Several studies contribute with valuable insights into agile teamwork performance. Currently, Scrum is dominating the industrial agile software development practices. Yet, there is a lack of studies that directly explores the role of team maturity and key components of the Scrum framework on being successful at Scrum. We investigate the impact of team maturity and four categories of the Scrum framework (team composition, Scrum values, Scrum roles, and Scrum events) on the perception of being successful at Scrum. Hence, we uncover and provide deeper insights into the characteristics and practices of what makes a team successful at Scrum. We carry out a large-scale and cross-sectional survey. We conduct Pearson's chi-square test of independence and logistic regression analysis for team maturity and the remaining variables on being successful. After surveying 182 Scrum team members, the results show that being successful at Scrum depends on the team maturity level. Team composition variables (fully allocated, low turnover rates, required skills and expertise, and self-management) and directing work in accordance with Scrum values (openness and courage) have an impact. All three Scrum roles are important. Particularly impactful are the developers’ ability to adapt their plans, the product owners’ mandate to prioritize, and the Scrum masters’ ability to ensure that all events take place. Following all Scrum events has an effect on the perception of being successful at Scrum. This work constitutes a valuable contribution to agile practitioners and organizations who are already involved in agile development or plan to pursue agility. Organizations can influence Scrum teams’ journey towards becoming successful at Scrum by ensuring the stability required to allow team maturation and decision-making relevant to team composition variables. This work also provides reflections that are useful for Scrum teams’ practices and internal dynamics related to values, roles, and events.