In order to study the galaxy population of galaxy clusters with photometric data one must be able to accurately discriminate between cluster members and non-members. The redMaPPer cluster finding algorithm treats this problem probabilistically. Here, we utilize SDSS and GAMA spectroscopic membership rates to validate the redMaPPer membership probability estimates for clusters with $zin[0.1,0.3]$. We find small - but correctable - biases, sourced by three different systematics. The first two were expected a priori, namely blue cluster galaxies and correlated structure along the line of sight. The third systematic is new: the redMaPPer template fitting exhibits a non-trivial dependence on photometric noise, which biases the original redMaPPer probabilities when utilizing noisy data. After correcting for these effects, we find exquisite agreement ($approx 1%$) between the photometric probability estimates and the spectroscopic membership rates, demonstrating that we can robustly recover cluster membership estimates from photometric data alone. As a byproduct of our analysis we find that on average unavoidable projection effects from correlated structure contribute $approx 6%$ of the richness of a redMaPPer galaxy cluster. This work also marks the second public release of the SDSS redMaPPer cluster catalog.
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