Expected fraction of clusters with radio halos with steepening frequency ν_s >  600 MHz and ν_s >  140 MHz in the redshift range 0.08 <  z <  0.33 (red and blue lines, respectively). Shadowed regions represent the uncertainty on the model predictions taking into account the statistical error associated with the limited size of the observed sample. Calculations have been performed for the following choice of model parameters: b = 1.5, ⟨B⟩ = 1.9 μG (where B = ⟨B⟩×(M/⟨M⟩)^b), and the fraction of energy channelled into particle acceleration η_t = 0.2 (see Cassano et al. 2012, and references therein). The observed fraction of clusters with radio halos in the two mass bins is overlaid (black lines) and refers to the three cases in Table 4 for the total sample. The dots represent the average mass of the clusters in the bins.