The Marginal Value of a Win

As fans, it is our expectation that our favorite teams will do the best they can to field the best possible team. In economics, a perfectly competitive market is dependent on perfect information (all consumers in a perfectly competitive market know the prices being charged by all the producers). The lack of honesty and forthrightness that baseball management often engages in produces a severe information gap between the decision makers and the paying (sometime) customers. This results in fans often judging actions taken by the baseball operations department as good or bad without the proper information to make an educated judgment. For example, the Yankees apparent decision to let Johnny Damon go in favor of Brett Gardner has angered many Yankee fans (I am a Yankee fan, just not a crazy ones) who expect General Manager Brian Cashman to sign an all star at every position. Whether Cashman's claims that the Yankees have reached the end of their budget is true or not (Yankee fans aren't used to such absurdities as budgets), the Yankees seem content with having the light hitting, quick footed Gardner manning left field.

The information gap causes fans to complain when the Yankees refuse to continue spending money at their previous pace. Aside from the fact that you'd expect fans to trust the General Manager who just won them a World Series Championship, there must be some information that the team has that tells them that spending an extra $9 million (estimated) is not worth the investment. Cashman must have realized that the extra potential win generated by Damon's VORP (Value Over Replacement Player) over Gardner's VORP is not worth $9 million. With FanGraph already projecting the Yankees to win close to 100 games, the marginal value of an extra win is small. Dave Cameron wrote about the Yankees' Win Curve on FanGraph.

A while ago, we talked about the marginal value of a win, and how it differs from team to team, changing the calculation on what a team should pay for a given player given what they already have on the roster. The wins that have the largest impact on playoff odds are in the upper-80s, so if you’re a slightly better than .500 club, adding another additional win or two can have a pretty dramatic impact on your chances of playing in October.

For a team that isn’t likely to contend, the marginal value of each win is pretty low, which is one reason why those teams often go young and give prospects a chance to play rather than upgrading the roster with more expensive veterans. However, the win curve has two sides where the marginal value of an additional win is low, and in New York, we may be seeing evidence of how a team responds when their marginal value of a win is way past the peak.

The Yankees have made a bunch of good moves this winter, adding Curtis Granderson, Nick Johnson, and Javier Vazquez to a roster that was the best in baseball a year ago. Their true talent level, as currently constructed, is probably that of a 100 win team. The Yankees are going to be very good in 2010.

So, perhaps we should not be so surprised that New York is bargain shopping in left field, avoiding the likes of Matt Holliday and Jason Bay. They are at the other end of the win curve, and it doesn’t make much sense to spend a lot of money there either. The marginal value of the 101st, 102nd, and 103rd win in terms of playoff odds is really quite small. And that’s approximately the upgrade that Holliday would represent over the current production that Gardner offers in left field.

The Yankees have entered the prime area of significant diminishing marginal utility. They are so good that adding another high quality player doesn’t help them that much in 2010, and because of the long term contract that is required, they’d be risking future flexibility to add wins that may actually matter for an upgrade that just isn’t necessary.

It’s a rational decision made by smart people who understand just how good their roster currently is. In the past, New York has pursued every big ticket free agent on the market because they represented a real, tangible improvement in their quest to bring home another championship. Given how well Brian Cashman has put together this roster, though, a big ticket left fielder is superfluous. He’s right to keep his money locked up. They just don’t need another good player.

The value gained by an extra win is not worth the value of Damon's contract. This combined with Yankee ownership not wanting to bring the 25 man payroll above $200 million explains Cashman's decision to end the offseason having only acquired Granderson, Vazquez, and Johnson. What a cheapskate!

-David