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The center determination of a galaxy cluster from an optical cluster findingalgorithm can be offset from theoretical prescriptions or $N$-body definitionsof its host halo center. These offsets impact the recovered cluster statistics,affecting both richness measurements and the weak lensing shear profile aroundthe clusters. This paper models the centering performance of the \RM~clusterfinding algorithm using archival X-ray observations of \RM-selected clusters.Assuming the X-ray emission peaks as the fiducial halo centers, and throughanalyzing their offsets to the \RM~centers, we find that $\sim 75\pm 8 \%$ ofthe \RM~clusters are well centered and the mis-centered offset follows a Gammadistribution in normalized, projected distance. These mis-centering offsetscause a systematic underestimation of cluster richness relative to thewell-centered clusters, for which we propose a descriptive model. Our resultsenable the DES Y1 cluster cosmology analysis by characterizing the necessarycorrections to both the weak lensing and richness abundance functions of theDES Y1 redMaPPer cluster catalog.

Dark Energy Survey Year 1 Results: Calibration of Cluster Mis-centering in the redMaPPer Catalogs