Watching UEFA football (aka soccer) league tournaments recently I've come to appreciate the format. Europeans have been doing sports longer than the U.S., might we learn something from them?
Under UEFA rules, teams play a home-and-home and the team with the most goals wins. In the event of a tie, the team with the most away goals wins. If still a tie, you go to overtime and then penalty kicks.
I think this would be great for NCAA basketball (and perhaps football). Most conference teams currently play a home-and-home. Let's declare the one with the most points the winner. An individual game would therefore matter less. The last possession of a game would receive less focus, which is currently the error in thinking in today's game. Teams would rarely play an overtime. An RPI would be less meaningful in favor of (arguably more accurage) rating systems like Sagarin that factor in points scored. We could potentially have less arguing in March about "these two bubble teams split during the regular season, which one is tournament worthy?"
I think you could make the NIT a pilot program for the format to help generate revenue for the schools and draw more interest to that tournament. If people like the format, hey, you could double the number of NCAA tournament games with the new format-- and make the outcome more accurate, similar to a playoff.
Another problem it would solve: Kentucky was an NIT #1 seed but had to play on the road at Robert Morris due to scheduling conflicts that week (the school was hosting the NCAA first round). Having a home-and-home would have solved that problem, they could have played in Lexington the following week.
How would it affect the strategies of the teams? The first game probably wouldn't be affected at all, but the tempo of the second game would likely be different than it otherwise might be. A team that got blown out the first game could be highly motivated to make up that margin the second. Behold the second half of Galatasaray-Real Madrid this week. Galatasaray went into the second half of the second leg down 4-0 in aggregate. RM then relaxed while Galatasaray attacked, quickly scoring 3 goals and making it quite exciting to watch.
Here's a fun experiment. Look at one of the home-and-home games your favorite team played this season. Total the points scored by each team and use away goals as tie-breaker. Using this format, who won? Do you think that method of determining the victor is a more accurate one?