Predicting daily patient volume is necessary for emergency department (ED) strategic and operational decisions, such as resource planning and workforce scheduling. For these purposes, forecast accuracy requires understanding the heterogeneity among patients with respect to their characteristics and reasons for visits. To capture the heterogeneity among ED patients (case-mix), we present a patient coding and classification scheme (PCCS) based on patient demographics and diagnostic information. The proposed PCCS allows us to mathematically formalize the arrival patterns of the patient population as well as each class of patients. We can then examine the volume and case-mix of patients presenting to an ED and investigate their relationship to the ED's quality and time-based performance metrics. We use data from five hospitals in February, July and November for the years of 2007, 2012, and 2017 in the city of Calgary, Alberta, Canada. We find meaningful arrival time patterns of the patient population as well as classes of patients in EDs. The regression results suggest that patient volume is the main predictor of time-based ED performance measures. Case-mix is, however, the key predictor of quality of care in EDs. We conclude that considering both patient volume and the mix of patients are necessary for more accurate strategic and operational planning in EDs.