Friday, June 01, 2007

Buyer's Fallacy

I know that free agency is still a ways away but I have been thinking a little bit about a term I picked up from an economics course this past year. One of my textbooks presented the idea of a buyer's fallacy in respect to sealed-bid auctions. The basic premise of the idea is that in a sealed auction the good for sale will always be sold for a higher price that it's actually worth.

Why? If you take ten bidders for the same good, you will have ten different estimations of what the buyer is willing to pay - ten different statemens of worth. While the textbook surmised that you could count on the average of the bids to be a reasonable estimate of value, some bids would be below it and some above it with only the single maximum bid taking home the good in question.

The analogy is obvious - here is a simple reason why salaries in the NHL are inflationary. By having an unrestricted free agency system you are in effect creating an auction destined to raise salaries, first for the UFAs and then for anyone at all who can justify a comparison to one of these players in contract negotiations. I'm not sure if RFAs can use UFA prices in arbitration this would only hinder but not stop the inflationary process.

As far as I can see it, there really is no problem here as long as NHL revenue increases. The cap will go up, teams will have money, and teams will spend it on their players of choice. What happens when the league stops showing revenue growth? When the cap levels off or drops? There is a 20% of the cap maximum for any individual player but what if contracts as a whole start drifting closer to that maximum?

I raise those questions but here is the open-ended one I'm most interested in reading opinions on from the many writers and visitors of this site: should the NHL have a method built into its CBA to directly stop or reverse inflation?

edit: as an update to Speeds' post below, the Oilers have let today's deadline pass without signing any of the players on his list.

11 Comments:

Blogger JavaGeek said...

Who is the author of that textbook?

"Buyer's Fallacy"?

Why? If you take ten bidders for the same good, you will have ten different estimations of what the buyer is willing to pay - ten different statemens of worth. While the textbook surmised that you could count on the average of the bids to be a reasonable estimate of value, some bids would be below it and some above it with only the single maximum bid taking home the good in question.

The price of a good should be set such that the market clears. Since all hockey players are unique their supply is one and the market will clear when the price is set such it is the minimum price such that only one team is willing to pay that price. In an economic sense, the market clearing price is the player's worth. The price that will clear the market is 1 cent above the second highest bidder. This is where the concept of a "Vickrey auction" comes from.

If a player's price was set at the average offer then 15 teams would be willing to pay for the player.

Example
Let's say a player (approximately worth $5M) was a UFA and all 30 teams were allowed to offer a contract (it cost them nothing (research) to bid and players wouldn't be 'insulted' by low offers). Many teams who would would be forced to use the player in a third line role would offer $2-3M for the player (15 teams). A few teams would offer $4.5M as the player wasn't a good fit (5 teams), but certainly better than the other $4.5M alternatives and would give injury protection. A number of teams knowing his true value offer $5M (9 teams).

Finally a team offers $5.5 as they really need that player and there aren't alternatives for that team.

What is that player worth: $4M? $5M? or $5.5M?

The team who offered $5.5M certainly believes he's worth the $5.5M, that team doesn't have a better use for that $5.5M and that makes that player worth $5.5M. Technically though that team could only sell the player to another team for $5M (if that was permitted).

6/01/2007 4:50 pm  
Blogger RiversQ said...

What happens when the league stops showing revenue growth? When the cap levels off or drops?

Well, that's why they have the escrow account. I'm not sure this is a big deal for the league.

I'll leave the economic theory to someone else, but with respect to team building, you'll always get more bang for the buck out of the price controlled players and you'll almost always get less value from the free market ones.

Essentially, I don't think it's possible for any team to save itself via UFA signings, at least not via multiple marquee signings. I would say the key is to have enough good price controlled players such that you have the cap space to buy the right free market players to fill the holes.

6/01/2007 8:58 pm  
Blogger MikeP said...

I agree with javageek - a player's value is whatever a team is willing to pay for his services. Ryan Smyth will be worth a lot more to some teams than to others this off-season.

And no, RFAs can't use UFA contracts as comparison points.

6/03/2007 11:29 am  
Blogger PDO said...

mikep:

What about a contract like Hemsky's where he signed away 3 of his UFA years?

6/03/2007 2:22 pm  
Blogger JavaGeek said...

What about a contract like Hemsky's where he signed away 3 of his UFA years?

I estimate that RFAs sign for approximately 75% of an UFA equivalent. In an economic sense it would be hard to figure out how they get to a 75% figure, but that's what it looks like.

So, Hemsky signed 6-year contract worth $24.6M = $4.1M/year
Three of those $4.1M are really worth about $5.5M and the other three are worth $4.1M, so if all the years were UFA years he would've signed for about:
$28.7M over 6 or about $4.8M/year.

6/03/2007 7:58 pm  
Blogger Showerhead said...

javageek: I am unsure of the author as I no longer have possession of his/her text. If you're curious though I'm sure it would only take a phone call or two for me to find out.

I understand what you're saying regarding the price of a good and grant that if a team pays a player X$ then it sets his price at that level. I think that the definition of "value" or "worth" in the context of hockey players would have to be different though from what someone was willing to pay. This could perhaps be a measure of "expected contribution to a team's expected winning percentage, relative to the current prices (yes prices) of other players in the league" if such a thing was easily possible. You could pay Joffrey Lupul $8m a year and hence set his price but for the sake of a hockey vocabulary that makes sense you should never be allowed to say he is "worth" that money.

PS - in that Vickrey example, what is stopping a bidder from curling his pinky to his lip, writing "one BILLION dollars" on a piece of paper, and walking away with the good for a price of bid#2 + 1 cent?

RiversQ - Good point re: escrow. Another idea I was thinking of though would be enough teams betting on continued revenue growth that too many players were signed long term at high prices to fit a legitimate team under a newly low cap. I think it's unlikely and I think that if it did happen the only consequence would be a redistribution of some of those players, but it's an entertaining doomsday scenario.

6/04/2007 2:01 pm  
Blogger speeds said...

I think that the definition of "value" or "worth" in the context of hockey players would have to be different though from what someone was willing to pay. This could perhaps be a measure of "expected contribution to a team's expected winning percentage, relative to the current prices (yes prices) of other players in the league" if such a thing was easily possible.

It's kinda hard to have this mean anything though.

If EDM's goalies were Dubnyk and Markkanen, while CAL's were Kiprusoff and Luongo, is there any reason to think CAL would be willing to pay as much for Giguere as EDM would via UFA? Giguere's "expected contribution to a team's expected winning percentage, relative to the current prices (yes prices) of other players in the league" is CLEARLY higher for the Oilers than it would be for CAL, which is exactly why EDM would bid more for him than CAL would.

Similarly, given EDM's D options for the PP, would it be terribly surprising if they value Souray more this summer than PIT?

NOTE: That doesn't justify paying Souray, specifically, 8 mil a year, but if Souray's true "value", to the average team, is 3.5 mil as a UFA this summer, it doesn't mean his value can't be 4.5 mil to EDM if Souray fits needs for the Oilers better than he would for a variety of other teams.

6/05/2007 12:13 am  
Blogger speeds said...

a baseball article on "winner's curse":

http://www.thediamondangle.com/archive/oct01/wincurse.html

http://en.wikipedia.org/wiki/Winner's_curse

6/05/2007 12:18 am  
Blogger Showerhead said...

And to think there was a catchy name like that going around. Thanks for the links, speeds, they fit in exactly with what I was going for. I suppose a significant difference between those simple models and free agency is that as you said, a player will have a different value to different teams... so while the contract offers may still form a range that approximate the average value and the winner may still be paying more than that average value the specific team and player fit must also be taken into consideration.

It's still inflationary though, is it not? I am still curious about the forces at play should salaries continue to rise while revenue dropped though I'm not necessarily worried about it in any way.

6/05/2007 12:25 pm  
Blogger JavaGeek said...

Winner's Curse:
Next time you find yourself a little short on cash for lunch, try the following experiment in your class. Take a jar and fill it with coins, noting the total value of the coins. Now auction the jar off to your class (offering to pay the winning bider in bills to control for penny aversion). Chances are very high that the following results will be obtained: (1) the average bid will be significantly less than the value of the coins (bidders are risk averse); (2) the winning bid will exceed the value of the jar. Therefor, you will have money for lunch, and your students will have learned first-hand about the "winner's curse". (Anomalies: The Winner's Curse by Richard H. Thaler).

The "winner's curse" cannot occur if all bidders are rational, so evidence of winner's curse in a market settings would constitute an anomaly. (Being rational isn't an easy task)
I think this point is the important topic for hockey, many GMs and owners aren't necessarily rational.

Secondly, "winner's curse" doesn't consider winning valuable. Some people are willing to pay to win an auction even if they know the auction is worth less than their bid (due to prestige). This is especially relevant in hockey, due to the benefits that result (fan interest, media coverage).

I would call "winner's curse" a tool to remove bad bidders (irrational bidders) from the market. Someone who wins a bid and then loses money will likely go bankrupt. Of course in the NHL owners are often slow to respond to bad GMs, or even encourage such activity (they like the big name players).

Buyer's Fallacy or Winner's Curse, stems primarily from lack of information. With a small "jar of coins" it simply isn't worthwhile to go and do a thorough estimation of the value (calculate volume of jar, average value of coins, average volume of coin, etc.). With hockey players the "intrinsic value" is debatable even after they retire (unlike the revenue from a oil well, or coins in a jar). Hockey players don't have an "intrinsic value", it varies by team, by era, by day, etc.

Inflation
In a "salary fixed" environment inflation beyond revenue is physically impossible. If one player is overpaid another has to be underpaid. This may explain the large jumps in salaries in the 90's though (I would debate that though).

In general the "winner's curse" should be "anti-inflationary". Think back to the first paragraph and imagine that professor auctioning off 10 jars to his students and showing the loss after each jar. The first jar will be overbid, the second jar will likely be overbid, but the students will eventually see what's happening and bid less and less, rather than more and more and it should stabilize to the point where the maximum bid is equal to the actual value of the coins.

Conclusion
However, I believe that owners and GMs have a better idea of the "intrinsic value" of a player than the fans and newspaper writers. There is no way to check the "intrinsic value", therefor, there is no way to determine if the contracts are the result of poor fan understanding of value or "winner's curse". Either way the difference would likely be small (1-10%) and the signed value should (on average) be the closest approximation we have to the "intrinsic value" of a player.

6/05/2007 10:27 pm  
Blogger MikeP said...

PDO - sorry, just saw this, but if you're still watching - I doubt it.

Hemsky's *next* contract will obviously count though.

I think that's part of the reason a signing like his is so valuable to the team. Probably drove staunch unionists like Todd M insane.

6/20/2007 9:16 pm  

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