Online group debates hosted in asynchronous threaded discussions can facilitate critical thinking between discussants (and increase deeper understanding of complex problems) by eliminating the need for turn-taking while formulating and presenting premises to support and challenge claims. Yet to be determined is to what extent does the current number of posts (premises from teammates, premises from the opposing team, supportive replies to premises, and opposing replies to premises) induce production blocking to disrupt the generation of new premises. Statistical discourse analysis was conducted on 1554 postings from online debates produced by four cohorts of students enrolled in an online graduate-level course. The resulting stochastic model revealed that: (a) the number of premises posted by the other team, premises posted by teammates, and supportive replies from teammates were associated with the largest to smallest drop in the likelihood of posting a new premise, respectively; and (b) the number of oppositional replies from the other team was associated with an increased likelihood of posting a new premise. These findings provide evidence to support the use of specific strategies for structuring and sequencing the argumentation task to generate larger numbers of premises to achieve a deeper and more thorough analysis of problems and claims.