What's the ideal Final Four team?

Every year, as we sort through the NCAA tournament bracket -- justifying selections and dismissing our putative losers -- we talk a lot about what it takes to win in the Big Dance, about what a team needs to have to make it to the Final Four.

There are tangible recommendations. Defense. Rebounding. Good guard play. (That's a big one. Guards are popular, and for good reason.) We also, of course, hear about intangibles. Toughness. Intensity. Focus. Experience. Will.

And we also hear about coaching: how coaches scout and analyze opponents, how they implement that information and execute on it, how they see the game as it unfolds, how they react.

And still, though we like to think we have these categories pegged, each year the NCAA tournament baffles us anew. Outliers abound. Why? Because four games -- the number you must win to reach the Final Four, unless you're VCU -- is just four games.

Compared to the regular season, it's an incredibly small sample size. Crazy things happen in small sample sizes, and the reasons -- again, look at VCU -- quite often make very little sense.

This is the distinct glory of the NCAA tournament specifically, and of basketball generally. For as much as we can quantify these teams' performances, for as much as we sift through scouting breakdowns and positional charting, the game is the game. Not only are there things about basketball we can never quantify -- in the same way you click with some pickup teammates and languish with others -- but in a given 40 minutes, anything can happen.

As advanced as your bracket analysis is, more often than not, you're probably going to be wrong. How great is that?

Still, we do our best. To that end, I decided to round up and analyze the Final Four teams of the efficiency era, from 2003 to 2011. Advanced analytics have changed the way we study this game. Dean Oliver's four factors -- and the simple, tempo-free breakdowns of the games they are based on -- have become the best ways to very quickly learn what makes a team tick. You probably know this already, but if not, the four factors are, essentially: shooting, turnovers, rebounding and how often a team gets to the free throw line.

Simple enough, right? Right. That's what makes the method Oliver helped pioneer so elegant (and why we're all thrilled to call him an ESPN employee). It's revealing, but also easy to understand.

A few things to clear up before diving into the numbers:

• What follows is entirely unscientific, and hardly the most advanced analysis you'll find out there. The most complicated thing that went into this -- besides me actually sitting down and counting up various team attributes, which was complicated because I swore off math after one pass-fail semester of college precalculus (I passed) -- was asking my Excel wizard of a roommate to calculate some averages for me in a spreadsheet. There is no secret sauce here. I have no proprietary, mind-blowing formulas to reveal. Just want to make that clear up front.

• All data came via Ken Pomeroy's KenPom.com, which you should definitely subscribe to if you want to know as much as possible about this here basketball.

• Many readers are by now plenty familiar with this stuff, but just in case you're not: effective field goal percentage is the same as field goal percentage, but with a weight for 3-point field goal accuracy built in, since 3s count more than 2s. Turnover rate is the percentage of a team's possessions in which it -- you guessed it -- commits a turnover. Offensive rebounding rate is the percentage of available possessions in which a team rebounds its own miss. And free throw rate (or FTA/FGA) is simply the number of free throws a team shoots divided by its number of field goals. It tells us how often a team is creating chances at the line. Cool? Cool.

So: What do the past nine Final Fours have to show us? What can we learn about this year's Sweet 16 teams, and their respective chances for advancement, from the teams that came before?

It's safe to say most of the teams that made the past nine Final Fours were near the top of the sport in offensive and defensive efficiency in each of their seasons, barring certain outliers and particularly hot tournament streaks (q.v.: 2011 VCU). So I decided to examine the four factors alone, to see if there has been some certain stylistic trend that repeatedly predicts success. The answer is, to paraphrase an Oasis album title, a definitive maybe.

As a snapshot, here's the average -- including both actual performance and average rank -- of all 36 Final Four teams combined. If you jumbled every Final Four team from the past nine years together into one entity, this would be it:

Average effective FG pct: 52.9 (Average rank: 58.2)
Opponent average eFG pct: 45.8 (Rank: 44.9)

Average turnover pct: 19.1 (Rank: 79.8)
Opponent average turnover pct: 20.8 (Rank: 167.7)

Average offensive rebounding pct: 37.6 (Rank: 61.0)
Opponent avg offensive reb. pct: 31.2 (Rank: 93.0)

Average free throw rate: 38.7 (Rank: 127.4)
Opponent avg free throw rate: 31.1 (Rank: 77.5)

What do these numbers say? Well, they're averages, and there are plenty of outliers in the mix, so they only go so far. But a few things stick out:

1. Forcing turnovers isn't a huge deal. By far, the lowest average ranking on this list is opponents' turnover percentage. This makes sense: Forcing turnovers is great, of course, but it's a bit unreliable, because teams that are really good at preventing turnovers are probably going to be able to do so even against a team that's particularly good at forcing them. It's the whole benefit of knowing where you're going. It's why NFL wide receivers get open all the time.

2. Shooting is a big deal. Relatively speaking, effective field goal percentage (or how well teams shoot, factoring in an added half-percentage point for 3-point FG%) comprises the highest relative average rankings of any two items on this list. Shoot well and prevent other teams from doing so. That sounds like a pretty good basketball strategy to me. Insightful stuff, right?

3. Rebounding the ball on offense is helpful. Well, duh. If you rebound your own misses, not only do you get second-chance opportunities around the rim and extra possessions, but -- and this feels especially important in tournament play -- you compensate for your off shooting nights with something that can be replicated on a nightly basis, no matter how hot or cold you are: effort on the offensive boards. More on this below.

4. Free throw rate? Meh. By far the lowest average offensive rank in the above chart is free throw rate, or how often teams attempt free throws as a percentage of their field goal attempts. You'd think this would be a major factor in tournament play, following the same logic as rebounding: When your shooting goes cold, you can battle through by creating contact, getting to the foul line, and making up the difference in easy points. But it turns out free throw rate, while nice, doesn't seem to matter all that much.

To dig in just a tad bit deeper, I went through and counted the number of teams that ranked in the top 25 in each of the four factors. Top 25 marks in free throw were almost shockingly infrequent: Only three Final Four teams in the past nine years have ranked among the nation's 25 best in that particular season in the statistic. (Those teams: 2010 Butler, 2009 UConn, 2005 UNC).

By comparison, eight of the past 36 Final Four teams ranked among the top 25 in their respective seasons in turnover percentage. Thirteen teams ranked among the top 25 in turnover rate.

And the big winner? Offensive rebounding rate. By my count, a whopping 19 of the past 36 teams to compete in the Final Four ranked among the best 25 in the country in offensive rebounding rate. There wasn't a single season in which at least one team ranked inside the top 25 in this metric wasn't in the Final Four. There were three years (2010, 2009, 2003) in which three members of the Final Four earned such glass-cleaning distinction, and one year -- 2008, when all four No. 1 seeds (Kansas, Memphis, UCLA and UNC) emerged from their various regions -- in which all four Final Four combatants ranked among the top 25 in offensive rebounding rate.

What does this tell us? That rebounding your own misses is a pretty solid tournament strategy.

Other than that? Well, look at the averages again. If anything, those numbers tell us something we already know: There are no guarantees in March. That goes for elite seeds (just ask Duke and Missouri), but it also goes for style.

Some teams progress through the tourney field by keeping turnovers low and slowing down the game, others do it by shooting the ball well as a baseline and extending the excellence from there, while some just flat get after the offensive glass on a nightly basis. With the possible exception of offensive rebounding rate -- in which only slightly more than half of the past eight 36 Final Four qualifiers were considered among the nation's 25 best -- there isn't one obvious stylistic template to follow.

Sometimes teams that dominate all season get to the Final Four. Sometimes teams that struggle for four months get hot at the right time. Sometimes teams make a buzzer-beater or two on their way, and the next thing you know, they're taking an unlikely crack at the title.

The lesson, as always: Crazy things happen in the tournament. And everyone -- well, almost everyone -- has a shot.

So what about the 2012 Sweet 16 field? We pulled each remaining Final Four hopeful's various four factors performance and compared it with the average Final Four team from the past nine years. Compared to those 36 teams, where does each team stand in each facet of the game, both on offense and defense? Have a look for yourself:

Average effective FG pct: 52.9

Above average: Indiana (55.1), Florida (55.0), Kentucky (53.8), Kansas (53.4), Michigan State (53.2)

Below average: Baylor (52.6), Ohio State (52.5), Syracuse (52.0), NC State (51.0), Marquette (50.6), North Carolina (50.0), Wisconsin (49.9), Xavier (49.8), Ohio (49.2), Cincinnati (47.9), Louisville (47.6)

Opponent avg eFG pct: 45.8

Above average: Kentucky (41.7), Wisconsin (42.0), Louisville (42.8), Michigan State (43.2), Kansas (43.7), Syracuse (43.9), North Carolina (45.0), Xavier (45.3), Marquette (45.4)

Below average: Cincinnati (45.9), Ohio State (46.1), Ohio (47.2), NC State (47.3), Baylor (47.4), Indiana (48.0), Florida (48.1)

Average turnover pct: 19.1

Above average: Wisconsin (15.1), North Carolina (16.0), Syracuse (16.0), Cincinnati (16.4), Florida (16.7), Kentucky (17.1), Ohio State (17.6), Xavier (18.5), NC State (18.7), Marquette (18.8)

Below average: Indiana (19.4), Kansas (19.4), Ohio (19.5), Michigan State (19.6), Baylor (20.5), Louisville (21.3)

Opponent avg turnover pct: 20.8

Above average: Ohio (26.3), Syracuse (25.0), Marquette (23.7), Louisville (23.1), Ohio State (22.4), Cincinnati (21.8), Baylor (21.3)

Below average: Indiana (20.6), Kansas (20.6), Florida (19.6), Michigan State (19.5), North Carolina (18.6), NC State (18.5), Xavier (18.4), Wisconsin (18.3), Kentucky (17.8)

Average offensive reb. pct: 37.6

Above average: North Carolina (39.8), Baylor (38.0), Kentucky (37.9)

Below average: Michigan State (36.8), Syracuse (36.6), Ohio State (36.0), Louisville (35.9), Cincinnati (35.8), NC State (35.6), Indiana (35.3), Kansas (34.7), Ohio (34.7), Marquette (34.2), Florida (34.1), Xavier (32.0), Wisconsin (30.7)

Opponent avg offensive reb. pct: 31.2

Above average: Ohio State (24.8), Michigan State (26.8), North Carolina (27.6), Wisconsin (27.7), Kansas (28.7), Xavier (29.9), Kentucky (30.2), Florida (30.4), NC State (30.4), Indiana (30.6)

Below average: Baylor (32.3), Ohio (33.9), Louisville (34.2), Cincinnati (34.4), Marquette (35.7), Syracuse (39.3)

Average free throw rate: 38.7

Above average: Indiana (45.2), Marquette (41.3), Xavier (41.2), Kansas (41.1), Kentucky (40.1)

Below average: Michigan State (38.1), North Carolina (37.8), Louisville (37.5), Ohio (37.2), Ohio State (37.1), NC State (36.6), Baylor (36.3), Florida (33.4), Syracuse (32.9), Wisconsin (30.8), Cincinnati (29.7)

Opponent average free throw rate: 31.1

Above average: North Carolina (21.6), Cincinnati (25.7), Kentucky (26.0), Ohio State (29.1), Syracuse (29.8), Florida (30.1), Wisconsin (30.1), Marquette (30.8)

Below average: Baylor (31.7), NC State (32.1), Indiana (33.5), Kansas (34.0), Louisville (34.3), Michigan State (34.7), Xavier (35.8), Ohio (42.7)