How individuals in a group move relative to one another can influence both their survival and fitness. Spatial positioning has been well studied in baboons (Papio spp.), which travel collectively in line formations called "progressions". Early studies of baboon progressions presented contradictory findings – some reporting random positioning of individuals, and others reporting non-random positioning, thought to protect more vulnerable group members. Here, we revisit this topic and use high-resolution GPS tracking data to study a chacma baboon (Papio ursinus) group’s travel progressions on the Cape Peninsula, South Africa. We identify 78 progressions over 36 days and find that progression orders are not random. We test four non-exclusive hypotheses to explain progression orders: vulnerable individuals position themselves in the middle of the progression (risk hypothesis), subordinate individuals position themselves at the front to gain better access to resources (competition hypothesis), dominant individuals assume leading positions (group decision-making hypothesis), or progression order is an emergent outcome of underlying social bonds (social spandrel hypothesis). We find no evidence that progression orders are adaptive responses to minimise an individual’s risk, maximise their resource acquisition, or are the result of decision-makers leading the group. Instead, we find that individuals’ positions are predicted by pairwise affiliations and social dominance, with more dominant individuals occupying central positions in progressions. This non-random structuring of individuals during progressions can be considered a side-effect or outcome of underlying social forces acting among the individuals, providing an example of a ‘social spandrel’ in collective animal behaviour.