For each cluster in the redMaPPer catalogue, the central galaxy identification algorithm of redMaPPer assigns five galaxies probabilities of being the central galaxy (CG) of the cluster ($P_{\rm{CEN}}$). These galaxies are ranked according to probability and are hereafter referred to as the CG candidates. The central probabilities are defined by using a luminosity filter, photometric redshift filter and a local galaxy density filter (discussed below). The product of these three filters produces the overall centering filter that is used to determine the central probabilities [see equation 67 of @Rykoff2014]. The redshift filter that is used in this equation is slightly broader than the cluster red-sequence filter in order to allow galaxies with slight colour offsets from the red-sequence to be considered as CG candidates, as it is possible for the CGs to have experienced residual amounts of star formation and therefore have bluer photometric colours [$\sim2$ per cent of the CGs in redMaPPer are blue; @Rykoff2014].

The galaxy with the highest $P_{\mathrm{CEN}}$ is not necessarily the brightest galaxy. This is because, apart from the luminosity, the local galaxy density around the CG candidate is also considered. Central galaxies are expected to be found in the highest density central regions of 