  I re-examine the relation between virial mass and concentration for groups
and clusters of galaxies as measured in a number of recent works. As previously
noted by several authors, low-mass clusters and groups of galaxies display
systematically larger concentrations than simple prescriptions based on pure
$n$-body simulations would predict. This implies an observed concentration-mass
relation with a substantially larger slope/normalization than expected from
theoretical investigations. Additionally, this conclusion seems to be quite
independent on selection effects, holding for both lensing based and X-ray
based cluster samples. In order to shed new light on this issue I employ a
simple spherical halo model containing, in addition to dark matter, also stars
and hot diffuse gas in proportions and with distributions in agreement with the
most recent observations. Moreover, I include the contraction effect
experienced by dark matter due to the cooling of baryons in the very central
part of the structure itself. The resulting modified concentration-mass
relation is steeper than the theoretical input one, because star formation is
fractionally more efficient in low-mass objects. However, the effect is
non-vanishing at all masses, thus resulting also in a larger normalization.
Overall the new relation provides a better representation of the observed one
for almost all catalogs considered in this work, although the specific details
depend quite significantly on the baryon fraction prescription adopted. Anyhow,
the same effect could also be produced by a redistribution of baryons within
the structure. Finally I use this simple model to show how the estimated
concentration of cosmic structures is expected to be overestimated as a
function of the radial range covered by the analysis. (abridged)
