Replacement players, VORP, salaries, and MRP

In a post on his blog, J.C. Bradbury argues, again, that a player's free-agent player salary is equal to his "MRP," which means "marginal value of production." That is, a player should be paid exactly the amount by which his performance increases the team's revenue.

And he seems to think that revenue is exactly proportional to the player's performance, rather than the player's performance as measured against replacement level. Because of that, he dismisses the concept of replacement value (and VORP). But I don't understand why he would do that.

The idea behind MRP is this: the more employees you hire, the less each one contributes to the bottom line. If you're running a Wal-Mart, you might want ten cashiers. If you hire an eleventh cashier, it might help a little bit: if there's a crowd of customers, fewer might leave the store if the lineups are shorter. But the eleventh is only useful in busy times, so he's worth less than the other 10.

The idea is this: suppose cashiers earn $30,000 a year. The first five or six might bring the company $70,000 in revenue each. The seventh might bring in only $60K. The eighth adds $50K, the ninth $40K, the tenth $30K, and the eleventh $20K. The eleventh cashier is actually losing the company money, so she never gets hired in the first place. And the last cashier hired brought in $30,000, which exactly matches his salary. Thus the equivalence: salary = MRP.

That works for Wal-Mart, but not for baseball. Why? Because in baseball, the number of employees is fixed, and so is the minimum salary. At Wal-Mart, if you have 11 cashiers, you figure that the 11th costs $30,000 but is bringing in only $20,000 in revenue. So you fire him. In baseball, you might figure that you're paying the 25th man $390,000, but he's contributing nothing to the bottom line (because he gets no playing time). So you want to release him. But you can't – there's a rule requiring you to have 25 men on your roster. And there's a minimum salary of $390,000. So you're stuck. In this case, the MRP of the 25th man is less than his salary.

It can work the other way around, too. Suppose you're a big-market team with lots of fans who love to win, and you figure that a 25th man, while costing only $390,000, is bringing in revenues of over a million. You'd like to hire a 26th player, who would bring in another $900,000 or so. But, unlike Wal-Mart, you can't go hiring that extra player. There are rules against that. In that case, the 25th man is earning less than his MRP.

So, in baseball, a player's salary could easily be more, or less, than his MRP.

The real-world equivalence between salary and MRP is

Salary = MRP

But that's a special case that just happens to apply to Wal-Mart. I would argue that the more general equivalence is

Salary over and above the alternative = MRP over and above the alternative

At Wal-Mart, the alternative is "nobody" – you just never hire the 11th cashier. That alternative has zero salary and zero MRP, so the second equation collapses into the first equation. But in baseball, the alternative is NEVER "nobody" – you have to fill the roster spot, whether you want to or not. The alternative is a player at minimum salary, creating a replacement-level MRP. It's one of the many freely available minor-leaguers. That means

Salary over and above the $390,000 minimum = MRP over replacement player

If you choose to define "VORP" in terms of dollars instead of runs, you get

Salary - $390,000 = VORP

Which, I think, is what's really happening in baseball.

J.C. doesn't agree with that formulation – he wants to stick with "salary = MRP". He wants to value marginal runs from zero, rather than from replacement value. But, I argue, that clearly leads to untenable conclusions.

For instance, suppose a marginal win is worth $5 million. Then a marginal run is worth about $500,000.

Suppose a replacement-level player creates 39 runs. At $50,000 per run, you'd expect him to cost $19.5 million. But you can pick up any one of these guys for $390,000! So "salary = MRP" just doesn't make sense.

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If you don't buy that argument, here's another one. Suppose you really, truly believe that a player earns his MRP. And suppose the 25th guy on your roster earns $390,000, the MLB minimum.

Now, halfway through the season, the union and MLB agree to double the minimum salary. The 25th guy gets to keep his job – after all, the team has to have 25 guys, and this is still the best one available. But now he's making $780,000.

His salary doubled, but his MRP, obviously, is exactly the same! So even if his salary was equal to MRP before, it certainly isn't now. Which means that there's no reason to have expected them to be equal in the first place.

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One of J.C.'s arguments is that not all replacement-level players are worth only $390,000. It could be that all the players eligible for the minimum are young draft choices, and you don't want to use up their "slave" years if your season is a lost cause – you'd rather save them for when your team is a contender. In that case, you might have to sign a replacement-level veteran for $1,000,000 or so.

To which I say: there is no shortage of mediocre veterans who can be had for $390K, that you would have to spend a million. If you DO spend a million, it's probably because you peg the veteran as better than replacement. The extra $610,000 is worth it if you expect about 12 1.2 runs better than replacement over a full season, which isn't a lot.

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By the way, you could argue that a player is never paid less than his MRP. In a sense, even if the 25th guy on your roster never bats, his presence contributes more than $390,000. That's because if you released him, and didn't call anyone up, the commissioner would fine you a lot more than $390,000.

But that's a trick technicality, and it's not what J.C. is arguing here.

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Finally, I am puzzled by J.C.'s dislike of VORP because, according to him, it's an insider term and hard to explain:

The big advantage of these is that I can have these conversations with people other than die-hard stat-heads ... I view VORP as an insider language, and by using it you can signal that you are insider. It’s like speaking Klingon at a Star Trek convention. I can signal to others who speak the language that I am one of you. But, the danger of VORP is that once you bring it up the discussion goes down the wrong path as the uninitiated have reason to feel they are being told they are not as smart as the person making the argument. It’s like constantly bringing up the fact that you only listen to NPR or watch the BBC news at dinner parties. The response is likely going to be the same, “well fuck you too, you pretentious asshole!”

But, as I think a commenter on J.C's site points out, "MRP" is also pretty jargon-y insider economist talk, isn't it? And it's a lot hard to explain than VORP. So I'm a bit confused by J.C.'s aversion to the term. How come sabermetric abbreviations are pompous, but economics abbreviations are not?

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See also Tom Tango's comments, here.