Comparison between the HB predicted by our model with predictions from other models presented in the literature: Cole & Kaiser (1989). Sheth et al. (2001), Tinker et al. (2010), and Comparat et al. (2017). We present both our benchmark model as well as the PBS predictions based on the HMF model of Euclid Collaboration (2023) used as a baseline of our model. Different columns correspond to different redshifts. The relative difference with respect to our benchmark model is presented in the panels in the second row. We adopted a composite scale for the residual plot to show the dynamic range of differences between the models: The scale is linear for values between [−10, 10] % and symmetric log outside. For reference, we show the zero line in black. The predictions of the models from the literature have been computed using the COLOSSUS toolkit (Diemer 2018).