Tuesday, January 31, 2012

NBA Team Alignment


Seven years ago, the NBA added its newest team, the Charlotte Bobcats, and realigned the league with three divisions in each conference. A few years after the Grizzlies moved to Memphis from Vancouver, Seattle lost its basketball team to Oklahoma City, and the new Northwest Division featured only one team truly in the northwest quadrant of the nation and one in Minnesota and another in Oklahoma. There are other oddities as well -- the aforementioned Grizzlies are in the "Southwest" Division, the desert city Phoenix is in the Pacific Division despite being hundreds of miles away, and likewise Toronto is in the Atlantic Division even though the closest they get to the Atlantic is raptor-filled lake Ontario. Next year will feature the New Jersey Nets moving to Brooklyn, and although it's akin to moving to a house down the block in the NBA landscape it hints at future developments.

Isn't there a better arrangement of NBA teams? What happens when a city like Charlotte or Sacramento loses their team? Or Seattle and Las Vegas gain one? With even a modest computer like mine, these questions can be tested with a little ingenuity.


Teams typically play the same schedule for 58 out of 82 games because they play every other team at least twice. They also have to play division opponents four times, and other teams in the division three to four. There is a significant difference between conferences, but divisions are essentially meaningless in terms of scheduling. Therefore, for computational simplicity, I will set the conferences first, and then organize the divisions.

In order to find the most efficient alignment of teams, first I had to calculate the distance between every NBA arena. This was surprisingly easy thanks to the internet and programming. The latitude and longitude of every arena was found online, and the distance between was calculated using the spherical law of cosines -- basically I found the length of an arc on two different points on a sphere using trigonometry. Teams, obviously, don't travel on perfect paths from on arena to the next because they need to access airports and hotels, but over large distances the effects are small. With some nice logical statements and programming, I compiled a 30 by 30 matrix of distances between teams. I used the Brooklyn arena instead of New Jersey, although it doesn't significantly matter, and for computational efficiency the calculation was for 29 teams and the Lakers' results were copied for the Clippers.

The next part was surprisingly difficult. A fifteen team conference doesn't sound all too large, but there are 15,510,000~ unique combinations possible. (As a side note, combination is a specific mathematical term to describe the scenario. A permutation cares about order, so a conference with teams X, Y and Z would be different than X, Z, and Y, while combination only cares about unique groupings.) I wouldn't be able to crank out that many calculations with ease without the aid of the Jeopardy! computer, so I locked in 11 teams on each coast to their respective conferences and left eight teams in conference purgatory, waiting for their ultimate judgement from the program.

Next I found the minimum number of total league miles between arenas giving a 1.8 weight to teams in the same conference and a weight of 1.0 to those in different conferences. The weighting is basically just saying teams play 2 games against teams in the other conference, but because one of those will be at home they only travel once, and at least an average of 3.6 games within conferences, but again they only travel on average 1.8 games. Note this simulates 80.4 games, which makes it apparent how little divisions matter, and essentially that any efficient method of organizing divisions only affects 1.6 games half of which are at home.

I also included scenarios for teams relocating to different cities -- the Grizzlies, for example, moving back to Vancouver and restoring the sanity of the team's name. Looking at the smallest metropolitan areas and which cities already have many professional teams along with population growth, another candidate for relocation is the Bucks in Milwaukee, and I had them move to Seattle, which is currently the largest metro area without an NBA team. The last scenario tested was a major relocation with the New Orleans Hornets moving to Seattle to become the Sonics, the Sacramento Kings to Las Vegas, and the Memphis Grizzlies to Tampa and hopefully changing their name (Tampa Panthers after the elusive Florida cat?) Those three organizations are having trouble attracting enough fans and keeping their business above the profit line.

Las Vegas doesn't have a pro team, has hugely growth, and the Las Vegas Kings is a great name; Seattle deserves its team back and New Orleans had negative population growth last decade and became the smallest market besides Salt Lake City; and Memphis is another small market while Tampa is another warm weather city athletes love with plenty of people and growth. These choices, however, were mainly an exercise in seeing how the league's alignment would change if teams moved. For the geographical coordinates, the old arenas were used for Vancouver and Seattle, while the city's coordinates were used for Las Vegas and Tampa Bay.


For reference, using the same conference alignment presently except with the Nets in Brooklyn, if every team traveled to every other team in its conference on average 1.8 times and once to teams in the other conference, they would have traveled 1,272,633 miles in total for an average of 42,421 miles per team. This does not include the extra games within one's conference, but again that amount is negligible for these purposes (only 1.6 games more on average per team per season.)

The most efficient conference alignment from the algorithm was Minnesota, Memphis, Oklahoma City, and New Orleans in the west, and Milwaukee, Chicago, Atlanta, and Indiana in the east ... which is exactly how it's already set-up. Basically, the conferences were already efficiently arranged. The entire operation wasn't fortuitous, however, since there's nothing wrong with proving the current system is best, and the best results are usually surprising.

The first alternate scenario also did not feature a shift in the conferences when the Grizzlies migrated back to Canada in Vancouver, although it's not surprising because Memphis was already in the Western Conference.  The total miles for the league was 1,329,218 miles, which was an increase of 4.4 percent from the present order, and an average of 44,307 miles per team. The Blazers would be happy for another team in the northwest, but the overall effects are fairly significant because Memphis is a centrally located city and Vancouver would be the furthest team from the center of the country. For minimizing travel, the most efficient placement of a single team would be near the center of mass, so to speak, of the conference teams and shifted to the center of the country for all the travel to the other conference. Memphis is in an ideal location in this respect.

The Bucks to Seattle scenario had a shift in the conferences, which is obvious since the Bucks were in the east and Seattle's a ways from the Mississippi. Only two teams would change conferences -- the Bucks to Seattle, and the Memphis Grizzlies to the east. The total miles from the league was 1,323,964 increased by 3.9 percent and an average of 44,132 miles. Once again, a team moving from the central of the country to one of the coasts would increase the total miles traveled by every team.

The Kings to Kansas City, predictably, decreased the total number of miles league-wide by 4.0 percent for 1,221,952 and an average of 40,732 miles. Surprisingly, teams didn't change conferences, as the Kings would stay in the west. Kansas City is geographically the center of the country, and even in the Western Conference it would still have a center location with Minnesota, Memphis and New Orleans east. A rule of thumb seems to be if you move switch teams from the center of the country to the outer edges league-wide traveling between cities would change by roughly 4 percent.

The most radical scenario with the Kings to Las Vegas, the Grizzlies to Tampa Bay, and the Hornets to Seattle featured again only one conference switch. The Hornets would stay in the west by going to Seattle, the Kings would also stay in the west because of Las Vegas, but Milwaukee would interestingly join the western conference while the Grizzlies in Tampa would join the east. The total miles increased by 3.7 percent to 1,320,134 with an average of 44,004 miles. Divisions would have to be completely changed, but that's a story for another section.


The NBA schedule is heavily dependent on which conference team occupies, but little about the specific division. 80.4 games are comprised of two with each opposing conference team and an average of 3.6 within the conference. The extra 1.6 games are added to teams within your division. The present conference alignment is the most efficient system in terms of minimizing travel distance between cities tested against seventy different combinations of eastern and western conference teams. The total travel distance of every team in the league was 1,272,633 miles (not including the extra 1.6 games.)

A few different team relocation scenarios were tested, and the results suggested that moving a team from the middle of the country to the outer edge would increase total travel distance by a fair amount but nothing too large (around 4 percent based on where the teams are.) Pairing a lonely city like Portland with Seattle wouldn't decrease travel distances for the league because of how far Seattle is from every other city. All four scenarios tested only switched at the most one pair of teams from each other's conferences, suggesting that the NBA's current alignment is mostly static.

This article is a little late in arriving, but I had trouble sorting the teams by division and as a result part two of this article will test for the most efficient alignments for divisions, their importance, and how relocations change those.

Thursday, January 26, 2012

Minnesota Timberwolves Deny Love Max Extension: Racism?

An all-star last year, the 23 year-old power forward, Kevin Love, has again improved. His offseason was apparently productive as he dropped a large amount of weight and increased his per game scoring average from 20.2 to 25.3 while leading the league in minutes a game. In fact, he has considerably improved every season he's been in the NBA, and he's a hard worker off the court, well spoken, and one of the best young stars. The likely western all-star starter, Blake Griffin, has regressed from his rookie year and his numbers pale in comparison to his young power forward counterpart. No other player in the NBA, actually, can be compared since he has the rare combination of three-point shooting prowess with over five attempts a game at a conversion of over 40% and elite rebounding collecting 13 per contest. The only similar player in the league's history is Troy Murphy, who never scored at the rate Love is. Having already had the first 30 point, 30 rebound game since Moses Malone, Love could become the first player to average 25 points and 13 rebounds since Moses himself in 1981-82.

So why didn't Kevin Love earn a max extension from his team? He's set to receive the maximum amount of money per year, but he didn't get the full five years. A new rule in the NBA says that each team gets a "designated player," for whom a five year extension can be granted after the rookie contract, but a team can have just one designated player at a time.Only the home team can offer this, helping out small-market clubs. If a young, hard-working power forward who's averaging 25-13 can't get the max deal, then who would?

Earlier, Russell Westbrook received a five year deal with his team Oklahoma City. There's no denying he has talent and could considerably improve his game, but it's hard to argue that Love isn't having the better season. Westbrook is a point guard without a reliable outside shot who relies on his athleticism, while Love is a phenomenal rebounder who's turned himself into a great outside shooter. Who will age better? There's no logical reason to assume the Thunder point guard will be the better player going forward when he hasn't shown it.

Westbrook takes more shots a game than Love, but he averages both less points per game and less on a per minute basis. He's always had problems with his shooting percentages, and even when he's bricking he'll hoist up shots. Love's scoring more because his shooting percentages are once again much better. These two western conference stars are inextricably linked as they both played together at UCLA, and their contracts hint at something the media feels uneasy discussing.

Kevin Love is a white American basketball player, and as such he's had to deal with people assuming he can't play. Said to be a bust out of college by many because the league was too athletic for him, he had a stellar rookie season with outstanding rebounding and great offensive potential. Fans regularly make jokes about white American ballplayers, and some like Scalabrine are a confused merging of disrespect for white players and glee whenever he makes a positive play like he's a dog who's learned fancy tricks, an oddity. There's no denying racial assumptions exist in basketball. Kevin did everything he could to better himself as a ball player, and maybe because of what he looks like management didn't see him as their designated player, the face of the franchise.

Minnesota is probably saving their max extension for Rubio, and as an international player he's faced with a different set of prejudices. With the success of foreign stars in winning championships from Dirk Nowitzki to Manu Ginobili and Tony Parker, and the MVPs given to Dirk and Nash, white foreign players are allowed to be superstars. In fact, the different culture may help these players develop because they're not as obsessed as race as we are. In places like Lithuania and Serbia with few Africans no one assumes how good someone is based on skin color; you just pick up the ball and prove yourself. There's no self-selection with the young athletes with regards to race.

Maybe Minnesota really does believe they need to save the 5 year max for Rubio or another lottery star. Love, however, is doing everything a designated player should do, averaging 25-13 a game. It's unclear why they chose to do this, including a fourth year option where Love can decide if he wants to leave or not. But you have to consider how they perceive Kevin Love's value and if any of that is tied to his skin color.

Monday, January 23, 2012

Free Throws and Hand Size: Are Big Hands Detrimental to Shooting?


One of the most common discussions on free throws is how bigger hands make it harder to shoot. Shaq has such big hands, people say, that it's impossible for him to be a good free-throw shooter no matter what his form is or how often he practices. Another player, Rondo, has very large hands, especially for point guard, and people excuse his poor shooting from the foul line and his outside jumpers. If this is true, then we should see a lower percentages as a player's hand size increase.

I think one credible explanation is how the ball is held between someone with (relative to the NBA) small hands and someone with large hands. When taking a free throw most people are able to easily grip the ball with both hands: one to provide the power and one for stability. When your dimensions are like Shaq's, it's harder to balance the ball as you release. Try shooting with a tennis ball for an extreme example. You're entirely using one hand to launch it, and it's generally harder to retain precision in the typical basketball shooting motion. (Of course, the tennis ball's smaller size will help you make the shot.) It's a reasonable explanation, and the hand size-shooting myth is prevalent among NBA fans because it feels right. One can't assume this is true, however, without objectively looking into the matter.


In order to systematically test the hypothesis that larger hands lower a player's free-throw percentage, you need lots of data. Fortunately, at the pre-draft combine they started collecting hand size from virtually every player. This was only started in 2010, but that still leaves a huge pool of guys to analyze. I could have also included players who have had measurements released to the public by the team or media; you can find plenty of these "facts" online. However, those are self-selected data and I would be compiling them one at a time, which is too slow of a rate for me.

Over the past two years there were 155 players with hand measurements, but only 21 with over 50 free throw attempts in NBA games. The hand sizes ranged from 11.25 inches long to 7.25 among players. Hand width was also measured but not for every player, so I didn't include it in the study. I did, however, use a few other explanatory variables. Since hand size correlates with height and therefore position, those were both used in the data. I also had age as a variable because players typically improve from the line as they get older, although these players are all rookies or sophomores. The height used was the pre-draft's height without shoes because the inflated with shoes number or whatever a team lists has more variation -- some guys gain an inch for their shoes, and some two.


The first results I'll discuss are for players with over 50 attempts and treating each player as a separate datum. Free-throw percentage was the dependent variable, and hand size, height, position, and age were tested as the independent variables in a linear regression. I tried every combination of the independent variables, and in every case hand size statistically insignificant. Even with just one independent variable the p-value for hand length -- it's the probability that hand length has zero effect on FT% -- was only 0.111. For reference, 0.05 is taken as statistically significant, and hand size correlates with position well enough that you'd think there'd be enough of a correlation for a better result. By contrast, using just height, the p-value was 0.016 and the R-squared value 0.27, meaning 27% of the variation in free-throw shooting percentage was explained by height alone.

The table below contains the 21 players with over 50 attempts arranged by hand size. There's a bit of a pattern where most of the best shooters have smaller hands, but it's not perfect. Aminu, in particular, has huge hands but he's shot well from the line. Likewise, Vasquez has tiny hands for an NBA player but he's been terrible. I also want to note that 21 samples are not large enough for a conclusive study, and in couple years there should be enough data. However, there is no overwhelming evidence to support the claim that hand size has a negative effect on free-throw shooting, and I think that's a fascinating preliminary result.

Free-throw %
Hand length (in)
Height w/out shoes
Larry Sanders
6' 9.25"
Al Farouq Aminu
6' 7.25"
Ekpe Udoh
6' 8.75"
DeMarcus Cousins
6' 9.5"
Ed Davis
6' 9"
Marshon Brooks
6' 4.25"
Trevor Booker
6' 6.25"
Wesley Johnson
6' 6.25"
Derrick Favors
6' 8.75"
Evan Turner
6' 5.75"
Greg Monroe
6' 9.75"
Xavier Henry
6' 5.25"
Eric Bledsoe
6' 0.25"
Gordon Hayward
6' 6.75"
Manny Harris
6' 4"
Paul George
6' 7.75"
John Wall
6' 2.75"
Kyrie Irving
6' 1.75"
Jordan Crawford
6' 3"
Kemba Walker
5' 11.5"
Greivis Vasquez
6' 4.75"

Perhaps a better method is to pool each free throw attempt into a hand size measurement. That way a rookie who only plays in a blowout will have his ten attempts be used with the rest of the group of players with his hand length. Luckily, hands were measured in discrete units instead of something more exact like 8.425" and there are only nine categories. The linear regression based on one independent variable, hand size, output a p-value of 0.326 and an R-squared of 0.137. Basically, there was no correlation, and the graph below illustrates the point. There isn't any designation of point guard versus centers, but pundits claim someone like Rondo shoots so poorly because of his large hands. One problem, however, with a smaller than ideal data set is that players with high attempts like John Wall skew the results, and that's why you're seeing such different results for each size.

Hand length (in)
Free-throw %

Another approach I tried was grouping the results by position and applying linear regression to each position. Unfortunately, there aren't enough players yet with hand measurements to subdivide the data even when lowering the free throw requirement to 20 attempts. The results, however, were so one-sided that I doubt more data would reveal a statistical significance between hand size within positions. Point guards, for example, a group known for their sweet shooting, had a tiny R-squared value of 0.0529 and a p-value for the hand length coefficient of 0.523. R-squared, to reiterate, is saying hand length only explains 5% of the variation in free-throw percentage among point guards, and that's a abhorrent result. There were only 10 point guards to qualify, but the same was true of each position. Again, there was no evidence to conclude that hand size was a significant variable in determining free-throw percentage. To illustrate the lack of association between size and free throws, Iman Shumpert was more of a combo guard so he wasn't included, but he has larger hands than any point, yet he's at 22/24 for the year.


The NBA athletes we see on TV are undeniably talented and earning more money than most of us will ever accrue in our lives. When we see a player making $10 million a year miss a free throw -- a shot even little kids can make -- we're angry and baffled. Surely he's been practicing for years, so why is he shooting 60% for the season? In asking that question some seek answers about how some players aren't able to make them during the flow of the game or that these athletes' hands are too big to accurately shoot. We can find examples like Duncan, who clearly has worked on his shot but often shoots under 70%, to fit our theory and confirm our own perceptions, but there are also counter-examples. Pau Gasol has enormous hands and palms the ball with ease, but he has an accurate jump shot and cleared 80% for the season multiple times. John Stockton is a point guard with large mitts, and he's at 82.6% for his career with a good three-point shot. Michael Jordan, known for using his big hands to dunk with flair, is even better at 83.5%.

The inclusion of hand size measurements for nearly every drafted player recently will lead to a better data set, and at the end of the year I'll redo the regression to see if anything changes. There are a couple other hypotheses that need to be tested. Maybe there's a hand size limit beyond which percentage plunges, but we don't have enough information for that yet. The players in the data are all very young and the results could change once they improve or, even their hand size is so problematic, flatline at a poor number. Within a couple of years we could get a definitive answer as more guys get measured and the ones that already have rack up attempts. However, based on the data right now, there is no evidence to support the hypothesis that hand size negatively affects free-throw percentage.

Saturday, January 21, 2012

A Young Center Crop Ready to Harvest

The Lakers-Magic Friday night game was supposed to showcase the league’s two best undisputed centers, but Bynum was a non-factor and Howard was a one-man wrecking crew with another 20-20 game. The coronation of Bynum as the rival center is mostly due to his uniform, as the Lakers are regularly featured on national TV, and his sweet, natural post moves. The center position is dying is a common refrain from the last 15 years, but this season unexpectedly a few young big guys have put together remarkable seasons.

Still Young and Very Good

Al Horford

Vital stats: 25 years old, per 40 mins: 17.4 pts, 10.6 rebs, 1.2 blcks, 3.9 asts, 58.5 TS%, 35.1 mins per game (2010-11)

Dwight Howard’s back-up in two all-star games is the perfect introduction to this list. The center position, like the point guard spot, is often contested because not every player follows the typical mold and some play major minutes at both frontcourt slots. Horford, however, was asked to start at center for most of his career and deserves credit for the work he has done. Before tearing a pectoral muscle, he was going for another typical Horford season – high efficiency scoring, solid rebounding, good passing, competent post game, nimble defense, and surprisingly great outside shooting. The latter will surprise most people who don’t watch the Hawks much (97% of NBA fans), but he shot 53% from 16 to 23 feet with 4.8 attempts a game a year after shooting 48%. This led the league, even Nowitzki.

Unfortunately, Al can only recover in time for the playoffs, if Atlanta can make it this year. Outside of his strangely amazing midrange game, there is nothing spectacular about his play, except that he’s above average in so many categories he deserves a spot in the upper echelon of NBA centers. No, he’s not Shaq, or Dwight Howard, but he’s been starting at center for his entire career and deserves the respect he’s earned.

Marcin Gortat

Vital stats: 27 years old, per 40 mins: 19.6 pts, 12.4 rebs, 2.1 blcks, 1.1 asts, 60.9 TS%, 30.0 mins per game

Gortat, who played under the shadow of Dwight Howard for years, is likely the league’s most underrated center. A low minutes per game hides one of the most effective offensive games for a player his size, and his defense is also above average. He’s everything you want from a center – he’s nearly 7 feet tall, he rebounds, he blocks shots, he scores well inside, he can hit a midrange jumper, he’s not a turnover machine, he stays out of foul trouble, and he has a great nickname: the Polish Hammer. Maybe playing against Howard in practice for three and a half years was the best training any young center could get.

The only worrying aspect to Gortat is his age, but he was stuck on the bench so long it was hard for him to emerge as a force inside. Coupled with Nash, they form one of the best pick and roll teams in the league because Gortat is quick on his feet, finishes well, and has a reliable jumper. With a 60.9 TS%, he needs to demand the ball more and score over 20 a game to reach his potential. Since Yao has retired and Duncan is declining just when he’s okay being called a center, Gortat could be called to an all-star game and would deserve the spot once he plays more minutes. With Nash and Hill still trying to get in the playoffs, the Suns need to play their talented polish center the time he deserves.

Andrew Bogut

Vital stats: 27 years old, per 40 mins: 15.4 pts, 10.2 rebs, 2.3 blcks, 3.4 asts, 46.9 TS%, 33.0 mins per game

As the NBA game has shifted to the guards with hand-checking rules allowing young, explosive players to get to the rim at will, big men have not only lost touches but have to deal with these speedy and athletic guards once they reach the paint. As such, defense has shifted from the perimeter to the post, where centers are extremely important defensively. Outside of Dwight Howard, the best defensive player in the league is fellow former number one pick Andrew Bogut. Even though his offense has suffered since his gruesome elbow injury, he’s still one of the most valuable players in the league.

NBA players get accolades and awards for pretty offensive games, scoring 30 pointers from every spot on the floor, even if they’re liabilities on the defensive end. If guys like Amare Stoudemire or Ray Allen can receive praises for one side of the court, then Bogut should receive just as much. Not only he is one of the best shot blockers, he also takes a boatload of charges, a rare combo, controls the boards, and has some of the best post defense in the game. Unlike many centers, he doesn’t pick up blocks by leaving his position too much or flying out at every shot. Milwaukee has been one of the best defensive teams for a while, and he is their anchor.

Offensively, he’s off to a slow start after a disappointing year, but he took time off for a personal issue and his shooting from 3-9 feet has been uncharacteristically inaccurate. Once he regains his form, he should be able to clear 50% from the field, and he’s one of the best passers at his position. He’s often pressed into a more difficult role, however, given the Bucks’ scoring problems. Of course, his offense isn’t his calling card, and every defensive metric rates him near the top. Regularized +/-, for example, has rated him in the top five defensively for the past few years. With Dwight Howard dominating the DPOY award, Bogut has received few awards for his play, but he’s so great at one end of the court he’s deserving of an all-star game once his offense recovers.

Roy Hibbert

Vital stats: 25 years old, per 40 mins: 18.5 pts, 13.7 rebs, 2.2 blcks, 2.6 asts, 54.8 TS%, 29.4 mins per game

Listed at 7’ 2”, there is no mistaking him for a power forward. With his tall, slender frame and long arms he can wall off the basket to any intruders, and is one of the better defenders in the league despite his problems with the pick and roll. He blocks shots, though not at a prodigious rate, but he alters so many and has kept his foul rate at a reasonable limit he’s an effective rim protector. Offensively he uses a hook shot and a turnaround jumper that are untouchable, and his range extends far from the paint; you’d like him to focus his efforts in the paint, however. After two years of improvements he’s one of the better rebounders in the game, and with his size he should be able to keep grabbing around 18.7% of the available rebounds.

Last year, however, Hibbert also started off on a similar torrid pace, but was dreadful, especially offensively, for the middle of the season.  He was diagnosed with asthma, explaining last year’s up’s and down’s, and has been playing at 30 minutes a game as a result. He has played 81 games two years in a row, and unlike other centers his size doesn’t have an injury history. If he can find a way to conquer his asthma he could put up surprisingly good numbers, but even so he’s a tall shot-blocker who can generate offense with underrated skill, as he’s a good passer and over 70% from the line for his career.

Marc Gasol

Vital stats: 26 years old, per 40 mins: 15.6 pts, 11.1 rebs, 2.4 blcks, 3.2 asts, 57.6 TS%, 38.1 mins per game

Like his brother, Marc Gasol is a well-rounded and skilled big man, able to throw an accurate and difficult pass and score in the post. He’s already known as one of the best centers and plays large minutes for a team that upset San Antonio last year, so I don’t need to discuss him at length. Unlike his brother, he’s a burly center whose greatest nemesis is his weight, but he’s mobile enough to be a plus defensively.
The Gasol gene limits Marc’s impact because he’d rather pass than shoot far too often despite high accuracy. His range moves out to 20 feet, but like most big men you’d wish he’d stay in the paint. His value, however, is still high enough that during one of his best seasons he could be awarded with an all-star berth and wouldn’t be a bad pick unlike recent “stars” Jamaal Magloire and Mehmet Okur

Andrea Bargnani

Vital stats: 26 years old, per 40 mins: 25.3 pts, 7.4 rebs, 0.8 blcks, 3.9 asts, 57.9 TS%, 35.2 mins per game

As a number one pick the Italian “Il Mago” Bargnani has been underwhelming for so long that many consider him a bust, but finally at the age of 26 in his sixth season he has a breakout season. Some may consider last year just as good because he was scoring roughly the same average at 22 a game. The differences are important but subtle. He’s shooting more but his scoring efficiency has skyrocketed to the point where his field-goal percentage is near 50% even though he’s slumping on his three’s and his increased aggression has resulted in more trips to the line. His defense, once pitiful, has improved – his +/- on defense is near 0 instead of the terrible -6.45 last year -- and while he may never be a good defender he managed to cut his turnovers and increase his number assists. Even his rebounding is a career high on a per possession and per game basis.

Bargnani is not a player I’d want to build a team around, but his scoring is finally valuable enough that you can occasionally forgive his defense. If the Raptors keep using this seven-footer as their center, he could earn at least one trip to the all-star game. (Another player listed shortly, however, could change his position.) While I still consider him overrated, he at least gives the media one more (offensively) productive center. He should study Dirk Nowitzki for how the German uses his outside shooting, height advantage, and agility to frustrate opponents, and Dirk’s underrated defense despite being as athletic as Bargnani.

Joakim Noah

Vital stats: 27 years old, per 40 mins: 14.2 pts, 12.6 rebs, 1.8 blcks, 2.7 asts, 57.9 TS%, 32.8 mins per game

I included last year’s stats because Noah’s been disappointing and you’d question my judgment if all you knew were his stats from this season. However, he’s fairly well known for a defensive minded center because of his college run at Florida and the Bulls’ success. He’s the perfect role player center for this era – he’s mobile enough to destroy the opponents’ pick and rolls, he controls the glass, he’s strong enough against most centers, and he generally stays out of the way on offense other than showing off his good passing skills. There were murmurs of him making the all-star squad last year, which would have been a change in thinking from how reserves are usually taken.

Noah bounces around the court with his ponytail bobbing up and down, his high energy coupled with his size terrorizing the other team’s offense. He’s one of the best help defenders and racks up more steals than others his size. Even though he has one of the ugliest jump shots in the game – it looks like when a little kid first learns how to shoot – he’s a better outside shooter than few other centers. Chicago is one of the best teams in the league because of their defense, and their starting center is one of the reasons why.

Forgotten but Promising

Jonas Valanciunas

Vital stats: 19 years old, per 40 mins: 20.0 pts, 15.0 rebs, 1.3 blcks, 0.5 asts, 75.2 TS%, 15.5 mins per game (2010-11 Euroleague)

Lithuania is the land of giants, and the next international star could be this guy. He’s the only player to achieve an MVP and Gold Medal in every one of his age-bracketed FIBA U-tournaments, where in the most recent one, the under 19 tournament, he averaged 23.0 points, 13.9 rebounds, and 2.7 blocks. The above stats are for only 15 games, but in other leagues he’s put up similar numbers although with more reasonable efficiency and more blocks. He's in the forgotten category because fellow international players like Rubio and Biyombo are receiving all the love, but Toronto fans haven't forgotten about Jonas. Listed at 7 feet tall with a 9’ 3” reach, he has enough size for an NBA center and plays near the paint with a soft touch and a nose for boards. He’s set to come over for the 2012-13 season, where he can push Bargnani out to the power forward spot, and give them an energetic and big center who can rebound and score inside.

Andris Biedrins

Vital stats: 25 years old, per 40 mins: 15.8 pts, 14.9 rebs, 2.1 blcks, 2.6 asts, 58.5 TS%, 35.1 mins per game (2008-09)

Biedrins was once one of the bright young centers in NBA, flanked by fellow A.B. initial alumni Andrew Bynum and Andrew Bogut, but considerably got worse after one of his best seasons when he was still only 22 years old. Ever since being as old as centers of the past used to be in their rookie years he’s been terrible and shot an impossibly poor 23.3% from the free throw line in the past three seasons. This year, however, he’s at least rebounding as well as he ever has and has made sure to shoot well enough from the field, at 73.3%, that he doesn’t even need to shoot free throws. At his best he’s a high-energy big man who can crash the boards at an elite level, block shots, and finish inside better than most. If he ever vanquishes his free throw demons, which are so disruptive it’s like a baseball player with the yips a la Chuck Knoblauch, he can be a very good mobile center many teams covet.

Greg Oden: 23 years old, per 40 mins: 18.6 pts, 14.2 rebs, 3.8 blcks, 1.5 asts, 64.7 TS%, 23.9 mins per game (2009-10)

A number one pick like other centers – Dwight Howard, Andrea Bargnani, Andrew Bogut – Oden is now thought of as a bust because the consensus number two, Durant, has turned into a scoring machine, while Oden has amassed only 82 games in his career so far. In between all the injuries he showed promise as a dominating big man, strong enough for rim shaking dunks but athletic with a talent for blocking shots and rebounding. In fact, in his short time in the league he was already rebounding and blocking at an elite level. He was also developing a post game, where his strength was too much for most centers and sending him to the line was no solution unlike others of his build, as he was 76.6% from the line in his second season. He fouled like crazy, but that’s common among young centers. If he was healthy he’d be one of the best defensive centers in the NBA with a potent even if still limited offensive game. Alas, he may never get a full season, and his potential as a dominant center is all but vanished.

Young Potential Stars
Andrew Bynum

Vital stats: 24 years old, per 40 mins: 18.5 pts, 15.9 rebs, 2.2 blcks, 1.5 asts, 54.5 TS%, 34.3 mins per game

Already in his seventh year, the young Bynum is finally delivering on his promise. While some people have been overrating his game – he’s only averaging 16 a game with a mediocre TS% -- he’s clearly working harder. He’s crashing the glass aggressively and setting a career high, running down the court to establish post position, and shooting more on a per minute basis than he ever has. He has a hook shot from either hand, knows how to pin someone trying to front him for a lob, and is a natural in the post. There are few players who are truly seven-feet tall, and Bynum was measured at 7’ at 17 years-old. Some reports say the Lakers measured him at 7’ 1” in bare feet later on, but most importantly he has a huge wingspan he uses to shoot over most players and grab rebounds from directly over the opponent’s head. Given his knee problems, the fact that he can reach 9’ 4” or higher – again, that was at 17 years old -- without jumping will be an advantage going forward.

However, contrary to all the media attention anointing the Lakers center as the next great one, he has performed below even his own standards offensively so far this season. His career high in minutes per game and shots per possession has masked his struggles. He has a true-shooting percentage of 54 this season after consecutive years of 59.3, 65.9, 59.8, 60.8, and 60.6. A higher amount of shots isn’t the blame – he’s at 20.6 for his usage % (ESPN’s version), barely beating his career highs of 19.0 and 18.9.

The future is uncertain for one of the most talented centers in the league. Bynum doesn’t know which team he’ll be playing for even a year from now, and he normally misses large stretches of the season with knee injuries. Players rarely “grow out” of their injury susceptibility – Ilgauskas and Grant Hill are exceptions, as many feared they’d never play again but managed to play well into their thirties while missing few games – but Bynum has a style that’s not based on vertical leaping explosiveness or speed. He has long arms and a soft touch around the rim with a handful of excellent post moves. Even at 24, he can’t jump anymore, and against big centers he can find himself getting rejected all too often. However, he’s playing a career high in minutes and if he can make it through the season it’ll be one of the best from a center in the NBA.

Greg Monroe

Vital stats: 21 years old, per 40 mins: 19.4 pts, 11.9 rebs, 0.7 blcks, 3.7 asts, 58.1 TS%, 32.3 mins per game

The Detroit Pistons post-Billups have been a basketball wasteland. They went from perennial conference contenders to disappointing and mediocre, but not terrible enough to land one of the top couple picks. Fortunately, they have a steal in Greg Monroe, drafted 7th overall, an offensively talented big man who’s on the small side for the position but uses superior positioning to grab rebounds and score inside. He’s a close second behind Dwight Howard and tenth overall in PER, a statistic that summarizes box score stats. Some may argue he’s a power forward, but two of their top lineups are with Jerebko as the other frontcourt player – the 231 lb Jonas brother is clearly not a center – and the third is with Jason Maxiell, a power forward listed at 6’ 7” who is only a center in weight. Monroe also hardly plays alongside Ben Wallace, who is himself an undersized center standing 6’ 9” only if he wears his big afro.  (Daye is another forward he plays alongside, and he’s listed at an impossible 200 lbs despite being 6’ 11”.)

Regardless of what you call Monroe’s position, he scores inside the paint with a nice touch off the glass, great pivot moves, a hook shot, and an ability to use either hand. His differentiating skill among young centers, however, is his passing. His 3 assists per game may not sound like much, but among centers he’s second in the league and nearly tied with Marc Gasol, who’s playing 6 more minutes a game. He’s only 21 and already one of the best passing big men since Brad Miller. Much of his improvement is from the in-between range (3-9 feet) where he’s jumped from 24 to 42% while more than doubling his attempts. With a developing midrange game and 82% from the line, he’s well rounded and in the running for best offensive center in the game.

There are only two aspects of basketball holding Greg Monroe back, and one of them is not even his fault. He’s only playing 32.3 minutes a game, pushing his averages down to 16 and 9 from the magic double-double mark of 18 and 10 per a modest 36 minutes. He also needs to be shooting more, as the true-shooting percentage mark of 58.1% without many turnovers would indicate. The second aspect, however, is defense, where he was awful last year as a rookie, and even with progress this season he’s still a liability. He’s too slow for a power forward, so that’s not the solution, and he’ll only lose quickness as he ages. He only blocks 0.7 shots per 40 minutes, but he does have quick hands and gets 1.3 steals per 40. He needs to add strength to defend competently; if he can be an average defender his offense will provide enough value. Nevertheless, he’s only 21 and should have a bright future in the league with a few all-star appearances, especially since defense is largely ignored there, and a season of 22-11-4(assists) likely.

JaVale McGee

Vital stats: 24 years old, per 40 mins: 15.7 pts, 13.3 rebs, 4.0 blcks, 0.5 asts, 51.1 TS%, 29.9 mins per game

McGee is one of the most frustrating players in the league. He still has no idea how to play correctly, and is only a starter because of his amazing physical gifts. When most people discuss centers height is mentioned as a requirement, but standing reach and wingspan are more important. You shoot, block shots, and contest with your hands, not the top of your head. McGee has a standing reach of 9’ 6.5”, meaning he can alter shots without leaving his feet and can dunk by only jumping one foot. Unfortunately, he still manages to be out of position leaping at every available ball he can see. That standing reach is the highest recorded in ten years at the pre-draft camp excluding two guys who aren’t in the league in Pavel “Pitutary Gland Malfunction” Podkolzine and Guy Marc-Michel. For comparison, centers typically have one in the range of 9’ 1” to 9’ 4”, and McGee bests everyone – DeAndre Jordan, Oden, Bynum, Hibbert, and Howard included.

JaVale, while not leading the league in blocks per game with only 30 minutes, needs to put on some muscle before he can physically be a plus defender, but his lanky frame allows him to be one of the best running big men in the game. Outside of his condor-like wingspan and athleticism there isn’t much to say. He takes too many jumpers for a guy who has trouble clearing 30% on those shots, he never passes, can’t shoot free throws, and he still goaltends. His TS% is typically higher, and last year it was a nice 56.6. There was some progress this year, however, with above average rebounding, and he does have a knack for inside shots. Few guys have the effective size of McGee and his athleticism, meaning no matter how many mistakes he collects the luminous sign of potential is always visible.

Brook Lopez

Vital stats: 23 years old, per 40 mins: 23.2 pts, 6.8 rebs, 1.7 blcks, 1.8 asts, 54.9 TS%, 35.2 mins per game (2010-11)

Lost in the injury and trade talks with Orlando, Brook Lopez was one of the most durable big men in the league, playing 82 games in each of his first three seasons while logging heavy minutes and an offensive burden. Offensively he’s a star, clearing over 20 a game with his post game and a decent jumper, and from the line he’s nearly 80% for his career. His shooting efficiency last year wasn’t noteworthy, but it was better in years past and he rarely turns the ball over for a center. However, he’s a bad passer, and once he learns how to pass out of the low block he should be a great offensive player.

The rebounds aren’t a misprint. Brook’s one of the worst for his position and size. He was outrebounded by Dwyane Wade, and in fact was at only 10% for his rebound percentage, meaning since there are ten players on the court he was exactly average for an NBA player despite playing near the rim and being one of the biggest players on the floor. He admitted he didn’t try on the boards, and apparently was playing through an injury that limited his ability to rebound. Defensively he’s also disappointing; he’s one of the slowest guys in the league and has yet to use his size well on that end of the court.

However, other plodding centers like Yao Ming and Roy Hibbert are able to use their size to be defensive pluses, and if Brook can at least be a wash at that end of the court he can be one of the most valuable centers in the game. If Brook and his twin brother Robin, an energy and defensive guy, were combined into one center, the hybrid Lopez would have already been an all-star. He’s recovering well from the broken foot, and probably should be back to full strength in not too long. Other iron men like Jordan, Malone, and David Robinson also missed most of a season with a broken bone, so it’s no indication Brook is the next Bowie or Oden. He’s one of the few keeping the scoring low post center alive in the NBA.

DeMarcus Cousins

Vital stats: 21 years old, per 40 mins: 20.7 pts, 15.6 rebs, 2.2 blcks, 1.1 asts, 50.2 TS%, 27.2 mins per game

One could argue that some guys on this list are power forwards and not centers, but Cousins has the opposite problem. He’s listed as a power forward despite being 6’ 11”, 270 lbs, and one of the highest standing reaches in the game at 9’ 5”. He’s a force inside, grabbing over 20% of every available rebound, and bullying his way to the rim. Unfortunately, he’s one of the most immature players in the league and tends to take stupid jump shots.

Unlike other players on the list, DeMarcus is a natural scorer and demands the ball. He backs down his opponent with his massive size into the paint, where he can spin to the baseline, throw a hook shot, or show off his nice shooting touch off the glass. His shooting efficiency is low, but that’s mostly because of his bad shot selection and the Kings’ inability to set up plays for him. Sacramento apparently has little knowledge of NBA positions, and they call their 6’ 6” scoring guard who can’t pass, Evans, their point. He also has problems with turnovers, but a lot of that is, again, poor decision making as he’s actually a deft passer. Cousins is reminiscent of Zach Randolph for the skill, scoring knack inside, and maturity, except that he has real defensive potential because of his long arms and strength. If he ever grows up he’ll be a perennial all-star for years.

Notable Postables

Omer Asik

Vital stats: 25 years old, per 40 mins: 8.4 pts, 13.0 rebs, 3.0 blcks, 0.9 asts, 60.2 TS%, 17.2 mins per game

Defensive stars who don’t leap at the ball every play for a blocked shot or steal are some of the better camouflaged players in the league. As the introduction to notable postables -- guys who definitely aren't stars but their play has warranted discussion -- Asik and Destroy doesn't get much playing time, but on other teams they’d be glad to start him because he’s one of the best defensive big men in the league. Despite being on a great defensive team, he’s had one of their best +/- numbers the past two years. Some people sneer at that advanced stat, but you can’t dismiss the fact that the Bulls’ defense is better when he’s on the court. He’s a big center who’s surprisingly nimble on his feet, able to thwart pick and roll’s, opposing centers have trouble scoring on him, and he’s a great rebounder. He won’t score much, but overall he can undoubtedly help a team. Chicago is reluctant to break up their nucleus for a trade, and as a result Asik could be stuck on the bench like Gortat for far too long; however, he’s one of the best defensive players in the league and a hidden gem.

DeAndre Jordan

Vital stats: 23 years old, per 40 mins: 9.5 pts, 10.4 rebs, 4.0 blcks, 0.3 asts, 63.0 TS%, 35.2 mins per game

The young center for the Clippers DeAndre Jordan is nearly leading the league in blocks and is on the receiving end of a few alley-oops. He may never be a star, but he knows his role. He rarely shoots from outside the paint, and in fact has only shot 27 times outside of 9 feet for his career. Defensively, the blocks are nice but he still has a lot to learn, but that’s typical among big guys who eventually become all-league defenders. He’ll learn to use his size to wall off the paint from invading guards and how to defend the post without fouling.

DeAndre Jordan’s value, in need in a nickname because Jordan is synonymous with someone else, is predicated on his long arms and athleticism. He was third in total number of dunks last year and shot 68.6% from the field. However, he’s one of the worst foul shooters in the game and has yet to clear 50% for a season. His rebounding, while solid, is disappointing given his long arms and jumping ability. Don’t expect him to join an all-star team, but he’ll be a valuable center for a long time, jumping from the weak side like Camby for years to come.

Spencer Hawes

Vital stats: 23 years old

I’m ready to call this a fluke or a contract year push, but the change is so remarkable I should be noting his play at the very least. After four years of being a low-efficiency and soft big man who lazily slings midrange shots, Hawes is putting up some of the best per minute numbers outside of Howard. His field-goal percentage, after toiling in the 45.9 to 46.8% range his whole career, has ascended to 58.8%. There is simply no rational explanation. He’s taking the same types of shots in the same proportions, and he credits his advancement to working out with Shawn Kemp. Somehow he has also improved in nearly every major statistical category. His rebound is above average for the first time, he’s passing more, he’s blocking significantly more shots, he’s turning the ball over less often, and the only blemish is shooting a lower percentage from the line than the field, although he’s only taken 16 free throws this year.

Looking closer at Hawes and his numbers, there is evidence that he’s playing over his head. From 16 to 23 feet he’s shooting 57%; the three years before it was 40, 40 and 39%. At 2.9 attempts a game, if he regressed to his historical average he’d lose over a point a game and his field-goal percentage would drop to 52.6. It would still be a career high, but he’s also shooting at a fishy 76% at the rim, which is normally a stat designated for the top finishers in the game. However, given that the changes are over most of his game, it’s reasonable to say he has actually become a better player. His PER, a statistic summarizing his box score numbers, won’t stay in the fringe all-star territory of 22 and should level off to something modest but valuable like 17 to 18.

Kendrick Perkins

Vital stats: 27 years old, per 40 mins: 8.1 pts, 8.8 rebs, 1.8 blcks, 0.9 asts, 60.2 TS%, 33 mins per game

The former Celtic is notable because of his post defense and tough game. Perkins will never be a big scorer down low, but I don’t think he ever wants to be one either. He’s the kryptonite to Dwight Howard and other huge centers, and he’s typically had sterling defensive +/- numbers throughout his career. His stats this season are ugly, but he’s normally in the 12 pts/12 rebs per 40 minutes area. He’s inert offensively, though he’s a high percentage finisher when he gets a good look. Over the offseason several players told tall tales of their great conditioning and workouts, but Perkins was one of the few who wasn’t lying: he looks like a completely different person, having dropped over 30 pounds. This should help with his injury problems and his lack of explosiveness, and he’ll hold down the fort in the paint for Oklahoma City or other teams for the next few years.

Byron Mullens

Vital stats: 22 years old, per 40 mins: 21.5 pts, 9.4 rebs, 0.8 blcks, 1.0 asts, 52.3 TS%, 23.1 mins per game

One of the biggest surprises this year is the great play from Byron Mullens for the Charlotte Bobcats. Boris “Ohh Eclairs” Diaw was comically the starting center, and it took only a few games  before the sweet shooting big man took his place. Most of his shots are long jumpers, and he makes an impressive 46% of them; he's also near 90% from the line. Overall he’s scoring at such a high rate that he would average 20 points a game with enough time, which would shock basketball fans everywhere. His overall shooting efficiency is low because he’s subsisting on longer 2’s, but he rarely turns the ball over and the Bobcats are so starved for offense his floor spacing is valuable.

With this entry I’m not exactly proclaiming Byron to be the next all-star center; rather I’m illustrating the surprisingly good years from a number of centers. He’s suspect defensively, but any center who stands a legitimate 7’ with a reliable jump shot will play in the league for a long time. On an odd note, he likes to play in prison rec leagues in the offseason – probably why he eschews low post work inside, lest he wants a shiv to the side. Charlotte was so desperate for a center they had to start the undersized Diaw, but they were blessed in finding that Byron Mullens was ready to be a real basketball player.

A League of His Own

Dwight Howard

Vital stats: 26 years old, per 40 mins: 20.9 pts, 16.7 rebs, 2.0 blcks, 2.5 asts, 55.9 TS%, 38.6 mins per game

I can't do a young centers list without Howard. Everyone knows the Orlando center, but I have to list him. His points are point this year, mostly because of his wayward foul-shooting -- he's been between 58.6 and 59.6% from the line the previous six seasons -- but he's an improved passer and his post game looks better. He gets a lot of flak for his robotic looking moves, but they're effective and his defense is outstanding. Shaq likes to pick on Howard's game, but the two supermen aren't comparable. Shaq was dominating offensively, but disappointing on the defensive end for the most part and missed too many games even in his prime. Howard, meanwhile, rarely misses a game and leads one of the best defensive teams the past few years even though he's basically their only good defender. He's an athletic phenom in the mold of David Robinson and Wilt Chamberlain; he's unbelievably strong  with a physique carved from Mt. Olympus but can jump and move like a much smaller player. 

The center position isn't dying like some would believe, and there are potential stars and solid studs already strewn about the league. Even if guards are taking more shots, the best spot on the floor to shoot is still near the rim, where centers typically operate. The all-star game in Orlando, home of the league's undisputed best center, will be a test to see how the media view the position and who's worthy of a selection. Nene, who would have been featured in this article if he weren't older than he seemed at 29, is one of the NBA's most underrated players, for example, but Bynum gets all the attention. A first time all-star from this list may make the team, and for some players it could be the first of many.

All statistics are as of January 20th, 2012. Honorable mentions include Al Jefferson, still just 27 but more of a power forward and can't defend. Ian Mahinmi has been playing well, his rebounding in particular, and he'll be watched to see if he continues his play. Tiago Splitter of the Spurs, who dumped Mahinmi, was one of the best players overseas for years and we're seeing glimpses why. Greg Steimsma has given Boston great shotblocking out of nowhere, but he's already 26. Andre Drummond, a year younger than other college freshmen, should find a place on this list in a year or two.