Baseball’s Arms Race and the Prisoner’s Dilemma

By very popular demand, guest blogger Steve Walters is back.  As noted before, Steve teaches economics at Loyola College in Maryland but remains a fan of his hometown Red Sox, Celtics, Patriots, and Bruins. Today he provides insights into the Clemens deal that you will not find anywhere else.

Imagine you’re a police detective and you’ve collared a couple of suspects—call them “Theo” and “Brian”—in a mob hit. They’re in separate interrogation rooms, and now your job is to get enough evidence to put these bad boys away for a long time.

You try to get them to rat each other out, but Theo—the mouthy one with a Boston accent—says “don’t you know about honah among thieves? We ain’t talkin’.”

You point out that you can send each of them upriver for a year (for parole violations) even if they keep quiet. But if one of them turns on the other, you offer to let that slide. They just laugh. Brian, a hard case from the Bronx, says “I can do a year standing on my head.”

Then you get creative. You let each thug start to wonder whether the other is a rat fink. You make each worry about doing life while the other goes into Witness Protection and gets a fresh start. Eventually, both start to crack.

True, keeping quiet is the smart play, collectively speaking—but Theo and Brian can’t make this decision jointly (because, thank heaven, high-priced lawyers aren’t involved). They’ll decide their strategy alone, and so they’ll put their individual interest above their joint interest.

And that’s the essence of what is known as “the prisoner’s dilemma.” Brian thinks “I can shut up and do my year… but what if Theo is ratting me out? I could spend the rest of my life behind bars! But if I rat him out first…” And Theo thinks the same thing. To protect himself against the worst-case scenario (taking the entire fall while the other guy walks) and/or to pursue the best-case scenario (walking while the other guy takes the fall), each punk spills his guts.

Bravo. But what, you ask, does this little discussion of interrogation tactics have to do with more interesting and important topics, like sports?

Well, it just might explain how Rogers Clemens’s agent, Randy Hendricks, got the Yankees to spend such a stupendous amount of money to bring the 44-year-old pitcher out of retirement—yet again.

Let’s first get the cost-benefit analysis out of the way: The Yanks reportedly will pay Clemens roughly $18.5 million for the remainder of the season. (His contract is for $28 million for the year, of which two-thirds will remain once the Rocket is in game shape.) But since the Yankees are already far over the threshold for MLB’s “payroll luxury tax,” they will pay another $7.4 million in payroll taxes as a result of this deal.

So Clemens is costing the Yanks about $25.9 million. Will that investment pay off, financially speaking? No. Freaking. Way.

Make no mistake, considerable extra revenue will flow to the Yankees once they get to start a sure-fire future Hall-of-Famer instead of dreck like Kei Igawa, Darrell Rasner, or Jeff Karstens every fifth day. Just nowhere near $25.9 million extra.

Using the methodology (and updated parameters) outlined in excruciating detail here…

“Market Size, Pay, and Performance: A General Model and Application to Major League Baseball,” by John D. Burger and Stephen J.K. Walters, Journal of Sports Economics, May 2003, v. 4, iss. 2, pp. 108-25.

…and a rosy assumption about how well Clemens will pitch this year, the most optimistic estimate I can make is that he’ll generate no more than $22.5 million in marginal revenue in the Bronx. Probably a lot less. And yes, that includes all likely revenue streams: more viewers on cable TV, enhanced chances of post-season booty, etc. Fantasize about “enhancing the Yankee brand” if you want to, but this deal is a $3.4 million loser for Boss Stein—at best.

But you don’t even have to do this type of math to know that the Yankees overpaid. The other major bidder in the Rocket auction—the Red Sox (Clemens’s hometown Astros apparently stopped talking with him at the end of spring training)—reportedly topped out at a pro-rated $18 million for the year, or no more than $12 million for the rest of the season. How did Hendricks get an extra $6.5 million from the Yanks? He put the “prisoner’s dilemma” to work for his client, expertly playing on the fears of the Yanks’ brass that their arch-rivals would nab Clemens.

The details have been splendidly reported by ESPN’s Buster Olney (see: “How the Yankees Landed the Rocket”)

In effect, Hendricks held Brian Cashman and Theo Epstein in separate interrogation rooms and made each worry about what the other might do. Here’s a telling episode from Olney’s account:

“The Yankees’ charter touched down in Texas last Monday [4/30] evening, and general manager Brian Cashman sent a text message to Randy Hendricks, the agent for Roger Clemens. ‘I just landed in your wonderful state.’

“Hendricks responded: ‘I’m out of town.’ And a couple of hours later, as Cashman dined with manager Joe Torre, he said, ‘I wonder if he’s at Fenway Park.’

“This was just one more anxious moment in the Yankees’ months-long pursuit of Clemens…”

The two key players in this prisoner’s dilemma-type game had two possible strategies. Bid low for Clemens, and he’d probably stay retired or, perhaps, pitch for the ‘Stros. Either way, that would have been OK for the Sox and Yanks, since then the Rocket wouldn’t have upset the competitive balance between the two A.L. East juggernauts. And both teams are gonna sell out all their remaining games anyway.

From both a baseball and financial perspective, then, bidding low made sense collectively. But not individually. Bidding high for Clemens held out the prospect of taking a competitive advantage in the A.L. East’s “arm’s race”—i.e., it gave the bidder a chance at the best-case scenario, baseball-wise. And it also protected against the worst-case scenario of having the Rocket pitching against you the rest of the year.

Ultimately, the Yankees decided they had to bid high. Very, very high.

Note, however, that this does not mean that Brian Cashman is a fool. Rather, thanks to the way Randy Hendricks set up this auction, Cashman was between a rock and a hard place: bidding high was an unappealing but unavoidable choice. In game theory jargon, it was a “dominant strategy.” Just not a cheap one.

That such situations pop up so often in baseball may be a reason that team owners earn relatively low yields on their investments (in addition to the possibility that they’re utility- rather than profit-oriented, discussed here last week in “Show Me the Wins”). It’s also a reason that savvy agents are well worth their money. A question worth pondering is whether a team that understood game theory could avoid these types of dilemmas—and the red ink that usually results.

Steve Walters

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