In recent years an increasing number of analyses of offensive language has been published, however, dealing mainly with the automatic detection and classification of isolated instances. In this paper we aim to understand the impact of offensive messages in online conversations diachronically, and in particular the change in offensiveness of dialogue turns. In turn, we aim to measure the progression of offence level as well as its direction - For example, whether a conversation is escalating or declining in offence. We present our method of extracting linear dialogues from tree-structured conversations in social media data and make our code publicly available. Furthermore, we discuss methods to analyse this dataset through changes in discourse offensiveness. Our paper includes two main contributions; first, using a neural network to measure the level of offensiveness in conversations; and second, the analysis of conversations around offensive comments using decoupling functions.