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!