Model of the standard deviation of photometry, as a function of apparent magnitude, shown in red. At every 500th target apparent magnitude, 10 σ model uncertainties ﹩( 10\nu _{m,\mathrm{model}\,}) ﹩ are shown in blue. Shown in green are the observed photometric standard deviations for the sample, with error bars suppressed for clarity. The black dashed vertical lines correspond to the break point magnitudes, where the linear relationship changes between photon statistics and flux overestimation from incomplete detections. These occur at ﹩J=16.53﹩, ﹩H=15.67﹩, and ﹩K_{s}=15.06﹩ and are within 1 σ of the mean M₁₀ magnitudes, corresponding to a >99% completeness for ﹩\mathrm{S}\,/ \mathrm{R}\,> 10﹩ in the PSC Cutri et al. (2006), § VI.2. Propagated uncertainties are dominated by the uncertainty in the observed photometric scatter. See § 3.2.4 for discussion.