Yesterday I was on Bloomberg Television, discussing the NCAA Final Four (and a bit of baseball) with Rhonda Shaffler. Let me expand briefly on what I said.

1. The Final Four is a Big Business for a Small Number of Schools

CBS pays the NCAA $6.2 billion – over 11 years – to broadcast the NCAA tournament. Each year that works out to more than $500 million in revenue. Part of this money – about $132 million – goes into a basketball fund that is distributed to conferences according to the success the conference teams have in the tournament. If your teams go far, you get more money. If your team or teams are eliminated in the first round, you get less. As a consequence of this distribution plan, the rich tend to get richer.

I think it’s important to note how the distribution of NCAA revenue conflicts with the primary purpose of the extensive (500 page) NCAA rule book. Throughout its history the NCAA has added rules in an effort to promote competitive balance. For example, colleges are prohibited from paying athletes because it’s feared that if athletes sold their services in a market, the richest schools would have the best players. And if that happened, the NCAA would not have competitive balance.

Of course, the NCAA as it stands today, does not have competitive balance. In January, the Social Science Quarterly published a paper by Jim Peach (“College Athletics, Universities, and the NCAA”). In this paper he states the following:

Competitive balance in men’s basketball will be measured here by appearances in the final four of the NCAA tournament since 1950. Only four teams (UCLA, North Carolina, Kansas and Duke) account for nearly a quarter (24.6 percent) of all final four appearances between 1950 and 2005. Thirteen teams accounted for half of all final four appearances. As with football, the concentration at the top in men’s basketball does not change much by decade.

Economic theory tells us that the labor market restrictions imposed by the NCAA are not likely to change the distribution of players or the level of competitive balance. Whether the players collect the money, or the money is collected by the schools, players are still going to migrate to wherever they generate the highest return. In other words, it’s not surprising that the same schools tend to win year after year.

This was true before CBS paid the NCAA billions to televise the tournament.  And it is still true today.

2. The Players Generate, but do not get, the Money

The prior discussion noted that college basketball players do not get paid. And I, like many other economists argue, that there is something wrong with an institution that takes money from athletes – many of which come from disadvantaged backgrounds – and gives it to coaches and universities.

Let me note a few sources where one can read more on this topic. Robert W. Brown – a professor of economics at California State University San Marcos – has published extensively on how much revenue a college athlete generates. With respect to men’s college basketball, Brown (along with Todd Jewell) found that in 1996 a player taken in the NBA draft generated more than $1 million per season for his college team. In other words, players like Greg Oden and Kevin Durant generate far more for their respective colleges than their athletic scholarship costs.

The discrepancy between pay and revenue generation results in a surplus, which appears to go to the coaches. This was a point made in the New York Times by Andrew Zimbalist (Looks Like a Business; Should Be Taxed Like One). Zimbalist, by the way, is the author of Unpaid Professionals, a very good book on college sports.

As I noted in the interview, the University of Alabama does not generate the revenues of the Miami Dolphins. Yet the Crimson Tide could offer Nick Saban a competitive wage. This is only possible because Alabama does not pay its players.

Brown and Zimbalist are not the only sports economists to comment on this issue. For more you can look in Economics of Sports (by Michael Leeds and Peter Von Allmen), Sports Economics (by Rod Fort), and Economics of College Sports (an edited volume by John Fizel and Rod Fort which has one article I authored). In addition, Randy Grant, John Leadley, and Zenon Zygmont have a forthcoming book entitled The NCAA and the Economics of Intercollegiate Sports (World Scientific). All of these authors explore in detail the labor market in college sports and conclude that players are indeed not being compensated for the revenue being generated.

3. The Final Four is Not an Engine of Economic Growth

Atlanta is hosting the Final Four. Cities campaign for the opportunity to host such an event. One might wonder, though, if this event impacts economic growth? Victor Matheson and Robert Baade investigated this question. Looking at data from 1970 to 1999, these authors found little evidence that economic growth was enhanced by a city hosting the Final Four.

Such a result is not surprising to those who have seen economists apply the methodology of public finance to the study of professional sports. Studies of the economic impact of stadiums and mega-events (such as Super Bowls), consistently find that sports do not generate substantial economic growth.

There are a few reasons for this result. Perhaps the biggest is the crowding out effect of sports consumption. Often sports consumption is simply replacing another potential item in a consumer’s entertainment budget. If the sporting event was not there, the consumer would simply enjoy some other form of entertainment. There is also the issue of leakages. For example, of a hotel raises its rates for a big event, these higher rates will often be transferred to a home office, not into the local economy.

All of this tells us that residents of Atlanta might enjoy the Final Four this weekend. But if the city spent tax dollars to host this event, it is not likely this investment will generate many returns.

4. And my picks….

Okay, I have problems with the structure of the NCAA. I think the player’s should be paid. And I do not believe cities should spend tax dollars to host the Final Four.

All that being said, I still intend to watch. Like a moth to the flame, I can’t stay away. So who will I root for?

I grew up in Michigan, but the Wolverines seem addicted to the NIT. I spent my teenage years in Nebraska, but the Cornhuskers were very bad this year. And the same could be said for my alma mater, Colorado State. Given that all my teams stopped playing some time ago, I need to find some reason to root for one of these teams.

My wife, thankfully, has provided a reason. Before the tournament began we each filled in our brackets. After the first four rounds, she has done slightly better than I. This is mostly because she tends to go with the seedings, only picking a few upsets here and there. I think I know something, so I pick more upsets.

Still, if UCLA can beat Florida, I will finish ahead of my wife. So on Saturday I will be rooting for the Bruins. And hopefully Ohio State – the team my wife and I both picked to win it all — will also make it to the Finals. If that happens, I can take some delight in having chosen the teams in the championship game.

All that being said, I do not think there is any criteria that would successfully predict the outcome of games where the competitors are so close in talent level. Each of the three remaining games should make for good television. It’s not good that the money this television audience will generate will go to rich schools (and not poor athletes). But the fact does not change the compelling nature of these games.

And now for some baseball…

I also talked a bit of baseball on Bloomberg. My story should be familiar to readers of The Wages of Wins. Money cannot buy championships in baseball. Again, payroll only explains about 18% of wins in baseball.

The Baseball Economist notes the reason why. I just received my autographed hard cover copy of this book (thanks, JC) and on page 194 it reads: “In the previous chapter we saw that a pitcher’s previous season performance explains only about 30 percent of his performance the following season. Similarly, in their book The Wages of Wins, economists David Berri, Martin Schmidt, and Stacey Brook report that a hitter’s previous season’s performance explains only about a third of his performance the following year.”

Both JC and The Wages of Wins authors find that baseball performance is difficult to predict. Consequently, it is difficult for baseball teams to know which players to spend their millions upon. When players do not perform as expected, teams with large payrolls do not get to win as much as they would like. Likewise, when players perform better than expected, teams like the Detroit Tigers (my team) get to go to the World Series. So although we might guess who we think is going to finish on top this season, as the season starts on Monday we don’t really know.

- DJ

If we compare player performance in the basketball, baseball, and football we see that over time, NBA players are the most consistent. Football players tend to be quite inconsistent.

Although NBA players tend to be relatively consistent across time, player performance can change. And each year the NBA has an award that theoretically rewards the player who made the largest positive leap in performance.

According to Kelly Dwyer at Sports Illustrated.com, the favorite for Most Improved player in the NBA this year is Kevin Martin. In 2005-06, Martin averaged 10.8 points per game. This year his per-game scoring average has leaped to 20.5. Of course, Martin has also seen his minutes increase from 26.5 per game to 35.4. So part of the increase in scoring is tied to his increase in minutes. Still, when we look at Martin’s per-minute scoring production, we see that he has improved from 0.407 points-per-minute (or 19.6 points per 48 minutes) to 0.579 (or 27.8 points per 48 minutes).

This leap in per-minute scoring, though, is not tied to increases in shooting efficiency. In 2005-06, Martin’s point-per-shot [(PTS-FTM)/FGA] was 1.08 and his free throw percentage was 85%. In 2006-07 he has also scored 1.08 points per field goal attempt and is converting 85% of his free throws.

So why is Martin scoring more? The key is shot attempts. In 2005-06, Martin attempted 0.286 field goal attempts per minute (or 13.7 shots per 48 minutes). This year his per-minute field goal attempts stands at 0.380 (or 18.3 shots per 48 minutes). Martin has also seen an increase in free throw attempts.

Of course, production is about more than scoring. When we turn to the non-scoring aspects of performance we see very little change in Martin’s per-minute totals. Certainly it is the case that Martin is a more productive player overall. His Wins Produced per 48 minutes [WP48] has risen from 0.161 to 0.226. But this improvement is only because this very efficient scorer is simply taking more shots per minute.

Well, if Martin is not “Most Improved”, who is? I have not looked at every player, but I suspect that we need to look no further than David Lee. In 2005-06, Lee posted a WP48 of 0.197. So like Martin, he was above average. This year, though, Lee has improved dramatically with a WP48 of 0.395.

Like Martin, Lee scored more per-minute without offering a significantly improved level of efficiency. Although increased scoring is part of Lee’s improvement, the biggest story can be seen in his rebounding numbers. Per-minute, Lee grabbed 0.268 rebounds in 2005-06. This year he grabbed 0.348 boards per-minute.

When we see a side-by-side comparison of Martin and Lee, it appears that this is an easy choice. Both players were good in 2005-06. Both players were better in 2006-07. But Lee has improved more than Martin. Martin has simply increased his shot attempts, which makes sense given that he is a very efficient scorer. Lee has both increased his shot attempts and taken a substantial leap forward as a rebounder.

Table One: Kevin Martin vs. David Lee

Of course there is one issue. Lee has only played in 56 games. Consequently, his Wins Produced has only increased by 9.4. If Martin can continue to play 35 minutes a night over the remaining games in the schedule, and his WP48 for the season can rise to 0.264, Martin should be able to match Lee’s increase in wins. Unfortunately, Martin would have to post a 0.486 WP48 over the remaining 12 games to make such a leap, and that seems unlikely.

Bloomberg Again

Tomorrow I will be on a guest on Bloomberg on the Economy, which is hosted by Kathleen Hays. Kathleen and I will be discussing the economics of the NCAA Final Four.

- DJ

The Wins Produced model begins with a simple idea.  Wins are a function of offensive and defensive efficiency.  This idea can be found in the work of John Hollinger and Dean Oliver.  And with a bit of math, you can show that wins are indeed a function of these efficiency metrics.

Once we see that wins are a function of offensive and defensive efficiency, a simple regression (of wins on the efficiency metrics) allows us to determine the value, in terms of wins, of the following statistics tracked for a player: three point field goals made, two point field goals made, free throws made, field goals attempted, free throws attempted, missed field goals, missed free throws, offensive rebounds, defensive rebounds, turnovers, steals, and personal fouls. Now the efficiency metrics are not only comprised of these player statistics.  From the wins regression we can also derive the value for the opponent’s three point field goals made, opponent’s two point field goals made, opponent’s turnovers (that are not steals), and team rebounds.  For the most part, these team factors are associated with defense.  Before I get to these team defense statistics, let me review two basic lessons from this wins model.

Wins are a function of offensive and defensive efficiency.  This is not only what theory tells us, but also the empirical evidence. The efficiency metrics explain 95% of wins and hence provide an accurate depiction of the quality of a team.

Each element in the efficiency metrics is linked to actions taken by the players on the floor.  It is the players who are responsible for made shots, rebounds, turnovers, team defense etc.. Thus, our wins model – because it accurately links these actions to wins – allows us to accurately value the contributions of an individual player. In sum, Wins Produced links all the elements of the wins model back to the players. Hence, Wins Produced also explains 95% of team wins.

For the player statistics, evaluating the player’s contribution in terms of wins is easy.   We simply need to multiply a player’s statistics by the corresponding value. The result of this calculation is then compared to the average performance at the player’s position.The team variables, which are associated with team defense, are not tracked for individual players.  So how can we incorporate these factors? Here is what we say in the book:

…we have constructed what we call the team’s statistical adjustment. We then follow a convention we have observed and personally employed in the economics literature. Specifically we allocate the impact of the team statistical adjustment according to the minutes each player was on the court.

The convention we followed was originated by Frank Scott, James Long, and Ken Sompii. In 1985 these authors published an article in the Atlantic Economic Journal examining the link between salary and performance in the NBA.  For the team factors employed in their model these authors simply allocated each factor across the players according to minutes played.   

What does that mean?  We don’t have a measure of defense for each player.  What we do have, though, is knowledge about how good the team played defense.  We argue that if a player played 15% of the team’s minutes, then he is responsible for 15% of the team’s defense [or specifically, the opponent’s made field goals, opponent’s turnovers (that are not steals), and team rebounds accumulated].

And this makes some sense.  Defense, especially in today’s NBA, is a team effort.  If your team is good at this, you should receive credit.  If not, you should be penalized.  The Wins Produced metric, by allocating the opponent’s made field goals, opponent’s turnovers, and team rebounds across the players, thus takes into account the quality of a team’s defense.So as one can see, the infamous team statistical adjustment is simply a measure of team defense.  Despite its simplicity, there has been a bit of confusion regarding what this is and how it impacts our results.  Let me try and answer these questions.

1.  Is this a “giant fudge factor”?

In simple terms, no.  Wins are a function of offensive and defensive efficiency.  The factors comprising what we called the team statistical adjustment are the opponent’s field goals made, opponent’s turnovers (that are not steals), and team rebounds.  In essence, this is the quality of the team defense. The players are the individuals playing defense, so they should get credit if a team does well or poorly with respect to this aspect of the game.

This factor has been described as an addition to our wins model designed to increase its accuracy.  That charge is false.  The opponent’s statistics are part of defensive efficiency, not an addition to the model.

People have also said that you could take points scored and a “team adjustment” and predict wins just as accurately as we do.  I do not know what the author of this statement means by a “team adjustment.”  If you employ the team factors listed above, this statement is false.  To demonstrate this point, I regressed wins on points scored, opponent’s three point field goals made, opponent’s two point field goals made, opponent’s turnovers (that are not steals), and team rebounds.  These five factors explained 79% of team wins, not the 95% that is explained by offensive and defensive efficiency.

Again, the team statistical adjustment is not some random factor we yanked out of our ass.  It is simply team defensive factors that must be accounted for in the measurement of defensive efficiency and player performance.

2. How does this impact our evaluation of players?

What I have mentioned, more than once, is that these team defensive variables do not have much impact on our evaluation of players.  PAWSmin, which is position adjusted win score, does not consider these team variables.  WP48, or wins produced per 48 minutes, does have these team variables.  The correlation between these two is 0.994.  So the team defense measures do not matter much in our evaluation of players.

3. Can you predict wins without the team defensive factors?

People have asked: Can you predict well without the team variables?  And my answer is “I don’t think so, but then again, I haven’t looked.”  Without the opponent’s field goals made, the opponent’s turnovers, and team rebounds, the wins model is mis-specified (in other words, you have left out relevant variables, which introduces a number of statistical issues for your model). 

Nevertheless, since people have been clamoring to know, I thought I would look.  Without the opponent’s field goals made, opponent’s turnovers, and team rebounds, we are explaining wins with the following variables: three point field goals made, two point field goals made, free throws made, field goals attempted, free throws attempted, missed field goals, missed free throws, offensive rebounds, defensive rebounds, turnovers, steals, and personal fouls. A regression of wins on these factors reveals that 84% of wins can be explained without opponent’s field goals made, opponent’s turnovers, and team rebounds. 

Of course the model is mis-specified and the results cannot really be used to evaluate individuals.  The easy fix to this problem is to specify the model in a fashion that is theoretically correct, which we did in The Wages of Wins. 

Getting Rid of the Team Adjustment

Is it possible, though, to do “better”? Maybe we can change how we allocate opponent’s field goals made, opponent’s turnovers, and team rebounds. 82games.com has several measures of how well a team’s opponent does when each player is on the court.  If we use one of these measures, we can scrap the team statistical adjustment (which allocates defense in terms of minutes played), and allocate the defensive variables across each player according to their ability to play defense.

I did this for the Washington Wizards.  82games. com reports how well the opponent scores with each player on the court.  The team surrenders about 104 points per game.  From 82games.com we see that when Jarvis Hayes is on the court the team gives up 106.2 points per game.  So by this measure he is a relatively poor defender.  In contrast, Brendan Haywood gives up 100.6 points, so he appears to be a relatively better defender.  Previously we are allocating the opponent’s field goals made and opponent’s turnovers in terms of minutes played, so each player – on a per-minute basis – was evaluated the same on defense for each team. There were differences across teams, but on any one team it was the same.

Now we have a measure that differentiates players on a team. What happens if we allocate the opponent’s statistics with the 82games.com measure of defense? The results reveal a difference, but not very big.

Table One: Examining the Impact of Team Defense with the Washington Wizards

Brendan Haywood improves, posting a WP48 of 0.133 when we treat every player the same and a mark of 0.142 when he is credited for his defensive ability.  Jarvis Hayes looks a bit worse.  In general, though, the results are very similar.This should not surprise.  There are apparently large differences in the defensive abilities of teams.  And these differences across teams are incorporated in the evaluation of players with Wins Produced.  Yet we found that with or without adjusting for these factors our evaluation of players was essentially the same.  Now when we do this for an individual team, we tell the same story.

The research at 82games.com, if it accurately measures individual defense, allows us to get rid of the team adjustment. The model still explains 95% of wins. It is also still tells the same story about player performance.  And what is that story?  The primary factors in evaluating a player are shooting efficiency, rebounds, and turnovers.    

A Comment on Baseball

The box score statistics in basketball are often discredited because these do not account for on-the-ball defense.  We can see defensive ability at the team level, but without the work at 82games.com we cannot get at the individual’s contribution.  Does the inability of the standard box score statistics to measure on-the-ball defense really matter in our evaluation of players?

I want people to step outside basketball for a moment and think about baseball.  In baseball there is the issue of fielding.  OPS and linear weights are measures of performance in baseball.  They both ignore fielding entirely.  Yet, very often (not always, but often) people discuss the merits of a player strictly in terms of his offensive output.

Of course there is also the issue of evaluating pitchers.  A pitcher cannot strike everyone out.  Pitchers depend on fielders.  Yet in evaluating pitchers, I often see people reference statistics (ERA, Wins, etc…) that do not separate the pitcher from his fielders. 

Imagine if we regressed wins in baseball on a team’s ability to hit, pitch, and field.  We would be able to explain about 90% of wins, which is what happens when you regress wins on runs scored – your ability to hit — and runs surrendered – your ability to pitch and field. 

Now let’s say you isolated a pitcher’s contribution from his fielders.  Then you regressed wins on runs scored (what the hitters did) and just the pitcher’s contribution.  How well would explain wins now?  I do not know the exact answer, but without any measure of fielding your explanatory power would have to be a good deal less.

Despite this issue, traditional measures of hitters and pitchers do not consider fielding. Is this a problem?  Should we throw out all the traditional box score statistics in baseball because they ignore fielding, a factor that must have some ability to explain wins?

The answer is of course not.  Yes, fielding matters.  But our evaluation of players will generally not change very much if we ignore this factor.  Barry Bonds and Manny Ramirez will still be great players.  Greg Maddux will still be a great pitcher. 

I think the same thing can be said for defense in basketball.  Yes some players are better at on-the-ball defense than others.  But if it truly mattered a great deal we would see vast differences in our evaluation of players when defense is included and when it is not.  We would also see that rebounding totals fluctuate for players dramatically depending on who their teammates were.  When we look at the data, though, we see none of this.

Perfect Models?

I want to return to a statement I made a couple of weeks ago.  Models are not supposed to be “perfect” (whatever that means).  When I and my colleagues construct models, we are trying to construct a simplified version of reality that allows us to focus on what is important (and answer the various questions we pose in our research).That is what I think Wins Produced does. It is a simple and accurate measure of performance, based on the theoretically sound idea that wins are determined by a team’s offensive and defensive efficiency.  This model ultimately tells us that wins are primarily determined by shooting efficiency, rebounds, and turnovers.  Yes, other issues matter.  But players who do not score efficiently, who fail to rebound (given their position), and/or turn the ball over excessively, will not help you win games.

Let me repeat what I said a few days ago:

Now it’s not the case that factors like blocked shots, assists, and personal fouls don’t matter. But none of these factors are as important as shooting efficiency, rebounds, turnovers, and steals. And once we see this, we can understand the outcomes we observe.

For example, the Rockets lost Yao Ming to a devastating injury, yet managed to maintain their winning percentage. Once we see the importance of rebounding, though, we can see how having an extraordinary rebounder like Dikembe Mutombo come off the bench mitigated the loss of Yao.

We also see why the 76ers improved after Iverson departed. Iverson has problems hitting shots and avoiding turnovers, so despite his scoring totals, our model tells us he does not produce as many wins as his star power suggests. In other words, we should not have expected a team that replaced Iverson with Andre Miler to get worse (as many people who focused on scoring predicted).

And on Collaboration

I have written a paper entitled “A Simple Measure of Worker Productivity in the National Basketball Association.”  An earlier working version of this paper – which details the math behind the Wins Produced metrics — was referenced in The Wages of Wins.  Later this year this paper should finally be published.  Although I am the solo author on this paper, one should not think that Wins Produced and the related models are only the results of my efforts.  As noted in The Wages of Wins, many conversations with Dean Oliver clearly impacted my thinking.   

In addition, a collection of co-authors also should be credited (or blamed, depending on your perspective).  At the top of this list are Martin Schmidt and Stacey Brook (co-authors on The Wages of Wins).  The Wins Produced metric has also been employed in papers I have written with Anthony Krautmann, Aju Fenn, Bernd Frick, Erick Eschker, Young Hoon Lee, Rod Fort, Michael Leeds, and Michael Mondello. 

This is how I described my tendency to collaborate at my website in April of 2006: Beyond my publication rate, we can also see that virtually all of my work is co-authored. Over the course of my career I have published research with eleven different writers, with Martin Schmidt being my most frequent collaborator.  In all, Marty and I have published twelve papers together.  One can look at this as I work well with others, or lack the skills to complete projects by myself.  I like the “works well with others” story, although my many co-authors might play up the “lacking skills” angle. 

Almost all of my work is a collaboration with someone else.  All of these c0-authors are accomplished researchers who have the corresponding list of academic publications as evidence of their abilities.  But even with their help, academic research still requires the help of more people.

My list of co-authors leaves out the various editors and referees who review our academic papers.  Research in academia is never a solo effort.  Other people comment and critique your work constantly, and these efforts improve the final product. Hence when people argue that I do not “collaborate” I am left very puzzled.  Academic research – be it in journals or at academic conferences – is always a collaboration.  And anyone with an understanding of academic research would see this point.

The Future

We are on the quarter system at California State University – Bakersfield.  This is a good deal in the fall, since we don’t begin until late September and finish around Thanksgiving. In the spring, though, it’s a bit of drag. Today we begin the Spring Quarter, which does not end until June.  This quarter I am teaching three classes. I also have a paper to complete for the Western Economic Association and several other research projects to finish.

All of this means that over the next 10 weeks, postings in this forum will be less frequent.  I will simply not have time to post as often as I have across the last year.  Hopefully this summer I will have time to resume posting on a daily basis. Thanks to everyone who makes this a part of their day.  Unfortunately, for a few weeks at least, this will no longer be a part of each day for me.

- DJ

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 NBA.com 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