The wide variation in upper limb motor impairments among stroke survivors presents a significant challenge to therapy. One approach is to customize treatment based on each individual’s particular movement capabilities. Past work in our lab successfully allowed patients to move any way they wanted, freely exploring while being facilitated by robot-applied forces that amplify their movement velocities. This thesis builds upon this framework by introducing a statistical approach, distribution analysis, for characterizing each patient’s patterns of movement during a special paradigm, free exploration, such that forces can be applied in a customized manner. Distribution analysis first builds a model of each individual’s unique motor deficits, which then informs the design of training forces that push each patient’s hand away from their typical movement velocities (i.e. higher probability bins) and towards their less visited velocity deficits (i.e. lower probability bins). We tracked the recovery of patients across weeks of such training using both clinical assessments and engineering metrics (Chapter II). As the success of any robotic intervention is often determined by whether patients are actively moving their affected limb, we relate their energetic contributions (quantified in terms of mechanical work) during training to their recovery outcomes and combine advanced multiple regression techniques to identify the most important biomechanical components of work (Chapter III). Lastly, we apply distribution analysis across a wider domain of variables (endpoint and joint kinematics, kinetics) and relate them to clinical measures, use them to classify stroke survivors and healthy individuals and describe the individual differences between stroke and healthy (Chapter IV). These findings represent a powerful set of new statistical modeling approaches for stroke therapy.