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December 22, 2009
The Real Curse
Supply, Demand, and Pricing
When is it a bad thing for a baseball team to win? On the field, of course, it never is. An extra-inning win may leave you with an overworked pen, for instance, but it's still better than having an overworked pen and losing. But when it comes to acquiring baseball talent, it is possible to lose by winning—something that economists call the "winner's curse." What we mean by winning in this case is having the winning bid for a player's services.
Of course, we don't often think of teams as being bidders. When we talk about the free agents market, we often talk about it as though teams are shopping for players on the open market—sellers set a price for their goods, buyers buy X quantity of goods based upon their reservation price, sellers adjust their price accordingly until they have maximized profit. There are certain qualities of that kind of a market that make it function properly.
Think about when you want to buy a car: when you go down to your local car lot, they have a variety of makes and models, all of which are to some extent or another a substitute for the other. Sure, a pickup truck and a sports car tend to appeal to different buyers, but both will get you to work; there are plenty of both besides. It's pretty easy for you to get an idea of what the car is worth. You can go to other car dealerships and see what they're selling similar cars for, and you can get a guidebook that will tell you the market value of almost any used car available based upon its condition. And everyone out there has access to the same resources to figure out what a car is worth. Each car has a roughly common value to everyone in the market for a car. That means each car is "worth" about the same to everyone, either as a trade-in, to resell it or simply to drive it.
Because these things are true, we can apply something called the "fundamental theorem of exchange," which states that people are likely to make an exchange that benefits both parties. Otherwise, why would both sides agree to a deal? If this were true in the market for baseball players, we would expect to see teams and players both mutually benefit from free agency. But how well does that reflect the reality we see?
So far this offseason we've seen the Mariners kick in a net $6 million to trade Carlos Silva to the Cubs for Milton Bradley. The Dodgers sent $10.5 million to the White Sox to unload Juan Pierre. The Blue Jays sent $6 million to the Phillies along with Roy Halladay. And none of that tops the August deal where the White Sox assumed over $61 million of Alex Rios's contact and the Blue Jays got nothing in return (except for the salary relief, of course—a lot of it). These are of course just the contracts that teams can get rid of, though. As much as they might like to, the Blue Jays are not going to be able to trade Vernon Wells. The Cubs can't get rid of Alfonso Soriano. No team will offer to take Barry Zito off the Giants' hands.
This raises the question: Why would teams sign players to these sorts of deals, if they are good at evaluating baseball talent and are rational actors? (And yes, we do think that MLB teams are pretty good at evaluating baseball talent, despite what you may occasionally hear on talk radio.) Simply put, the market for baseball players isn't much like the market for cars at all. It differs in some pretty significant respects:
Because of this, the market for baseball players seems to more closely resemble a sealed-bid auction than it does a market. Since the person who wins that sort of auction is typically the person with the largest bid, it stands to reason that the person who "wins" is in fact the person who overbids. This doesn't have to be the case, of course, but there is a tendency for things to behave this way.
This doesn't require you to be bad at evaluating players on the whole. But forecasting baseball players is at best imperfect, so anyone—even a major-league team, which has both the most resources and the greatest incentive to get it right—will be wrong at least some of the time. As it turns out, when you make those mistakes in a player's favor, those are the times you're most likely to actually sign that player. It's difficult for us to quantify how exactly this impacts the market for free agents—remember, most dollar-value estimates of a baseball player's worth are based upon actual free-agent salaries. So if the market is distorted, the model won't be able to figure that out.
There are ways to figure out a player's value without looking at other free-agent salaries, typically through a marginal revenue product model , where you compute the dollar value of a win to a team and go from there. This approach is fraught with problems as well. First, we lack a lot of information about team finances that would be useful to know in such an analysis, and second, there is the problem that not all wins are created equal from a marginal revenue standpoint. As a result, you have to figure out a baseline for comparison; economist Andrew Zimbalist, for instance, in his book Baseball and Billions, figured marginal revenue products compared to the average player. But then you're left trying to figure out the MRP of an average baseball player. I don't honestly think that we're at a point where we can firmly attribute differences between an MRP model and observed salaries to an actual cause rather than a problem with model specification.
So let's speak more broadly about the issue for a moment. Teams can account for the effect of the winner's curse and account for it in their bidding for free agents. Let's go ahead and suppose for a minute that some teams do, and some teams don't. (I think that's a reasonable theory, although certainly not the only one available. At this point it doesn't matter much either way, because it helps us to illustrate useful principles.)
The teams that do would seem to clearly benefit from the actions of those teams that don't, right? Sure, except that free-agent contracts are used as guidelines to set appropriate salaries for players in arbitration. If you ever wanted to know why the Pirates would non-tender Matt Capps, that's why: every time some other team signs a short reliever to an inflated contract, its more money you have to pay to hold on to your own guys. (And if you've ever wondered why your team refuses to offer such-and-such departing free agent arbitration… yeah, that's probably part of it as well.) Plus, you see the prices get driven up on free agents in general, making it more expensive for you to sign guys you do like but have appropriately valued.
So how do you prevent other teams from suffering the winner's curse? Realistically, you have two options. The first is one that the Player's Association would probably file (and win) a grievance over, because it's essentially collusion. If you end the information asymmetry—in effect, having teams tell each other what free agent offers they're making and at what price—you would tend to see a reduction in the offers made to free agents. Because of what happened the last time the industry tried to do that unilaterally, during the '80s, and the $280 million penalty they agreed to pay to settle the matter, let's just assume that this isn't an option.
The other solution would be to make more players free agents. By having more free agents, you would see an increase in the number of close substitutes available, and you would have more comparable players being signed in order to establish a player's market rate. In many ways, teams may be hurting themselves financially by keeping so many players off the market, either by signing long-term deals or by controlling a player's rights for six years prior to free agency. A market where all players were free agents every offseason could be cheaper for teams.