Deal or No Deal and incoherent views of "trade value"

Apparently, Broncos receiver Brandon Marshall is on the trade block, according to Shutdown Corner. The headline of his piece is called "You just cannot get equal trade value for Brandon Marshall." That's not a per se inaccurate statement, but it presumes you know what "trade value" is. Presumably, by the way it is used in the post, "trade value" equals the value of the productivity or talent the player is capable of. But we all know that a player's "value" is influenced by many factors aside from their raw talent, including his salary, his adaptability to what other teams do, and, particularly in Marshall's case, the likelihood that he will be around to perform and not caught up in the legal system. Shutdown Corner:

Look at it this way: If the Broncos pay Marshall and hang onto him, one of two things happens: He either stays healthy and out of handcuffs and is an extremely productive player, or he ends up suspended or in court again, in which case, the Broncos don't get the value they should.

If the Broncos trade Marshall, though, they also don't get the value they should. Period.

So the only possible way to maximize what you get from him is to roll the dice, keep him around, and hope you get the best out of him. In any other scenario, the Broncos lose.

The italicized conclusion does not follow from the premises, and largely contradicts #1, that they keep him and "he ends up suspended or in court again." The key issue is that there is something they "should" get. Should Marshall be "worth" more, based solely on his talent? Yes, but the fact that he isn't is due solely to himself; it is not something the Broncos have any control over. They must take their troubled receiver as they find him.

Indeed, while value of a player is some estimate of their probable production, that value is a calculation their talent and capability multipled by their risk of injury, off the field trouble, discontent, etc. You don't produce if you're not on the field, and we've seen otherwise talented players be traded for peanuts or released because they weren't "worth" what they were being paid. See Terrell Owens.

Trade or No Trade? The upshot is that SD's conclusion -- that the Broncos must keep Marshall -- doesn't follow, because it confuses "maximizing" expected gain with maximizing the possible gain, two very different things. This is a common cognitive defect, particularly after someone experiences a setback or dramatic loss in value, much like the Broncos just have as their star receiver has been in increasing amounts of legal trouble.

The show Deal or No Deal provides a great example. Much has been written about the show from a behavioral economics perspective. I will assume people are familiar with the show's basic premise that someone selects a case, and then takes other cases off the board which whittles down the possibilities of what are in his case. Throughout the show, a "banker" offers the player a certain amount of money to walk away, based on what possible values remain in play.

Let's say our contestant -- let's call him Sonny Chiba -- has four cases left, with possible values of $10, $100, $500, and $50,000. The case he just chose took $100,000 off the board, so he is reeling a bit and is no doubt upset about the money he just saw evaporate. The banker gives him a new offer: $16,000, significantly down from the previous one.

What should Sonny do? Take it of course. The expected value from the four cases is only $12,652.50, and moreover he has only a 1/4 or 25% chance of having more than $16,000 in his case. In the actual game, this is not an uncommon circumstance at all; the banker is usually generous after a big blow late in the game. But you know what the studies show? After a big loss that dramatically cuts the contestant's expected value and, in turn, the banker's offer (even if it is in fact still a generous one given the circumstances), contestants repeatedly reject the offer. Why? Because all they can think about is that big $50,000 maximum, and how it will compensate them for what they lost. Nevermind that it is unlikely, and that they are staring down a better offer. (I ignore here the fact that $16,000 might be too paltry for some players. Fine, repeat the scenario with 10, 500, 1,000 and 250,000, where the player has just had 500,000 taken off the board.)

Denver's Choice. No offense to SD (who I very much like as a blogger, and I am merely nitpicking out one random statement in a blog post), but his rationale seems to be that the Broncos must keep Marshall because there's a chance it might all work out and he'll be a pro-bowler. That is the same trap that our contestant fell into in our Deal or No Deal example.

Now, this doesn't mean the Broncos must trade him either; we don't know the corresponding offers with as much certainty as Deal or No Deal, either. And he's right that the Broncos probably won't get a fantastic offer because of Marshall's off-the-field problems, but that's to be expected. If believed, SD's logic would be to expect other teams to have traded for Mike Vick or Plaxico simply because of their immense talents without regard to the probability of their spending all or part of the season in jail, or otherwise or caught up in the legal system.

The upshot is that "trade value" should not be confused with the maximum possible upside. Yes, Marshall has big upside, but all the risks surrounding him bring that value down, just as it does for Plaxico, Pacman Jones, Vick, T.O., or even guys on the total straight and narrow who are an injury risk. Just because a player might be great, or has the potential to be great, does not necessarily make their trade value better than another player. There's a difference between upside and realistic expectation.

What it means is that the Broncos -- or another team that might trade for Marshall -- must understand not only what he is capable of but what baggage and risks are attendant as well. In other words, if the Broncos get what they think is a good deal, they should take it. And if Marshall winds up making the pro-bowl elsewhere, then they can (or at least should) be able to safely say that they made the best decision they could under the information they had.

Sonny Chiba could say the same thing if, after he took the banker's offer of $16,000, Howie Mandel opened his case to reveal $50,000. That's just how the game goes. It doesn't change the fact that his decision was undoubtedly the correct one.

What I've been reading

1. The Bunch Attack: Using Compressed Formations in the Passing Game - by Andrew Coverdale and Dan Robinson. Sometimes you have to go back and re-read the bible. The title now is a bit anachronistic -- the idea of the "bunch" revolutionizing the passing game is so 1997 -- but this book is still probably the best exegesis on the passing game out there. Of course, also check out Coverdale and Robinson's three volume series on the quick, or three-step passing game.

2. FDR: The First Hundred Days - by Anthony Badger. Can be read in about a day, and I learned things I previously did not know.

3. Notes from Underground- by Dostevsky. I enjoyed this translation by Richard Pevear and Larissa Volokhonsky. Word is that this is one of Mike Leach's favorite books. No comment on any possible parallelism between Leach and Notes's famous opening line, "I am a sick man . . . I am a wicked man."

4. Nudge: Improving Decisions About Health, Wealth, and Happiness - by Richard Thaler and Cass Sunstein. Thaler is the big behavioral economics guru (famous in football circles for doing a behavioral economic analysis on the NFL draft with Cade Massey of Duke*), and Sunstein is a law professor who specializes in administrative and regulatory law (though his writing is prolific and his interests varied). They were colleagues at the U of Chicago, but Sunstein moved to Harvard and now has been nominated to head the Office of Information and Regulatory Policy, which primarily reviews proposed regulations for efficacy and consistency with government wide policies. Sunstein is also a potential future Supreme Court nominee, though it is unlikely he would be tapped to replace Justice Souter.

About the book: I liked it, but I'm not raving. It takes a couple of behavioral economics' biggest or best ideas and stretches it out over the course of the book. I think it would make a great article (indeed, it has made several) but the book is uneven. The early chapters read like a high school level or at best freshman undergraduate level explanation of ideas like anchoring, availability, and representativeness -- all important heuristics to understand, but stretched out too long. But then, the book switches course to specific applications, and its choices are the minutiae of some rather byzantine laws and regulations, from Medicare Reform to potential social security reform. These are not gripping chapters.

I leave aside the broader political questions hovering over the book in terms of judging it (and the book tries mightily to stay apolitical). I note that Thaler and Sunstein call their approach "libertarian-paternalism" -- the idea is that we want to maintain maximum choice but nevertheless design the architecture in a way that makes it easier for people to make the right choices, or even if they make no choice at all. The only vaguely political comment I do have is that Thaler and Sunstein spend a lot of time justifying the "paternalistic" aspect to would be libertarians who are skeptical of all government interference. And indeed, there is much criticism of the book from this faction. But, since the book's initial conception, the political winds have shifted somewhat, and I would have enjoyed a more thorough defense of the "libertarian" half of their approach. The authors are committed to free choice, yet they mostly assume that everyone is with them on the point. This is not to say they are not, but debate is always good -- where there's light there's usually also heat.

5. On Writing Well, 30th Anniversary Edition: The Classic Guide to Writing Nonfiction - by William Zinsser. Blogging is great, but it's probably time I figured out what professionals, who have spent careers writing non-fiction, think and try to do.


* This deserves its own post, but economist Kevin Hassett has developed NFL draft rankings based on the Massey-Thaler paper. Who did the best in the 2009 NFL draft? I'll let Hassett and Thaler. Via the Nudge blog:

Hassett identifies four winners: New England Patriots, Denver Broncos, Detroit Lions Lions, and New York Giants.

New England’s coach, Bill Belichick,…ditched his first-round pick altogether and loaded up on four second-rounders. In addition, he traded some of his later picks for other teams’ second-round picks next year. The big news is that the Giants maneuvered to get two second-round and two third-round picks, elevating their final scores.

The big losers were the Washington Redskins, the New York Jets, and the San Francisco 49ers.

The Redskins once again revealed their extreme economic ignorance, trading away their second-round and fourth-round picks…The Jets made a classic error, falling in love with University of Southern California quarterback Mark Sanchez and virtually guaranteeing they will have a large number of undrafted scrubs on their roster. Given the high salaries at the top of the draft, Sanchez will probably not generate much value above that demanded by his salary, even if he becomes a superstar.

Thaler loves the Patriots draft and also gives a positive review to the Cleveland Browns. After entering the draft with the 5th pick overall, the Browns traded down three times to take center Alex Mack with the 21st pick, plus defensive end Kenyon Coleman, quarterback Brett Ratliff, safety Abram Elam, a second round pick from the Jets, and sixth round picks from the Buccaneers and the Eagles. That’s a lot of chances to pick up some solid starting players. Football pundits didn’t think so highly of the Browns draft, but none of them are economists.