Baseball free agency and the winner's curse
The so-called “winner’s curse” is a phenomenon that affects the most common type of auctions where, it is frequently observed, winning bidders tend to overbid. This overpricing substantially reduces the bidders’ winnings below the levels predicted by game theory, often leading to losses rather than profits.
The concept of a “winner’s curse” was first documented in the early 1970s when three petroleum engineers looked back at historical data and observed low financial returns for successful bidders in auctions of oil and drilling rights in the Gulf of Mexico.1 The premise was that the winners—the one(s) who most overestimated true value—were “cursed” by paying too much for the leases. It’s a concept that continues to be prevalent today in everything from wireless spectrum auctions to corporate takeovers. But does it also apply to sports salaries, and specifically to baseball’s free agency market?
If you think about the way baseball free agency is set up—veteran players offer their services to the highest bidding team—it’s a classic auction-type scenario. And while it’s easy to recognize the extreme cases of owners overpaying free agent players (e.g., Kevin Brown receiving $105 million from the Dodgers for a seven-year contract in 1998; Denny Neagle netting $51 million from the Rockies for a five-year contract in 2001, and Albert Belle’s $65 million, five-year Orioles deal in 1999, just to name a few), it leads us to ask the question: Does the “winner’s curse” also apply to baseball’s free agency marketplace?
But before we get to the analysis, let’s review a bit of history. Up to the mid-1970s, Major League Baseball players could only sign contracts with their current team; the only way a player could negotiate with another team was to be either released or traded. There was what was called a “reserve clause” in each player’s contract that bound a player to a single team for a long period, even if the individual contracts he signed nominally covered only one season. While players had been challenging the reserve clause in baseball contracts for years, it wasn’t until 1975 that they achieved a breakthrough. Two players—Andy Messersmith and Dave McNally—refused to sign contracts, and then played through the 1975 season with the hope that they would then be free to sign as “free agents” with any team the following year. The owners objected and the case went to arbitration.
Arbitrator Peter Seitz eventually ruled for the two players. His rationale was that since the reserve clause language contained within players’ baseball contracts did not explicitly state that it could be applied to a season in which the athletes played without a signed contract, the reserve clause was then extended for one season and not in perpetuity. After a lengthy court battle and subsequent lockout by the owners, both sides came to an agreement over the rules governing free agency.
Today, players can apply for free agency after six years in the major leagues. Those with more than two but fewer than six years’ playing time can ask for salary arbitration in cases where a contract agreement can’t be reached. Only players in their first two years are subject to total contract control by the owners—although the collective bargaining agreement sets minimum salaries for those players.
So let’s get back to the original question. When a player hits free agency and essentially auctions his services to the owner, do these types of auctions exhibit similar “winner’s curse” results? According to extensive academic research performed over the past 20 years, the evidence is mixed, depending on how player performance (value) is quantified.
One way to look at the question is to use some of the more traditional measures of player performance. For everyone but pitchers, these include on-base percentage (OBP), battling average (AVG) and slugging percentage (SLG). While it’s quite easy to compare a free agency subset against the much larger sample of all major league hitters in terms of relative performance, factoring in the winning bid price (salary) for free agency players vs. the average salary of the larger sample makes the analysis much more difficult.
For pitchers, it becomes even more difficult to answer the question, given that the more popular pitching statistics (wins, losses and earned run averages, or ERAs) are dependent to a large extent on the overall quality of the team and the defensive capabilities of their teammates on the field when pitching. And as with the non-pitcher free agency analysis, adding the additional variable of salary makes the analysis even that more difficult.
So if examining individual statistics of free agency players doesn’t seem to shed much light on the question, what does?
Rather than looking at the question from an individual statistical reference, perhaps it’s better to look at it from a bidder’s perspective. The owners—the active participants in these free agency auctions—don’t really care about individual statistics. Sure, it’s nice to have your new free agent look good statistically, but that alone doesn’t guarantee investment success. So maybe the analysis needs to look at how that winning bid incrementally affects bottom-line results. A dollars-in (salary) compared to dollars-out (marginal return on the player’s performance) analysis seems to make the most sense.
Fortunately, a couple of smart economists from Loyola College in Maryland looked at the question from just that perspective. In a paper published in 2007, titled The Existence and Persistence of a Winner’s Curse: New Evidence from the (Baseball) Field, 2 authors John D. Burger and Stephen J.K. Walters examined the vast amount of player and team data and then created a refined measure for an existing term used to describe a player’s contribution. This term—marginal revenue products (MRP)—describes an estimate of a player’s marginal contribution to team revenue.
The process for estimating the MRP involves two steps: (1) econometrically estimating the relationship between a team’s output of wins (which may be a proxy for the quality of the spectacle fans are consuming) and its revenue in order to obtain the marginal revenue associated with each extra win, then (2) multiplying this by the player’s marginal output of wins. 3
One aspect that became obvious from the research was that the size of the team’s market directly affected the size of a player’s marginal contribution. In essence, what the research showed was that the marginal value per win for large-market teams (New York Yankees, Los Angeles Dodgers, etc.) was far greater than that for small-market teams (Kansas City Royals, Pittsburgh Pirates, etc.). In fact, the failure to recognize this relationship was a major deficiency in most previous studies.
Additionally, the research verified previous findings that owners consistently failed to discount the negative effect of inconsistent performance (i.e., in a free agent’s recent performance, inconsistent years—one great year sandwiched between two mediocre years was valued pretty much the same as three consistently good years). This variance constitutes risk—something the owners failed to factor into their bids. Here’s what Burger and Walters had to say:
Despite two decades of experience making large bets on outcomes in the free agent market, winning bidders continued to fail to discount their bids for inconsistency/risk. What is more, small-city teams failed to limit their bids to levels consistent with players’ MRPs in their markets; teams in below-median-sized markets actually lost money, on average, on the contracts they signed. 4
The discrepancy in the marginal revenue associated with each extra win between large- and small-market teams is significant. For example, the authors estimated that the marginal revenue associated with a win by a large-market team (e.g., New York Yankees) was valued at $2.5 million, while the same win for a small-market team (e.g., Milwaukee Brewers) was worth less than $1 million. Because of this difference, the research indicated that large-market teams broke even (on average) for their free agency signings over the past 20 years, while small- (and even middle-) market teams lost money—and lots of it!
What is the bottom line in all of this? Does the “winner’s curse” apply to baseball’s free agency marketplace? The most important factor in determining the answer is the size of the particular team’s economic market. There is no clear evidence that the “winner’s curse” affects large-market teams, but for small-market teams, a strong case can be made that these owners significantly overbid for free agent players and thus suffer a “winner’s curse.” By blindly paying for star power without taking into consideration what their particular market can support, they ultimately end up striking out.
1 Capen, E. C., Clapp, R. V. and Campbell, “Competitive Bidding in High-Risk Situations”, Journal of Petroleum Technology, 23 (1971).
2 John D. Burger and Stephen J.K. Walters, “The Existence and Persistence of a Winner’s Curse: New Evidence from the (Baseball) Field”, International Association of Sports Economists, Working Paper No. 06-25 (October 2006 Revised: July 2007).
3 Burger and Walters.
4 Burger and Walters.