Human evaluation of modern high-quality machine translation systems is a difficult problem, and there is increasing evidence that inadequate evaluation procedures can lead to erroneous conclusions. While there has been considerable research on human evaluation, the field still lacks a commonly accepted standard procedure. As a step toward this goal, we propose an evaluation methodology grounded in explicit error analysis, based on the Multidimensional Quality Metrics (MQM) framework. We carry out the largest MQM research study to date, scoring the outputs of top systems from the WMT 2020 shared task in two language pairs using annotations provided by professional translators with access to full document context. We analyze the resulting data extensively, finding among other results a substantially different ranking of evaluated systems from the one established by the WMT crowd workers, exhibiting a clear preference for human over machine output. Surprisingly, we also find that automatic metrics based on pre-trained embeddings can outperform human crowd workers. We make our corpus publicly available for further research.