Informational gain obtained for our X-ray fitting results. Top row: Distribution of the Kullback-Leibler divergence for hydrogen column density, photon index, and observed X-ray flux. The solid black lines show the distribution for sources with more than ten net counts in their X-ray spectra; the grey shaded areas show the distribution for sources with fewer than ten net counts. The vertical dashed red lines show D_KL = 0.5. Bottom row:D_KL vs net counts for the same three parameters in the top row. The symbols are colour-coded according to the source survey (blue: XXL-North; red: CCLS; orange: CDF). The horizontal dashed red lines again show D_KL = 0.5. Right column: Four examples of the log N_H posterior distribution (grey histograms) obtained from our X-ray spectral fits, for different D_KL values. The horizontal dashed lines show the flat prior distribution assumed in our analysis.