Operative parameters of La Fuenfría Hospital such as: hospitalized patients; daily admissions and discharges were studies for the hospital as a whole, and for each hospital’s service unit (henceforth called ‘services’). Conventional statistical analyzes and fractal dimension analyzes were performed on daily In-Patient series. The sequence of daily admissions and patients staying on each service were found to be a kind of random series known asrandom walks(Rw), sequences where what happens next, depends on what happens now plus a random variable.Rwanalyzed with parametric or nonparametric statistics may simulate cycles and drifts which resemble seasonal variations or fake trends which reduce the Hospital’s efficiency. Globally, inpatientsRws in LFH, were found to be determined by the time elapsed between daily discharges and admissions. The factors determining LFH R were found to be the difference between daily admissions and discharges. The discharges are replaced by admissions with some random delay and the random difference determines LFHRws. These findings show that if the daily difference between admissions and discharges is minimized, the number of inpatients would fluctuate less and the number of unoccupied beds would be reduced, thus optimizing the Hospital service.