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.

  4. Take a player’s total PECOTA projected WARP score over the life of the contract. Compare, contrast, and let stew.

Player               Years      NPMV     WARP      $/Win         +/-

Guzman, Cristian       4    $14,461K     14.7      $984K   +$17,041K
Drew, J.D.             5    $48,569K     29.1    $1,669K   +$13,792K
Eckstein, David        3     $8,866K     10.2      $869K   +$12,992K
Koskie, Corey          3    $15,300K     12.2    $1,254K   +$10,845K
Renteria, Edgar        4    $36,056K     20.2    $1,785K    +$7,232K
Kent, Jeff             2    $15,978K     10.5    $1,522K    +$6,523K
Hidalgo, Richard       1     $4,684K      5.1      $918K    +$6,245K
Garciaparra, Nomar     1     $7,684K      6.0    $1,281K    +$5,174K
Hernandez, Orlando     2     $7,193K      5.8    $1,240K    +$5,237K
Lidle, Cory            2     $5,533K      4.9    $1,129K    +$4,968K
Vizquel, Omar          3    $10,772K      7.1    $1,517K    +$4,443K
Beltre, Adrian         5    $56,752K     28.2    $2,012K    +$3,681K
Martinez, Pedro        4    $48,156K     24.1    $1,998K    +$3,489K
Miller, Damian         3     $7,198K      5.1    $1,411K    +$3,731K
Castilla, Vinny        2     $5,484K      4.2    $1,306K    +$3,516K
Hermanson, Dustin      2     $4,752K      3.6    $1,320K    +$2,963K
Burnitz, Jeromy        1     $4,684K      3.4    $1,378K    +$2,602K
Clement, Matt          3    $23,401K     12.0    $1,950K    +$2,314K
Schoeneweis, Scott     2     $4,459K      3.2    $1,394K    +$2,398K
Finley, Steve          2    $13,050K      7.1    $1,838K    +$2,165K
Cormier, Rheal         2     $4,508K      3.0    $1,503K    +$1,921K
Millwood, Kevin        1     $6,684K      3.9    $1,714K    +$1,674K
Kline, Steve           2     $4,752K      2.9    $1,667K    +$1,355K
Dye, Jermaine          2     $9,291K      4.9    $1,896K    +$1,209K
Alou, Moises           2    $12,318K      6.0    $2,053K      +$540K
Wilson, Paul           2     $7,388K      3.7    $1,997K      +$541K
Wells, David           2     $7,193K      3.6    $1,998K      +$522K
Matheny, Mike          3     $9,104K      4.3    $2,117K      +$110K
Cabrera, Orlando       4    $28,609K     13.3    $2,151K      -$108K
Radke, Brad            2    $16,954K      7.8    $2,174K      -$239K
Leiter, Al             1     $7,684K      3.3    $2,328K      -$612K
Lieber, Jon            3    $19,112K      8.5    $2,249K      -$897K
Lowe, Derek            4    $18,371K      7.9    $2,325K    -$1,441K
Perez, Odalis          3    $21,972K      9.5    $2,313K    -$1,613K
Wright, Jaret          3    $19,112K      7.8    $2,450K    -$2,397K
Benitez, Armando       3    $19,589K      7.7    $2,561K    -$3,195K
Beltran, Carlos        7   $101,367K     45.3    $2,238K    -$4,290K
Glaus, Troy            4    $40,710K     17.1    $2,381K    -$4,065K
Percival, Troy         2    $11,097K      3.2    $3,523K    -$4,347K
Benson, Kris           3    $20,542K      6.1    $3,368K    -$7,470K
Varitek, Jason         4    $36,056K     13.2    $2,732K    -$7,769K
Milton, Eric           3    $23,401K      7.0    $3,343K    -$8,401K
Delgado, Carlos        4    $47,226K     17.9    $2,638K    -$8,866K
Pavano, Carl           4    $36,009K     11.5    $3,131K   -$11,365K
Ortiz, Russ            4    $29,540K      8.0    $3,693K   -$12,396K
Sexson, Richie         4    $45,364K     12.7    $3,572K   -$18,148K
Ordonez, Magglio       5    $66,753K     16.4    $4,070K   -$31,608K

Two columns here require additional explanation:

  • $/Win, just as you’d expect, means marginal dollars spent per marginal win.
  • +/- is a measure of market value. As it works out, the aggregate $/Win spent on the 47 players was around $2.14 million. We can use this number to determine how overpriced or underpriced a particular player was relative to the rest of the market. Take Kris Benson, for example:
    • Projected WARP over contract lifetime: 6.1
    • Projected contract amount @ $2.14 million / win: $13,072K
    • Actual contract amount (NPMV): $20,731K
    • +/- : $13,072K – $20,731 K = -$7,470K

    That is, PECOTA estimates that the Mets overpaid for Benson by approximately $7.5 million.

This is an awful lot of data to digest, so take a moment if you need. In the meantime:

  • Cristian Guzman is not who I’d have guessed would have topped the “best value” list. However, he does have three big things going for him: he’s young for a free agent, he’s a shortstop who plays his position very well, and he was signed for a relatively modest amount. This does not mean that Guzman is a good player, or that he has an especially favorable projection; he’s been worth about 18 wins over the four previous seasons, and PECOTA expects him to be worth slightly less than 15 wins over the four seasons to come. But it does mean that he’s a reasonably good value, especially when compared to someone like Orlando Cabrera. If there’s a problem with the signing, it’s not that Guzman’s was a bad contract on its face, but rather that it’s with the wrong team–the Nationals aren’t well positioned to take advantage of the three or four extra wins he’ll give them.
  • Speaking of that sort of context, it’s also important to consider when looking at the results we get for someone like Corey Koskie, whose signing we’ve criticized pretty heavily. Right player, right price…but wrong team. On the other hand, it does seem at least possible that the market has overcorrected for years of overpaying for marginal talent, and there are now some bargains to be found among second-tier players.
  • The best of the “major” free agent signings appears to be J.D. Drew. While PECOTA is usually not very kind to players with substantial injury histories, it’s worth remembering that almost every veteran player carries some injury risk, and Drew has at least demonstrated an ability to play well when he does take the field. It’s also worth noting that a fair number of Drew’s comparables–guys like Brian Giles–had late peaks.
  • Projected dollars per win, by number of contract years:
    1-Year Contracts: $1,448K
    2-Year Contracts: $1,749K
    3-Year Contracts: $2,036K
    4-Year Contracts: $2,370K
    5-Year+ Contracts: $2,298K

    For all the noise teams have made about wanting to avoid risky long-term signings, it hasn’t translated into a change in behavior. Nomar Garciaparra provides a perfect illustration of the principle; PECOTA does not expect him to age particularly well, but he comes out as one of the best values of the winter because the Cubs haven’t burdened themselves with extra contract years.

  • While contract length makes a difference in terms of value, the “hometown discount” does not. Eight players on this list–Garciaparra, Cory Lidle, Rheal Cormier, Paul Wilson, Brad Radke, Odalis Perez and Jason Varitek–resigned with their original clubs; in the aggregate they were about $4.7 million overpriced. This is hardly a comprehensive study of the issue, of course, but the trade-deadline rationalization that you’ll sometimes hear when an expensive veteran is acquired–“He’ll see how nice it is to play every day in Our Town, and he’ll sign cheaply with the Townies in the future”–appears to be just that. Indeed, Jason Varitek‘s case seems to suggest that a hometown player will sometimes have additional leverage in free-agent negotiations.
  • Position makes a difference. According to our reckoning, pitchers were a collective $45.8 million overpaid, while position players were underpaid by the same amount. Pitchers have at least four distinct strikes against them when it comes to the free agent market:
    1. Pitchers are more likely to get hurt then position players are, making them riskier long-term bets.
    2. Major-league teams do not do as good a job of predicting how pitchers are going to do as compared with position players because of the effect of defense on pitching statistics and the (mostly luck-based) differences between ERA and PERA, which are poorly understood.
    3. Major-league teams also do not do a particularly good job of understanding the role of defense; while run prevention is 50% of the game, pitching itself is a fair bit less.

    4. Because just about every team could use a reasonable pitcher, while some teams might be prevented from bidding on, say, a catcher if they have a skilled incumbent at the position, the bidding on pitchers tends to be more active.

    There’s an argument, of course, that all of this is academic; in order to acquire a free-agent pitcher, you don’t get to pick his contract amount in a vacuum, but rather have to outbid all the other clubs. That is, while pitchers are overpaid as a group, the problem may be so institutionalized that a rational team will need to overpay them a little bit themselves. Nevertheless, picking up a value pitcher like Hernandez or Cory Lidle, while reserving your most expensive acquisitions for position players, seems like an awfully good way to attack the market.

  • Relief pitchers appear to be particularly overpaid. I actually cheated a bit by multiplying the WARP scores for the free agent relievers by 50%, in order to account for their pitching in higher-leverage situations. (While the version of WARP you see on the Davenport player cards makes a similar adjustment, the version I use for PECOTA does not). Nevertheless, the four high-leverage relievers on the list combined to be overpaid by nearly $8 million.
  • I also had to cheat a bit for Carlos Beltran, because his contract was seven years long, and PECOTA ordinarily only projects five years outward. Beltran’s projected WARP scores for years six and seven (5.0 and 4.6, respectively) are based partly on rolling his projected stats a couple of years forward and seeing what happens, and partly on some educated guesswork. With that in mind, I think it’s fair to regard his contract as about value-neutral; missing the mark by $4 million on a $119 million contract isn’t very much, especially if Beltran’s signing provides some benefits for the Mets’ marketing department. If the Mets lost a little bit on Beltran, they gained it back on Pedro Martinez.
  • Which teams had the best and worst winters?
    Nationals       +$20,557K
    Dodgers         +$17,261K
    Blue Jays       +$13,243K
    Mariners        -$14,468K
    Diamondbacks    -$16,461K
    Tigers          -$35,955K
  • This is old news now, but the Magglio Ordonez signing stands heads and shoulders above the pack as the worst deal of the winter. Just for kicks, I decided to run a separate PECOTA projection for Mags that assumed that his performance in 2004 was the average of what it had been in 2002 and 2003. That is, it assumed that he’d never gotten hurt, nor suffered from the attendant performance decline.

    If we make that rather generous consolation, then Ordonez’ projected WARP over the five-year period comes out to 27.8 rather than 16.4, meaning that he’d still have been overpaid by around $7 million. Injuries are one of the more difficult forecasting problems, and a lot of the players on the “overpaid” list are coming off injuries; it’s possible that PECOTA is overstating the case for someone like Sexson or Ordonez. But when teams don’t appear to be discounting at all for the risks going-forward associated with recent, substantial injuries…well, that should give you an idea why Will Carroll’s analysis is such an important part of Baseball Prospectus.

  • Last but not least: this analysis does not provide an answer to the question of whether all free agents are overpriced: is $2.14 million for a win too expensive? That’s a subject for another article, but I suspect that it almost certainly is.