  In this paper, we examine the statistical soundness of comparative
assessments within the field of recommender systems in terms of reliability and
human uncertainty. From a controlled experiment, we get the insight that users
provide different ratings on same items when repeatedly asked. This volatility
of user ratings justifies the assumption of using probability densities instead
of single rating scores. As a consequence, the well-known accuracy metrics
(e.g. MAE, MSE, RMSE) yield a density themselves that emerges from convolution
of all rating densities. When two different systems produce different RMSE
distributions with significant intersection, then there exists a probability of
error for each possible ranking. As an application, we examine possible ranking
errors of the Netflix Prize. We are able to show that all top rankings are more
or less subject to high probabilities of error and that some rankings may be
deemed to be caused by mere chance rather than system quality.
