  The diffuse light within galaxy groups and clusters provides valuable insight
into the growth of massive cosmic structures. Groups are particularly
interesting in this context, because they represent the link between galactic
haloes and massive clusters. However, low surface brightness makes their
diffuse light extremely challenging to detect individually. Stacking many
groups is a promising alternative, but its physical interpretation is
complicated by possible systematic variations of diffuse light profiles with
other group properties. Another issue is the often ambiguous choice of group
centre. We explore these challenges using mock observations for 497 galaxy
groups and clusters with halo masses from $~ 10^{12} \textrm{M}_{\odot}$ to
$1.5 \times 10^{15}\textrm{M}_{\odot}$ at redshift $0.1$ from the Hydrangea
cosmological hydrodynamic simulations. In 18 per cent of groups with at least
five galaxies above $10^{9} \textrm{M}_{\odot}$ in stellar mass, the $r$-band
brightest galaxy is not the one at the centre of the gravitational potential;
line-of-sight projections account for half of these cases. Miscentring does not
significantly affect the ensemble average mass density profile or the surface
brightness profile for our sample: even within ambiguously centred haloes,
different centring choices lead to only a 1 per cent change in the total
fraction of diffuse intra-group light, $f_{\textrm{IGL}}$. We find strong
correlations of $f_{\textrm{IGL}}$ with the luminosity of the central group
galaxy and halo mass. Stacking groups in narrow bins of central galaxy
luminosity will therefore make the physical interpretation of the signal more
straightforward than combining systems across a wide range of mass.
