Nba nerd

The Myth of the Free Replacement-Level Player

Calculating the fair value of an NBA contract has been a tough nut to solve. In a lot of our work, we use some short hand by calculating the total payroll paid to all players, and divide by the total number of wins. There are obviously some big problems with this, and the biggest is opportunity cost. A player like Monta Ellis might produce some wins, but he plays 3000 minutes in which some other player would produce more wins. So it's tempting to use wins above a replacement-level player as the measurement of what you pay for. But this is even more deeply flawed.

The FiveThirtyEight website tries this approach. In an article about Carmelo Anthony's contract, Nate Silver tries to translate wins to salaries:

But we should be dividing $55 million by 25 wins instead, which comes out to $2.2 million per win. Where do these numbers come from? The $55 million represents the money a team spends above and beyond the minimum contracts for a 12-man roster,3 and 25 is the number of wins it takes to go from replacement-level (16 wins) to league average (41).

This is on to something clever, but there is a big problem here. I talked with Professor David Berri about this. He's best known for creating the Wins Produced metric, but he's also a professor of economics. His initial take:

If you study labor economics (a course I have taught) you will not find anyone saying that a worker's value is: Marginal Revenue Product of worker - Marginal Revenue Product of Replacement.   Your value is just your value.  There is no replacement worker.

Think of it this way.  Imagine you are hired to sell cars.  Now imagine your new boss tells you: "We have found that anyone coming off the street can sell 2 cars a month.  So we will not pay you for the first two cars you sell, since that is what a replacement worker would do.  Your pay is determined by everything you sell after 2 cars."  Would you buy that story?  Would you work for free? 

Ok, there's a solid point -- even the bad workers get paid. I am sure most of you can think of a colleague or two in your work environment that this applies to. And when you consider poor performers, you need to consider that in the vast majority of markets, you cannot simply walk out on to the street and get a replacement; even in markets with abundant supply of labor, there are at the least transaction costs to replacing workers.

Of course, in markets where labor supply is scarce, like professional basketball, there's no such thing as a big basket you can just reach into to pull out a couple of replacement players. Obviously talented, yet unemployed, players exist, but finding them isn't trivial. JC Bradbury made this point pretty clear in baseball several years ago:

I’ve written quite a bit about my dislike of replacement level over the years. You can see posts that I have written on the subject herehere, and here. But, I thought I’d briefly summarize my reasons for rejecting replacement-level theory in a single post.

— If there was an abundance of talent at the bottom of the league, then the frequency of poor play on the inferior side of the talent distribution should be evident. But as the distributions below indicate, the distribution of talent is bell-shaped.


So we can see that the assumption that replacement-level players are "free", or even "readily available at the league minimum", has essentially no basis in economic theory.

Of course, this is just the beginning of the problem. The next part of the problem is that wins don't necessarily translate to profit.

Let's use the 76ers as an example. They won 19 games, which means they literally were a collection of near-minimum-level players. They also paid damn close to the minimum salary last year. They managed to get above the salary floor by trading for players like Danny Granger and Earl Clark near the deadline, but they were only on the hook for pro-rated parts of those contracts, and they bought out those players for less than that. So let's assume for argument's sake that they paid the minimum salary, which means they were big beneficiaries of luxury tax payments (which are paid to teams under the cap).

Between fixed revenue streams like the luxury tax, profit-sharing and TV contract revenue (remember that low ratings affect the TV's revenue, not the team's TV licensing revenue), and semi-fixed revenue sources like season tickets (which were purchased well before the epic 26-game losing streak), it is probable that the 76ers made money last season, despite their awful record.

Clearly, if a team can make money winning 19 games, then it should pay its players even if they are all awful! So, as you can see, assigning a fair market value to a contract is a hard problem to solve!

Dave Berri's examples are irrelevant. A business in the real economy is not constrained on the number of workers it hires. It can expand the payroll as long as doing so generates more profit. A sports team is not in this situation. If a car factor or a dealership was limited by law to a 15 worker roster, then they would start caring about the replacement level worker as well. I'm surprised that this isn't obvious to Professor Berri.
" markets where labor supply is scarce, like professional basketball"

The labor supply is scarce, but the labor demand is scarcer-er-er. There are 347 NCAA I college basketball teams. Presumably all players on these teams would like to play basketball professionally. Even if you just count the starters on these teams, it's a number almost 4 times greater than all the roster spots in the NBA.

The graph you copy from JC Bradbury looks to me like a bell curve above the average, but it's not quite bell shaped below it. The population is more dense toward the average and the low-performer tail is thinner than it should be. Let's imagine the selection process for replacement players. Teams trying to pick out the best freely available players, but they sometimes make mistakes in their evaluations. And sometimes a player will perform below his innate talent level due to random variation. Such players are then discarded and a new one is drawn from the replacement pool. In this process it would be no surprise that a graph of performance will show a number of performers who are below the replacement level. Maybe even a larger number than those who are above replacement if the scrubs are discarded very quickly.

If you read the comments below Bradbury's post, you will see this objection, and a number of others. JC Bradbury is an iconoclast in the baseball sabrmetric community and not somebody who the others listen much to. If you quoted Tangotiger's opinion on the replacement level, you would be on a much better footing as far as authority goes, except Tangotiger's opinion would be for replacement level. Though maybe argument from authority is not what you were going for.
" it is probable that the 76ers made money last season, despite their awful record.

Clearly, if a team can make money winning 19 games, then it should pay its players even if they are all awful! "

I don't understand the last sentence. If a team can make money being lousy, maybe it should pay its players as little as possible because their performance doesn't matter.

More importantly, the amount of profit a team makes is not generally considered in performance analysis. The problem usually is posed like this: "My team wants to win the championship. It can use the amount of resources specified by the league cap rules to do so. How can it allocate them most efficiently to achieve that goal?" Profit is not considered. It's a question we are most interested in as fans. Fans don't care about the owner's profits.

Certainly, it's possible to run a team quite profitably as a cheapskate loser. Donald Sterling did this for decades. Jeffrey Loria of baseball is another example. But nobody wants other owners to copy them. I've yet to see a stats analyst argue that wins aren't important, but squeezing the most profit out of a team is. Are you going to be the first?
To sum up, there are three arguments in this article against replacement level. The first and third are irrelevant and the second is based on a dubious analysis of the data.
Well, bubba just beat me to everything I was going to say. First about replacement level being necessary because of the fixed roster, and also about Bradbury being regarded pretty poorly in this field. I'm kind of shocked to see this blog post from you guys actually.
I see value in discussing which personnel moves are profitable for an NBA franchise. If no one has ever raised that topic, addressed that question, or argued from that perspective, I would be proud to claim the mantle by being “first.” Sadly, I doubt it’s available. I suspect this subject has been discussed at great length. The reason we debate these academic points – given that the actual decision makers do not give a flip about our opinions or our conclusions – is because we seek valid, testable answers to questions such as: was it really stupid for the Knicks to give Carmello that much money? Said question can be considered & answered in a variety of ways. One very valid perspective, perhaps the most valid, considers the free agent signing (or re-signing) from the standpoint of a team trying to win the 2015 NBA title. But that’s not the only valid perspective. You can argue short term v. long term consequences. Or, you can argue that seemingly-counterproductive salary moves are rational because the owner’s goal is to profit, not win titles. Of course, as a hoops fan, I hope my team’s owner wants to win. I am very satisfied with my favorite team’s ownership (Go Spurs). Yet, if you could show me that some other owner’s roster move was crazy profitable– esp. if you show me that a certain move essentially maximizes that franchise’s near-term profit, I’ll concede that said move was rational or even smart -- from a certain point of view. I’m not going to call some guy a gibbering idiot if/when the outcome of his decisions are very profitable. I might hate that dude for choosing money over basketball success, but I can respect that perspective. The NBA is a business. On the other hand, some moves accomplish neither goal: they don’t make dollars and they don’t make sense. When a team pulls such a bone-headed move, folks can legitimately call it out as foolish. Hence, investigating and understanding a move’s profitability, not just its strategic, title-winning utility, seems a necessary precursor to castigating the GM’s intelligence. No?
"I might hate that dude for choosing money over basketball success, but I can respect that perspective. "

You respect that perspective in a team you're not rooting for. If the Spurs started doing that, you'd just hate the owner.
Whoa Bubba! You need a blog post thats a lot of commenting.
Being a cheapskate owner of a losing team is a self-limiting strategy. It's essentially freeloading off the hard work the other teams are doing of promoting the sport. It's possible because, unlike Europe, American sports leagues are quite socialistic, with revenue sharing and no relegation. However, if many owners start freeloading like that, than the league revenues would drop, the league will start losing fans, and either the league will die, or it will change the rules to make freeloading unprofitable. For example, AFAIK, NBA set up a salary floor in response to Donald Sterling. Thankfully, not a lot of owners have tried to go down this path.
Why aren't D-League players and the like considered replacement level? They get signed to 10-day contracts at the league minimum generally when teams have injury issues.

The baseball argument is obviously wrong, every team has a stable of minor league players who can be called up and if they are lacking at a position, it is simple to trade for another team's replacement level guys. This season, Oakland traded $1 for a player, isn't that pretty much the definition of replacement level?

I do think that calculating the expected production of a theoretical replacement player is difficult. You should read the fangraphs glossary to see how they calculated theirs.
"I do think that calculating the expected production of a theoretical replacement player is difficult. "

You're right. Baseball-Reference and Fangraphs used different replacement levels for years, and only compromised on a common baseline recently. However, Patrick is trying to deny replacement level altogether.

"The baseball argument is obviously wrong, every team has a stable of minor league players who can be called up "

While the pool of people who can be used to patch up a roster on a moment's notice during the season is smaller in basketball than in baseball, if you want to sign a replacement player during the offseason, you have a lot of choice: European free agents, college graduates, over the hill veterans.
"[W]ins don't necessarily translate to profit."

Want more evidence of that? The Lakers reportedly profited over $100 million after tax and revenue sharing for the 2013-14 season, despite just 27 wins:

This is the problem with salary-based player evaluation. We keep thinking that NBA teams are in the business of winning games, but they're really in the business of entertaining and making money. Winning helps the bottom line but it's not the only contributing factor.
Regarding Prof Berri's comment - does he really think that, in the "rel world" (i.e., non-sports employment), compensation is not structured so as to require some minimum threshold of performance? To be sure, usually employees are given some straight salary. But the incentive compensation structures with which I am familiar all require a threshold of performance before paying out.

So, in the NBA, this would translate to: anybody coming in out of the D-League can perform at replacement level and is paid minimum salary. To be paid anything above minimum, you need to produce in excess of what a player coming out the D-League would provide. I don't see that as particularly controversial, do you?
Regarding wins and profit - isn't the point that, even if a team can make a profit with 19 wins, it is likely to make an even greater profit with more wins?

That's not always the case, of course. (Hello, Brooklyn Nets, of the 45 wins and $144 million loss.) But in general, more wins should be correlated with higher profits, I'd think.
A few thoughts...

1 - On the topic of compensation, exchanging payment for work is typical. If you offered to pay the average Joe off the street in the car sales example nothing for average performance, he would reward you with an equivalent amount of work: none.

One can think of compensation as having two parts: the base level of compensation required to get people who are qualified to do the job at the average level to do the job at all (and this varies by profession, based on supply and demand), and the performance incentives where performance above the average is rewarded.

Obviously this is not allocated in the same way across all industries (witness retail with commission-based pay, so it's all performance, witness government jobs where it's all seniority and scale based so performance above a non-firing level doesn't matter, and witness weird hybrids like finance where traders can make a salary but a bonus equal to 10x their salary depending on results, but with a high probability of getting fired if you underperform).

However, to say replacement level activity is worth nothing is obviously untrue, unless the replacement level is literally not putting a player on the court and having an empty spot.

2 - The constraint on employment matters in two ways for NBA teams, and thus means value over replacement must be considered: one, you can only have 15 players on a team (and not even all available at once), and more so, you can only have 5 guys on the court at once (unless you want some to get suspended for coming off the bench to throw down). As a result, your real win condition (and the wins produced research around playoff basketball referenced on this site confirms this) is having the 5 best players possible (realistically, 7ish players). Your 12th player being replacement level vs. just above replacement level probably has near zero value, but on the flip side, your 5th player being replacement level vs. just above replacement level has significant value.

I suspect it's non-trivial to model this, but you would need a marginal contribution to team model for each player based on allocated playing time in order to measure the real value of performance above replacement level (and it would vary by team and position, annoyingly). So what you really want is the "marginal" NBA player to be the guy at the cusp of getting playing time, not just being on a roster.

3 - This all assumes the right players are being given playing time in the first place. It's actually very possible that the current high-minutes rotation of the NBA is worse than replacement level (whatever that is) if you believe coaches do not allocate minutes to their best players. Also, establishing the value of players would then depend on coaches actually playing them. What is the value of a 3x above replacement level performer that George Karl refuses to play? Can you have a sub replacement-level coach...?

4 - I think we have to assume a constant starting position to evaluate moves of "trying to win." If we get off the beaten path and into things like "the Lakers signed Kobe because it's profitable", fine (and possibly true), but if you want to go that route, you need a model to describe the actual goals of each owner and as a result each player will have a different value to each team (this is actually what is probably happening, but not that useful in terms of understanding which players help you win championships).

... Jay Bilas would be impressed with the length of this comment.
A marginal revenue model isn't terribly useful because you can't just hire more basketball labor for your team; a player requires fixed capital, a NBA roster slot and minutes, to be productive.

This is analogous to hiring machine operators for your machines; you are hiring basketball players to use your 15 roster slots and ~20,000 minutes. By default, you pay them the market clearing price for the corresponding productivity (the NBA minimum for 'replacement level' wins). Players who can make better use of those minutes can demand rents for their labor.

Calculating what that market clearing, no rent productivity is, is not trivial, but the intuition and model behind it is pretty solid.

"If you quoted Tangotiger's opinion on the replacement level, you would be on a much better footing as far as authority goes, except Tangotiger's opinion would be for replacement level."


A guy who doesn't even go by his real name has more authority on a sports economics question than J.C. Bradbuy, a published economist and Department of Exercise Science and Sport Management at Kennesaw State University! You're using an appeal to authority to support your argument, but you're doing even that poorly.
Shawn, the fact that no one know who TangoTiger is and that his work stands on it's own shows you something. Hyping up Bradbury being a "published economist" instead of discussing the merits of his replacement value arguments in comparison to Tango (and every other sabermatician ) is the appeal to authority.
No, dropping a name to support your argument is an appeal to authority. I'm just pointing out that Bubba is not appealing to someone most people would consider an authority. I'm not making an argument myself, just pointing out how the difference in credentials makes Bubba's appeal laughably unconvincing to a stander by.
Sorry, typo

difference in credentials --> ludicrously, bordering on satirically, stark difference in credentials.

If you want an actual argument, here it is. The people in this forum are pretty familiar with Bradbury's work, and tend to find it to be high quality. The assertion that TigerNacho's work is self-evidently better than Bradbury's sounds rather dubious, especially since Bubba's representation of the argument is both overconfident and woefully unconvincing.
Some of you are confusing *wages* with *productivity*. Perhaps I confused this issue by mentioning fair market value. But what we are trying to calculate here is each worker's (player's) marginal production. And we can unequivocally state that nowhere in econ is a replacement-level worker (player) considered to have a marginal revenue product of zero. That's why the concept of "replacement-level worker" that you can pick up off the street simply does not exist.


You are close to being censored. This isn't because your comments are mostly grossly misguided. It's just because you are using the comments section as your own blog.

"The labor supply is scarce, but the labor demand is scarcer-er-er. There are 347 NCAA I college basketball teams. Presumably all players on these teams would like to play basketball professionally."

This number of NCAA players, or players at any level for that matter, who WANT to play pro ball does not constitute the supply of labor. Desire is irrelevant, or there would be more labor supply for brain surgeons, astronauts, and professional athletes. Google for "Economic Rent."

Demand for NBA-level basketball talent is absolutely higher than the supply. I'm not sure how anyone could possibly argue otherwise with a straight face.

"A business in the real economy is not constrained on the number of workers it hires. It can expand the payroll as long as doing so generates more profit."

I'm confused. Are you claiming that the NBA is unique in that it suffers under diminishing returns to the marginal productivity of labor? Or that if the NBA had unlimited roster spots, each team could generate more wins or more revenue?

Both claims are ridiculous; I'm just wondering which of those claims you think makes Dr. Berri's work irrelevant.

Finally, regarding JC Bradbury, what Shawn said. Apparently the SABR people don't think highly of JC. That inclines me, in turn, to think higher of JC.

One last thing:

"A marginal revenue model isn't terribly useful because you can't just hire more basketball labor for your team; a player requires fixed capital, a NBA roster slot and minutes, to be productive."

It's Marginal Revenue PRODUCT. The difference is not semantic.

But I'm confused again. Are you claiming that most firms don't employ both labor and capital? Are you claiming that most workers don't require capital to be productive for their firms? Would you raise your hand in a labor econ class and make either of those claims?
Wait, he's going to get censored because of the length of his comments? Why? What's the rationale behind that? How is his comment length a negative thing?
Perhaps Patrick doesn't want to pay $40+/mo (I believe he uses Heroku which is expensive) to host blog posts that he feels are below his standards for quality.

If Bubba wants his opinion to live on the internet, nobody is stopping him from hosting them himself.
30 PA's eh........nice sample size constraint. That's the equivalent of 6 FGA.
I expected a weak excuse when i asked those questions, but the $.01 it costs for his extra paragraph or two exceeded my expectations. Though to be fair, it was just you speculating. It may not actually be Patrick's reasoning (in fact, I doubt it is) Anyway, having the discourse be here is clearly more advantageous than having him respond in his own blog..... Hope this wasn't too long.
I remember a year or so ago I actually got curious about whether there really were enough "replacement-level" or "average" players around so that every team could fill out its roster to the point that, theoretically, every team would have the same record of wins and losses (everyone is 0.500).

I actually found that not only does each position have varying levels of "talent" (in terms of # of players with ~0.099 WP48) but also that there were not enough "average" players to "go around."

I forgot why exactly I thought that this was relevant to the discussion above, but if anyone sees a connection than let me know, and if it's irrelevant then I'm sorry for wasting your time haha
A word limit in the comments looks like it would be a great move. These comments are long winded.
"Apparently the SABR people don't think highly of JC. That inclines me, in turn, to think higher of JC."

Perhaps Mr. Minton is referencing some behind-the-scenes beef between various parties within the sports analytics community? How very interesting, I love gossip as much as the next guy! Very inside-baseball (pun intended).
@boing3887 Although the way 'replacement level' is used seems to vary, a replacement level player is almost always worse than an average level player. Based on the baseball definition of replacement level where a team of replacement level players would have a winning percentage of .294, I'd roughly guess that an NBA team of replacement level players would win about 24 games and have an average wp48 of around 0.0588. But, that is a very sloppy estimate that does not account for the differences between the NBA and the MLB.

One thought occurred to me when looking at Bradbury's graph. This is a very restricted range we're looking at because only professional level players are included. What would the distribution of talent look like if players who were just outside of this range were included?
Berri's comparison is wildly off base. The labor market for car salespeople is structurally very different from the one for basketball players, and it's either disingenious or dumb to gloss over that.

Basketball players must be paid a minimum salary. There are thousands of candidates who are in similar, lower-grade leagues across the world, with records of their performance easily accessible online. Not only that, but it's probably fair to assume that a majority of the people who have 'the talent' to play basketball professionally are engaged in trying to. If not, it's still clear that a far greater share of the potentially productive basketball labor force are engaged in trying to make the NBA than are the potentially productive car sales labor force in trying to get a job selling cars. Oh, and nobody signs a contract to sell cars for a year.

That minimum contract? That very literally says, "Anyone we pick out of the d-league can spend minutes on a basketball court, so we're only going to pay you (whatever the minimum salary is) to put minutes on the court". The expectation is that if you happen to be a better-than-replacement player, you might get a better contract in the future. But the team can't actually avoid paying a player it employs for being less productive than replacement level, because there's a salary floor.

Further still, the evaluation of productivity is still up for debate, so, unlike the car salesman, we can't say, "Well, you scored 5 baskets, and that's two more than someone else would with your minutes, so you get a 2-basket commission, plus your 3-basket replacement salary".

Hell, it's a longstanding argument from your colleagues here that many of the players playing basketball outside the NBA have the chance to be decent .100 wp/48 guys, but get passed over in favor of aging, below-par vets.

Lastly, I think that this quote: "So we can see that the assumption that replacement-level players are "free", or even "readily available at the league minimum", has essentially no basis in economic theory." conflates 'replacement' and 'average', and that's a mistake that undercuts the point. Replacement-level IS what you expect from the league minimum. It literally means: this is what you have access to at all times, this is the player you can hire to fill in a roster spot. Sure, sometimes you strike gold, sometimes they're below the average replacement player, but the whole concept is based around the idea that there is a ready and waiting pool of labor to be had for the minimum.
I might leave a longer comment on this at the WoW Journal. But many of you are confusing how one measures marginal productivity with how salaries are determined in the marketplace. Those are separate issues.
I'm concerned why there are so many people who think that there is an abundance of replacement level players readily available. There is a finite supply of "NBA level" players, and the majority of them are in the NBA.

This reminds me of a few years back, when people were asking of the championship Kentucky team was better than the (then worst) Charlotte Bobcats. The answer was a resounding HELL NO, and that was the best college team in the country. The best D-League players struggle to find roster spots at the end of the bench, in the NBA. The majority of those guys are simply not NBA caliber.

Remember, Brian Scalabrine after he retired took on the best street ballers in the Boston area, including collegiate players, AND ANNIHILATED THEM. Scalabrine during his career was only borderline replacement level, this was well after he retired, and he was playing players substantially younger who play competitively.

I'm not bubba, but I agree with at least his first comment. You said this:

"Are you claiming that the NBA is unique in that it suffers under diminishing returns to the marginal productivity of labor? Or that if the NBA had unlimited roster spots, each team could generate more wins or more revenue?"

And then this:

"And we can unequivocally state that nowhere in econ is a replacement-level worker (player) considered to have a marginal revenue product of zero."

Bubba is not making either of the claims that you listed in the first comment that I've pasted above, he is stating that the NBA is unique in that a replacement-level player can indeed have a marginal revenue product of zero. Given the constraints of 48 minutes per game divided among 5 players at a time,

To use Dave Berry's car dealership example, consider a car dealer who is limited to 5 salesmen. If he has a full salesforce, a marginal worker can only be hired if he fires a current worker. If his new worker is not more productive than the worker he needed to lay-off, his marginal revenue product would indeed be zero!

Surely we can agree that the fact that labor economics does not consider the concept of a replacement-level worker does not mean that the concept cannot exist in strictly regulated, non-standard markets, such as the NBA.
Patrick, xavier, and probably some others,

I can make the argument that there are "an abundance of NBA-level players available" with a straight face because "NBA-level player" doesn't have a definition outside of "players who play in the NBA," or "players on an NBA roster."

There don't seem to be large pool of players who can produce 1.0 win shares per 48 minutes, but we must clearly define the group of NBA-level players to include players with a lower WS/48, if 1.0 is the average.

As has been stated above, the replacement level player is that guy who is available to play. I also agree with bubba that if we were to define this player more strictly, we should do it based on those who are on the cusp of earning minutes (not on the cusp of earning a roster spot), meaning that we would be looking at players already on NBA rosters. Making them NBA-level players!
Dave Berry,

"I might leave a longer comment on this at the WoW Journal."

If you do write more about this please plug the article in your twitter feed! I would like to better understand the differentiation you reference.
People seem to be misapprehending the Gaussian distribution (i.e., bell curve) of player talent that Patrick is talking about. There is no ocean of players from which one can draw "replacement" players at a moment's notice. The supply of labor in the NBA is so limited, especially among big men, that there sometimes straightforwardly is no one in the world who can perform a particular role for you at anything like a "replacement" level. Want an example? If you needed rim protection right now- if you needed to add a replacement-level true center- whom would you select? If there really are "replacement players" whose price we can essentially ignore by focusing purely on the "marginal productivity" of "non-replacement players," then there should surely be one true center wandering around who can protect the rim and crash the glass at the level of a "replacement" NBA starter. Top of my head, there is no such player; there certainly is no long list of NBA-level big men who can be called upon at will to provide "replacement-level" productivity.

Also, please don't censor people for the length of their posts; people are always coming in here trying to "refute" WP or whatever, and they always seem to wander off eventually. But hey, it's your website.
First, I have to say the level of commenting here is very high. The author of this blog should take pride that he can attract such level of discourse.

Secondly, bubba makes excellent points and has an excellent grasp of the concept. If he's ever kicked out of commenting here, I'd love for him to find a home at my blog. If readers are somehow dismissing what he's saying, they have essentially formed an opinion on limited information.

Thirdly, bubba's points don't rely at all on an appeal to authority. The merits of his points stand on their own.

Fourthly, Dave Berri's characterization of the car salesman is inaccurate. An above commenter made the point about a fixed number of salesman, which is a good way to say it. I have made the point on my blog, which I will repeat here. I have added in upper case what he should have said (I am not using case to denote screaming) :

"Think of it this way. Imagine you are hired to sell cars. Now imagine your new boss tells you: “We have found that anyone coming off the street can sell 2 cars a month AND THAT WE CAN PAY THAT PERSON THE MINIMUM FEDERAL WAGE. So we will pay you THE MINIMUM FEDERAL WAGE for the first two cars you sell, since that is what a replacement worker would do. Your BONUS pay is determined by everything you sell after 2 cars.” Would you buy that story? Would you work for THE MINIMUM FEDERAL WAGE AND EARN A HEALTHY COMMISSION IF YOU ARE MORE THAN MINIMALLY COMPETENT?"

Finally, if you want to understand replacement level, play Fantasy sports.
Again, many of you -- including TangoTiger -- are not understanding the difference between measuring productivity and the process by which wages are determined. This really is standard labor economics, which unfortunately many of you do not understand. I will see if I can find time to teach the difference this weekend.
For those interested, I had a very very lengthy discussion with Rodney Fort. I have posted the entire discussion on my blog. For those who want to learn more about replacement level, please read it:
Tangotiger (and others),

The idea that NBA teams are "limited" to 15 players in a way that other firms are not "limited" to finite numbers of employees doesn't hold up. A car dealership with 5 salesmen cannot magically decide to add another 25 salesmen unless its financial situation changes dramatically, perhaps through the assumption of a great deal of debt. All firms operate with more or less fixed capacity to sustain particular headcounts; NBA teams are not unique in this regard. I look forward to Prof. Berri helping clarify some of this.
Dave, and others, please read the exchange I had with Rodney Fort. He noted several times in that exchange how he was enlightened by it, so it would be helpful for everyone to read the exchange.
I'll read it. Again, no one (I think including Bubba) is trying to be a dick here, but it's no good just talking past each other. But, seriously, people need to take into account the overwhelming impact of the relationship between supply and demand in the NBA labor market; in particular, I reiterate that Patrick's most salient point in the original post was on the bell curve of NBA player productivity. Once you keep in mind the distinction between "wages" and "productivity," I think it will become clear why "replacement level players" are not a rational basis on which to determine the pricing of contracts.
"but it's no good just talking past each other"

Exactly. Which is why you will enjoy the discussion I had with Rodney.


"are not a rational basis on which to determine the pricing of contracts"

That is your theory. But in actual practice, replacment level is exactly how they are being priced by MLB teams and have been in the past. I've tracked the offseason signings every year since... I think 2008... and they've followed it pretty well.

And the only signings that don't match up are those that end up blowing up in the face of the team (e.g., Ryan Howard).

An economist once said that what they do is theoretical, and it only makes sense if it matches the empirical. If you haven't been able to wrap your mind around the idea that the replacement level model corresponds to the behaviour of GMs in MLB, then you should ignore what you think the theory should be and instead create a model that matches reality.

And that's what I've done with Replacement Level. And it's the same model that is used in Fantasy Sports.

As for the bell curve of performance, it's explained thusly:
Marginal productivity (of wins) is clear on a team level; one game between two teams produces one win.

Marginal productivity is not at all clear on an individual level; you cannot simply have one player play more minutes whole holding all else constant, and while you could have one player play less minutes holding all else constant (I.E., putting 4 guys on the floor) I'm comfortable proposing that case doesn't give a particularly useful measure of individual productivity. It just doesn't make sense to model marginal productivity on a player level - teams play basketball games, not individuals.

It's a unit of analysis problem that arises when factors of production cannot be substituted for each other.
It seems like the fundamental issue here is context. Is the goal to maximize wins, to maximize revenue, to maximize profit, or maybe something else? If there's no agreement on that, further discussion is silly.

My understanding - as such - is that the perspective that is usually taken here is to maximize the return (in terms of wins) in exchange for salary cap (not actually money).

For example, it's been suggested by authors here that the Lakers would have done well to amnesty Kobe. The notion of paying a player (especially a very good one) not to play really only makes sense if you consider it in terms of salary cap, rather than wages.

Silver is pretty clear that he's considering wins per salary cap expenditure. The criticism that marginal profit - rather than marginal wins - should be considered seems a bit hypocritical when that's the typical notion here.

> So we can see that the assumption that replacement-level
> players are "free", or even "readily available at the league
> minimum", has essentially no basis in economic theory.

Most NBA teams have a set of substitute players ready to step in when a starter gets injured. If we consider 'replacement level' to the expected performance of a substitute, then it's pretty clear that replacement level players are readily available, and, as far as I am aware, these players are typically paid close to the league minimum.

Naively, we'd expect that the NBA players are (mostly) the best 500 (or so) basketball players in the world. If the population at large is roughly normally distributed in terms of basketball talent, we'd expect that the population NBA players are one of the tails of that distribution. (It seems like the ERA chart in Bradbury's article is closer to what we should expect to see in the NBA: Almost all the best players are already seeing floor time, and we should expect that a 'replacement player' is near the bottom of the league's performance range.

I'm a little confused by the notion of a 'fair contract' too. For example, we can say that all the NBA contracts are made in accordance with the NBA's rules, and are, thus fair. (Fair in the same sense as a 'fair trial'.) On the other hand, the compensation of players isn't linear with marginal revenue or point margin, so the salaries are unfair because they're not commensurate to the players' contributions.

The owners of NBA teams want to (in a generalised order):
1. Signal they are filthy, filthy rich.
2. Have a toy to play with.
3. When it comes to money, they want to increase the value of their asset, e.g. they don't want to make $10 mil a year, they want to double the value of the franchise every few years and earn the capital gains.

Not every owner wants this, but that's pretty much the gist of it.
Of course there are replacement level 'centers' in the D-league. They are called 'shooting guards'. Teams readily substitute shooting guard minutes for center minutes when they don't have a natural center available (or, if you will, they substitute a PF for center, a SF for PF, etc).

Yes, this is way worse than playing even a bad center. It is why bad centers continue to get paid very well - the next best option is terrible.
BPS has made precisely my point. You don't not pay people for the work that "would have been" done by a "replacement." That's just not how this works.

"The idea that NBA teams are "limited" to 15 players in a way that other firms are not "limited" to finite numbers of employees doesn't hold up. A car dealership with 5 salesmen cannot magically decide to add another 25 salesmen unless its financial situation changes dramatically, perhaps through the assumption of a great deal of debt. All firms operate with more or less fixed capacity to sustain particular headcounts"

This to me is not a compelling counterargument. While a car dealership can't magically add another 25 salesmen, it *can* potentially add another 25 salesmen given the right circumstances present them self. That isn't the case in the NBA - roster sizes are arbitrarily restricted, they are not restricted because of a team's financial circumstances, so it is still accurate to say that NBA teams are limited in a way that other firms are not.

The obvious question then is does this difference in restriction matter, and I think it does. Front offices would most certainly add additional players to their roster if they could, but they can't - not because of a cash-flow issue but because of the arbitrary roster limit. I remember reading an article two years ago during "Linsanity" where Daryl Morey was talking about Jeremy Lin, whom he had cut before the season started. He said that he would've loved to had keep him on the roster but he simply couldn't solely because of the roster cap.

Consider a hypothetical financial portfolio that contains 10 investments (investment A, investment B...investment J). You are interested in adding investment K to your portfolio. Now here's the twist - God says you can only hold a maximum of 10 investments. Under normal circumstances you would've added K to your portfolio without thinking twice, but now the cost of adding K has just gone up significantly - not only does K have to be a good investment on its own terms but now it has to be a better investment than A...J. This is the problem that all professional teams face - it is not just a matter of whether or not a player is worthy of being on a roster based solely on his skill level proportional to his salary, but is he worthy of being on the roster over the player that would have to get cut in his place. To solve this problem you have to first decide if this player is unique in the sense that a player of his caliber won't be available when you do have an open roster spot - i.e. is he above "replacement level"?

"While a car dealership can't magically add another 25 salesmen, it *can* potentially add another 25 salesmen given the right circumstances present them self [sic]."

This would only be a material difference if the distinction created an incentive for the car dealership to overpay unproductive employees in the short term in order to expand in the long term. Since no such incentive exists, we can't make arguments by exception to the behavior of NBA teams in this regard. As I said, all firms have to contend with limitations on headcount and consider the productive value of various employees whom they might employ at various prices. In particular, your argument that "front offices would most certainly add additional players to their roster if they could, but they can't - not because of a cash-flow issue but because of the arbitrary roster limit" ignores the fact that total team productivity can grow only logarithmically, even with exponential growth in total payroll, due to the opportunity cost associated with individual players consuming minutes that might go to other players. Since all terms have to contend with market-imposed restrictions on total headcount, the NBA is not a special case. To argue that NBA teams are unique in having to choose between employees within a total limit of compensation that must be expended is to conflate the evaluation of marginal productivity with the pricing of contracts.

All of this says nothing about the basic misconception here that employers do not, or should not, pay employees for work that "would have been done" by a "replacement." If you are a car salesman who can produce 10 sales per month, you will not entertain job offers that dramatically discount your production up to a certain level; you will not, as one poster suggested, agree to be paid the federal minimum wage for your first 2 sales before earning market-determined prices for your final 8. The market pays for absolute production, and labor sellers such as NBA players are in a position to negotiate (within, in the NBA's case, the confines of the CBA) the terms of their employment. If you're a big man with a prospective NBA WP48 of .100 or above, you can demand to be paid for the ten percent of possible wins that you produce for your team, along with any other production you might bring along after that.

There is no such thing as a replacement NBA player.

P.S. Sorry for the long post but several people commented on my comments and I had to respond
Since all *firms* have to contend with market-imposed restrictions on total headcount*

Edits would be super cool.
Again, we are not talking about a market-imposed restriction. In the same way that a salary cap results in players being arbitrarily under-payed in aggregate, a cap on roster size results in players being arbitrarily underemployed in aggregate. The market isn't saying you can't sign a 16th player, it's not that you don't have the money to sign a 16th player, it's not that there isn't a talented enough player to fill that 16th roster spot, God is saying you can't sign a 16th player.
As for your point about the opportunity cost of giving a player minutes, that's irrelevant. The opportunity cost that matters here is whether or not its worth it to give a player the potential to play minutes.
The constraint is not number of players on the roster, but rather, number of players on the court (or field or ice). There are a limited number of jobs. Not just limited, but limited and fixed. This is unlike any of the other industries.

If other industries don't increase their workforce when demand warrants it, new companies will be created to fill in the void. This doesn't happen in pro sports.

Not only that, but the skillset doesn't transfer to other industries.

And all of that gets priced based on the idea that whatever the best free agent player willing to work for the league minimum is the "replacement level" player. Maybe you object to the term and want to create a better term. That's fine.

But you can't deny the existence of reality. You need a theory to fit reality. If you want to propose an alternative theory that explains how players get paid, then propose it.
First, let me say that I don't support the idea of banning anyone for lengthy or allegedly uninformed comments, because I enjoy the variety of opinions here and anyone who doesn't can skip down. Secondly, Tangotiger, it is exciting to see you here and I am a big fan of your work.

Ok, let's say first that a replacement level player is a player whose cost is $507,336 of team funds and functionally $0 of salary cap space (an empty roster spot exerts a $507,336-the rookie minimum-cap hold, so signing a player to a rookie minimum deal does not affect the cap situation). The alternative is to leave roster spots 13, 14 and 15 open, saving $1,522,008 in team funds and $0 in salary cap space. Knowing the cost of a replacement level player, we now need a performance baseline. Here's the baseball estimate ( A team could sign Boban Marjanovic at the replacement level cost, who Arturo's research suggests would be a top 5 NBA player. Obviously looking at the most productive replacement options isn't a good idea. Instead, I suggest we define NBA replacement level by examining the performance of players who have played within $50,000 of the rookie minimum salary AND who no assets were spent to acquire (a second round pick paid the rookie minimum had more spent on him and therefore doesn't fit the definition of replacement). I suspect that these players would be at about 0.010 WP48.

Why is this valuable? Well, if a team pays the 10-year veteran minimum ($1,448,490) for a 0.010 WP48 player, and the player that THEY would have signed internationally, from the UDFA pool, or from the d-league would have produced 0.010 WP48, then that team just wasted $941,154 of team funds (and $0 against the cap if they're over the cap because of the minimum salary exception). The point is that teams should not expend additional assets (funds, cap space, picks, tradable players) to acquire players whose production is equivalent to the production of someone whose price is $507,336 of funds and no other assets.

I think almost everyone would agree with my point in the last paragraph. The disputes come mainly around clarifying replacement level, which I tried to do in the earlier paragraph, and around using replacement level to evaluate real players. A yearly cycle of replacement players (using my previous .010 guess and a flat 2000 MP) would produce 2.1 wins over the course of 5 years and cost $2,720,573. Jimmer Fredette (25 yo, 0.002 WP48), appears poised to produce at about that level, and I would therefore estimate his 5 year value at $2,720,573. A player who would post a 0.015 WP48 over 5 years would be worth 3.1 wins, or 1 WAR, and, going off Arturo's numbers, about an additional $1,946,000. No one thinks that means he should be paid $1,946,000 over 5 years; THAT'S A STRAW MAN. I do think, however, that a team acquiring a 0.015 WP48 player should only give up 1 win's worth of assets instead of 3.1 win's worth.

If we keep expanding this we run into problems like the Gladiator Effect (, which is a major problem with all win-based valuations. However, I do think that WAR can be an effective tool for NBA evaluation, and I think that you were unfair, Patrick, in characterizing WAR as claiming either that replacement level is free or that there are replacement players sitting around ready to be acquired.

You also got sloppy in the last paragraph; as regular readers know and as other commenters have pointed out, most franchises operate at a loss and offset that by appreciating in value. I bet that sale prices and franchise values would be best predicted by wins, even though wins might not correlate to profit. Given that there is a correlation (though weaker since the implementation of the cap floor) between spending and winning, and a correlation between winning and revenue, and profit is essentially spending minus revenue, there is probably no relation between wins and profit.
As an example of who is a replacement level player are all these players who signed a minor league free agent contract (page down a bit):

Endy Chavez might be a good example, but just take an amalgamation of the dozens of players in that list.
Tangotiger, I think we are in agreement in principle, just disagreeing in scope. I think it's a bit too narrow to use the number of players on the court as your constraint. Ultimately the job they are paying them for is not to play but to potentially play, which makes the roster constraint impossible to ignore when pricing a contract.
Nathan: thanks for the kind words. I an enjoying the discussion here.

Thanks for laying out concrete terms and separating your concerns into production, asset cost, and monetary cost.
I'm not saying that the roster size is not a variable at all, especially since players don't play all 48 minutes. At the same time, if the roster size was 30 or 40 or 80 players, and you made the minimum salary 50,000$, then this wouldn't affect the salary of the top players.

The primary variable is that you can't add more players on the court, which is unlike any other business. When those business can generate more profit, they can potentially hire more workers, and the economists here can tell us all about that.

But, what happens when you are prohibited from increasing your workforce and you have the best workforce in the world, and that workforce has no other place to go?

Well, they will get paid one dollar more than the next best worker who wants to join that workforce.

And he will get paid proportionate to his production ABOVE that person who wants to join the workforce.

If an existing economic theory exists to explain all that, great. If it doesn't, then someone should create it, because right now, we're calling it "Replacement Level" theory.

Or if you want, Fantasy Sports.
I agree that factoring in roster size doesn't generally effect the salary of the top players, but the lower you go on the depth chart the more crucial roster size becomes, and this theory can't explain those contracts. And even for top players I would argue that roster size matters, because again, you are paying for potential minutes that have yet to be played, not for minutes that are actually played. NBA players aren't paid by the minute, you have to price in the risk of that player not playing and to do that you need to consider whether or not it's worth the roster spot when that player can't play. I don't think the theory is wrong, just that it is incomplete. It can be made more powerful by expanding the constraint and pushing the underlying reasoning of the theory to its logical conclusion.
No one said it was complete. But it is the best thing we've got right now. I've yet to see anyone propose a better model.

As for roster size: as I said, yes, it all matters. The model is tuned for specific constraints. If the NBA or MLB would suddenly increase the roster size by 10 players, then the model would need to be adjusted.

At the risk of coming off too nitpicky/argumentative (because we're just debating the margins, but since you made the initial effort of pointing out the distinction I feel a need to justify my rationale), if the primary constraint that you're concerned with is the fixed number of players on the court/field/ice, rather than the fixed size of the roster, then I would say that I am proposing a better model.

Imagine two players - one is LeBron James, who has no history of serious injury and has impeccable off the court behavior - your model would do a perfectly fine job of accurately pricing his contract because the risk of injury and/or injury is minimal. Now consider the second player - a LeBron James clone, let's call him "LeClone" that has been in the league for as long as LeBron has and has put up exactly the same stats up until this point. There is only one difference, LeClone has a serious defect. At any given time there is always an x% chance (the actual number doesn't matter for the purpose of this thought experiment) that his entire body will lock down rendering him utterly useless and a literal waste of a roster spot, and a y% chance that his body will revert back to normal (again, at any given time). I would think that a model's whose primary constraint is roster size would be more accurate than a model whose primary constraint is players on the court. To say that the latter is paramount I think misconstrues what a professional athlete's job actually is.
*injury and/or SUSPENSION*

I do agree that an edit button would be nice...
I can't fault NathanLazarus' argument and would like to see a statistical analysis of those minimum players. You could also look at everyone on 10-day contracts.
I do not think we should take into consideration the profitability of any team. we should be trying to predict the cost of a win not the return on investment for buying a win (which varies wildly by club). as such I think the 76ers example is poor.

I find it interesting how, what you are actually trying to calculate is, how much is the market incentive perverted by the league regulation. this has major real world application.

id suggest that where Nate Silver's formula really falls of the table is in the case of bigmen. good luck finding a "replacement level" big. my guess and i say guess as I have not looked at D league numbers is that there just might be a replacement level guard (maybe). but as we get larger and closer to the basket and the talent pool shrinks more rapidly, the replacement level player idea will start to show a major flaw in that these bigs required simply do not exist.
I find this post to be somewhat boring. I don't know, maybe that's just my opinion. I was hoping you would make an analysis-type of post detailing how teams would look in the 2014-2015 season(given the recent trade rumors). Especially the Miami Cavaliers.
Patrick: Based on your comments about the 76ers, I don't think you actually disagree with the concept of replacement level all that much, at least as a description of what teams actually do. You say the 76ers were a 19-win team, and essentially paid their players league-minimum salaries. That's perfectly in sync with the idea of replacement level. If Dr. Berri's analysis were correct, then a 19-win collection of players should have a payroll of almost half the league average, over $30 million (since it wins nearly half as many games as an average team). But it seems pretty clear that a 16-19 win team can be assembled for far less than that, as in the case of the 76ers.

Perhaps such teams "should" pay their players more, as you suggest. But it does not appear that there is enough demand for such players to make that happen in practice....
If you're using a replacement level model you don't calculate a single WP48 value as 'replacement level' for all positions. WP48 is essentially 'wins against average' at each position, with average being 0.100. If you want 'wins against replacement', you calibrate it differently; and since the difference between a replacement level and league average player at each position is different, you have to calibrate them all independently.

So, yes, a league average center will have a higher wins against replacement than a league average shooting guard. That's consistent with our intuition and how contracts are actually handed out, yes?
BPS, that's correct. Just as WP uses an average at each position, WAR (or whatever we want to call it's equivalent for basketball) would have to do the same. If a "replacement level" point guard has a WP48 of .050 and a "replacement level" center has a WP48 of -.050, this is going to make a .200WP48 center more valuable than a .200WP48 point guard. Because no matter how hard it is to find centers, you can find them somewhere. And if they are worse, you adjust your baseline accordingly.
The problem i see with using a replacement player as a metric is that comparing an average player to "replacement" level will necessarily not being comparing equal minutes.

is it really feasible to compare say Beverly who played 1751 minutes at a very near average .107 wp48. to say A.J. Price... who barely made his roster(the definition of replacement level.) and played all of 99 minutes at -.111 wp48

by this metric we would say we should compare Beverly to having A.J. Price X17 on your team. so are we supposed to compare him to this replacement level player or the added minutes that the closer to average players will necessarily have to play to make up the 1751 minutes that Beverly played?

if we compare him to an AJ price that plays the same number of minutes are we just assuming that the team in question is attempting to lose? And, if that is the case, how can i apply that to the real world at all?
at some point if a team replaces their roster with what some here are calling replacement level players... ... the team wins zero games.
I don't follow NBA, but I wouldn't want to presume a single player is representative of the class of players that would play for the league minimum as a free agent.

That said, a team of such players would probably have a team win% of .100 or something. It wouldn't be zero. It might be zero in the NFL though.

Anyway, if it is .100, that sets the replacement level at -.080 wins relative to average per 48 player minutes.

And be careful about using "observed" wins per 48 minutes. That's not the same thing as true talent wins.
TangoTiger, if i cant use observed wins where should i draw my numbers from, and more importantly where are you drawing yours. observed wins may be flawed, but "observed talent" most certainly is.

where are you getting this .1 win percentage from? If i put a top line team together from any D League roster i am likely to get a team that is gonna have major trouble protecting the rim, and be at best inadequate from all other spots.

my point with AJ price and a starter like beverly was simply that the players we are talking about are usually played many many fewer minutes than average players. who are usually starters or rotation players. any minute played has to come from somewhere.. so it makes no sense to compare say Lebrons value to a bad forward that plays 1/20th the minutes , we should be comparing them both to the league average first and then if we want to compare dollar value we should compare their salaries to their performance relative the average. this is the natural way to do this. trying to fit the value of a player against an abstract concept which in practice will clearly create a flawed team (in a basketball sense not ina talent sense) is backwards.
@Shilelea - I don't mean to speak for Tango, but I believe his "observed wins" point is just about regression to the mean. The worst observed performance in MLB or the NBA is going to be a very bad player where we also saw their 5th percentile of performance. The same goes on the top end - it's why no mainstream MLB projection system projects above 40 HRs for anyone. The 40 HR guys are the best hitters who also "got lucky" (or whatever else you want to call it apart from repeatable talent).

Calculating NBA replacement level is much harder than MLB, and it's possible than an NBA replacement level team would be much worse than most people think. Pelton's WARP stat for instance picks a 10 win team as replacement level (, but it's possible to imagine this is too high or too low. This doesn't really address the existence or salience replacement level performance however - it may just be possible that replacement level in the NBA is indistinguishable from 0 (although I do not believe this to be the case).
Actually, the way I do the comparison IS to compare to the average first. THEN, I make the adjustment between average and replacement level.

We compare to the average because we know what the average performance is, and we also know how much the average player gets paid.

We also know how much the league minimum is, and we can make a pretty good estimate as to the talent level of those players.

Yes, we get "true talent" wins by regressing "observed" wins. A player who has below average observed wins is LIKELY to have received more bad breaks than good breaks, and so, we need to regress those observations.

If you can check your resistance at the door, you'll find it much more enjoyable to get on Replacement Level Expressway.
Except, In the NBA almost all observed statistics can be explained by the season before. (baseball and ice hockey make far more sense to start regressing data to the mean)

You guys have still not addressed this seeming non existant talent pool you are talking about.

Basketball is not so plug and play as baseball is, as substitutions are more free flowing. replacing a slightly below average player with a player worthy of the league minimum will most likely cause more time on the floor for other players on the roster not our replacement.

how is adjusting our salary for what we can get for minimum dollar going to make our predictions more accurate when, we have no way to calculate how good or bad these players actually are at the NBA level?

also this check your resistance at the door and trust us comment, makes me think you are in some sort of cult.
I said to check your resistance at the door because your responses seem to be that you will shoot down everything I am saying. So, I am getting to the point that I have moved this discussion forward as much as I can.

So, let's take a step back if you are willing and see if we can agree on the basics. The theory is that talent follows this:

Do you agree with this?
talent level is a measure of what exactly? I am not familiar with this metric.

I assume you have set .99 to be your "theoretical replacement level player"?
if that is the case talent level is based on what underlying stat?
Many teams made money because of the massive luxury tax paid by the Nets. (~$80 million). The owner of the Nets made money because of the deals involved with moving the team to Brooklyn.
Posting on behalf of Tangotiger:


“From Tangotiger: I can’t post to this blog from the office during the day, so I asked a reader to post this in my place.

Talent is just some non-descript number to facilitate the illustration. In this PARTICULAR illustration, the value of “1.00” was set to describe an average MLB player, with all MLB players in the 0.80 to 2.00+ range. But the number itself doesn’t have to mean anything real (for now).”
if the crux of the lets just use wins produced per dollar argument is this? "the talent pool is actually top heavy" wouldn't it make sense to measure actual player performance in terms of some sort of wins metric. I assume that this is where your graph is going, and i'll be curious to see where the measured talent pool lies and also if the assumption that it looks the same for every sport lies true. to me this would be less important however than using WARP to predict change in wins and see how closely it follows actual measured success. The problem with this is that we know that the success of prediction is going to closely mirror the reliability of the underlying metric or metrics used to predict real value which really has little to do with whether or not we adjust for a replacement player constant.

either way should, if the underlying assumptions about what causes wins are correct, expose bad contracts relative to their position. so the question i have is whether or not our replacement contract is necessary or even damaging in the case of comparing value cross position.
Shilelea, I believe it's necessary for comparing cross position because even if you use a metric like Wins Produced which measures against average production at the position, you need to know how bad the replacement level player at the position is to price the contract. For example, say an average center produces 5 wins per 2,000 minutes and an average point guard produces 5 wins per 2,000 minutes. But say there are "replacement level" point guards available out there who can produce at a level of 2 wins per 2,000 minutes, while the "replacement level" centers available would produce 0 wins per minute. This leads us to value (and pay) the average center more than the average point guard. Due to their scarcity (as a few people have oddly pointed to in an argument AGAINST replacement level valuation), centers in this example become more valuable and we should see them paid accordingly.

As Tango has pointed out, this become obvious in fantasy sports. It is why Quarterbacks are generally not taken in the first round of fantasy football drafts despite scoring the most points in most formats.

Excellent explanation, as well as the example with the Fantasy QB.
In fantasy football typically the you have far far fewer participants than in the league itself, meaning that viable replacement options actually do exist. If there were say a 40 man fantasy league I suspect you would see the QB position filling first. As suddenly there is no longer a bunch of average talent available at replacement. in that case the difference is between having one and not having one. This is how basketball is with regard to rim protectors, there is no replacement, typically as i think someone else here pointed out a bigless team makes an undersized forward play center, and a Small forward try to play Forward and then they play an extra wing The problem here is now your all star forward isnt a forward anymore, hes a bad center.

It'd be akin to baseball having like 60 people in the world capable of pitching at the ML level and letting the first basemen take over the extra pitching duties, and then adjusting every pitching contract based on the price of a replacement level 1st baseman.
Dave Berri's description for question #5 here is perfect. It's exactly what we've been talking about in baseball circles.
can we agree that the accuracy of wins over replacement is simply going to mimic the accuracy of whatever your metric is in comparing wins across a specific position.

we can also agree I assume that wins at certain talent levels probably do not follow a linear dollar curve (especially when we consider salary caps and minimums. not to mention artificially low rookie contracts, that further confound the difficulty of zeroing in on the win production of a minimum wage player.)

where we dont agree i guess is that I do not think that comparing a player to the minimum will be in any way more accurate than comparing them to the average, and in cases where the minimum is playing out of position or going without the comparison could unintentionally create a flawed metric.

it could be that my assumption on there being a gross shortage of talent is flawed.
can we agree that the accuracy of wins over replacement is simply going to mimic the accuracy of whatever your metric is in comparing wins across a specific position.

we can also agree I assume that wins at certain talent levels probably do not follow a linear dollar curve (especially when we consider salary caps and minimums. not to mention artificially low rookie contracts, that further confound the difficulty of zeroing in on the win production of a minimum wage player.)

where we dont agree i guess is that I do not think that comparing a player to the minimum will be in any way more accurate than comparing them to the average, and in cases where the minimum is playing out of position or going without the comparison could unintentionally create a flawed metric.

it could be that my assumption on there being a gross shortage of talent is flawed.
my last post is missing punctuation in a couple key areas, it should read. "and in cases where the minimum is playing out of position or going without, the comparison could unintentionally create a flawed metric. "
I'll respond based on my knowledge of MLB and NHL, as I don't follow the economic structure of NBA.

1. I haven't discussed the method of calculating wins, just that *once you have that*, then you'd use the WAR framework.

2. No, if you follow it logically, the wins to dollar conversion must be linear, if and only if, you use the WAR framework. I've had dozens of these discussions. I'm not going to rehash it here. Feel free to search my blog. Or you can work it out yourself.

3. Yes, obviously CBA-imposed restrictions on rookies, arb-eligible players, etc adds a variable. We can handle that within the framework of WAR to dollar conversions by applying multipliers for players at each service level.

4. If you create a logical rational method of establishing positional adjustments, then we won't have an issue. In baseball for example, we compare a SS to the average SS and a 1B to the average 1B, and then apply a positional adjustment to put SS and 1B on the same scale. So, we can get to the point you want.

Indeed, I would say that if someone were to pay you to create a framework, you would come up with the WAR framework yourself, one that handles all the variables you are bringing up. Try it! I'm sure you'll succeed.
Tangotiger! I'm a fan, have been a regular lurker on your blog for years. Not a commenter before this, but happy to see you here, another blog I love:

Couldn't the problem be that you aren't understanding how replacement value in the nba works? You are arguing for replacement value, and they are arguing that replacement level players don't exist. Or, that by wp48, replacement level for individuals who earn the minimum is so wildly divergent that it's insane. The nba is different than the mlb!
On my blog, I'm trying to come up with a FIRST step as to what is a replacement-level player. Again, as a first step, I took the 241 players with the most minutes or the 241 players with the most minutes/game. If they qualify in either, I put that as part of the "regular" group. That gives me 270 players. The other 200+ players that played would be considered the "replacement level" group.

Now obviously, when you have 200+ players, you will find some exceptions of guys that maybe shouldn't belong in there, but we're trying to use empirical data here to come up with some tangible illustrations. I would hope that 90% of the players in that group you guys could all agree are guys on the bubble.

If all players were free agents, the argument would be that those 200+ players would each earn under 1 million$. So, a team that wanted to just field warm bodies would let the other 270 players go, and just select randomly from this pool of 200+ players. And this would cost them 10 million$.

Now, I understand there are salary floor considerations, etc. That's an extra step to add to the process, but it doesn't invalidate the basic idea.
Whoa! TangoTiger! You blew my mind!
A positional adjustment where we compare players against other player at their position? That's genius that is.

I wonder why Dave Berri never thought of it while writing Wages of Wins or Dean Oliver while writing Basketball on Paper.


Let me quote The Basics ( at you:
"The Basics
All articles use Wins Produced and WP48 [Wins Produced per 48 minutes] to evaluate player’s performance.* This measure uses three key components to evaluate a player:
The player’s per minute box score statistics
The player’s team’s per minute box score statistics
The average performance at the player’s position (PG, SG, SF, PF or C)
A full explanation can be found here. To give a general scale, an average player has a WP48 score of 0.100. The very best players in the league usually have a WP48 over 0.300. To put this in perspective; an average player who plays a full season at 40 minutes a game would generate around 6.83 wins for their team. In contrast, a player posting a 0.300 WP48 would generate about 20.5 wins at 40 minutes a game over an 82 game season."

Arturo, Patrick, Dre: in case you can't be bothered to read Tangotiger's blog, the current argument there is that an NBA team entirely composed of dudes who had 10-day contracts last yearcould win on average 14-15 games (, scroll down to bottom of comments). Care to comment on that, using your own data?
Arturo, thank you for providing this reminder that Wins Produced -- Professor Berri's measure of marginal product in the NBA -- relies on comparing a player's productivity to that of an average player (and then adding a constant). But now we have a contradiction: Prof. Berri says in his post "In calculating marginal product, we simply look at what the additional worker adds to the firm’s output. WAR, though, does not take this approach. WAR is a player’s production of wins minus a replacement player’s production of wins. But this is not how we measure marginal productivity." It would be just as true to say that marginal productivity is not usually measured by comparing a worker's production to that of an *average* worker -- and yet that is exactly what Berri does in calculating WP.

WP thus compares a player to the productivity of a player who is exactly .100 wins per 48 worse than an average player. Those arguing for replacement level are using a slightly higher benchmark. But conceptually, the two approaches are identical (as Nate has tried to point out). In neither case is a player simply "added to the firm," but rather is compared to the production of a hypothetical alternative. Claiming that replacement-level metrics somehow violate the teachings of labor economics, while Wins Produced does not, is just inane.
Arturo, Guy is right on that point, WP and a WAR model based on WP are in concept the same.

I do not think that evaluating a roster based on a WAR model will yield any better results than simply a WP model. (if i subtact 5 from X=Y i get X-5= Y a line with same slope.) In contract evaluation i would venture to say that unless there is such a shortage of bigs that the theoretical replacement player has to be placed really low in relation to others, the two are gonna mimic one another. Whether or not it makes sense to use either metric for contract evaluation is irrelevant to this claim.

This being said i find it dubious to say that we can even measure a replacement player or that as a concept it makes sense to assume that you can get any level of production on average from a replacement. The Chaotic nature of the bottom producers in the NBA makes any such evaluation as to what the value of a replacement is extremely limited.
Long time. Actually, It's a bit different (I feel like we've had this conversation before). Wins Shares compares every player against average performance and assumes a team of average performers gets you to win half your games (Dean does some leveling of the stats to get everyone's value to line up) . Wins Produced makes the same assumption about average player but sets up the comparison by the five classic roles on the floor.

Both are very good linear assumptions and in fact deeper studies I've done suggest that the values for players in reality line up to what the linear assumption is.

My own POP48 is meaner and looks at how much a player is better than his average opponent (which of course is how all the Plus/Minus measures judge this).

Actually, you can choose to set your reference to what ever you want. Some Blogger did it for Wins Produced four years ago

There's even another guy in the comment section ;-)

It's funny to me because I'm actually quite friendly to alternate takes on the models. I just find that in general the linear assumption (adjusted for role either thru coefficients or thru construction) is perfectly fine. As long as you remember that basketball is about the short supply of tall people.

I'll point you to this table from the draft model:

The implication (and again the research) suggests that there is a significant pool of NBA level talent. I'd think you get much closer to 41 wins with some effort and a minor league strategy. In the first year.
I also wanted to mention, you know who also used replacement level players?
Arturo said:
"Whoa! TangoTiger! You blew my mind!
A positional adjustment where we compare players against other player at their position? That's genius that is. "

What I actually had said:
" In baseball for example, we compare a SS to the average SS and a 1B to the average 1B, [b]and then apply a positional adjustment to put SS and 1B on the same scale[/b]. "

The key part is the second half of that. That is, while it's obvious to compare to a particular position or role, the more important part is how to align those roles along the same scale.

Pete Palmer in The Hidden Game presumed that each position is equally valuable, and so ensured that the average LF = average SS. It's was an assumption. One that doesn't work.

However, I reasoned otherwise. And putting players of different positions and roles along the same scale is an important step.

I don't know how it's handled in basketball analysis, but this is an important consideration to address, if it hasn't.

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