The transition to a cleaner and smarter electricity system is being spurred by new policy approaches aiming at delivering a decentralized, digital, and decarbonized energy future. This calls for the adaptation of incumbent technologies, policies, and actors, as well as for the introduction of new system components. The changing role of electricity distribution systems, and of distribution system operators, has been a focal aspect of recent market design efforts, given the critical role of network infrastructure and the importance to adjust its operations, and regulatory framework. We build on a novel dataset from 124 DSOs and apply a methodology combining Factor analysis and a Tobit model to evaluate the role of market, regulatory, investment, and firm-level factors on technological, business model, and market design adaptation. Our results indicate that hybrid regulatory models contribute to DSOs adaptation. Investing in smart grids is found to have a positive effect on adaptation. Regarding firm-level characteristics, the results indicate that unbundling does not affect adaptation, however larger DSOs are found to be better able to adapt. These findings provide timely empirical evidence for advancing regulatory and policy approaches toward the adaptation of incumbents in a rapidly changing electricity sector.