uncertainty on $R_{\mathrm{merge}}$ is determined using the standard propagation of errors.

Semi-analytical models, for example [@Conroy2007; @Puchwein2010; @Laporte2013] have shown that $30-80$ per cent of the companion’s stellar mass ends up in the ICL during a merger with the BCG. During a merger, we assume that 50 per cent of the companion’s stellar mass is transfered to the BCG [$f_{\mathrm{mass}} = 0.5$; also used by @Liu2009; @Liu2015; @Burke2013; @Lidman2013]. To account for the possible range of $f_{\mathrm{mass}}$ values, we assign an uncertainty of 20 per cent to our assumed $f_{\mathrm{mass}}$ value of 50 per cent (i.e. $f_{\mathrm{mass}} = 0.5 \pm 0.2$), which is propagated through to the measured fractional mass growths. In order to calculate how much mass $(\Delta M)$ major mergers add to a BCG from redshift $z_{i}$ down to $z=0$, we use the following: $$\Delta M \, (z = z_{i} - 0) \, = \, R_{\mathrm{merge}} \times T_{\mathrm{LB}} \times \langle M_{\star} \rangle_{\mathrm{com}} \, (z_{i}) \times f_{\mathrm{mass}} 
\label{eq:delta_M}$$ where $T_{\mathrm{LB}}$ and $\langle M_{\star} \rangle_{\mathrm{com}}(z_{i})$ respectively gives the lookback time and the average stellar mass of the companions at $z_{i}$.

The fractional contribution $(F)$ made by major mergers to the stellar mass of a present day BCG, denoted $\langle M_{\star} 