BD-PSNR, and more generally BD-VMAF or BD-quality, is the quality-gain twin of BD-rate. The same two rate-quality curves can be read two ways: read the gap horizontally - the bitrate difference at equal quality - and you get BD-rate, the bitrate saving; read it vertically - the quality difference at equal bitrate - and you get a BD-quality number, BD-PSNR if the metric is PSNR, BD-VMAF if it is VMAF. Bjontegaard's original 2001 note defined both; the paper's title is literally about average PSNR differences. The sign convention flips relative to BD-rate: a positive BD-quality is good for the test encoder, meaning more quality at the same bitrate. The catch is that a quality gain is harder to act on than a bitrate saving, because a value like 2 dB means different things at different bitrates, which is why streaming teams usually report BD-rate - bitrate maps directly to bandwidth and cost.
