Solar proton events have been studied for over thirty years and a great deal of lore has grown around them. It is the purpose of this paper to test some of this lore against the actual data. Data on solar proton events now exist for the period from 1956 to 1985 during which time 140 events took place in which the event integrated fluxes for protons of energy > 30 MeV was larger than 105 particles cm 2. We have studied statistical properties of event integrated fluxes for particles with energy > 10 MeV and for particles with energy > 30 MeV. Earlier studies based on a single solar cycle had resulted in a sharp division of events into 'ordinary' and 'anomalously large' events.Two such entirely separate distributions imply two entirely separate acceleration mechanisms, one common and the other very rare. We find that the sharp division is neither required nor justified by this larger sample. Instead the event intensity forms a smooth distribution for intensities up to the largest observed implying that any second acceleration mechanism cannot be rare. We have also studied the relation of event sizes to the sunspot number and the solar cycle phase. We find a clear bimodal variation of annual integrated flux with solar cycle phase but no statistically significant tendency for the large events to avoid sunspot maximum. We show there is almost no relation between the maximum sunspot number in a solar cycle and the solar cycle integrated flux. We also find that for annual sunspot numbers greater than 35 (i.e., non-minimum solar cycle conditions) there is no relation whatsoever between the annual sunspot numbers and annual integrated flux.