I'm still learning my way around here so I'm not sure what the most appropriate way to cross post stuff I write on VandySports is. Please bear with me.
So, you can read the antecedent discussion here if you wish. force10jc gives voice to something a lot of us are thinking about this week: "I see Butler playing for a National Championship as a 5-seed and can't help but ask why not us as a 4-seed." Here's my detailed discussion -- NOT an answer to the question, but rather a discussion of the method I'd use to answer the question -- because at the end of the day, I think it's largely an overreaction to a small sample of data. (Just because I'm calling it an overreaction doesn't mean I don't wonder this too!)
I think there's some element of luck and some element of merit. However, to keep us focused on the latter, here's a far more interesting question to me: How is that Butler is the 12th most efficient team in the land and Vanderbilt has topped out at 23rd (2004) or more recently 35th (2007, 2010)?
If you're consistently in the top 12 in efficiency over a decade, you're much more likely to make a FF than if you're consistently between 20th and 30th.
So then, the primary way Butler is so efficient is absolutely awesome defense. In the broad category of defense, they do all the following well (top third of D-I) but in descending order of rank: rebound defensively (14th), make the other team miss shots, cause turnovers, avoid fouling. They're much shorter than Vanderbilt but much better at DReb so I'd start there.
I get that [we're] looking for bigger-picture trends, and I love big-picture trends, but sometimes I fool myself into imposing a pattern without considering all the facts. So I'd keep drilling down like this, getting to the fine-grained facts and then building back up to see if the big picture is supported by them. To wit: Does VU typically rebound defensively less well than our height would suggest? 2009 was an exception, but in 2007, 08, and 10 it's a marked weakness. That's not a ton of data but enough to strongly suggest it's a perennial problem.
Why didn't we D-rebound well in 2010? Suppose it's because we had a somewhat unmotivated starting center and lacked a big-man coach. Does VU usually recruit apathetic big guys? I'd suggest not, so that's not a pattern, but I'm open to being convinced. Has VU had a big-man coach in the past? No, so that might be a pattern.
Etc. etc. as long as you want to go -- that's how I would approach it. I'd deal with efficiency and its components rather than Final Fours and their components because it's hard to measure everything that goes into a Final Four, including dumb luck, but it's relatively easier to measure the components that explain most of what makes a team efficient.