Past research has modelled statistically the language of the Homeric poems, assessing the degree of surprisal for each verse through diverse metrics and resulting to the HoLM resource. In this study we utilise the HoLM resource to explore cross poem affinity at the verse level, looking at Iliadic verses and passages that are less surprising to the Odyssean model than to the Iliadic one and vice-versa. Using the same tool, we investigate verses that evoke greater surprise when assessed by a local model trained solely on their source book, compared to a global model trained on the entire source poem. Investigating deeper on the distribution of such verses across the Homeric poems we employ machine learning text classification to further analyse quantitatively cross-poem affinity in selected books.