Last month, I looked at the effect of Louisville's offense on its defense. When a Louisville offensive possession ends, they get to set up their press. Setting up their defense makes it dramatically more difficult for opponents to score. Both field percentage and turnover percentage are influenced by the Louisville press.
The one and done nature of the NCAA Tournament does not allow for teams to have an off night. Poor shooting can knock a heavily favored team out for good. A poor shooting night is fairly difficult to control because it happens to all teams at some point. Going back to the Louisville example, a team is going to be even more vulnerable to an upset if their bad shooting also affects their defense.
I looked at the 10 teams with the best NCAA Championship odds according to Vegas Insider (note: the odds were made before the Michigan-Michigan State game). I then took these 10 teams and compared their opponent's shooting efficiency when they make a shot leading to the defensive possessions versus when they don't. This data comes from hoop-math.com:
As you can see, Indiana and Louisville's defenses are most negatively influenced by missing shots. This does not account for the extra turnovers caused by the Louisville set defense, so Louisville is probably more dependent on making shots than Indiana. On the flip side, Michigan and Arizona's defenses hardly change regardless of their previous offensive possession. Defense is not quite Michigan's specialty (41st in AdjD), but Arizona is definitely respectable (23rd in AdjD). Thus, Arizona may be less susceptible to a bad shooting night because of strong "transition" defense than other championship contenders. I'll attempt to take a closer look at this in the near future.