(selected from the GMBCG catalogue). The SALT pairs are not different from those in the photometric pair sample since the same $r_{\mathrm{sep}}$ and $\Delta m_{\mathrm{i}}$ criteria have been used to select pairs in both samples. The only difference between these two samples is the redshift requirement used for the SALT pair selection. Since the BCGs are bright, red galaxies, they are very likely to be observed by the SDSS spectroscopic surveys, so we do not expect a bias against spectroscopy for these galaxies. The number of pairs observed with SALT should therefore be representative of the number of pairs in the photometric sample.

The uncertainty on $f_{\mathrm{pair}}$ represents the 68.3 per cent $(1\sigma)$ binomial confidence limit and is calculated using the beta confidence interval as described by [@Cameron2011].

The mass growth of the BCGs {#sec:mass_merger_growth}
---------------------------

We now continue on to the main aim of the paper, measuring the merger-inferred stellar mass growth of the BCGs as a function of redshift. In order to do this we first calculate average stellar masses of the BCGs, denoted $\langle M_{\star}\rangle$, in each redshift bin. The uncertainties on $\langle M_{\star}\rangle$ are determined using bootstrap resampling with 1000 realizations.

We estimate average merger timescale, 