April 7, 2005

Lies, Damned Lies

Looking Back at the Market

by Nate Silver

A total of 47 free agents were signed this winter to contracts of $5 million or more; the aggregate commitment made to those players exceeded $1 billion. It goes without saying that that's the sort of money that could make or break a couple of franchises for years to come; nevertheless, one gets the sense that the decision to offer certain of these contracts might as well have been made with the help of a Ouija Board. Just how much are the Tigers overpaying for Magglio Ordonez? Did the Mets get a good deal on Pedro Martinez? Is Jim Bowden as dumb as we've made him out to be?

One of the nifty things about PECOTA is that it projects performance more than one year into the future; I don't know of any other system that does that, or at least not one that's available publicly. One-year projections are fine for a lot of things, but they can be absolutely misleading when you're using them to make a decision with a longer time horizon than that, such as determining who to retain for your keeper league or which free agent to sign to a $50-million contact. Let's take a look, for example, at the year-by-year WARP projections for the six free agents who were signed to contracts totaling $50 million or more this past winter:

                  2005   2006   2007   2008   2009
Carlos Beltran     8.5    7.9    7.0    7.0    5.3
Adrian Beltre      6.7    6.0    5.6    5.1    4.8
J.D. Drew          7.2    6.7    5.7    5.2    4.3
Pedro Martinez     7.6    6.1    5.4    5.0    3.0
Carlos Delgado     6.4    4.8    3.7    3.0    2.1
Magglio Ordonez    5.1    3.8    2.9    2.8    1.8

TOTAL             41.5   35.3   30.3   28.1   21.3

% of 2005 Value   100%    85%    73%    68%    51%

By three years into the contract, every one of these players can be expected to have lost about 25% of his value between deterioration in performance and deterioration in playing time; by the time we go five years outward, the player may have lost nearly half his value. It's easy to forget just how many things can go wrong with a baseball player, especially a veteran free agent whose best years are usually behind him; the more years you go out, the more likely one of those things is to happen.

We're talking in generalizations here, of course, when we should be talking about specifics. I went ahead and analyzed each of the 47 free-agent contracts as follows:

1. Take the lifetime guaranteed value of the contract, as reported by ESPN.

2. Subtract $316,000 for each year of the contract, in accordance with the minimum salary. Since WARP is a measure of marginal performance, it follows that we should be looking at marginal expenditure, and not the amount that a team is obligated to spend on each of its 25 roster spots.

3. Discount future years of the contract at a rate of 5%, in order to reflect the time value of money; Steps 2 and 3 combine to give us something I'll call Net Present Marginal Value, or NPMV.

   Two brief caveats here: I'm assuming that payments are spread equally over the life of a contract, simply because more detailed information is hard to come by. I'm also picking 5% for a discount rate when I could equally well have picked a different number, but it shouldn't make a ton of difference.

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