In protein structure prediction it is essential to score quickly and reliably large sets of models by selecting the ones that are closest to the native state. We here present a novel statistical potential constructed by Bayesian analysis measuring a few structural observables on a set of 500 experimental protein structures. Even though employing much less parameters than current state-of-the-art methods, our potential is capable of discriminating with an unprecedented reliability the native state in large sets of misfolded models of the same protein. We also introduce the new idea that thermal fluctuations cannot be neglected for scoring models that are very similar to each other. In these cases, the best structure can be recognized only by comparing the probability distributions of our potential over short finite temperature molecular dynamics simulations starting from the competing models.