Total hip and knee replacements are the most common orthopedic procedures performed due to osteoarthritis. Pain is an intrinsic symptom accompanying osteoarthritis, persisting long before surgery, and continuing during the preoperative and postoperative periods. Appropriate pain management after surgery determines the comfort, duration, and cost of hospitalization, as well as the effectiveness of postoperative rehabilitation. Individual differences in pain perception and tolerance in orthopedic patients remain an important research topic. Therefore, the aim of this study was to investigate the predictors of analgesic requirements (morphine, acetaminophen, and ketoprofen), including individual pain threshold and tolerance, body mass index (BMI), diabetes, and beliefs about pain control in patients undergoing elective hip or knee arthroplasty using a multilevel regression model (N = 147, 85 women, 62 men, 107 after hip replacement, and 40 after knee replacement). Results: Higher pain tolerance was associated with a lower dose of morphine per kg after surgery. Patients undergoing hip surgery received a lower dose of ketoprofen than patients undergoing knee surgery. The more the patient believed in personal pain control, the stronger the negative relationship between pain tolerance and morphine requirement. The lowest doses were given to patients with the highest pain tolerance and the greatest belief in personal control. Factors such as belief in pain control and pain tolerance should be considered in comprehensive postoperative pain management in orthopedic patients to reduce opioid doses and, thus, side effects.