KOBE BRYANT was never going to go gently into that good night. On November 29th the shooting guard for Los Angeles Lakers of North America’s National Basketball Association (NBA) published a poetic ode to his sport announcing he would retire after this season. It was a fittingly attention-grabbing goodbye for a player who attracts reporters to his sagas and scandals just like he pulls the ball towards his hands with the game on the line. Mr Bryant is most notorious for being accused of rape in 2003: he admitted to cheating on his wife but insisted it was consensual, and Colorado prosecutors dropped the charges. His other extracurricular antics, while much less serious, have still rankled fans, like his aborted attempt at a rap career and an ill-advised fashion photo shoot. And on and around the basketball court, he has publicly feuded with Shaquille O’Neal, a star teammate; said he’d rather “play on Pluto” than continue to toil for the Lakers; was caught on national television insulting a referee using a homophobic slur; and at least twice refused to shoot for long stretches of games in childish, sulking protests.
Perhaps the only point on which the general public can agree regarding Mr Bryant is that he is one of the greatest players in NBA history, and a lock to be enshrined in its Hall of Fame. But fittingly for the sport’s most divisive player, even this one seemingly self-evident truth is a topic of fierce debate among modern quantitative analysts. As Mr Bryant turns the remainder of his final season with the hapless, losing Lakers into a nostalgic farewell tour, the most pressing question about the man who calls himself “Black Mamba” is whether he was ever really any good at basketball.
On the surface, Mr Bryant’s résumé looks impeccable. He is the sport’s third-leading scorer of all time, having passed Michael Jordan earlier this year. He posted the highest points-per-game average (35.4 in 2005-06) in a season since 1986-87. He is one of only two players in history to have scored at least 80 points in a single game. He won the 2007-08 Most Valuable Player award, and has been chosen for the league’s annual All-Star Game 17 times in his 20 seasons. And lest he be accused of not being a team player, his clubs have won five championships.
Nonetheless, Mr Bryant has prominent spreadsheet-wielding detractors. The most vocal is probably David Berri, a professor at Southern Utah University and the author of a book on sports statistics called “The Wages of Wins”. For years Mr Berri has been writing articles and giving interviews arguing that the Lakers’ shooting guard falls far short of the elites at his position, is the league’s second-most overpaid player and is a poster child for fallacies in how the public understands the sport. And sure enough, four days after Mr Bryant announced his retirement, Mr Berri published another screed entitled “Kobe Bryant Is an All-Time Great, Unless You Do The Math”.
The case against Mr Bryant is not hard to make. Simply put, it holds that he is a chucker: a player who shoots at every opportunity no matter how tightly he is defended, and misses far too frequently. While nobody would put Mr Bryant in the chucking class of, say, J.R. Smith, there is no doubt that he throws up a hefty share of bricks: in fact, he has missed the most shots of any player in history. Over his lengthy career, his true shooting percentage (TS%)—essentially the share of his shots that are successful, after adjusting for the value of three-pointers and free throws—is .552. That is slightly above the league average of .531, but hardly exceptional: league leaders are usually around .700, and a mark of .552 would have ranked in just the 66th percentile last year among players with at least 1,000 minutes.
Because Mr Bryant shoots so frequently—during his career, around 32% of his teams’ possessions have ended with the ball in his hands, the fourth-highest mark in league history—he essentially drags his entire club towards this good-not-great level of offence. That could potentially mean forgoing higher-percentage shots for his teammates. Wins Produced, a statistic developed by Mr Berri that he claims is a comprehensive measure of a player’s value, places a heavy emphasis on “efficient” shooting and is quite unimpressed with Mr Bryant: his highest single-season rank in this metric is tenth, and he placed in the 40s or 50s during many of his peak years.
The other main line of criticism against Mr Bryant involves his defence. Although the league’s head coaches have elected him to the NBA’s All-Defensive Teams 12 times, the limited statistics available do not back up that reputation. Mr Bryant has never produced lofty numbers of steals, which have a stronger association with winning than any other statistic published in standard box scores. In contrast, a true ball-hawk guard like Tony Allen appears on the steals leaderboard year after year. Moreover, the Lakers as a team have rarely excelled when it comes to stifling opposing three-pointers, one of the hallmarks of a team with strong perimeter defence—for example, the San Antonio Spurs led the NBA in fewest three-pointers allowed for three straight seasons while employing the famed stopper Bruce Bowen. From 2004-05 to 2007-08, Los Angeles was mired in the middle of the pack in three-point defence. Only after adding the lockdown defenders Trevor Ariza and later Metta World Peace to play alongside Mr Bryant did they see marked improvement in the category.
So does Emperor Kobe have no clothes? Is the foremost scorer of his generation merely a ball-hog who can’t be bothered to get back on D, and owes his championship rings to Shaq and Pau Gasol? Is Kobe Bryant not even the best American professional athlete with his surname and first initial? Not necessarily. And it’s not only Lakers fanboys and statistically illiterate dinosaurs who leap to Black Mamba’s defence.
Mr Berri’s efficiency-driven approach has itself come in for plenty of scorn from fellow analysts, who object that it fails to account for the interdependent nature of a team sport like basketball. The primary retort is that there is not an inexhaustible supply of high-value shots—dunks and layups at the rim, as well as uncontested three-pointers—just waiting around for savvy players to pluck them. Instead, such opportunities arise as a result of disrupting opposing defences, typically when a player either breaks away from the man guarding him or represents such a potent threat that opponents must double-team him.
The league’s most efficient scorers are rarely versatile offensive threats. They tend simply to hang around the three-point line or the basket, and hope that their more skilled teammates can lure away pesky defenders and then deliver them the ball. In each of the past two years, Kyle Korver, a deadly long-distance marksman, has led all full-time NBA players in both TS% and the percentage of his basketsthat were assisted (meaning that he made a shot immediately after receiving a pass). In 2011-12 Tyson Chandler, a lumbering big man, pulled off the same feat. Players in this genre can prove extremely valuable, so long as they are paired with a playmaker and a self-starting scorer. But if you put five of them on the court at once, there would be no one able to generate high-percentage opportunities, and their efficiency numbers would plummet.
The flip side of this equation is that efficiency statistics severely underestimate the contributions of dynamic offensive players who can create their own shots and force opponents to react. Using this interpretation, the reason why Mr Bryant is only moderately efficient is that he draws a disproportionate share of attention from defenders, thus enabling his teammates to get better looks at the basket—a trade-off often referred to as the “usage-efficiency curve”. In 2011 Nate Silver, a statistical analyst then writing for the New York Times, tested this theory on Carmelo Anthony, another seemingly inefficient high-volume scorer. The impact was nothing short of enormous: Mr Anthony’s fellow Denver Nuggets posted a TS% 3.8 percentage points higher during the seasons they played alongside him than they had in other years. That is a bigger gap than the difference between the 2014-15 NBA average TS% and that of the league leader and eventual champion Golden State Warriors. Not for nothing did Mr Silver say that Mr Anthony, so often accused of selfishness, was in fact the “ultimate team player”. Only by proving to opponents that one man cannot guard him effectively—a demonstration that may require a few missed shots—can a team’s top scoring option force other defenders to abandon their men in order to help cover him.
Another point in support of Mr Bryant is that not all missed shots become lost possessions. Again, because volume scorers present such a threat that defences must scramble to stop them, opposing players often find themselves far from the optimal position to secure a rebound if the ball bounces off the rim. And given the formidable rebounders Mr Bryant has played alongside, including Mr O’Neal and Mr Gasol, his teammates have recovered his misses at a far higher rate than the league-average errant shot, often in positions close to the hoop that lead to easy baskets. The Lakers have been so successful in converting Mr Bryant’s misfires into second-chance points that Kirk Goldsberry of Harvard nicknamed the phenomenon the “Kobe Assist”.
Such dynamic interactions can never be captured fully by simple box-score figures. Fortunately, in recent years far more granular data about the NBA has become available. The performance of every five-man lineup and that of its opponents is now available on the league’s own website. In theory, these numbers should make it possible to measure a player’s entire impact on both offence and defence, fully counting his effect on teammates. Basketball players are substituted in and out of games every few minutes, resulting in a dizzying array of lineups. Over the course of a season, around 60,000 different combinations of ten men on the court occur, each yielding a specific scoring differential. Using a fairly straightforward (though quite large) multiple regression, analysts can estimate how much each individual impacts his team’s overall scoring margin, holding the other nine players constant. This method, called adjusted plus-minus, is often cited as the gold standard of basketball statistics, though it comes in many flavours (with one easily available on ESPN’s website) and with numerous caveats.
Plus-minus numbers are now available going back to the early 2000s, covering most but not all of Mr Bryant’s career (a list of one well-respected version called Regularised Adjusted Plus-Minus (RAPM) is available here). The story they tell is likely to disappoint both Mr Bryant’s partisans and haters. On the whole, they make Mr Berri’s critique look misguided. According to RAPM, during the past 15 years, swapping Mr Bryant in for a league-average player would have improved a team’s scoring by 5.83 points per 100 possessions. That is an outstanding mark, enough to transform a middling club into a low-end title contender. However, it is not quite consistent with Mr Bryant’s image as the foremost offensive player of his generation: Steve Nash, Chris Paul and of course LeBron James (the sport’s universally recognised greatest player) are all above 6.5.
Moreover, RAPM also supports the naysayers regarding Mr Bryant’s defence. It finds that adding him to a club would actually increase its opponents’ scoring by a bit over one point per 100 possessions. That hardly makes him a dire defensive liability: a true sieve like Stephon Marbury inflated rivals’ production nearly four times as much. But it does make his All-Defensive Team awards look spurious, and puts a low ceiling on his total contributions when compared with players who excel on both sides of the ball.
Combining offence and defence, RAPM ranks Mr Bryant as the NBA’s 19th-best player on a per-minute basis over the past 15 years, with a net contribution of 4.77 points per 100 possessions. (Predictably, Mr James is first, at 9.25, and a typical minimum-salary journeyman, freely available to any team who wants to hire him, is around negative two). No one but the egotistical Mr Bryant himself would object to his scoring lower than undisputed greats like his former teammate Mr O’Neal. But even his doubters might be surprised to see him below an unheralded, modestly-paid defensive specialist like Amir Johnson, whose score of 5.49 comes in 11th.
There are two good reasons to believe these figures may sell Mr Bryant short. One is a statistical problem called “multicollinearity”, which refers to the difficulty of disentangling the impact of teammates who almost always play at the same time. Mr Bryant has spent the majority of his career sharing the Los Angeles backcourt with Derek Fisher, a nice point guard who is no one’s idea of an elite talent. RAPM sees Mr Fisher as something of a hidden star: his score of 2.93 is comparable to those of big names like Chris Bosh and Mr Gasol. Suspiciously, Mr Fisher posted some of his lowest annual RAPM marks from 2004-07, precisely the three seasons when he was not on the Lakers. Is RAPM assigning credit to Mr Fisher that rightly belongs to Mr Bryant? If so, Mr Bryant should shoot up the rankings.
The other argument in support of Mr Bryant is that his lacklustre defensive performance may be by design. There is no prize for having the best record in the NBA: the only thing that matters is success in the playoffs. Although middling clubs must fight all 82 regular-season games fiercely in order to qualify for the playoffs, the best teams are assured of a high seed and tend to rest their players strategically to keep them in peak form once April rolls around. Mr Bryant is too dedicated a competitor—or perhaps too congenital a narcissist—to sit out large chunks of the season, as ageing stars on the San Antonio Spurs do every year. However, playing defence is exhausting and offers little glory. It is entirely plausible that Mr Bryant is simply trying to preserve his energy in one half of the game, in order to expend it on his quest for both scoring titles and championships. There is circumstantial evidence to support this theory: Mr Bryant’s career Defensive Box Plus-Minus, which estimates defensive plus-minus using box-score statistics, is negative 0.5 during the regular season but positive 0.7 in the playoffs. Perhaps he really has turned up the heat on D when a title was on the line.
Even if one dismisses these claims, however, one area remains in which Mr Bryant is an undisputed champion: longevity. Unlike big men, whose height advantage does not diminish with age, guards depend on quickness and tend to lose a step by their early 30s. But Mr Bryant, whose conditioning and work ethic are legendary, was essentially the same player at age 34 that he was at 20, and every year in between. As a result, even though he may not quite have been the superstar that his scoring figures would indicate, his total contributions exceed those of many better-rounded players with higher peaks. According to figures at Basketball-Reference.com, Mr Bryant’s career is the NBA’s 16th-most valuable since 1973-74—appropriately, one spot below that of his frenemy Mr O’Neal. No one, least of all Mr Bryant himself, would consider him an exemplar of the aphorism that slow and steady wins the race. But the data strongly suggest that Black Mamba was far more of a tortoise than a hare.
