The transient ELF(~50--5000 Hz) magnetic field radiated by lightning discharges across North America was continuously measured at Duke University during the summer of 2000. In total, 881 sprite-associated lightning discharges over 17 days were analyzed. We report in detail on 76 sprites for which we could reliably determine the lightning charge moment change from the ELF data at the time of sprite onset. The charge moment change for the initiation of a sprite is found to be as low as 120 C km. By folding together the charge moment distributions of sprite-producing lightning and all positive lightning, we find that the probability of sprite generation for lightning with >1000 C km charge moment change in 90%, while the sprite probability for lightning with <600 C km charge moment change in <6 ms is <10%.