NBA Babble Babble

Posted on March 21, 2007 by


NBA Babble and Win Score had added a couple of new features. You now have the following options in viewing the Win Score of NBA Players.

Win Score stats by team
Win Score stats by day
Win Score stats by player
Win Score stats for every game, every player

Of course Jason Chandler’s website does more than provide a player’s Win Score. It also reports Position Adjusted Win Score (PAWS), Position Adjusted Win Score per minute (PAWSmin), and Wins Produced per 48 minutes [WP48]. For all players you can look at this for the season or by individual game. So this is a really neat site for those interested in seeing more of the analysis introduced in The Wages of Wins.

As you look over the data, you will see some differences between what Chandler reports and what I report in this forum. Specifically, Chandler does not calculate WP48 in the same fashion and hence reports slightly different numbers.

To avoid any confusion, I thought I would briefly review how we calculate WP48, as it is reported in The Wages of Wins. Along the way I will answer a few comments from critics and show that the simple approach Chandler takes give you virtually the same results we report.

The WOW Approach to WP48

Connecting Wins to Offensive and Defensive Efficiency

We should begin with the very first step. Both John Hollinger and Dean Oliver argue that wins are determined by a team’s offensive and defensive efficiency, or how many points a team scores and surrenders per possession. I have written a paper entitled, “A Simple Measure of Worker Productivity in the National Basketball Association” (which was a working paper when the book was published but should be finally published later this year). This paper demonstrates that what Hollinger and Oliver assert is true. Via some fairly simply math, one can show that wins are indeed all about offensive and defensive efficiency.

I note this because the first step in building an empirical model is to establish theoretically the relationship between what you are trying to explain and what you think does the explaining. Hollinger and Oliver both asserted that the efficiency measures explained wins, but neither attempted to show that this must be the case. In the aforementioned article I try and show that I think the math is clearly on their side.

Blocked Shots and Assists

Once we statistically link wins to offensive and defensive efficiency, we then can determine the value, in terms of wins, of points, rebounds, steals, field goal attempts, free throw attempts, turnovers, and personal fouls. What is missing is blocked shots and assists.

Of these last two factors, the value of blocked shots is the easiest to determine. Part of defensive efficiency is the number of made field goals by the opponent. One can show that blocked shots impacts how many shots the opponent makes, and by estimating this relationship you can thus connect blocked shots to wins.

Assists are bit trickier. The basic theory behind an assist is that one player is taking an action the increases the productivity of a teammate. We find that the empirical evidence supports this claim. As your teammate’s assists increase, your overall productivity rises. We can use this relationship to estimate the value of an assist.

Now it is important to see how we incorporate assists into our model. As we detail in The Wages of Wins, the value of an assist represents a transfer between players. What we do is subtract the value of assists from each player, and add back that same value to the players who get the assists.

It is important to note that the value for assists that we use is not determined arbitrarily, but is determined by our model of individual player productivity. Now one of our critics noted that you could change the value of an assist and not alter our forecast of wins. Of course the critic fails to offer an alternative model to arrive at the value of an assist. Rather, this person simply asserts that changing assists does not change the forecast.

It certainly is clear, if you have read The Wages of Wins, that assists are not used to forecast wins. Our forecast of team wins from the Wins Produced model appears on page 110 of the book. Our discussion of assists occurs on page 117. From this it is obvious that assists are not necessary to forecast wins.

Why is this? Once again, assists are a transfer of credit from player to player. We are looking at production after the game has happened. The production is already there. The assists just tell us something about who should get credit for that production.

The fact that assists are not used to forecast wins is quite clear if you read The Wages of Wins. Unfortunately, our critics either cannot read, or are not interested in reporting what we do accurately (more on that in a moment).

Calculating WP48

Once we have ascertained the value of each statistic, we can now calculate WP48. To do this, you need the following three elements.

  • A player’s statistics, valued in terms of the impact these statistics have on wins.
  • The average performance at a player’s position
  • The value of team statistics, an adjustment that allows us to account for the quality of a team’s defense and the pace the team plays.

We note in The Wages of Wins, that a player’s value is primarily determined by the first two elements, or a player’s statistical production relative to the average performance of a player at that position.

Despite making this clear in the book, there is still some controversy surrounding the last step, or the team adjustment. It has been suggested in some circles that the team adjustment is a giant fudge factor. As we note in The Wages of Wins, and as I have noted in this forum, the team adjustment is not what drives Wins Produced.

To see this point, consider PAWSmin. PAWSmin is simply Win Score per minute, adjusted for the position the player plays. PAWSmin does not have any team adjustment at all. WP48, as noted, does have a team adjustment. If the team adjustment were truly that important, these two values would be very different. But as I noted a few weeks ago, the correlation between WP48 and PAWSmin is 0.994. Yes, there is a 0.99 correlation between the player evaluation with and without the team adjustment.

This result indicates quite clearly that player performance is indeed all about what the player has done relative to the player’s position. The team adjustment is not driving our player evaluations.

The NBA Babble Approach

All the steps I describe to calculate WP48 take a bit of time. I have reached a point where I can download the data for a team from and determine each player’s WP48 on that team in about five minutes. To update this after every game – which Jason Chandler wishes to do – would be very time consuming. There are 30 teams. If all played the night before it would take you 150 minutes to update the stats.

Fortunately, there is an easier way. Because PAWSmin and WP48 are essentially the same, you can estimate WP48 with the following formula:

WP48 = 0.104 + 1.621*PAWSmin

This formula is obviously quite a bit easier than all the steps I described earlier. As you scan Chandler’s calculations you will see a great deal of similarity between what he reports and what I report when I calculate WP48. Again, I use the actual values of the statistics in terms of wins and the team adjustment. Chandler uses the simple equation reported above. The results, though, are quite close (with the big differences actually driven by how Chandler and I consider position played).

Persistence of the Team Adjustment Critique

On page 108 of The Wages of Wins is the following three sentences:

“In general, the team statistical adjustment is quite small for each player and therefore this adjustment does not substantially alter our rankings of players across teams. To illustrate this point, the correlation coefficient between player production unadjusted for team statistics and then adjusted for team statistics is 0.99. In simple words, whether you adjust for the team statistics are not, the player rankings are essentially the same.”

So we note the unimportance of the team adjustment in the book. We have noted this more than once in this forum. Yet last week, at NBA Babble and Win Score, there was the same critique in the comments.

Why does this criticism keep appearing? It’s important to note that the group that most often attacks The Wages of Wins is associated with the plus-minus approach to evaluating NBA players. This group of people is in the business of selling a non-box score based measure of performance to NBA teams. The premise behind their business is that the box score statistics the NBA tracks do not allow one to evaluate NBA players. The Wages of Wins suggests, quite clearly, that the box score statistics do tell us a great deal about the productivity of individual players.

Unfortunately if you are in the business of selling a non box score based method, The Wages of Wins presents a significant problem. The analysis in The Wages of Wins is essentially free. The teams already have the box score data. The book, which was published by an academic press, can be checked out for free from a university library (or perhaps your own public library, or perhaps you can borrow from a friend). Given this reality, certain elements in the plus-minus crowd (and I am not referring at all to Wayne Winston, the originator of this approach who has always been perfectly pleasant in various e-mail exchanges) feel the need to attack both The Wages of Wins and its authors. And given the money involved this seems understandable. After all, if the box score statistics can tell you who is “good” and “bad”, then a business based on a non box score approach is clearly threatened.

Summarizing Wins Produced Again

My sense at this point is that we have addressed the primary critiques of Wins Produced. Let me close by re-iterating what I think our model is and is not. Wins Produced is a measure of how productive a player has been in the past. It is primarily driven by a player’s ability to shoot efficiently, rebound, and create and avoid turnovers (again, relative to what the average performance at a player’s position). It is designed to be both accurate and simple and hopefully furthers our ability to use the data generated by the NBA to investigate various aspects of economic theory. In other words, Wins Produced is a research tool.

Now that we see what Wins Produced is, let me state again what it is not. Wins Produced tells us how productive a player has been, but it does not tell us why a player was productive. In this sense, it does not replace coaching or scouting. In my view, the job of a coach or scout is not to tell us how productive a player has been (the data tells us that), but why the player was productive, and furthermore, whether or not there is anything one can do to change what a player does on the court.

Our research has shown that for the most part, players are what they are. Still, it is possible for player performance to change. Factors that can cause a player to be more or less productive include the productivity of teammates, injuries, stability of a team’s roster, and coaching. Yes, coaching has been found to statistically impact performance. What is not clear is how coaching matters? Hopefully, as we continue in our research into the economics of sports, further light can be shed on that question.

– DJ