <  0.4 suggest they are in relatively dynamically unrelaxed systems.