As the COVID-19 pandemic motivated a shift to virtual teaching, exams have increasingly moved online too. Detecting cheating through collusion is not easy when tech-savvy students take online exams at home and on their own devices. Such online at-home exams may tempt students to collude and share materials and answers. However, online exams' digital output also enables computer-aided detection of collusion patterns. This paper presents two simple data-driven techniques to analyze exam event logs and essay-form answers. Based on examples from exams in social sciences, we show that such analyses can reveal patterns of student collusion. We suggest using these patterns to quantify the degree of collusion. Finally, we summarize a set of lessons learned about designing and analyzing online exams.