Upper panel: Probability density function (pdf) of the systematic offset parameter, η, in our cluster sample. The gray band ranges between the 16th and 84th percentile of η in the entire sample. Bottom panel: Median η of each cluster (as indicated in the vertical axes) according to the α_turb ≥ 0 model, with error bars corresponding to the 16th and 84th percentiles. For reference, η = 1 (no offset) is indicated with a red vertical line.