Aristotle and Callisthenes were not the first authors to write on the history of the Pythian Games at Delphi. There was a slightly earlier work on this subject by the historian Menaechmus of Sicyon. It is necessary to consider this work in some detail in order to clarify its relationship with the Aristotelian Pythionikai and to establish the ways in which Aristotle's and Callisthenes' treatise on the Pythian Games broke new ground.

The list of Aristotle's work compiled by Hesychius contains one significant piece of information that is not found in the version of the list transmitted by Diogenes, the statement ἐν ᾧ Μέναιχμον ἐνίκησεν attached to Πυθιονίκας βιβλίον. This statement was evidently taken from Andronicos' treatise on the Aristotelian corpus (first century) and added to the Hesychian list by one of its editors.

In his analysis of this material, Paul Moraux understood ἐνίκησεν to mean that the amphictyons held a competition to produce a Pythionikai in which Aristotle and Callisthenes outdid Menaechmus. As Angelos Chaniotis has pointed out, this is unlikely because there is no evidence for contests of this sort at Delphi or anywhere else in the Greek world. August Brinkmann had made the same suggestion at an earlier date and pointed to the competition that the Messenians held for a war memorial at Olympia, the result of which was the Nike of Paionios.