## May 22, 2006

In the New Yorker, Malcolm Gladwell reviews a new book by economists trying to horn in on the kind of analyses done by amateur sports statisticians. Gladwell pass along their debunking of the value of the famous 6'-0" Philadelphia guard Allen Iverson, a seven time All-Star and four time scoring leader:

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.

I'm sure that Iverson gets a lot of credit for being incredibly good for his size, and that he really isn't that valuable a player, but it's pretty silly to say he was only the 91st best player in the league in his MVP season, the year he carried a mediocre 76ers team to the NBA Finals.

Basketball is simply a hard game to understand statistically. One obvious problem is something that economists ought to be able to grasp: diminishing marginal returns on shooting. The three economists downgrade Iverson because, even though he scores a lot of points per game, he has a below average shooting percentage. But, clearly, one reason for that is because his teams don't have a lot of other offensive options, so the defense plays Iverson tightly, and he takes more desperation shots than his teammates because he is The Man on the team, and that's what The Man does.

Similarly, Wilt Chamberlain shot only .506 from the floor the year he averaged an incredible 50 points a game in 1961-62, compare to .727 in his last season, 1972-73, when he averaged only 14 points per game. Same guy, but completely different strategies led to very different results due to diminishing marginal returns on shooting.

Gladwell doesn't mention another conclusion that might make you wonder about the methodology. Matt Yglesias writes:

If you want to see a truly controversial claim, check out this 1999 paper by one of the book's authors looking at the 1997-1998 MVP race. The leading candidates were Michael Jordan and Karl Malone. They conclude that Malone had a superior season, worth 18.83 wins as opposed to Jordan's 16.44 wins. Fair enough.

They say Jordan actually only had the sixth-best season. Numbers four and five were David Robinson and Tim Duncan respectively. Then it gets a bit wild. Number three on the list is Jayson Williams! And number one on the list . . . better than Jordan, Barkley, Robinson, and even Malone -- Dennis Rodman whose 20.79 wins make him far and away the league's top player in the 97-98 season.

In 1998, Rodman led the league in rebounding with 15 per game, but averaged less than 5 points per game, which is awful. But Jordan was there to take up the offensive slack.

Rodman had been basically given away by San Antonio as a troublemaker three years before, but the Chicago Bulls picked him up cheap in the hopes that Jordan's vast prestige and formidable personality could intimidate Rodman into contributing to the team. And that's what happened, as Jordan, Pippen, and Rodman won three consecutive titles. As soon as Jordan retired for the second time after the 1998 season, Chicago got rid of the Rodman freak show. He played 35 games over the next two seasons, then retired.

One way (although certainly not the only way) to think about would be how would a team of all Jordans do and how would a team of all Rodmans do? Five Jordans would win the NBA championship. Five Rodmans would probably set the the NBA record for lowest number of points scored against, but they would certainly set the record for the least points scored because by 1998 Rodman couldn't shoot at all.

Here's their Basketball Win Score formula, and it's easy to see why Rodman gets overrated:

Points + Rebounds + Steals + ½Assists + ½Blocked Shots

– Field Goal Attempts – Turnovers - ½Free Throw Attempts - ½Personal Fouls

They overrate rebounders because there is nothing that gets subtracted from rebounding, so rebounding is treated as pure profit, whereas for other positive outcomes, they subtract the costs of generating those outcomes:

- whereas from Points they subtract Field Goal Attempts and 1/2 of Free Throw Attempts

- from Steals they subtract 1/2 Personal Fouls

- from Assists (and only 1/2 of assists!) they subtract Turnovers

- and from 1/2 of Blocked Shots they subtract Personal Fouls.

- But, there is no countervailing measure of what a player is sacrificing by concentrating on rebounding (other than 1/2 of the occasional loose ball foul). Thus, they overrate players like the late career Dennis Rodman who did very little on offense except rebound (and set screens). Because Rodman wouldn't take the open 12 footer because he concentrated solely on rebounding on offense, Jordan had to take a lot of fall-away 18 footers with both his own man and Rodman's man in his face. Thus, Jordan got subtracted from his Win Score a lot of Field Goal Attempts that he took because Rodman wasn't around to shoot. But there is nothing subtracted from Rodman's positive totals to account for this.

One way to account for this might be to subtract points scored less than average. For example, if the average team scored 100 points per game that year, that averages out to 20 points per man on the court (100/5=20). Rodman played about 3/4ths of each game that year, so he should have averaged 15 points per game if he was an average scorer. But instead, he scored less than 5 points per game, which is 10 points per game below what would be expected of the average player who plays 75% of the available minutes. So, subtract either the missing 10 points or some fraction of that.

In general, I've noticed that Ph.D. economists, who all have to be really good at dealing with abstract equations full of x, y, and z to get their doctorates, aren't as good as they need to be at thinking about how the human beings they model in their formulas actually behave.

Perhaps the authors have refined their methodology since this 1999 paper, but, in general, what I've heard of this new book reminds me a lot of Pete Palmer's 1984 book "The Hidden Game of Baseball," in that both of them used a single synthetic statistic for evaluating every player in history. Palmer's results were interesting and most of them reasonable, but his Holy Grail statistic ("linear weights") kept coming up with too many weird findings, like Roy Smalley Jr. being one of the best baseball players of all time.

Palmer's book was a heroic attempt but too ambitious for the sabremetric state of the art in 1984. Bill James' less ambitious methodologies were more productive at the time. I don't know enough about basketball statistics to say if the same is true for this new book that Gladwell takes on faith, but knowing Gladwell's track record in recent years, I'd have to be awfully skeptical of it.

In general, this sounds like another example of the arrogance of economists, which has always existed, but now examples of it get a lot more (and a lot more credulous) mainstream publicity in the wake of Freakonomics.

#### 1 comment:

Anonymous said...

I'm Steve Landtroop. Idid play by play for Rodmans 3 years @ Southeastern Oklahoma State-Durant. Marty Blake, the famed NBA scout noted one night that we were watching the most dominate rebounder to play the game and nobody in the NBA knows it.