Poussin's sketch was not intended as a faithful representation of the sculpture, but to be stored and referred to, as part of his visual repertory of antiquities, which was extensive and which made its presence felt in most of his paintings.
The sketch by Poussin served as a preliminary study, rather than an exact representation, and was intended for storage and future reference, as it was one of many examples from his extensive repertoire of classical antiquities that he often incorporated into his paintings.