Valuing wins

Baseball Prospectus' Matt Swartz posted a fantastic article this week on the valuation of player contracts in Major League Baseball:

If baseball free agents were in a typical, perfectly competitive market like those you see in the first chapter of your introductory economics textbooks, the price per win would have to be linear. Basic economic theory of perfectly competitive markets would say that anything other than the same price for all wins would create arbitrage opportunities where teams could perpetually trade their way to the top of the league.

Later on:

In the case of baseball free agents, there are two main reasons why the baseline’s assumptions don’t apply. First, these markets aren't thick enough that teams can sign and trade players so easily and quickly swap out players for others like investors can do with shares of Microsoft. There are only so many teams, and there are limits to making this kind of move in general. Second, you can't employ 60 Garret Andersons on a team and suddenly become the best team in baseball. There are only 25 roster spots, and only so many players can realistically get enough playing time to realize their true value.

This a subject that I've given a lot of thought lately, to the point where I may actually do some original research on the matter in the near future.

In any case, my intuition is that teams should pay disproportionately more for a seven win player than a five win, three win, or one win player. I have a hard time seeing a team trading Alex Rodriguez for ten or twelve players barely above replacement level unless they are also saving money in the deal. I think Matt's reasoning is spot on: there are only twenty-five roster spots. You can't show up with sixty one WAR players and expect to make the playoffs.

That being said, I think there are really two questions here:

1. What do teams pay for wins?
2. What should teams pay for wins?

Any approach that uses existing contracts as its basis, like Matt's, is going to end up answering question number one. I'm really more interested in question number two. Unfortunately, answering question number one is much easier: we have a whole lot of data on how players performed (and how they were expected to perform) and what they were paid. The question is essentially positive. Question number two is a normative question that involves a variety of assumptions about why teams pay players. I'm not going to delve into those here.

I'm not sure if Matt's article is subscriber only or not, but if it isn't, it is worth your time.

Twenty-five days until pitchers and catchers report!

**EDIT** I had originally misspelled Matt's last name. I've fixed that.