Sunday, December 21, 2008

How should we value closers?

J.C. Bradbury, a man who writes a blog that combines two of my favorite subjects, baseball and economics, has put up a couple of posts so far this offseason decrying what he believes are the inordinately large salaries being given to closers.

His chief problem is that relievers, even the best ones, save so many fewer runs than starting pitchers that it seems ridiculous to offer relievers salaries that even approach the salary of a comparably elite starter. The usual response to this is that relievers pitch in "high leverage" situations, which is to say that the best relievers often pitch in situations where each run is of magnified importance. I think we can all agree that it is less damaging to give up a run when you are leading by 15 in the top of the ninth than when the game is tied in the bottom of the ninth.

J.C. does not agree that leverage, which amounts to a simple usage pattern for relievers, should factor in to their salaries:
I have considered the impact of leverage, but I don’t think leverage can explain the vast differences in my estimates and what is happening in the market. Leverage is a product of outside factors when a pitcher faces the same rules during all times of the game. The quality of his pitching is the same in the 5th inning as it is in the 9th.
He concludes (emphasis mine):
Another factor is that better pitchers in earlier innings affect the leverage in later innings. So, a good starter preventing runs as an impact on reducing leverage later in the game by creating bigger leads. I’m not sure exactly how to value that. So, I believe that the proper method is to treat all pitcher innings the same, while acknowledging that some elite relievers have some extra value in that they could be used in more valuable spots. But this value doesn’t necessarily come from when they pitched in the past.
J.C. is certainly right that it doesn't matter when a reliever has pitched in the past. All that matters is how a reliever can be used in the future. I will also admit that I myself have struggled with how to deal with the question of leverage when assessing player value, both in a past sense (how much reliever X contributed to a team's success) and in a future sense (how much reliever X will be worth to me next year).

I want to leave aside the question of past performance for now. I think that J.C. is in error to not factor leverage into future player value. Let me offer an analogy.

Let's say that I have been offered a prize of $1,000,000.00 if I can win a race from New York to Los Angeles. After a couple days of driving, I'm only a couple hours from Los Angeles and comfortably in the lead, by perhaps an hour or two. Suddenly, I find that I have a flat tire. Worse, I have no spare, since I dropped it to lighten my load and increase my fuel economy. I'm stuck in the middle of nowhere with no way to get going again.

But wait! Just when it seems that all hope is lost, a man pulls up beside me with tires for sale. He knows about my predicament and the prize waiting for me at the end of the race. If I act now, my lead will still be comfortable and I can cruise to the finish line in peace.

So I ask my savior, "How much for a spare tire?" He replies, "Only $750,000.00."

Obviously that tire did not cost that much to make, nor would it be worth that much at just about any other point in the race. Nonetheless, that tire is almost certainly worth that much at this point in time because I have no other options. I can either accept a prize of $250,000.00 or receive nothing. In fact, one might say that my enterprising benefactor is giving me a good deal, since I should probably be willing to accept almost up to the entire $1,000,000.00.

The situation is slightly more complicated when there are multiple tires (or relievers) on the market and multiple people bidding for them, but the principle is the same. How you intend to use a tool and the situation in which you might use it most certainly impacts how much that tool is worth, even if that tool is a pitcher.