Rating Basketball Players

Malcolm Gladwell has an interesting book review this week that is availiable online in The New Yorker:

But how do we know that we’re watching a great player? That’s an easier question to answer when it comes to, say, golf or tennis, where players compete against one another, under similar circumstances, week after week. Nobody would dispute that Roger Federer is the world’s best tennis player. Baseball is a little more complicated, since it’s a team sport. Still, because the game consists of a sequence of discrete, ritualized encounters between pitcher and hitter, it lends itself to statistical rankings and analysis. Most tasks that professionals perform, though, are surprisingly hard to evaluate. Suppose that we wanted to measure something in the real world, like the relative skill of New York City’s heart surgeons. One obvious way would be to compare the mortality rates of the patients on whom they operate—except that substandard care isn’t necessarily fatal, so a more accurate measure might be how quickly patients get better or how few complications they have after surgery. But recovery time is a function as well of how a patient is treated in the intensive-care unit, which reflects the capabilities not just of the doctor but of the nurses in the I.C.U. So now we have to adjust for nurse quality in our assessment of surgeon quality. We’d also better adjust for how sick the patients were in the first place, and since well-regarded surgeons often treat the most difficult cases, the best surgeons might well have the poorest patient recovery rates. In order to measure something you thought was fairly straightforward, you really have to take into account a series of things that aren’t so straightforward.

Basketball presents many of the same kinds of problems. The fact that Allen Iverson has been one of the league’s most prolific scorers over the past decade, for instance, could mean that he is a brilliant player. It could mean that he’s selfish and takes shots rather than passing the ball to his teammates. It could mean that he plays for a team that races up and down the court and plays so quickly that he has the opportunity to take many more shots than he would on a team that plays more deliberately. Or he might be the equivalent of an average surgeon with a first-rate I.C.U.: maybe his success reflects the fact that everyone else on his team excels at getting rebounds and forcing the other team to turn over the ball. Nor does the number of points that Iverson scores tell us anything about his tendency to do other things that contribute to winning and losing games; it doesn’t tell us how often he makes a mistake and loses the ball to the other team, or commits a foul, or blocks a shot, or rebounds the ball. Figuring whether one basketball player is better than another is a challenge similar to figuring out whether one heart surgeon is better than another: you have to find a way to interpret someone’s individual statistics in the context of the team that they’re on and the task that they are performing.

In “The Wages of Wins” (Stanford; $29.95), the economists David J. Berri, Martin B. Schmidt, and Stacey L. Brook set out to solve the Iverson problem. Weighing the relative value of fouls, rebounds, shots taken, turnovers, and the like, they’ve created an algorithm that, they argue, comes closer than any previous statistical measure to capturing the true value of a basketball player. The algorithm yields what they call a Win Score, because it expresses a player’s worth as the number of wins that his contributions bring to his team. According to their analysis, Iverson’s finest season was in 2004-05, when he was worth ten wins, which made him the thirty-sixth-best player in the league. In the season in which he won the Most Valuable Player award, he was the ninety-first-best player in the league. In his worst season (2003-04), he was the two-hundred-and-twenty-seventh-best player in the league. On average, for his career, he has ranked a hundred and sixteenth. In some years, Iverson has not even been the best player on his own team. Looking at the findings that Berri, Schmidt, and Brook present is enough to make one wonder what exactly basketball experts—coaches, managers, sportswriters—know about basketball.