Passive agents in ancient Greek exhibit a well-known alternation between dative case and prepositional phrase. It has long been recognized that grammatical aspect plays a crucial role in this alternation: dative agents preponderate among aspectually perfect predicates, prepositional phrase agents elsewhere. Although the importance of grammatical aspect is undeniable, it is not the only factor that determines the realization of passive agents. The identification of other factors has proven challenging, however, not least because previous researchers have lacked methods for assessing the relative importance of determinants that influence the realization of agent phrases. In this paper, I use Bayesian mixed-effects logistic regression to provide a multifactorial account of differential agent marking in Herodotus, according to which the realization of passive agent phrases is conditioned by the relationship between semantic role and referential prominence (Haspelmath 2021). Dative agents are favored in clauses where semantic role and referential prominence are aligned (i.e., the agent is referentially prominent or the patient is referentially non-prominent). By contrast, prepositional phrase agents are more likely when semantic role and referential prominence are at odds (i.e., the patient is referentially prominent or the agent is referentially non-prominent).