Win Curves and Player Pricing

As expected, there were two basic responses to yesterday’s news that the Tigers had agreed to pay Prince Fielder $214 million over the next nine seasons:

1. “That’s just way too much money.”

2. “As long as he helps them win, the cost is irrelevant.”

I’m part of the group that says the former, as I simply don’t think that the Tigers are going to get a very good return on their investment in Fielder, and if they had this kind of money to spend to upgrade their roster, I think there are far better ways they could have used that money to produce a better team overall. However, while I think the second point ignores the fact that signing Fielder wasn’t the only option available to to the Tigers, I understand the desire to focus on total wins rather than cost efficiency. After all, the point of baseball is to win a championship, not to finish first in the $/WAR standings. Efficiency is a method to help create a championship caliber roster, but it isn’t the goal in and of itself.

And, those that argue in favor of the deal are arguing from a premise that holds some truth – the Tigers were absolutely in a position where each marginal win is significantly more valuable than the average. I referenced the win curve theory in the post yesterday, but it’s worth expanding on briefly. If you’re not familiar with the concept of the win curve, this article by Vince Gennaro from 2007 is a good place to start. I’ll highlight one of the important passages:

A team’s location on the win-curve — their absolute level of wins — has a dramatic impact on the value of a win. To understand the power of the win-curve location, you only have to look as far as the marginal revenue of a Twins team in playoff contention. A five-win improvement for financially challenged Minnesota, from 86 wins to 91 wins, would yield $6.8 million in incremental revenue. When comparing this revenue estimate with teams who are striving for respectability (78- to 83-win category), their marginal revenue is greater than all teams except the Mets. The location on the win-curve is so important that it often trumps market size as the key driver of a team’s marginal revenue opportunity.

As Gennaro’s data shows and is generally understood by most fans, the wins that get you from good team to great team are worth a lot more than the wins that get you from bad to good. As the word curve implies, the value of a win is non-linear, and peaks between the 85-95 win levels, where the marginal return on each additional win is significantly higher than on wins below 84 and above 96 – those wins don’t move a team’s playoff expectations needle all that much.

Given the Tigers roster after the Victor Martinez injury, they projected as a mid-80s win team, and were at least somewhat vulnerable to upstart runs by the Indians and Royals. Even as division favorites, their chances of stacking up against the contenders from the East and West in the playoffs weren’t very good, so taking real steps to upgrade the roster was the right decision. The wins that the Tigers bought with Fielder are more valuable than an average win, and thus, the decision to go after those wins was justified.

However, player pricing is not solely driven by a team’s internal valuation of the marginal value of wins added to their franchise. The cost of wins in free agency is determined by the aggregate demand for wins by all 30 teams in a given winter, and of course by the supply of wins available. Regardless of the value of a win to a specific team, they only have to offer an amount some degree higher than the next best offer in order to buy wins in the market. For instance, the Red Sox need for another starting pitcher and their position on the win curve means that a pitcher like Roy Oswalt is likely worth far more than $8 million to their franchise in 2012, but since the market for his services is significantly depressed, they don’t have to pay him based on their rate of return – they just have to pay more than what he could get to sign somewhere else.

When determining whether a team should spend money on a particular player, we cannot simply focus on the value of wins that the player should be expected to provide to that franchise. That certainly belongs in the discussion, but you also have to factor in the price for wins in the market, as that price is essentially the cost of an alternative option. The price for wins in the free agent market over the last few years has been between $4-$5 million apiece. Based on a projection of Fielder producing about +25 wins over the next nine years, the Tigers paid about $8.5 million per win. You’ll have to believe that inflation is going to go bananas to believe that this contract isn’t going to turn out badly in the long run.

You can justify some amount of overpay based on their current position in the win curve and the return that they can expect to get from those wins. The fact that Martinez’s injury happened so late in the off-season, after most of the quality free agents had already signed elsewhere, is also a mitigating factor. However, those are reasons to pay $6 million per win, not $8.5. They justify overpaying a little bit – the Tigers overpaid by a lot.

The value of a win is important to understand, but you cannot simply ignore the market price of wins in determining whether a contract was a good idea or not. The Tigers spot on the win curve justifies higher than average expenditures to improve their team for 2012, but it doesn’t justify signing Fielder instead of just pursuing a combination of Edwin Jackson and Carlos Pena, who could have improved the team to the same degree without requiring anything close to the same level of long term financial commitment.

Whether a contract is justified or not depends on both the value and the relative price of wins. Focusing solely on one is simply not a good way to evaluate the worth of a deal. You have to look at both.