Digital studies of drama have tended to emphasise the written text and network analyses. As theatre scholars, we have approached the field from a different perspective by focusing on levels of presence. This includes the embodied presence of not only the speaking characters, but also the non‐speaking characters and the imagined characters mentioned by characters present on stage. This in turn includes another embodied presence, namely that of the audience, which actively engages with the text in performance and gives presence to these imagined characters. We also emphasise the implicit performance, the spatiality of the play and the maintenance of the temporal dramaturgical structure. The study is based on the 37 plays of the Danish‐Norwegian playwright Ludvig Holberg (1684–1754), published during the period 1723–1754. Holberg's comedies were heavily influenced by Italian commedia dell'arte and stock characters, or masks, were central to his plays. In this article, we discuss the question of how we can analyse levels of presence in drama texts via digital drama analysis, both from a historical and dramaturgical point of view. Our article points to a number of potentials as well as shortcomings of digital drama analysis and to the necessary synergy of close and distant reading.