Ratio of all-particle and bound-only SO masses for host halos (top row) and subhalos (bottom row), low and high redshift, and low and high masses (defined as ﹩0.5\lt \nu \lt 1﹩ and ﹩1.5\lt \nu \lt 2﹩). In each panel, the colored lines show histograms of the radius ratio for four mass definitions. Since ﹩M\propto {R}^{3}﹩ for SO definitions, the logarithmic differences in radius are three times smaller. For host halos, the definitions agree for the vast majority of halos, but there is a tail toward high ratios caused by halos that are close to another, larger halo. In such cases, the all-particle mass can encompass much or all of the other halo’s mass. As expected, this effect is more common for lower-threshold definitions such as ﹩{R}_{200{\rm{m}}}﹩, at low mass, and at high redshift. The all-particle masses of a large fraction of subhalos are ill-defined; the cutoff of the distribution around a ratio of 1000 is partly caused by SPARTA’s algorithm. The dependence on mass definition is even stronger for subhalos, with high-threshold definitions such as ﹩{R}_{500{\rm{c}}}﹩ performing better. However, high thresholds also lead to more subhalos for which no mass can be found at all, which are excluded from this figure. See Section 5.3 for details.