The Marginal Value Of A Win

This post is inspired by a question Sky Kalkman raised on twitter. Specifically, he wondered about the wisdom of the Rays paying $7 million for Rafael Soriano, when the franchise has proven time and again that they are capable of finding bargains for below-market rates, eschewing the going rate for wins and building a contender on a shoestring payroll.

I like the move and think it was a good one for Tampa Bay, even though it’s not an efficiency maximizing move from the perspective of the price of wins. They’re going to pay Soriano about $4 to $4.5 million per win for 2009, which is certainly not a discount, and is actually above the going rate that we have seen for most players signed this year. Additionally, the $7 million he will earn would represent nearly 11 percent of the total team payroll from 2009. That is a significant allocation of resources to give to a closer.

However, the Rays are not in a league average situation. Their position in expected outcomes is quite a bit different than most teams. They have the talent of a contender, but share a division with New York and Boston, which drives down their chances of making the playoffs. As such, they have to protect themselves from variance more than most clubs will, as a bullpen implosion (like they had in 2009) can essentially derail their chances of playing in October.

Soriano adds a win or two to the roster, which may not sound like much, but the win that he’s bringing is extremely valuable, given the precarious nature of the Rays playoff odds. By adding a premium relief ace, they’ve insured, to an extent, against a disaster. The security that he brings doesn’t offer the same reward for the dollar that you may find by taking a flyer on a young, unproven, power arm, but the Rays don’t need more upside as much as they need less downside.

We talked a bit about this a few weeks ago, but the composition of a team’s talent and their relation to their division opponents can have a pretty significant effect on their internal marginal value of a win. A win to the Rays is significantly more valuable than a win to the Astros because of the respective effect of that win on the odds of either team making the playoffs.

Because of where they stand, it makes sense for the Rays to pay the market rate for wins, because that price is lower than the value they’re getting from that win. It does not make sense for the Astros to pay the market price, because the return they will get on those additional wins is below the going rate. If Tampa Bay and Houston pay the same price for the same player, it will be a good deal for the Rays and a bad deal for the Astros.

We cannot use the price of wins in the market as the guide for what every team should be willing to pay for a win. It will never deviate too tremendously from the average (no one, not even the Yankees, should pay $10 million per win for a player), but teams do have their own internal marginal values of a win, and they won’t equal the going rate of wins in the market for all 30 teams.

Tampa Bay should be insuring against bad outcomes at the expense of the best one, which is what they did with Soriano. It was the right move, even if it doesn’t offer the opportunity to be a huge bargain.