agreement between the two. However, the black points do show slightly more spread overall. This indicates that the halo properties we have chosen to use here may not fully encapsulate the mapping to $N_{gal}$, i.e. we are still missing some information that is relevant to the halo-galaxy relationship. This should not be surprising as most of our parameters ($N_p$, $M_{200}$, $\sigma_v$ $v_{max}$) are effectively mass tracers. The ratio of $R_{1/2}$ and $R_{200}$ (calculated easily from $M_{200}$) can be thought of as a measure of concentration, effectively the ratio of 2 radii that are defined in the same way for all halos. Concentration is known to trace mass [@NFW96], but has also been found to correlate with halo environment [@Wea06; @GS07; @Mea07]. One can imagine that in addition to mass, spin and environment, there are additional factors (branching from the full merger history of the halo) that might affect $N_{gal}$. Fortunately, it appears that any other factors are not completely orthogonal to the halo properties used in this study. As shown above, our parameters seem to capture most of the halo-galaxy mapping, at least in the context of the Millennium simulations.

Finally, we can perform a feature selection to identify, within 