Tuesday, March 27, 2012

The Winner's Curse

As the funstravaganza (not a real word) that is NFL free agency winds down, I am reminded again that there is a structural reason that free agent contracts in every sport pay more than players are “worth.” It turns out that the reason is slightly more complicated than: The owners are all crazy (though it still explains why Daniel Snyder, in particular, is crazy). The exception to this is the late 1980s in baseball, when owners agreed to simply not offer contracts to free agents from other teams. This actually happened, you can look it up. It bears mentioning that if this were attempted today, the internet would melt.

Econ 202

This phenomenon is known in economics as the Winner’s Curse. In the late 1950s a bunch of oil companies were wondering why they didn’t make any money on offshore wells. The leases for these places were auctioned off competitively by the government, with each company doing an analysis of what they thought the asset was worth and putting in a bid that they felt would make them a good return on their investment. That’s all well and good if everyone knows what the asset is worth, but that’s not what happened. The big firms were losing out on bids to the newer, little guys, and the little guys who won the leases weren’t making any money, even though they found oil in some of the leases. After several decades of this a few engineers from Atlantic Richfield Co. (later ARCO and even later BP) stepped back to analyze these outcomes and the cause jumped out at them. Capen, Clapp and Campbell identified the culprit as the Winner’s Curse.

In the auctions of offshore leases, each bidder had the same (limited) knowledge of the value of each lease up for bid. They might be more or less optimistic but they were working from the same data. The only additional piece of information that such a bidder could receive is the outcome of the auction. In other words, they wouldn’t know if they were too optimistic or pessimistic until they got to the auction. Those who ended up winning belatedly realized they had been too optimistic about the value of the asset (Hellooooooo Mr. Snyder).
Normal Distribution - Mean 10, StDev 1

The picture above shows the plot of likely offers for a free agent with an intrinsic value of 10. Again, what’s important is not that the average of the offers equals 10 but that they are in fact distributed because no team knows the intrinsic value so they come in at various points on the curve. The player and his agent will have no trouble deciding which offer to pick among the options below (the green one!).

I see the Redskins have entered the bidding...

Sports World Complications 

If everyone knew precisely what a player was worth (if Daryl Morey ran every front office) then the bids would be totally equal or would vary depending on the value of a player to a particular situation. For example, Dwight Howard would be more valuable to the Celtics than the Lakers because he would take minutes from Jermaine O’Neal in Boston as opposed to Andrew Bynum in LA. This team-specific value can also be present in the NFL, though the fact that some players are more valuable to some teams can be a security blanket for those owners (sorry Dan, still you) who are consistently deluded about the “one missing piece” they need. Baseball, on the other hand, tends to be a bit more team-neutral about where a player can add the most value with the exception of aging sluggers being more valuable to American League teams.

The Winner’s Curse is a part of any system in which assets are auctioned to the highest bidder. The free agent and salary cap systems in place in American sports have additional quirks that prevent teams from even trying to evaluate players rationally. Going back to the original example, if the oil company didn’t see a lease at an appropriate price, they would close their wallets and move on. The owner who does that (a bigger problem in baseball, hello Royals, Orioles, Indians, Pirates) shoots himself in the foot because it’s a giant white flag from a marketing perspective – at least until the revenue sharing check shows up as some of these teams are inexplicably among the most profitable in baseball. Multi-year contracts screw this up more because you can only sign the players who are out there even though this may soak up cash that would otherwise be available in future years. If you are a basketball team with enough space for two great players but the only ones available are Charlie Villanueva and Ben Gordon, that’s what you get. If you are a football team that needs to spend 89% of the cap at a minimum, you spend it on free agents or cut an extra check to the players – given the same out of pocket, wouldn’t you rather have the extra players?

One final quirk that pushes contract values is the repeated game aspect of the system. If a team drives too hard a bargain with an agent they may be blocked from future deals with that agent and his other players. In a single game the team might have a dominant strategy of holding out and going scorched earth, but this is unlikely to be the case (fair enough, this part is on both sides) given that they must continue to deal with agents in the future. The reason I’m so confident that this bias acts in favor of the agent comes back to the publicity factor. Agents can absorb bad publicity with no impact to their bottom line and act as shields for their players. Organizations get dragged down by this bad publicity and it can dissuade marginal fans from supporting the team.


Basically, the system is structured so that the owner most irrational (to the expensive side) about the value of a player will always win – barring any hometown discounts or desire to become global icons.

From the players’ side, almost every single thing in their life is telling them to take the money. Their agent is pressing them to take it so they can get a couple extra bucks. Other players want them to take it because it raises the comps for their upcoming contracts. Family, friends and hangers-on want them to take it because they want a piece of it, directly or indirectly. The players union wants them to take it because they are the players union.

From the teams’ side, there are at least competing priorities but they still appear weighted towards overpaying. Even the most loyal fans are unwilling to prefer delaying gratification in most cases – they’ll say they are but they’re not. Team owners, who should be the voice of reason in this discussion, are often the ones with the shortest time horizon of all (see Snyder, Daniel). The result is a chart like this one demonstrating a strong correlation between building through the draft in the NFL (with all its inherent salary advantages) and team success. Good teams have to work extremely hard to avoid the quick fix (who wants a "D" or, god forbid, an "Incomplete" in the Free Agency Grades????).

The easiest way out of this, ironically, is the collusion attempted by the baseball owners in the late 1980s. Within the scope of actual solutions, collective bargaining agreements represent the owners’ best chance to handcuff themselves in free agent bidding. Unsurprisingly, they always seem to find a way out.

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