Continuity of care refers to the practice of capturing, sharing, and effectively using knowledge about the diagnosis and prognosis of a patient over time. Prior studies have established a positive association between continuity and quality of care. However, because previous measures have focused on the patient rather than the provider, there is no widely-accepted metric for evaluating provider performance in this context. Furthermore, existing measures frequently rely on statistical formulations that may be difficult to interpret in a clinical setting. Analytics-driven decisions must be both explainable and transparent in order to be trusted. To address this issue, we propose an explainable analytics framework based on Markovian theory for assessing provider performance. Two explainable, transparent, and pragmatic measures from Markovian theory are presented: sojourn time (number of visits with a provider before changing to another) and recurrent time (number of transitions that take place before returning to a provider). Higher-order Markov concepts are incorporated into the scoring, such as when a patient sees another provider due to scheduling conflicts, urgent care, etc., but promptly returns to the primary provider. We also generalize this higher-order model to accommodate unique weights for each provider. The proposed model elucidates the inner mechanics of Markovian theory in order to achieve explainability, and provides interpretable scores for evaluating provider performance which increases trust and transparency in analytics-driven decisions.