I think the hat tricks may be undercounted. 67 did it 2008-2010, making finals each time. There may be more!
Put together some stats because I'm done with finals and don't know what to do with myself. Only 21 teams have even been on Einstein 3 times. Of those, only 4 have made it to Einstein 3 times in a row (you guys got all of them). The only active streaks are 1678's (3) and 1114's (2).