The teams that make the Final Four will most likely be the ones that had the easiest path to the Final Four. UConn's top teams that made the Final Four played a 10 seed (Gonzaga 1999), an 8 seed (Alabama 2004), a 3 seed (Missouri 2009), a 5 seed (Arizona 2011) and a 4 seed (Michigan State 2014). UConn didn't have to play the highest potential seed in their region to make the Final Four in those years. Arguably, the 2014 run was against the highest seeds of any of UConn's Final Four runs, which made sense since UConn was a 7 seed that year. UConn only played the 2nd highest potential seed once in that stretch. Places where UConn got stopped on its way to the Final Four: 1990 (Duke 3 seed), 1995 (UCLA 1 seed), 1998 (UNC 1 seed), 2002 (Maryland 1 seed), and of course, 2006 (George Mason 11 seed). UConn played really well in both the 1995 Final Eight and the 2002 Final Eight, but the opponent was just too good. You know the best way to avoid playing other top teams before the Final Eight? Get a higher seeding.
5 or fewer teams of every seed 5 or worse have made the Final Four in the history of the NCAA Tournament. 13 4's, 17 3's, 30 2's and 59 1's have made the Final Four. Part of that is that the higher ranked teams are generally better, but a big part is that it is hard to beat a lot of good teams in a row, so the further a team can go before having to face top competition, the better.