1.16.2007

Dave Berri's Dismal Science

Ever since Malcom Gladwell first endorsed The Wages of Wins in the New Yorker last summer, Dave Berri’s secular science of Iverson-bashing has been subject to an endless stream of criticism from pro basketball’s actuarial heavyweights. ESPN’s John Hollinger , Salon’s King Kauffman , and APBR’s Dan Rosenbaum have all traded blows with Berri and his co-authors, leading Dan Shanoff to name Wages of Wins the most controversial sports book of 2006. In many ways, the volume of criticism directed at Wages testifies to the durability of its thesis. Everyone seems to agree that the book is flawed, but no one can definitively say why. The reason for the stalemate, I believe, is a confusion over the nature of the flaw. The problem with Wages isn’t the statistics – its the economics from which they derive.



As Mathew Yglesias has wisely noted , the central issue in Wages is the weak correlation between payrolls and wins. Numerous empirical studies have demonstrated that increases in NBA payrolls do not correspond to increases in team success. Given that player salaries are determined by conventional measures of productivity – in particular, scoring – Berri argues that these measures must be flawed: otherwise, higher payrolls would mean greater productivity, and by extension, wins. The aim of Wages, then, is to develop a more accurate model of player productivity – one which could, if adopted by GMs, eliminate the disjunction between wages and wins, and thereby usher in a more economically efficient league.

I won’t go into detail about Wages’ methods, which are well summarized here . The basic idea is to use regression analysis to estimate a single measure of players’ marginal productivity, called ‘Win Score’ (WS). The crucial difference between Win Score and existing metrics (like PER) concerns the valuation of scoring. Unlike conventional measures of offensive efficiency, which penalize players only for the shots that they miss, Berri recognizes that even when a shot is made, a resource – a possession – has been expended. Because teams average roughly 1 point per possession, a 1pt opportunity cost is deducted for each field goal attempt, regardless of whether it goes through the hoop. Thus, when Kobe Bryant shoots 26-50 for 52pts, his marginal impact on team wins (52pts – 50pos = +2) is the same as that of Ronny Turiaf shooting 2-2 for 4pts (4pts – 2pos = +2), or Andrew Bynum grabbing 2 defensive rebounds (2pos = +2).



Now, the economics. Suppose that Berri is basically correct, and that Win Score is an accurate measure of players’ marginal productivity. According to orthodox economic theory, the “price” (i.e. wage) that players receive in an efficient market should be determined by their Win Score. However, recent economic models have demonstrated that the existence of this “efficient market”, and its capacity to correctly “price” player inputs, depends on a highly unrealistic assumption: namely, perfect information. For a GM to sign a player on the basis of his Win Score, he must first know, with relative certainty, what a player’s Win Score will be.

In his book, Berri argues that player productivity can be predicted, with sufficient certainty, on the basis of past performance. Using data from 1994-2004, he shows that Win Scores from the previous season are highly correlated with current performance (R-sq = .70). The problem with this line of reasoning is that “Win Score” as such doesn’t actually exist, but is instead a composite of various inputs. Now, suppose we distinguish between scoring input (points – true shot attempts), and non-scoring input (rebounds + steals - turnovers….). When we reexamine Berri’s 1994-2004 data, we find that non-scoring production is almost perfectly consistent from year to year (R-sq = .85). Yet when we consider scoring production alone, the correlation between past and current performance is much, much weaker (R-sq = .30). Thus, contrary to the assumptions of Berri’s economic model, the ability of GMs to accurately “price” a players’ scoring production is a highly uncertain (i.e. risky) business. From the perspective of players, the risk involved in scoring production appears even starker. Except for super-efficient producers (i.e. Shaq or Duncan), even above-average career shooters face a significant risk of ending a given season with negative scoring production, and thus, scoring income. Berri’s data shows that in any two season interval, over 30% of all players switch between positive and negative scoring Win Scores.

The uncertainty of point production has profound implications for Berri’s analysis. Under the assumption of perfect information, efficient scorers know whether they will shoot efficiently each season, and thus will continue to shoot up to the point where it becomes unproductive for the team. In reality, however, players are uncertain as to their actual scoring efficiency, and as such will be risk-averse when attempting to maximize that aspect of their income. Thus, if scorers were to be paid the true value of their marginal products – if economic rewards were distributed on the basis of Win Score – there would emerge a profound divergence in what teams and players perceive as an optimal level of shot attempts. Insofar as their investment is ‘diversified’ across the entire roster, teams will prefer that the above-average scorer shoot liberally, despite the occasional below-average season. In contrast, the player, fearing the possibility of a sudden career-ending injury, and thus relatively more risk-averse than his employer, would likely under-invest in shot attempts – if not eschew scoring altogether – rather than risk a negative scoring year.



The problem of underinvestment is further compounded once we consider that players themselves can, at any given moment, choose between scoring (risky) and non-scoring (risk-less) production. Thus, rather than take a high-percentage field-goal attempt, a player may opt for a potential assist (WS = +.5), or focus on grabbing an offensive rebound (WS = +1). The problem here is analogous to the one identified by economist Joseph Stiglitz in his analysis of the sharecropping system. Stiglitz argues that in situations where workers can choose between more- and less-risky farming techniques, there will arise “a conflict of interest between the landlord and workers. At any specified share contract, the landlord wants only to have the worker choose whatever technique or crop maximizes expected output; the worker is willing at the margin to sacrifice some mean output for a reduction of risk”. For above-average scorers, shooting will generate more overall career utility than, say, offensive rebounding. Yet offensive rebounding may nevertheless be more attractive since it poses essentially no risk of a loss. If scoring was “priced” on the basis of Win Score, even the most efficient shooters would likely under-produce on offense, choosing instead to maximize other, less-risky forms of production.

Berri and Co. are certainly correct in their claim that scorers are overpaid relative to their marginal impact on team wins. Yet in their rush to offer a correction, the authors never fully consider why this is the case? Why is it that scoring statistics explain 63% of player salaries, while equally-important possession statistics (i.e. rebounding) combine to explain just 1%? To the extent they address these questions, Berri and his co-authors fall back on an unconvincing appeal to the “bounded rationality” of GMs. They argue that the “myth” of scoring’s importance has only survived because people in the NBA do not process information efficiently, and that once they are exposed “to new and better information”, their decisions will change accordingly. In other words, the reason mangers overpay for scorers is that they haven’t read Wages of Wins!

The recognition that scoring is a uniquely risky mode of production, and that determining its “price” is fraught with uncertainty, affords a far more convincing explanation of its disproportionate value and compensation. What first appears as irrational, suboptimal behavior under the orthodox assumptions of neoclassical economics can now be understood as economically rational (if not perfectly efficient) outcomes in situations of uncertainty. Consider the question of why scoring is valued more than possession statistics, even though their marginal effect on wins is the same. Traditional economics tells us that in equilibrium, the price of labor depends on its quality (i.e. marginal productivity): if scoring and rebounding are equally productive activities, their prices should be equivalent. In contrast, Stiglitz and other economists have shown that in situations of uncertainty, quality often depends on price: here, workers with a certain labor capacity will only expend the necessary effort if they are paid an above-market wage. Put simply, the production of points in the NBA – due to the relative uncertainty of success – requires that scorers receive more than the value of their marginal product. Otherwise, players with the capacity to shoot efficiently WOULDN’T TAKE THE RISK OF TRYING TO SCORE.



By way of conclusion, let me just say that there is something peculiar about three academic economists second-guessing the propriety of NBA salaries. Well-paid professionals of all other persuasions are rarely subjected to such skepticism. Asked to account for the exorbitance of CEO compensation, for example, and your average economist will more likely cut off his own arm than conclude it anything other than optimally wealth-enhancing. Compared to CEOs, one would think that high-scoring basketball players – whose performance is subject of infinitely more surveillance, and who negotiate their contracts with infinitely less bargaining power – would be worthy of at least the same benefit of the doubt. Yet Berri and Co. simply jump to the conclusion that these players are overpaid.

The reason, it seems to me, is that below its ostensibly neutral surface, Wages of Wins is as much ideology as science. Note the familiarity of Berri's targets (Melo, AI), his conspicuous affection for "Playing the 'Right Way'" (see Chapter 10), or the undisguised moralism of the title’s jeu de mots. Or consider the following from the authors' blog :

Certainly NBA coaches, like Auerbach, are aware that rebounds, shooting efficiency, and taking care of the ball are important. But players can see that the highest paid are the scorers. And players also see that the money still comes even if they perform poorly with respect to many of the other parts of the game Auerbach knew led to wins and championships. So next time you see a player focus more on how many touches he has and less on winning, remember the incentives the players face. And ask yourself, what would you rather do, collect millions or win a basketball game?

The irony of this passage is that it recognizes (albeit tacitly) that the quality of scoring production is a function of its above-market “price”. Yet rather than exploring the obvious conclusion – that such incentives are necessary for motivating scorers’ labor – the authors instead retreat to the well-trodden canard of player selfishness. What we have in Berri’s book, then, is Calvinism masquerading as social science – not the other way around.

66 Comments:

At 1/16/2007 5:13 AM, Anonymous Anonymous said...

Thank you! Finally someone produces an intelligent analysis of Wages of Win, rather than the crap that passes for analysis on most sites. I don't necessarily agree with your conclusions, but I'm very pleased to see such a thorough and analytical post.

 
At 1/16/2007 5:20 AM, Anonymous Petey said...

It's crucial to note that Berri's weighting of the numbers is arbitrary.

Did I mention this is crucial?

One can use Berri's methodology while massively overweighting blocks to show that Alonzo Mourning "produces the most wins" of any player in the NBA, and the numbers will align perfectly. Team wins will still align with reality. Deciding which statistics are most important in a system like Berri's is utterly subjective.

Berri, on the other hand, overweights rebounds. In order for us to agree with Berri's weightings, we have to credit Berri's subjective understanding of the NBA game.

Most importantly, Berri goes to extreme lengths to obfuscate the subjective nature of his weightings. HIs attempts to give the impression that his weightings are based on objective criteria are what make him a con man, not just wrong.

Dan Rosenbaum has ably shown the nature of the fraud, not that anyone has paid much attention.

-----

And tangentially, does anyone on the planet actually accept that Dennis Rodman "produced more wins" than Michael Jordan, or that Caron Butler "produces more wins" than Gilbert Arenas?

 
At 1/16/2007 5:33 AM, Blogger SilverBird5000 said...

Petey- good point. I doubt many readers of Wages caught this admission, burried in footnote 28:

One should note that our explanatory power in the regression of wins on efficiency measures is the same as what one uncovers when you regress wins on points scored and allowed per game

In other words, one could use the same methodology as Berri and arrive at the conclusion that points alone are important for winning. As you note, Rosenbaum has been on this since Day 1.

That said, just because Wages' weighting is arbirary doesn't necessarily make it wrong. What makes it wrong, I think, is the economics, not the methodology.

 
At 1/16/2007 5:35 AM, Blogger SilverBird5000 said...

make that footnote 28 of Chapter 6 (pg. 244).

 
At 1/16/2007 10:05 AM, Anonymous Anonymous said...

Generally well said, but I believe you and the book you decry (which I have not read) are missing one large independent variable in the regression of contracts: profit production. True, the argument is based in win shares, or the effectiveness of on the court play, but contracts are not completely comprised of on the court ability. What we could presumably call off the court ability (jersey sales, ticket sales, tv revenue, etc.) also factor into contract negotiations, and have a real impact both on the court, and through the ultimate evaluation of a player in the leagues mind, price. Accordingly, AI may have a poor win share, but his added value is far greater than all of his teammates combined.

 
At 1/16/2007 10:10 AM, Anonymous Anonymous said...

Thanks for publishing the first critique of Wages of Wins that has some validity. One small point to quibble with (which I'm guessing Berri will more than quibble with if he responds to this post): Win Score is their easy to calculate measure. It is the more refined WP that they make their claims of predictive power.

That said I appreciate your talking about the need to create an incentive to score. While I don't think that your criticism necessarily undermines Wages of Wins powers as a tool of analysis, it does undermine the idea that its system should be adopted by the NBA and perhaps fatally undermines it's criticism of the linkage between scoring and salaries.

 
At 1/16/2007 10:20 AM, Blogger SilverBird5000 said...

kidscoach-
You're right that Wins Produced is the more refined of the two measures. However, the relation between the WP coefficients and the WS coefficients is the same. So, according to Win Score, a 2-point FG, Rebound, and Steal all equal +1. According to WP, they all equal (roughly) +0.033. So I don't believe the difference between the metrics changes my critique.

 
At 1/16/2007 11:03 AM, Blogger Steve Sailer said...

Berri missed the basic economic concept of declining marginal returns when it comes to shooting. When Wilt Chamberlain scored 50 points per game in 1962, he shot .506 from the field. When he scored 14 points per game in 1973, his shooting percentage was .727. Same guy, just fewer and thus less risky shots. That was a coaching decision that Wilt should concentrate on quality rather than quantity of shooting in 1973.

If Berri's beloved Kevin Garnett shot as much as Kobe Bryant, his shooting percentage would go down too. But Garnett's team might win a few more games per year if he was less efficient and more productive. It's not like Garnett's teammates are taking up the slack when he makes 7 of 11 for 17 points.

 
At 1/16/2007 11:09 AM, Anonymous Petey said...

"Put simply, the production of points in the NBA – due to the relative uncertainty of success – requires that scorers receive more than the value of their marginal product."

I think it's all a lot simpler than that.

Berri just radically underweights the value of scorers in terms of winning basketball games.

Scorers don't need to be overpaid to compensate. With a less insane statistical weighting than Berri's, top scorers would get paid lots without any overpayment being necessary since top scorers create lots of wins.

----

But that said, I do think your pegging of Berri as Calvinism run amok, (I'd just say he's a playa-hater), accounts for why Berri has subjectively chosen to weight his stats in the way he has.

 
At 1/16/2007 11:11 AM, Anonymous Anonymous said...

Is over overinvestment in shooting by high percentage shooters and underinvestment by low % shooters necessarily a bad thing?
If you track Berri's stats carefully, you'll notice that most high % shooters with high win scores (and, after all, it is win score, not shooting efficiency, that berri wants to map to salary) excel in other aspects of the game (rebounding, assists, steals, etc...). So if an above average shooter dips below average one season, this should be offset by other aspects of his game. This will certainly decrease his Win Score, but the decrease in productivity shouldn't be as significant as lower productivity that results from a poor shooter with a low WS who takes an unreasonably large number of shots. Further, it's unclear to me that underinvestment is necessarily a bad thing. For players who are poor shooters and have low WS, getting them to focus on other aspects of the game may not be a bad thing. For poor shooters with high WS, getting them to engage in less risky behavior for bigger payoffs also may be a good thing. For example, if Allen Iverson took less shots and passed the ball more to high percentage shooters (to boost his assists and WS), this would probably be better for the Denver Nuggets than him taking 40-50% of the shots. Also, if someone like Jason Kidd (high WS, terrible shooter) took less shots and focused more on being a pure point guard with exceptional rebounding skills, this would probably be better for the Nets.

Part of the problem with your critique is that risky behavior is typically encouraged because of its potential upside. Part of what Berri is getting at, though, is there really is no potential upside to overcompensating bad shooters who take a lot of shots. The most egregious example being Allen Iverson.

Also, Berri is proposing a more statistically rigorous (perhaps flawed) approach to evaluating and predicting player performance. Though this means some NBA salaries will be decreased, others will correspondingly be increased. So I'm not exactly sure what your salary beef is. Berri isn't attacking NBA salaries in the aggregate (or even star salaries), just who should be getting star salaries.

Finally, I think there is a way of justifying Auerbach's model without resorting to the "well-trodden canard of player selfishness." If a player scores a lot of points, he gets a reputation for being a scorer whether he scores efficiently or inefficiently. If he scores inefficiently, this will create a huge distortion because he will get a disproportionate number of shots based his final tally as opposed to his per-possession efficiency. Again, the obvious example is Allen Iverson. It's not his selfishness that is the problem; rather, it is other players misplaced confidence in his ability to make the most out of every possession that Auerbach's model helps overcome.

 
At 1/16/2007 11:31 AM, Blogger SilverBird5000 said...

Is over overinvestment in shooting by high percentage shooters and underinvestment by low % shooters necessarily a bad thing?

No, but underinvestment by high % shooters is. As I argue in the post, most high % shooters won't know, with any certainty, whether or not they will shoot efficiently in any particular season: in any given two-year interval, 30% of players will swing between red and black vis-a-vis the scoring element of Win Score. So, if players were paid exactly according to that metric, many high % shooters would be risk-averse and thus underinvest in scoring.

As for the question of whether underinvestment in scoring would be a bad thing per se...From the perspective of teams, no. But from the perspective of David Stern, it would be a hugh problem. Take an extreme example: it would be easy to argue against the introduction of the shot-clock on the grounds that it leads to more inefficient shot selection. Without it, though, the league could kiss those multi-billion dollar t.v. contracts goodbye. An entire game-theory paper could be (has been?) written on the inherent conflicts between individual team and league-wide interests.

Lastly, I wasn't criticizing the 'Auerbach model' itself, just Berri's reading of it.

 
At 1/16/2007 12:17 PM, Anonymous Petey said...

"Part of what Berri is getting at, though, is there really is no potential upside to overcompensating bad shooters who take a lot of shots. The most egregious example being Allen Iverson. "

Right. The thing I don't understand is why Iverson doesn't pass more to good shooters like Steve Blake. Why would Iverson take 21 shots when Blake was converting so much more effectively than he was? And why wouldn't George Karl orient the offense to get Blake 30 - 35 shots per game?

"Also, Berri is proposing a more statistically rigorous (perhaps flawed) approach to evaluating and predicting player performance."

The problem isn't that Berri's model is flawed. Any pure statistical measurement of individual NBA players is going to be flawed. The problem is that what Berri is doing isn't "statistically rigorous" by any reasonable definition of that term.

He's subjectively valuing certain stats over others, while doing his utmost to avoid discussion of his subjective choices. There are many terms that are applicable for that kind of approach, but "statistically rigorous" is certainly not one.

 
At 1/16/2007 12:24 PM, Anonymous Anonymous said...

Instead of the shooter getting essentialy 1 pt for a basket based on expected FG% and no other player besides the direct assist man getting any credit, I think it would be better to fully allocate the 2 or 3 pts with perhaps 50% credit to the shooter, 20% to the assister and 10% to the other 3.Or something close to this.

I think +/- scoring should move from the other way- from 5 equal shares- to a similar credit split.

It neither makes sense to give the shooter full credit or to give everyone equal credit. The exact split can be argued but something in that middle range seems more realistic/fairer to me.

 
At 1/16/2007 12:24 PM, Anonymous Anonymous said...

Back in the days when people used to argue whether Magic Johnson or Michael Jordan was the best player in the NBA (am I showing my age here?), Jordan critics used to say that Magic could have scored just as many points if he had been equally selfish / surrounded by lower-quality teammates and shot as often as Michael. In response, Phil Jackson made a similar point: that Jordan was so good that he could shoot twice as often as anyone else and still maintain a better than league average shooting percentage. Jordan was creating more average-percentage shots than anyone else in the league was capable of.

 
At 1/16/2007 12:25 PM, Anonymous cw said...

One thing I have been thinking about is that all of these methods use shooting 100% as the optimal in shooting efficiency. But because that is not how it really works in BBall (people hardly ever shoot %100) a better measuer of optimal efficiency would be the leauge average for position or, maybe just something like 48% -50%, for 1s, 2, 3s, and 50% tp 55% for centers. This way you are actually comparing players vrs other players rather than against some mythical standard that is very rare achieved in real life.

Another thing. While the statistical side of it is fun and interesting, I wonder how many people involved int his ever played much actual basketball. I think I see mistakes based on incomplete understanding of subtlties of the game. Take scorers for instance. If you are on a team with someone like Iverson or Michael Redd, it's kind of a double-edged sword for most of the game and then a real good thing at other parts. It's a really really good thing to have a guy who can create a reasonable shot at the end of close games and in those diffficult to quantify times when you "need a bucket." BBall is a really dynamic sport. Lots of things can strongly effect the course of a game. Psychology is one of those. There are times in the game when you really need to score some buckets. The other team is pulling away, what you are doing isn't working, you coach can't come up with the right adjustment... and the game is on a tipping point between you competing and demoralization. At points like these it's really good and to have an iverson, who can carry the offense for a while whie you regroup. On the other hand, if your gunner takes over the game too much, the rest of the team will start to stand around (these are all clieches, but all really true). Not to have everyone involved in some meaningful way in the offence is sub-optimal. You can still win games but not as many as you could if everyone was suffficiently involved. This is why the Wiz (sorry matt) are not going far. As a rebutle, you might say, look at Wade though, what he did last year. I think that was kind of an aberation, though. I think that was a better example of demoralization on the Mavs part. Plus Wade does a good job of balancing between taking over and keeping everyone involved.

Anyway this kind of contrast between team and individual offence would be something interesting to look at statistacally.

 
At 1/16/2007 12:25 PM, Anonymous Anonymous said...

this isnt really an academic response, but these incentives for how to play seem at least partially ridiculous. Jkidd can be 10 times a worse shooter than he is, but when he is wide open for a j from 15 feet, he needs to shoot, not look for an assist. i know the argument against stats has been made 1000s of times, but its not the way the game unfolds

 
At 1/16/2007 12:53 PM, Anonymous Carlos said...

Another point is that Berri puts a lot of emphasis on the fact that payroll doesn't correlate well with wins, and concludes that GMs don't understand well what wins games. That seems right superficially but what he forgets is that the NBA is anything BUT a free, unregulated labor market. It's probably one of the most regulated labor market that you can think of and in top of that, the regulations are expressly designed to produce the kind of inefficiency he criticizes. The draft, the free agency rules, the regulation about contract length and maximum salary, the salary cap, the luxury cap, all have the declared purpose of limiting the influence of money in winning. ¿Maybe that has something to do with the issue?

 
At 1/16/2007 1:00 PM, Blogger T. said...

Taking a look salary list (http://hoopshype.com/salaries.htm) it seems as if Berri's central thesis of salaries being linked to scoring doesn't really seem to hold up.

 
At 1/16/2007 1:05 PM, Anonymous Anonymous said...

My problem with the use of "shooting efficiency" as a worthwhile metric is that it a player's efficiency is that it is considered an intrinsic quality.

Illuminative example: Tony Parker, Amare, and Eduardo Najera are all shooting over 50%, and all are above-average shooters for their positions. Thus, they are all 'efficient' scorers and should be well-paid/encouraged to shoot more, right?

Well, Tony Parker creates his own shot by driving the lane, so his efficiency seems to be a part of his game. And, recalling some of Amare's most dominant performances, it seems like he can shoot a great deal and still be efficient.

But Eddie, much as I love him as a player, scores mostly off offensive rebounds or cuts facilitated by guards' penetration of the lane. So, even if he wanted to, he couldn't just decide to take more shots and have a prayer of continuing to score efficiently. His high shooting % is a product of extrinsic factors--his role in the offense.

To close with a quick defense of AI: the way he passes, he should be averaging 15 assists since the trade. I watched the Nuggets-Rockets game, at which he scored the team's first 10 points, and, believe me, it was not for lack of trying to get his teammates involved--they just couldn't hit an open shot.

 
At 1/16/2007 1:06 PM, Anonymous paper tiger said...

petey- your steve blake-AI question just points out another of berri's problems. you ask why AI doesn't pass more to the more efficient blake, but doesn't the model need to account for the fact that blake may be more efficient because AI is drawing the defense and creating the efficient shots for others? you have to shoot alot (including bad shots) to be able to have that effect. and i know the model gives credit for assists, but this sort of impact is more than just the dime.

on another note, i think it's bizarre when a big scorer is injured (or suspended) and folks wonder about how the team is going to "replace" their scoring. like a team averaging 110 with a 30 point guy should suddenly be averaging 80 without him. that makes it seem like his points are coming in addition to everyone else's rather than instead of. somebody is going to still get those shots. (granted, the degree of the effect depends on the missing player, their efficiency and their role in the offense, etc). and i think berri's model shares that flawed way of thinking, especially with the way things are weighted. certainly in re: his thoughts on scoring, but maybe more with rebounds and steals being equal. when a shot is missed somebody is going to get that rebound. there has to be a rebound on the play. steals are different- when artest rips someone, there's no way to say that happens without him on the floor.

 
At 1/16/2007 1:22 PM, Anonymous Petey said...

"doesn't the model need to account for the fact that blake may be more efficient because AI is drawing the defense and creating the efficient shots for others?"

Bingo.

Hence my modest proposal for having the ultra-efficient Blake shoot 30 times a game.

It's no accident that Blake had a career game in his second outing with Iverson. Iverson has the most valuable attribute that exists in the NBA - the ability to force the defense out of straight-up coverage in an attempt to contain him. If you can catch and shoot when left wide-open, playing with Iverson is going to make you look very, very good. Ask Kyle Korver if he wasn't a helluva lot happier two months ago.

I'm looking for Blake to be outstandingly productive all season when playing alongside Iverson and 'Melo, in a somewhat similar way that Mikki Moore is suddenly an all-star when running alongside Kidd, Jefferson, and Carter.

 
At 1/16/2007 1:33 PM, Anonymous Petey said...

"To close with a quick defense of AI: the way he passes, he should be averaging 15 assists since the trade. I watched the Nuggets-Rockets game, at which he scored the team's first 10 points, and, believe me, it was not for lack of trying to get his teammates involved--they just couldn't hit an open shot."

If the assist rule was changed so that a pass leading to a shooting foul were considered an assist, I think Iverson would benefit more than any other player in the league.

Given the way Iverson scrambles the defense, a lot of his inside passes result in shooting fouls, which don't accrue to his assist total.

I'd love to see someone find a way to run the numbers on that one.

 
At 1/16/2007 1:42 PM, Anonymous Anonymous said...

See, you let Petey in the door, and the whole neighborhood goes to hell...

Seriously though I heartily second the comment above which questions Berri's understanding of basketball on anything more than a numerical level. Petey hints at it in his defense of AI, but Berri makes no effort to understand the interaction between players. While he may well have an excellent understanding of how stats on a team level contribute to wins (but seriously, how hard is it to say 'shoot a high percentage, rebound, don't turn it over?'), Berri makes no effort at all to allocate the credit for those outcomes amongst the players on the floor. For Rodman to get a rebound, somebody had to miss a shot, and presumably the other 4 players had something to do with that (or maybe they didn't, maybe the guys just missed. But the thing is, we don't know). Yet Rodman gets all the 'credit' in Berri's system.

Basketball is not baseball, where everything can be atomized, counted, and analyzed individually. It's just not, the game is too dynamic to allow that level of analysis. And the hubris to think otherwise is the real root of Berri's wrongness.

 
At 1/16/2007 1:58 PM, Blogger salt_bagel said...

If the assist rule was changed so that a pass leading to a shooting foul were considered an assist, I think Iverson would benefit more than any other player in the league.

I'd guess the biggest beneficiaries of that rule are whoever makes the most post entries to Tim Duncan.

My take on these objective measures is this: If you want to consider the value of rebounds, steals, etc. as equal to the value of a possession, shouldn't you acknowledge that the expected value of a possession for your team is directly tied to your offensive efficiency? Isn't it correct to say that a Camby offensive rebound has a greater value if Iverson happens to be on the floor than if not? You can only expect so much return from shifting resources from scoring ability to, say, offensive rebounding before it the strategy loses profitability.

Also, I think that very few of the stat gurus take into account the capacity these stars have for shouldering an offensive load. Anon 12:24 hit it on the head with the mention of Jordan producing quality shots at such great numbers despite using more and more possessions. I still think Dean Oliver gives a great explanation for this when he talks about individual possession stats and possession usage. For example, the most efficient offensive players in the league are always the 3-point specialists, i.e., Blake and Korver. However, you can easily track their efficency as a function of possession use, and see that it falls off dramatically as usage goes up. Whether this is just the nature of all 3-point specialists or something about a particular player doesn't matter. Either way, you just can't expect to give this type of player more possessions at the expense of the scorer like Iverson, or Jordan. To me, its this capacity that differs and has value over and above what is measured as a plus/minus number.

Lastly, I haven't read anything in this thread about the supply side. Scorers are just more scarce, right?

 
At 1/16/2007 2:02 PM, Anonymous Anonymous said...

Dean Oliver

I'm glad you brought him up, because unlike Berri, or to a lesser degree, Hollinger, he's very upfront about where and how statistical analysis of basketball is insufficient to be especially meaningful, especially WRT to what we have learned to expect from the SABR approach to baseball.

 
At 1/16/2007 2:16 PM, Anonymous Petey said...

"See, you let Petey in the door, and the whole neighborhood goes to hell..."

Perhaps so, but my swag is phenomenal.

When I hit the "Submit Comment" button, I don't even stick around to watch the comment fly through the internets. I just turn around and walk away with a scowl on my face. I know my comment is going to hit nothing but the bottom of the net.

 
At 1/16/2007 2:20 PM, Anonymous v said...

There's a lot of talk about Michael Jordan in the comments, and I think it's entirely misplaced. Berri has stated multiple times that his stats clearly establish Jordan as the greatest SG of all time, and given the margin between his greatness and other SG, a strong statistical case can be made for him as the greatest player of all time.

That Berri's model makes Iverson less appealing has been taken by some to imply that this must also mean Jordan was inefficient. Nothing could be further from the truth. Throughout his career, Jordan was a high efficiency shooter (unlike Iverson). Also, Jordan could rebound and pass (averaged almost 6 boards and 6 assists per game throughout his career). These are pretty impressive for a SG, whose main function is to score. Finally, Jordan had relatively few turnovers a game. There seems to be a high correlation between TO and number possessions. The players who turn the ball over most also tend to be the players who score the most and are on the floor most. Given that, it's amazing that Jordan didn't turn the ball over more.

Iverson has become an above passer recently. But outside of that, the only other area where he excels is steals. He's still an inefficient shooter and can't rebound.

The shouldering comment strikes me a bootstrapping argument. People shoulder burdens because everyone think they are the one to shoulder the burdens. But if everyone is wrong about this, then they are shouldering the burden when they shouldn't be. The mere fact that AI tried to will Philly to victory could be less due to his actual greatness and more due to the fact that everyone believed he was great and their only hope and made him shoulder that burden.

The other thing I don't understand is how obvious it can be to everyone that Berri's model is wrong. The book came out last year. He made predictions at the beginning of the year. At the end of this year we'll have some evidence of the predictive power of his model.

But that aside, do people really doubt that scoring is way overvalued?

 
At 1/16/2007 2:27 PM, Anonymous Petey said...

"Berri has stated multiple times that his stats clearly establish Jordan as the greatest SG of all time ... a strong statistical case can be made for him as the greatest player of all time."

Given that Berri's model says that Jordan produced fewer wins than another player on Jordan's own team, you've lost me.

 
At 1/16/2007 2:42 PM, Anonymous v said...

http://dberri.wordpress.com/2006/12/04/on-jordan-and-rodman-again

 
At 1/16/2007 3:00 PM, Anonymous mensch said...

I am really knock-over over by all the commentary worthy of talmudic scholars----too bad we don't the same grey matter figuring out how to extricate the nation from the Iraqui bog.

 
At 1/16/2007 3:01 PM, Anonymous Anonymous said...

It would be interesting to track those players who switch between positive and negative scoring Win Scores. It would be nice to filter out those players who benefit from playing with a star (did that player find more minutes due to that increases scoring production, thus leading to less time on the floor with said star player or did that player leave to a new team where he could be the "guy").

Using regession analysis is a tough thing to do in basketball, it cant be looked at like baseball, its more dynamic, and it looks like, from the surface of things, that Berri has approached his methodology in this way.

 
At 1/16/2007 3:09 PM, Anonymous Petey said...

"http://dberri.wordpress.com/2006/12/04/on-jordan-and-rodman-again"

Ugh.

Read it carefully. Berri is saying that Jordan is extraordinary for a SG, but his model still has Rodman "producing more wins" than Jordan during their time together.

He's not denying Jordan's greatness, he's just saying Jordan in his prime was the second most valuable player on his own team.

Similarly, I'd guess Berri would admit that Arenas is an exceptional player for a 6'4" combo guard even though his model says that Caron Butler "produces more wins".

Berri has made some subjective decisions that make his model radically overvalue rebounds and radically undervalue scoring. These subjective decisions have no statistical basis outside of Berri's whims, and they make his model wildly bizarre.

 
At 1/16/2007 3:18 PM, Blogger Kirk Krack said...

what is the address for the SB5k English Civil War blog?

 
At 1/16/2007 3:21 PM, Blogger Brown Recluse, Esq. said...

http://theenglishrevolution.blogspot.com/

 
At 1/16/2007 3:22 PM, Anonymous tom said...

I haven't read the book but from this post, it sounds like Berri came up with this bunk Wins Score equation to support his Iversons-are-overpaid campaign as silverbird suggests. Can someone who's read the book explain his justifications for this model?

 
At 1/16/2007 3:31 PM, Anonymous Anonymous said...

Can someone who's read the book explain his justifications for this model?

Since payroll does not correlate to wins, he's trying to find what does. And, I have little beef with his findings on a team level. As I said above, it's not rocket science: shoot more efficiently, rebound, don't turn it over - the problem is that his lack of knowledge of basketball (as opposed to basketball statistics) leads him to do very silly things in terms of valuing players as opposed to teams.

 
At 1/16/2007 3:34 PM, Anonymous stickpiano said...

Maybe I'm just reiterating something said earlier, but it also seems like scorers are MUCH harder to replace than players who would do well under Berri's formula.

It's much easier to find David Lee's than it is to find AI's.

Also, anecdotally (and this has been suggested elsewhere), AI and other scorers see better defenders and more double teams which has an adverse effect on shooting percentage. However, if one player is drawing the main attention of the defense that would have a positive correlation on the offensive efficiency of the other four players. Is Anderson Varejao really that good? No, he's an average NBA big with awesome hair and energy, but every time LeBron drives to the bucket, his defender rotates over to contest the shot. Take away his uncontested dunks off of LeBron hand-offs and his FG% would plummet.

Does all of this mean that scorers should pass more? Not necessarily, because if they stopped scoring, they'd stop getting the double teams.

Okay be nice. First time commenter.

 
At 1/16/2007 3:39 PM, Blogger Kirk Krack said...

thanks...best website on the internet!

 
At 1/16/2007 3:45 PM, Anonymous Anonymous said...

Players may perceive passing up some tough shots (to reduce misses) as a useful stat and income maximizing strategy but the better GMs and advisors if they watch enough tape will assess this aspect of the game. Maybe it is underconsidered and uncharted but I dont think it is completely absent from consideration. Guys with this behavior dont tend to get or keep jobs on the good teams or at least it may affect their role and playing time.

 
At 1/16/2007 3:51 PM, Anonymous tom said...

So is it safe to say that Berri's model, like most economic models, is based on a set of naive assumptions that knowingly excludes a number of crucial elements for the sake of simplicity and ease of explanation? I guess that means that the real purpose of this post is to expose Berri for the Iverson hater he is.

 
At 1/16/2007 3:51 PM, Anonymous v said...

petey,

actually, you should reread my comment and the post. Quote from the Berri post:
"Of course when one looks at standard deviations about the average, Jordan was still more productive than Rodman."

Point of my post: while Rodman may have produced more wins when Jordan and him played together, you have to adjust for position when evaluating how players from different positions compare with each other. Given the rebound bias in Berri's model, forwards who can rebound exceptionally well and are high percentage shooters will produce a lot of wins. This, however, DOES NOT mean that there is any priority between positions.

Given Jordan's productivity for his position, it's plausible to argue he was more important during the Bulls stretch than Rodman, because Jordan did things no other guard could do (just like Magic's ability to play the point well made the Lakers so dominant in the 80s). Power Forwards are supposed to rebound. SG are not supposed to be exceptional rebounders.

So I don't think it's logically inconsistent to say Jordan was better than Rodman, once you adjust for position, even though Rodman generated more wins than Jordan.

Kidd is a perfect example of this in the modern era. Kidd is unique in that he is a PG who can pass exceptionally well and rebound like a small forward. You can't just replace Kidd with another point guard. There are no point guards in the league who can do what he does.

 
At 1/16/2007 3:55 PM, Anonymous Anonymous said...

To followup and be clear- passing up a tough shot with enough time on the clock for someone to get a better one is a good behavior. (conversely, taking a marginal shot too soon can be various degrees of a negative.) Passing up a tough shot on a rapidly expiring clock when the probability is high that the team will end up with a worse shot or no shot is a harmful choice. It is a judgment call for the player and the observer. Neither will be perfect but those who have been around the game long enough and are successful have to get a feel for this.

 
At 1/16/2007 3:58 PM, Anonymous Anonymous said...

Given the rebound bias in Berri's model, forwards who can rebound exceptionally well and are high percentage shooters will produce a lot of wins.

Given this, wouldn't one look some askance at the model itself?

 
At 1/16/2007 3:59 PM, Anonymous Anonymous said...

And this makes no sense at all:

So I don't think it's logically inconsistent to say Jordan was better than Rodman, once you adjust for position, even though Rodman generated more wins than Jordan.

Better necessarily implies more contributions to winning, otherwise we might as well be watching Streetball.

 
At 1/16/2007 3:59 PM, Blogger salt_bagel said...

The shouldering comment strikes me a bootstrapping argument. People shoulder burdens because everyone think they are the one to shoulder the burdens. But if everyone is wrong about this, then they are shouldering the burden when they shouldn't be.

That's what the hypothesis is, but some prior work (Oliver is one) produces evidence against this.

It seems to me like the existing analysis shows that the big scorers (Jordan, Wade, maybe not Iverson) are the only ones who can shoulder the load. The lesser players can only produce at high efficiency for fleeting moments or in very specific situations. All the rest of the production is due to the creation that comes from high-quality scorers (or even more rarely, an enabler such as Magic or Nash).

At the very least, one should admit that individual players' production levels are more interdependent than these metrics assume. The best example the argument about how much partial credit the players should get for a bucket when one passes to the other. It's very hard to separate the two contributions and do so accurately for each instance.

You can carry the same logic to the team-wide level. It must be the case (to me, anyway) that part of the measurable production of someone like Kyle Korver actually originates from being on the same floor as AI. The difference between the stats gurus is that some realize this, try to measure it as best as possible, and admit that it's inexact; while others gloss over it and use the stats as if each individual player is the sole generator of his own stats.

 
At 1/16/2007 4:06 PM, Blogger salt_bagel said...

Does anyone else find that the frame of argument is partly driving the controversy? You could do the same statistical analysis, but title it Why doesn't a player as good as Allen Iverson win as much as he should?, and the people's take on it would be totally different. Whether that's conscious or unintentional, it's still on Berri.

 
At 1/16/2007 4:12 PM, Anonymous Anonymous said...

Stickpiano- The idea that it is difficult to find scorers has always been a point of contention for me. I've often wondered how many current NBA players, if placed in the right system where there would be no fear of failure in taking missed shots, couldn't be dynamic scorers. Don't forget that players like Tony Delk and Tracey Murray have gone for 50 points in a game before. Obviously no one expects them to keep up that kind of pace, but if every play was run for them, what kind of scorers could they be? We'll never know. How often does reputation dictate performance, rather than performance dictating reputation?

 
At 1/16/2007 4:22 PM, Anonymous Anonymous said...

To take or not take a tough shot is based on ability and role. Some are instructed to pass in these situations and some listen and some don't. Guys who are supposed to shoot these will probably catch heat from the coach if they don't and it might affect their next contract.

Spurs are a good example of a team stocked with veterans now in smaller roles who previously took more of tough shots and so while they pass to the primo guys when they can, they are also experienced enough and good enough to make a good % of the tough shots they should take for the good of the team.

On AI he bounces from being good in the clutch to somewhat weak but I think dominating the clutch shots leads to deference, lack of guts and overloaded defenses. i've looked a lot at clutch shooting stats but just recently just to also looked at team win % in the clutch duriong a star's time on the court to set the star's behavior- and impact- in context. This year Iverson clutch shooting went from 40% eFg in Philly to 50% in Denver but team % in clutch has been 17% in both places. In most of the previous years Philly with Iverson were close to .500 in the clutch. Ok but not a dominating closer.

I

 
At 1/16/2007 4:53 PM, Anonymous Anonymous said...

Denver with Melo (before Iverson) was winning 44% of the clutch minutes (down from 60% the previous season). With Melo and AI will it be 60%, 50%, 44%, or lower?

All the minutes count of course. Team with AI at PG is doing much worse on win % with AI at PG.
With Melo and Smith back does AI play more PG? Do the early results change? His PG/SG time split is a challenging question as it always has been.

 
At 1/16/2007 5:01 PM, Anonymous Anonymous said...

should be... Team with AI at PG is doing much worse on win % than with AI at SG.

Melo back next week then the we begin to get deeper into the story. will the AI trade make team better? Playoffs will be the main answer.

 
At 1/16/2007 5:12 PM, Anonymous PCA said...

Excellent work Silverbird. My only complaint is that this post led me to spend an hour reading the comments on Gladwell's blog in response to his odd defense of the Enron execs.

 
At 1/16/2007 6:06 PM, Anonymous Petey said...

"With Melo and Smith back does AI play more PG? Do the early results change? His PG/SG time split is a challenging question as it always has been."

Yup.

If I were George Karl, I'd want him spending a serious chunk of his time off the ball doing his Rip Hamilton schtick.

I loved the Steve Blake deal because it seems like a perfect way to get Iverson off the ball with Blake playing the role of Eric Snow circa 2001.

The question for me is where to find J.R. his tick once 'Melo gets back.

 
At 1/16/2007 6:46 PM, Anonymous Anonymous said...

From what I've seen, they aren't JR's shots/minutes to lose. Extra-practice one-on-ones with Melo aside, he got killed by the Spurs just being run through screens.

Steve Blake not only runs the ball upcourt (which some of us have been waiting for for years, no thanks to Miller/Boykins), but he also generally shoots only after first passing the ball off and then getting it back. Blake/AI looks promising, and like where the team is headed for now.

As for Melo's return, it's definitely not clear where the minutes will go, but they certainly aren't JR's to lose. In my opinion, he's going to need to develop as a ballhandler and as a man-to-man defender to earn his time.

And that's all I want to hear about analysis of "nuggets with AI", since the other guys on the floor for those "clutch minutes" are Linas Kleiza and Diawara...

 
At 1/16/2007 7:00 PM, Anonymous Anonymous said...

I think that a rotation of AI, Melo, JR and Blake at the 1-3 (with maybe some minutes from Diawara as well) will do fine.

My concern is whether Blake will continue to shoot as well as he has done so far. Past performance all the way back to Maryland says no, but we'll see.

 
At 1/16/2007 7:05 PM, Anonymous Petey said...

"And that's all I want to hear about analysis of "nuggets with AI", since the other guys on the floor for those "clutch minutes" are Linas Kleiza and Diawara..."

I dig Kleiza. He's horrible right now, but I could see him evolving into someone with a Nocioni vibe.

And while I'm looking forward to the Real Nuggets showing up next Monday, I've gotta say that I thoroughly enjoyed watching the CBA Nuggets of Iverson, Boykins, Kleiza, and Diawara. They weren't ever going to win many games, but they were competitive and compelling.

"they aren't JR's shots/minutes to lose. Extra-practice one-on-ones with Melo aside, he got killed by the Spurs just being run through screens."

Yup. He did look absolutely awful on both sides of the ball in the Spurs game, but J.R. is just an excitable boy, and it was his first game back from the suspension.

I agree with you on his larger weaknesses, but he's still got some high level talent, and the Nuggs need to find minutes for him if they want to compete with the big boys of the West come playoff time.

With a healthy Nene and a productive J.R. who knows his role, I can see them giving a real series to Dallas or S.A.

 
At 1/16/2007 7:13 PM, Anonymous Petey said...

"My concern is whether Blake will continue to shoot as well as he has done so far. Past performance all the way back to Maryland says no, but we'll see."

His career NBA 3pt percentage says yes.

-----

He brings up the ball. He does a bit of distributing and playing traffic cop between Melo and AI in the halfcourt. He helps run the transition offense. He knocks down wide open 3pts at 40%. And he chases the Tony Parkers and Devin Harrises and Leandro Barbossas of the world on defense.

Voila! All of that is within Steve Blake's game. And if he can play within that game on a reliable basis, he's going to make a career for himself over the next 5 months.

 
At 1/16/2007 7:49 PM, Anonymous Anonymous said...

Voila! All of that is within Steve Blake's game. And if he can play within that game on a reliable basis, he's going to make a career for himself over the next 5 months.

I hope so, because what team wouldn't want Bubbles' boy Johnny running the point?

 
At 1/16/2007 8:28 PM, Anonymous Anonymous said...

I can wrap my head around the fact that Jordan was "better" than Rodman even when Rodman was generating a higher WS. I'm no statistician, but it does seem, as some here have said, that comparing players' "Win Scores" to others at the same position is much more instructive than looking at cross-positional comparisons, particularly when you consider the overweighted nature of the rebound. In fact, I take this into account when considering any of these sabermetrically influenced attempts at valuing basketball players.

I also agree with the notion that this metric lacks greatly in that you can't account for differences in offensive efficiency for each basketball action given who's on the floor. One Suns posession when Nash is on the bench has measurably lower expectations than those when he's bringing the ball up, obv. This is why I'm a fan of the plus/minus in hockey, even with all its warts (the defensiveman bias, etc.).

 
At 1/16/2007 10:38 PM, Blogger tegwarrior said...

quick hits:

if win scores can't be compared across players, they hardly seem like an effective catch-all tool for considering player worth when crafting a team/ salary scale.

economists would say this whole project suffers from a 'missing markets' problem. where's the really effective data on defensive play (i.e. yes there are steals and blocks, but the not so simple act denial defense or causing your man to shoot terrible percentages routinely are not tracked/ trackable). besides, how do you separate one individual's contribution within the team framework on that end. this is all something worth paying for.

marginal anything is not determined by quality as is stated above- the relative scarcities and the relative prices (values) determine marginal contributions. listen to athletes talk, and they'll tell you successful rebounding is more a result of effort than skill (assuming they're right). which can be restated as: rebounders are plentiful, cutting their wages (regardless of the value one puts on rebounding).

and let's all just admit that it's a bit silly to penalize a player for shooting (missing: yes, shooting: no). shooting is, oddly enough, the only way to score. yes, you shoot and you 'lose possession'. or rather, you trade possession for an opportunity at points. but given the shot clock, you were going to lose that possession anyway, might as well get some points for it. comically, the ideal team might just run around for the whole shot clock trying to get fouled, making the first free throw, missing the second and hopefully rebounding the miss to repeat all over again. this is how 5 rational guys in a contract year would behave?

 
At 1/17/2007 12:09 AM, Anonymous danny said...

A little economic sociology is desperately needed among the moneyball wannabees. It's pretty obvious that the actors in an NBA game are not playing according to a rational calculus but operate according to cultural scripts that place different kinds of value on the various economic variables being tracked. A charge taken by Battier is not always just a turnover or foul, and a block by Mourning may not just be a failed possession. It might instead be something that instils doubt in the minds of the offensive player about driving the lane, and this will change the offensive strategy and then what kinds of shots are available to the team, and the relative effectiveness of different kinds of scorers.

As mentioned by others above, what scorers like Kobe, AI and even the hated Arenas bring to the table is not purchaseable off the shelf: the ability to be a threat, which changes the fabric of the game. This is why Marion has never been considered an MVP candidate while putting up the numbers.

The statistical arguments are interesting in terms of trying to develop heuristics that provide shortcuts to qualitative analysis, but at the end of the day, just as in macroeconomics, there is little truth to be found there, merely an epistemology which lacks the conception of human space and time. Which is why you ain't gonna meet chicks at yr fantasy sports gig.

Nice takedown in the article though!

 
At 1/17/2007 1:17 PM, Anonymous Rich said...

The basketball team, as a firm, is supposed to accomplish two goals rather than just one. Everyone here is talking about one goal, winning games, and ignoring the other, which is to turn a profit in conventional business terms. I assume that all personnel decisions are made with both of these factors in mind, and it's not at all surprising that in a given market it's determined that bringing in the stereotypical selfish scorer will fill the seats, raise the ad rates, and increase profitability, even in the absence of any positive impact on wins vs. losses. only a certain kind of market, for instance, will value a "win the right way" team (the mirror-image stereotype) even if it's successful n the court.

In hockey terms, winning championships by using the neutral-zone trap will fill the seats in (e.g.) Detroit, but it probably won't in Nashville.

 
At 1/17/2007 3:14 PM, Anonymous Anonymous said...

We have a trade! Golden State just got a whole lot more Free Darkoer.

 
At 1/18/2007 9:07 PM, Anonymous Anonymous said...

This all just points up the fundamental problem with the current fad for economic orthodoxy dressed up as sociology of the future: it's still all the same crowd jumping up and down saying that something just is - it is! it is! - because their precious model says so. Economists are just fishing for ways to save a discipline that pooped out on fresh insights five seconds after the General Theory hit the racks by colonizing other fields. You know how people sort of chuckle down their sleeves at Derrida now? That's Levitt and Landsburg and Berri and all these other clowns tomorrow. Resist!

 
At 3/06/2007 4:13 PM, Blogger Lesser Idiot said...

There is a massive level of misunderstanding of the claims of Dave Berri in these comments here.

1. the weights are not arbitrary
2. the correlation doesn't hold for just points scored, it holds for points scored AND allowed, which can be measured on a team basis, but not for individuals, and it amortizes the net effect of all the blocks, steals, turnovers, and rebounds, and fouls.
3. Thing are not "just is! it is!" because they say so, they are that way because they have predicitve power. That has real practical usefulness, it is real tangible evidence that the model is good.

The author of this post has made the most twisted and insane argument i have ever heard to try and continue believing that the NBA doesn't overvalue scoring.

It is a fact as plain as day that the NBA is failing to properly evaluate the producivity of players who score a lot with low efficiency. If you take the time to understand the math you can know it too.

 
At 9/16/2008 1:30 AM, Blogger Jackline said...

Hi Nice Blog .This labor time tracker is used to track the time and attendance of employees, and at the same time track labor activity against specific parts, jobs, and operations.

 
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