Comparison of different model predictions for P(N_g | δ_m) against measured counts-in-cells distributions in mock galaxy catalogs for a pair of example HODs that have sub-Poisson scatter (top row) and super-Poisson scatter (bottom row) at δ_m = 0. Within each row, the three panels show model fits (solid curves) for the different parametrizations of P(N_g | δ_m) given in Eqs. (1), (2), and (4). Left column: Best-fitting model with linear bias only; i.e., a simple Poisson distribution. Middle column: Model with linear bias b and density-dependent stochasticity α₀, α₁, which decouples the mean and variance of the distribution. Right column: Stochasticity model with galaxy bias modeled to second order in δ_m. Shaded histograms show the measured distributions of galaxy counts in cells for three narrow bins of width 0.05 in δ_m. Each histogram is an average over 200 mock galaxy catalogs. The underdense (−0.3) and overdense (0.38) bins are set to the most extreme values of δ_m for which each bin still contains at least 1000 of the 160 000 cylinders in the simulation box. Stochasticity values α₀ and α₁ for the two HODs (as measured in the model with quadratic bias) are given in the top right corner of the last panel in each row.