We've done sports, movies and music, each time in early may (like before the 15th). We have seen some groups around (mostly at the pool), but they haven't been bothersome in the food courts or late at night/early AM. Maybe we've just been lucky, but they haven't seemed to be huge groups or that numerous. My personal theory on this has always been that early May is when schools are winding down, so the older kids have exams and end of year testing, etc. so can't miss school to go to WDW. But that's just a theory. The last two years we've gone in May, none of the AS resorts has had all their buildings open -- low occupancy, so no need to have them all open. I have encountered large groups at these resorts at other times of year, however. Maybe may is just slower, or we're just lucky.