Projection effects, whereby galaxies along the line-of-sight to a galaxy cluster are mistakenly associated with the cluster halo, present a significant challenge for optical cluster cosmology. We use statistically representative spectral coverage of luminous galaxies to investigate how projection effects impact the low-redshift limit of the Sloan Digital Sky Survey (SDSS) redMaPPer galaxy cluster catalog. Spectroscopic redshifts enable us to differentiate true cluster members from false positives and determine the fraction of candidate cluster members viewed in projection. Our main results can be summarized as follows: first, we show that a simple double-Gaussian model can be used to describe the distribution of line-of-sight velocities in the redMaPPer sample; second, the incidence of projection effects is substantial, accounting for $sim 16$ per cent of the weighted richness for the lowest richness objects; third, projection effects are a strong function of richness, with the contribution in the highest richness bin being several times smaller than for low-richness objects; fourth, our measurement has a similar amplitude to state-of-the-art models, but finds a steeper dependence of projection effects on richness than these models; and fifth, the slope of the observed velocity dispersion--richness relation, corrected for projection effects, implies an approximately linear relationship between the true, three-dimensional halo mass and three-dimensional richness. Our results provide a robust, empirical description of the impact of projection effects on the SDSS redMaPPer cluster sample and exemplify the synergies between optical imaging and spectroscopic data for studies of galaxy cluster astrophysics and cosmology....
