Self-determination theory (SDT) is one of the most well-known approaches to achievement motivation. However, the three basic psychological needs of SDT have not received equivalent attention in the literature: priority has been given to autonomy, followed by the need for competence, with research into relatedness lacking (Bachman and Stewart in "Teach Psychol" 38: 180-187, 2011. doi: 10.1177/0098628311411798). One new educational setting where relatedness may be particularly important is massive open online courses (MOOCs), which provide unprecedented opportunities for either relatedness or isolation. The purpose of the research was to use Bayesian networks (BN) to establish probabilistic relationships between learners' basic psychological needs in the context of one MOOC. The majority (59 %) of participants (N = 1037; 50% female and 50% male) were under 45 (age range was 18-74 years). This sample represented approximately 88 regions and countries. Participants completed a revised Basic Student Needs Scale (Betoret and Artiga in "Electron J Res Educ Psychol" 9(2): 463-496, 2011). In order to reveal the best structural understanding of SDT within a MOOC learning environment, analysis of the data involved the development of a BN probabilistic model. The best fitting BN model included autonomy, competence, and relatedness--resulting in a probabilistic accuracy of 77.41%. Analyses revealed participants with high autonomy had an 80.01% probability of having a moderate level of competence. Relatedness was distinct from the autonomy and competence relationship. The strong inter-connections between autonomy and competence support existing research. The notion that relatedness may be a distinct need, at least in this context, was supported and warrants future research.