The availability of tracking data in football presents unique opportunities for analyzing team shape and player roles, but leveraging it effectively remains challenging. This difficulty arises from the significant overlap in player positions, which complicates the identification of distinct roles and team formations. In this work, we propose a novel model that incorporates a hidden permutation matrix to simultaneously estimate team formations and assign roles to players at the frame level. To address the cardinality of permutation sets, we develop a statistical procedure to parsimoniously select relevant matrices prior to parameter estimation. Additionally, to capture formation changes during a match, we introduce a latent regime variable, enabling the modeling of dynamic tactical adjustments. This framework disentangles player locations from role-specific positions, providing a clear representation of team structure. We demonstrate the applicability of our approach using player tracking data, showcasing its potential for detailed team and player analysis.