Relation between the parameters of the sigmoid and M₁₀ in Eq. (1), for 500 samples from the MCMC chain: the inflection point, x(M₁₀) − Eq. (2), on the left; the inverse slope, y(M₁₀) – Eq. (3), at center, and the skewness, z(M₁₀) – Eq. (4), on the right. The magnitude of 50% completeness, x(M₁₀) is well approximated by M₁₀. Fields with fainter M₁₀ have a steeper (smaller y(M₁₀)) and more symmetrical (z(M₁₀) towards 1) selection function. Examples of resulting sigmoids are shown in Fig. 3 for a range of M₁₀ values.