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Bracket Math

Kyle Terada-USA TODAY Sports

You knew I was going to find a way to "nerdify" the process of filling out the brackets, didn't you? In preparing to fill out my bracket, I decided to look back through the KenPom archives to see if I could develop a statistical profile of past Final 4 participants and champions as a guide to help decided who should get moved forward, and who should get sent packing. What follows on the other side of the break are the results of this analysis, which focused on both the efficiency margins (offensive efficiency - defensive efficiency) of the last 32 Final Four participants, as well as their individual offensive and defensive rankings.

In the first table, you will find the average offensive efficiency (OE) and defensive efficiency (OE) rankings, and the average efficiency margins (EM) for the last 32 Final Four participants as well as the last 8 National Champions.

Final Four Champions
Avg. OE Rank 12.3 2.9
Avg. DE Rank 14.2 8.4
Avg. Eff. Margin 31.6 35.5

Next, the table below begins to set some of the thresholds that will be used to develop the criteria that will be used to judge the field in this year's tournament by looking at the number of teams that made the Final Four (or won the title), despite failing to reach certain levels of excellence.

Teams with: Final Four Champions
EM > 28.0 22 (68.8%) 7 (87.5%)
EM > 34.0 13 (40.6%) 6 (75.0%)
OE Rank > 10 12 (37.5%) 1 (12.5%)
DE Rank > 10 16 (50.0%) 2 (25.0%)
OE Rank > 20 8 (25.0%) 0 (0.0%)
DE Rank > 20 5 (15.6%) 0 (0.0%)
OE Rank > 40 3 (9.4%) 0 (0.0%)
DE Rank > 40 2 (6.3%) 0 (0.0%)
OE Rank > DE Rank 20 (62.5%) 7 (87.5%)

Based on these data, it is now possible to set the "rules" that will be used to identify the teams most likely to reach the Final Four this year, and most importantly, which team, or teams, is most likely to win it all.  For a potential Final Four team, what you should look for is a team the ranks in the top 20 in both offensive and defensive efficiency and has an EM greater than 28.0  For a potential champion, you just up the thresholds to a top - 10 ranking in both offensive and defensive efficiency and an EM greater than 34.0, but also add in a third criterion that singles out teams that have a better OE ranking than they do a DE ranking.

So now that the criteria is set, lets take a look at the top-4 seeds in each of the four regions.  My reason for only looking at the top-4 seeds is simple: a 4-seed or higher has been the champion the last 22 years (with a 1-seed winning 15 of those titles).

Seed/Team Region OE Rank DE Rank Eff. Margin
#1 - Ohio St. East 1 10 35.8
#2 - UNC East 37 7 23.5
#3 - Syracuse East 17 16 25.3
#4 - Kentucky East 7 22 27.8
#1 - Pitt Southeast 6 21 28.7
#2 - Florida Southeast 16 40 22.3
#3 - BYU Southeast 8 37 25.2
#4 - Wisconsin Southeast 2 63 28.0
#1 - Duke West 5 3 32.7
#2 - SDSU West 24 4 27.4
#3 - UConn West 21 31 21.9
#4 - Texas West 19 1 28.6
#1 - Kansas Southwest 4 12 31.9
#2 - Notre Dame Southwest 3 62 27.4
#3 - Purdue Southwest 18 8 26.9
#4 - Louisville Southwest 36 5 24.4

Parity is an overused term, but this year it may actually be true.  Applying the criteria set forth above, there are only four teams that meet the both standards used to define a Final Four contender: Ohio State  in the East, Kansas in Southwest, and Duke and Texas in the West.  Three other teams meet one of the two standards: Pitt (Southeast) has and EM over 28.0 (28.7), and Purdue (Southwest) and Syracuse (East) each have top-20 rankings in both OE and DE.  And that is it.  (Wisconsin is right at the EM-threshold, but as will be showed shortly, there is another reason why they would not be a strong choice to make the Final Four.)

The field for viable champions is even smaller, as only Ohio State is ranked in the top-10 in both OE and DE, has an EM greater than 35.0 and is better on offense than it is on defense.  I realize that coming up with the tournament's overall #1-seed as the odds on favorite to win the tournament is hardly cutting-edge, but then again, the tournament's overall #1-seed has only won once in the last 8 years, so maybe it is.

Some other thoughts:

-In the East, West and Southeast, the 4-seeds all have the second best EM in the region.  This could make for several very interesting 1/4-games in the Sweet 16 and would make good choices for an upset pick.

-In 2003, Texas (DE-rank: 44) and Marquette (DE-rank: 101!!) both made the Final Four despite questionable (at best) defenses.  Since then, no team with a DE-rank over 30 has made the Final Four.  This is bad news for, UConn (31), BYU (37), and Florida (40), and terrible news for Notre Dame (62) and Wisconsin (63).  [Memo to basketball commentators: Wisconsin plays slow! They are not a good defensive team!!]

-The news for Louisville (OE-rank: 36) and North Carolina (OE-rank: 37) is almost as bad, as only 3 of the last 32 Final Four participants had an OE-rank over 30, though Butler (OE-rank: 50) did pull it off last year.

Looking more specifically at the Heels, their road is rough.  Based on EM, they should be the slightest of favorites in a 2nd-round match-up against Washington, though the home-state crowd and the fact that the Huskies play really fast should be significant advantages.  After that, they are looking at the likelihood of being slight underdogs against Syracuse and (possibly Kentucky), and a fairly significant underdog against Ohio State.  Of course, things could also go completely crazy and UNC could end up beating LIU, Georgia, Xavier and Clemson in a walk to the Final Four...