Recently, Ken Pomeroy added a new feature to his site called "Game Plan". If you don't frequent www.KenPom.com, you're really missing out. No one does a better job of taking easily misused box score statistics and converting them into efficiency (i.e. Duke's bad field goal percentage being outweighed by incredible offensive rebounding numbers last season). It's really interesting to see where different teams fit in (for instance, would you have guessed Washington is the fourth most efficient team in the country?), and you can learn a whole lot from usage numbers and some of the more "advanced stats."
Anyway, Game Plan is essentially a table that goes looks at a team's efficiency game by game instead of averaged out over the season. Below the table are the correlations between a specific stat and the team's offensive and defensive efficiencies. So for Kansas effective field goal percentage is strongly correlated to offensive efficiency and effective field goal percentage defense is strongly correlated to defensive efficiency, which makes a lot of sense. Kansas' worst offensive efficiencies came at Michigan, against Nebraska, against USC and against UCLA (not surprisingly those were some of Kansas' closest games). A little more surprisingly the Jayhawks' worst defensive performances came against Arizona, Baylor, UCLA and USC (though Baylor can be counted as a garbage game, as it was a blowout).
For Texas effective field goal percentage and offensive rebounding percentage correlate strongly to the team's offensive efficiency. Likewise, effective field goal percentage defense and turnover percentage defense correlate strongly to Longhorn defensive efficiency. Texas' offensive duds came against USC, Lamar, Michigan State, North Florida and Pitt. USC shouldn't surprise you, but I was a little surprised to see that the Longhorns were so inefficient against Michigan State (though their defense was tremendous). As for defensive duds Coppin State, USC, Rice, Connecticut and Pitt lead the way. Not surprisingly, all three of Texas' losses are in that bunch.
In conclusion, both of these teams rely on shooting well and making their opponent shoot poorly. Texas also relies on offensive rebounding and turning their opponent over. So statistically speaking, the keys of the game are definitely effective field goal percentage, rebounding and turnovers. That's not surprising, but the statistical evidence definitely gives them more weight in my opinion.