We make an estimate of the likelihood function for the Higgs vacuum expectation value (vev) by imposing anthropic constraints on the existence of atoms while allowing the other parameters of the standard model to also be variable. We argue that the most important extra ingredients are the Yukawa couplings, and for the intrinsic distribution of Yukawa couplings we use the scale-invariant distribution which is favored phenomenologically. The result is successful phenomenologically, favoring values close to the observed vev. We also discuss modifications that can change these conclusions. Our work supports the hypothesis that the anthropic constraints could be the origin of the small Higgs vev.