Everybody stay calm... Allen Iverson is not actually a terrible player A review of "The Wages of Wins" by David Lewin, 7/29/06

There have been a couple of different types of reactions to the new book, "The Wages of Wins" by David J. Berri, Martin B. Schmidt and Stacey L. Brook. The most common reaction has been people who have not read the book dismissing it solely because they do not like its conclusions. This is a reprehensible reaction, as one should not dismiss an idea solely because it defies conventional wisdom. America's best sportswriter Bill Simmons did this, writing: “we get carried away with basketball statistics nowadays, as evidenced by the new book that rated Allen Iverson as the 90th best player in the league during his MVP season.” I was quite disappointed in the usually stats friendly Simmons for writing this without providing any evidence for why the system was wrong.

The second type of reaction has been to blindly agree with the book, because it sounds like a good idea, without closely examining its methods. Malcolm Gladwell of the New Yorker did this. He strongly agrees with the scientific, empirical spirit behind the book and because of this touted the book without checking with experts in the various fields to see whether the studies were well executed.

The third type of reaction to the book is the one I had. I love the effort that the book represents. I love the idea of using regression analysis to develop a basketball rating system instead of just arbitrarily making one up. I love the scientific method. What I am not in love with is the many mistakes made in the application of these ideas to sports. The heart of this book is the basketball ratings system called "Wins Produced". I hope that by explaining the problems with this system I can contribute to the effort to create a better one.

When I first read the book and saw the conclusions drawn from this system I got the sense that they were a little off, but I couldn't quite put my finger on it. The system seemed to give little credit to scorers and a ton of credit to rebounders. Some players have negative values. It is never stated that “Wins Produced” compares players to some baseline. It is to be inferred from this that in the case of players with negative wins produced the team would be better off without them, playing 4 on 5. Faced with these and other unlikely results many people have said that the system was worthless and moved on.

Just saying that the system is wrong is not enough. If the system was created through a completely valid process then it should be correct, whether or not we like the results. The question is then, why do the results of the "Wins Produced” system differ so greatly from conventional wisdom?

The "Wins Produced" system is a traditional linear weights system. The major difference as mentioned previously, is that instead of simply assigning values to the various individual statistics available the coefficients are determined through regression analysis. This is a good idea. The problem is in the execution.

Team stats totals that are available for individual players (points, rebounds, steals, but not points allowed because that stat is not tracked for individual players) are regressed against wins. This yields a value for each stat in terms of wins. A point is said to be worth .033 wins, other values are assigned to other stats. The result is the best measure of team quality that does not use points allowed. It is nothing more than this. Unfortunately the goal is to create a system that evaluates individual players, not teams.

To get to this end, the authors make a leap of logic that is highly questionable. They decide that the value of every stat is the same on a team level as it is on an individual level, i.e. basketball is simply five games of one on one. This is where the system becomes debatable. The assumption that basketball is five games of one on one may be correct, or it may be incorrect. I suspect the latter. A few examples will illustrate why I feel this way.

"Wages" states that the average NBA offensive efficiency is approximately one point per possession. Based on this, the system is built such that scoring at one point per possession contributes nothing towards winning, because a team that scores at this rate is an average team. Essentially it suggests that you can trade one possession for one point at any time, and that scoring at the league average rate is worthless. On a team level this is somewhat true. Every team will use all of their possessions, the efficiency at which they use them determines whether they win or not. However, at an individual level, this is a problem. Possessions don't just get used, someone has to use them otherwise the team gets a shot clock violation. Using possessions at a league average rate has value because it is better than a shot clock violation.

Claiming that scoring one point per possession is worthless ignores a basic tenet of economics: supply and demand determines value. There are very few people in the world that can score one point per possession in the NBA. In fact, assuming that the league average is one point per possession as stated in the book, half the players in the league score below this rate. So, the NBA can fill only half of the league with players who can score above one point per possession. It seems clear that being the 225th best player in a league that requires 450 or so players is not worthless. In fact it tends to be worth about three to five million a year in the NBA.

This is a recurring problem with linear weights systems. They do not take into account replacement level. What would replace a player if he were not there? Is it nothing? Is it a worse player? Is it a league average player? There is good reason for the system to struggle with this concept as it is regressed at the team level, and replacement level is not applicable at the team level.

Here’s an example of how this is problematic. In the Author's blog, "The Wages of Wins Journal" Berri stated that Kobe's scoring this year did not contribute as much value as many people think it did (although it was certainly valuable) because he was not very far above league average efficiency. This statement suggests that if Kobe were removed from the Lakers, that the Lakers would get league average efficiency (one point per possession) on the possessions that Kobe would have used. He is not all that valuable because he does not exceed this by very much. The system does not specify what Kobe is being replaced by, but we can draw the assumption that he is either being replaced by a player who, no matter how many possessions he uses, produces one point per possession, or that Kobe's teammates, in his absence increase their scoring efficiency and score one point per possession while playing four on five. This seems a tad unreasonable to me.

A similar, but somewhat opposite problem arises with rebounding. The "Wins Produced" system considers defensive rebounds to be worth a possession, and therefore one point. At a team level this is undoubtedly true. If you don't get the defensive rebound then the other team will get it. This is one fewer possession you have compared to the other team. On an individual level this is a questionable claim. To illustrate lets do the same thing we did with Kobe above, this time removing Ben Wallace from the Pistons. What he is replaced with?

Well, since a defensive rebound is said to be worth a possession, the implication from the "Wins Produced" system is that you would lose all those possessions, and that the other team would get all of those rebounds. This is probably not a valid assumption. If we replaced Big Ben with a player from the NBDL then the new guy would get at least some boards. If we replaced Wallace with nothing but air his teammates would still grab some of those boards. Still other rebounds would go out of bounds and be credited as team rebounds. So, the assumption here is that unlike with Kobe's scoring (where he was replaced with a guy who scored at league average level or his teammates played better playing four on five) here Wallace is replaced with a guy who not only doesn't rebound, but also ensures the other team gets every rebound Wallace would have gotten. This goes a long way towards explaining why the "Wins Produced" system is so high on players like Wallace and Chandler.

There is a lot of debate over whether scorers like Kobe cause their teammates to score more efficiently and therefore should get simply for using possessions. So far no one has proved it one-way or the other. There is also debate as to whether rebounders like Wallace and Chandler create more rebounds for their team or simply steal them from teammates. This is where on court-off court data, derided in the book, comes in.

There is no doubt in my mind that regression analysis is a more accurate way to determine the value of player statistics than just guessing. However, it is imperative that the regression is set up properly, which in this case it is not. In order to determine how much a player helps his team win it does not make sense to regress team statistics against wins and then apply that to players. Better perhaps would be to regress player's individual statistics against his on court-court influence. While not perfect, this gives a better picture of how scorers affect their teammates’ offense and how rebounders effect team rebounding. All in all “The Wages of Wins” is a good read and offers many clever insights but it falls short in terms of real groundbreaking analysis.

About the Author:
David Lewin is an 19 year old student at Macalester College in St. Paul, Minnesota. His interests include basketball, basketball statistics, football, and football statistics. He has also written for Football Outsiders and Pro Football Prospectus 2006. He can be reached at dlew33@yahoo.com