In Neural Machine Translation, it is typically assumed that the sentence with the highest estimated probability should also be the translation with the highest quality as measured by humans. In this work, we question this assumption and show that model estimates and translation quality only vaguely correlate. We apply Minimum Bayes Risk (MBR) decoding on unbiased samples to optimize diverse automated metrics of translation quality as an alternative inference strategy to beam search. Instead of targeting the hypotheses with the highest model probability, MBR decoding extracts the hypotheses with the highest estimated quality. Our experiments show that the combination of a neural translation model with a neural reference-based metric, B leurt , results in significant improvement in human evaluations. This improvement is obtained with translations different from classical beam-search output: These translations have much lower model likelihood and are less favored by surface metrics like B leu .