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We present a study of unprecedented statistical power regarding thehalo-to-halo variance of dark matter substructure. Using a combination ofN-body simulations and a semi-analytical model, we investigate the variance insubhalo mass fractions and subhalo occupation numbers, with an emphasis on howthese statistics scale with halo formation time. We demonstrate that thesubhalo mass fraction, f_sub, is mainly a function of halo formation time, withearlier forming haloes having less substructure. At fixed formation redshift,the average f_sub is virtually independent of halo mass, and the massdependence of f_sub is therefore mainly a manifestation of more massive haloesassembling later. We compare observational constraints on f_sub fromgravitational lensing to our model predictions and simulation results. Althoughthe inferred f_sub are substantially higher than the median LCDM predictions,they fall within the 95th percentile due to halo-to-halo variance. We show thatwhile the halo occupation distribution of subhaloes, P(N|M), issuper-Poissonian for large <N>, a well established result, it becomessub-Poissonian for <N> < 2. Ignoring the non-Poissonity results in systematicerrors of the clustering of galaxies of a few percent, and with a complicatedscale- and luminosity-dependence. Earlier-formed haloes have P(N|M) closer to aPoisson distribution, suggesting that the dynamical evolution of subhaloesdrives the statistics towards Poissonian. Contrary to a recent claim, thenon-Poissonity of subhalo occupation statistics does not vanish by selectinghaloes with fixed mass and fixed formation redshift. Finally, we use subhalooccupation statistics to put loose constraints on the mass and formationredshift of the Milky Way halo. Using observational constraints on the V_max ofthe most massive satellites, we infer that 0.25<M_vir/10^12M_sun/h<1.4 and0.1<z_f<1.4 at 90% confidence.

Statistics of Dark Matter Substructure: III. Halo-to-Halo Variance