In this talk, an extensive experimental study of a Statistical Machine Translation system, Moses, from the point of view of its learning capabilities is presented. Very accurate Learning Curves are obtained, by using high-performance computing, and extrapolations of the projected performance of thesystem under different conditions are provided. Our experiments suggest:

1. The representation power of the system is not currently a limitation to its performance,
2. The inference of its models from finite sets of i.i.d. data is responsible for current performance limitations,
3. It is unlikely that increasing dataset sizes will result in significant improvements (at least in traditional i.i.d. setting),
4. It is unlikely that novel statistical estimation methods will result in significant improvements.

The current performance wall is mostly a consequence of Zipf's law, and this should be taken into account when designing a statistical machine translation system. A few possible research directions are discussed as a result of this investigation, most notably the integration of linguistic rules into the model inference phase, and the development of active learning procedures.