The alternating warm/cold phenomena in the Pacific, known as El Niño–Southern Oscillation (ENSO), is characterized by large perturbations to the worldwide climate. Indices have been defined to characterize this phenomenon. However, the commonly used indices contain an unwanted effect from the annual cycle that can be reduced by digital filtering. Using a filtered ENSO index NL on data from 1856 to the present allows more accurate calculations of various quantities to be made. New results are (1) the distribution of positive values of NL is Gaussian. Thus, large-magnitude El Niño events come from the tail of this distribution and not from some rare external perturbation. (2) The probability of occurrence of an El Niño of any magnitude can be calculated. A 1997–1998 El Niño will occur once in approximately 70 ± 20 years, while an El Niño 25% larger will occur once in approximately 700 ± 200 years. (3) The distribution of negative values of NL deviates from Gaussian because of a deficiency of large La Niña events. (4) Examination of the 20 largest El Niño events since 1856 shows that there is no increase in the frequency of such events with time.