"AllEventsCount" (aka "EventsCount") returns the overall number of events throughout the evolution (
the Length of "AllEventsList").
"GenerationEventsCountList" gives the number of events per each
generation (Length mapped
over "GenerationEventsList"):
In[] := WolframModel[{{1, 2}} -> {{1, 3}, {1, 3}, {3, 2}},
{{1, 1}}, 5, "GenerationEventsCountList"]
Out[] = {1, 3, 9, 27, 81}