Asynchronous online discussions (AODs) are widely used in hybrid courses and online education. AODs with high levels of interaction can enhance students' cognitive development and knowledge construction, providing a solid platform for the development of deep learning and critical thinking skills. However, few empirical studies have been conducted on the effectiveness of asynchronous online discussion methods. In this study, AOD was used as the pre-class activity of offline oral output. With social network analysis (SNA) and quantitative analysis, we compared the effect of three different facilitation strategies in AODs on students' interaction level, as well as examined the correlation between individual students' interaction patterns in AOD and their critical thinking ability assessment in EFL public speaking. According to the study, peer-facilitated asynchronous online discussions can significantly improve network density and centrality, increase strong associations between members, and facilitate sub-group formation compared to teacher facilitation. Meanwhile, node strength had a more significant positive correlation with the subsequent performance of critical thinking ability in EFL public speaking than node degree.