Balancing Act: Evaluating the offensive balance of title winners

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I just hope that history does not omit the other, vital part of Wildcats' legacy: that their balance was as noteworthy as the brevity of their college experience. During Kentucky's run to New Orleans, there was this constant juxtaposition of sinisterness and harmony -- at the same time Calipari was being accused of killing off some idealized concept of the student-athlete, and being black-hatted by the fact that two of his previous Final Four trips had been vacated, the best team of his coaching career was playing some of the most balanced, unselfish basketball ever seen in an NCAA tournament.

And that led me to wonder something at the Superdome: Was Kentucky the most offensively balanced title team of this era? It's not the sort of question that can be definitively answered on deadline, and so I let it slide, but on a slow week in June, there was time to revisit it, build a dossier of data, and figure out where the Wildcats actually stand.

The most effective way to assess offensive balance is through possession usage -- the percent of possessions a player ends by making or missing a shot, or committing a turnover. A perfectly harmonious team would have a usage distribution of 20-20-20-20-20 across its lineup, while a team with a ballhog and four role players might have a 35-17-16-16-16 distribution. By applying a business-analysis formula called the Herfindahl Index, which typically measures market-share concentration, to basketball usage data, we can assess how much teams stray from that 20-20-20-20-20 model. The lower the Herfindahl (HHI), the more balanced a team is; the higher, the more unbalanced. Usage data is available for the past 16 champions, from Arizona's 1996-97 title team onward; while that doesn't exactly constitute an "era," it does provide a decent sample of modern-day champs.

For each team, I averaged two HHI figures -- one across the top five players in percentage of minutes played, and the other across the top six players -- to come up with a final balance score. (The complete chart doesn't appear until the end of the story, for the sake of suspense.) Counting down, these were the three most balanced title teams in the sample:

Top Six in Rotation (Poss%): Mario Chalmers (19.6), Brandon Rush (21.6), Russell Robinson (16.6), Darrell Arthur (24.1), Darnell Jackson (19.9), Sherron Collins (21.1)

Chalmers hit the biggest shot for these Jayhawks and played the most minutes, but he was the second-lowest possession-user in an unselfish rotation. It's incredibly rare to see a team with three NBA-prospect guards (Chalmers, Rush and Collins were all highly regarded at the time) with usage rates near 20.

Top Six in Rotation (Poss%): Wayne Turner (19.2), Scott Padgett (20.1), Jeff Sheppard (21.7), Allen Edwards (19.4), Nazr Mohammed (24.1), Heshimu Evans (20.5)

Tubby Smith's first Wildcats team was a classic, no-star crew, lacking a Lottery Pick or a first-team All-America rep. The only champs since to fit the same, unsung profile are 2009-10 Duke, whose best player, Jon Scheyer, was a second-team All-American and a second-round pick in the NBA draft.

Top Six in Rotation (Poss%): Marquis Teague (21.1), Anthony Davis (19.2), Doron Lamb (18.2), Michael Kidd-Gilchrist (21.4), Terrence Jones (22.3), Darius Miller (18.7)

So there you have it: Kentucky '12 is the most balanced title team of the past 16 years -- and potentially much longer than that, if the data were available to prove it. To have top-two draft picks using just 19.2 and 21.4 percent of possessions is not in any way normal. This is what's more typical: The No. 1 pick in 2011, Kyrie Irving, used 27.2 percent of Duke's possessions, and the No. 2 pick Derrick Williams, used 28.7 percent of Arizona's. The No. 1 pick in 2010, Kentucky's John Wall, had a usage rage of 27.3, and the No. 2 pick, Ohio State's Evan Turner, used 34.3.

Now, who were the most unbalanced champions during the same period? One school makes two appearances in an all-Big East top three:

Top Six in Rotation (Poss%): Kemba Walker (31.4), Alex Oriakhi (17.9), Jeremy Lamb (19.2), Roscoe Smith (14.2), Shabazz Napier (20.8), Jamal Coombs-McDaniel (17.5)

Before actually running the numbers, this was my guess for the team with the least balance, because Walker (at 31.4) is the highest possession-user in the database. He and Duke's Jason Williams were the only title-team starters with usage rates above 30 percent. The late-season emergence of Jeremy Lamb and Shabazz Napier, who hovered near 20 percent usage, was what prevented these Huskies from taking the unbalance crown.

Top Six in Rotation (Poss%): Ricky Moore (12.9), Kevin Freeman (18.4), Richard Hamilton (29.6), Khalid El-Amin (25.8), Jake Voskuhl (16.3), Edmund Saunders (16.9)

When your leader in minutes played is a defensive stopper who never looks for points (Moore), your big men do role-player dirty work, and your backcourt is dominated by a shot-happy point guard (El-Amin) and a guy who'd go on to be one of the NBA's most prolific shooters (Hamilton), you're bound to be unbalanced. It didn't stop the Huskies from pulling off a mega-upset over Duke in the final, and establishing that when it comes to title-team construction, Jim Calhoun is the anti-Calipari.

Top Six in Rotation (Poss%): Carmelo Anthony (27.8), Gerry McNamara (18.5), Hakim Warrick (22.4), Kueth Duany (19.9), Jeremy McNeil (9.8), Craig Forth (13.8)

The Orange's designation as the most unbalanced title team of the past 16 years has as much to do with the minuscule usage rates of rotation back-enders McNeil and Forth as it does with 'Melo's outsized offensive role. When you have two regulars who are no threat to shoot, you create a dangerously unbalanced dynamic -- one that required a freshman's transcendent performance to result in a national championship.

(It's worth noting that the mid-season addition of Billy Edelin -- who finished seventh on the team in overall minutes played, and thus fell outside the scope of this study -- altered the Orange's rotation. Because Edelin used 21.2 percent of possessions, one could reasonably argue that UConn '99 is the most unbalanced team, but I wanted to stick to a firm set of rules for analysis, rather than make team-by-team exceptions.)

Top Six in Rotation (Poss%): Tyshawn Taylor (27.6), Elijah Johnson (17.3), Thomas Robinson (29.5), Travis Releford (13.8), Jeff Withey (17.9), Conner Teahan (14.0)

This is my favorite footnote to the '11-12 season: Had the Jayhawks managed to upset Kentucky in the final, they would have gone down as the second-most unbalanced champs. Robinson and Taylor formed such a powerful offensive duarchy that everyone else was relegated to sub-18-percent roles. But they fell to a Kentucky D that keyed on T-Rob, and a Kentucky offense with such a multitude of options that it rendered defensive game-plans futile. On that Monday night in New Orleans, it was Doron Lamb who led the Wildcats in scoring, but really, it could have been any of their top six. While balance is not always better, when you are historically loaded with soon-to-be pros, and they are selfless enough to engage in a historically great balancing act, you have to like your odds.

(Lower average = more balanced. HHI-5 = Herfindahl index of possession usage across top five players. HHI-6 = Herfindahl index of usage across top six players.)