Subtraction {#bs}
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In this work, the method we adopt to correct for contamination in the stacking data is called “background subtraction”. The background is decontaminated by considering a mean local background around each cluster in an annulus at a projected radius $r_1 < r_p < r_2$, where $r_1$ and $r_2$ are the inner and outer radii, respectively, and the contaminated galaxy properties at the center can then be removed by subtracting the same galaxy properties of the background. This method has been widely used to compute the luminosity function, e.g. [@bar07], and has been demonstrated numerically to be able to accurately recover the underlying luminosity function selected in three dimensions [@val01]. We adopt the method to explore galaxy properties for photometric redshift samples, similar to the approach used in [@loh08] and [@li09]. We stack galaxies around group centers within a redshift slice for which the redshift difference between galaxy and group has to be smaller than the photo-$z$ accuracy, i.e. $|z - z_{\textrm{grp}}| \leq \sigma_{\Delta z/(1+z_s)}$, where $z$, $z_{\textrm{grp}}$, and $\sigma_{\Delta z/(1+z_s)}$ are galaxy redshift, group redshift, and photo-$z$ accuracy, respectively. The position of the brightest cluster galaxy (BCG) is selected as the center. From the center, the inner 