As startups and micro teams adopt real-time collaborative instant messaging solutions, a wealth of data is generated from day to day usage. Making sense of this data can be a challenge to teams, given the lack of inbuilt analytical tooling. In this study we model the distributions of duration, inter-arrival time, word count and user count of real-time electronic chat conversations in a framework, where these distributions can be used as an analogue to service time estimation of problem determination. Using both an enterprise and an open-source dataset, we answer the question of what distribution family and fitting techniques can be used to adequately model real-time chat conversations. Our framework can help startups and micro teams alike to effectively model their real-time chat conversations to allow high value decisions to be made based on their collaboration outputs.