What's a Free Agent Worth?
I have been troubled for a couple of years with the consensus belief in the sabermetric community that free agents are worth between four to five million dollars per Win Above Replacement (WAR). For the ESPN Stats and Info blog, Tom Tango of Inside the Book stated that "the value of a win on the free-agent market is between $4 million and $5 million dollars." In a recent New York Times piece, Sean Forman of Baseball-Reference.com wrote, "2009 free agents received nearly $4.5 million per win added." Led by Dave Cameron's input, Fangraphs has based its dollars per win value at approximately $4M for 2007, $4.5M for 2008 and 2009, and $4M for 2010.
I respect all three of these esteemed analysts. However, I believe there is a flaw in applying $4 million, $4.5 million, or $5 million to estimate the value of all free agents. To see if I could set the record straight, I began by using ESPN's Free Agent Tracker to create a database for the 2009-2010 crop. Of the 201 free agents last year, 121 signed MLB contracts, 66 inked MiLB deals, and 14 retired. For the purposes of my study, I excluded free agents who signed for less than $3 million per season. Most of these players were part-timers, backups, pinch hitters, or injured. In hindsight, the best of this lot included Alex Gonzalez, Kevin Gregg, Miguel Olivo, Kelly Johnson, John Buck, Jim Thome, and Jonny Gomes. In addition, I eliminated foreign players Aroldis Chapman, Noel Arguelles, and Ryota Igarashi, as well as Colby Lewis, who played in Japan in 2008 and 2009.
All in all, there were 53 free agents who qualified, a sampling that captured the most significant signees between the 2009 and 2010 seasons. The players in the table below are ranked by their total compensation. I also included the number of years, the average annual salary, the average Fangraphs WAR for the 2007-09 period, and the average annual dollars per WAR.
Let's take a look at Matt Holliday. He signed a seven-year contract with the St. Louis Cardinals for $120 million, equal to an average of $17.142 million per season. Holliday averaged 6.1 WAR during 2007-09. As a result, he was paid $2.80M per WAR.
Based on $/WAR, the major outliers were relievers John Grabow ($37.5M), Mike Gonzalez ($13.95M), Fernando Rodney ($11M), Rafael Soriano ($9.06M), Jose Valverde ($7.78M), and Billy Wagner ($7M), all of whom had a higher $/WAR than Jason Bay ($6.88M), the highest-paid position player based on the average WAR for 2007-09. It's pretty obvious to me that there is virtually no correlation between the salaries of relief pitchers (be it closers or setup men) and WAR. As a result, I believe it makes sense to exclude them when trying to determine what a free agent is worth. Nonetheless, I have calculated the arithmetic mean, weighted average, and median $/WAR including and excluding relief pitchers.
Here are my findings:
- The arithmetic mean $/WAR for all players was $4.36 million. Excluding relief pitchers, it was $2.88M.
- The weighted average $/WAR for all players was $3.03 million. Excluding relief pitchers, it was $2.73M.
- The median $/WAR for all players was $2.95 million. Excluding relief pitchers, it was $2.73-2.80M.
I realize this study is based on one year only. In addition, the salaries may have been negatively influenced by the overall economy. That said, no matter how you slice and dice it, excluding relief pitchers, the average free agent signed for about $2.7-$2.9M/WAR last offseason. I believe this finding is significant in that most analysts have routinely used $4.5M per win added.
Based on their performance in 2010, the biggest bargains from the list above were Marlon Byrd ($1.22M/WAR), Adrian Beltre ($1.41M), Orlando Hudson ($1.61M), and Placido Polanco ($1.62M). Beltre and Hudson are free agents once again. The biggest busts were Chone Figgins ($15M/WAR), Randy Wolf ($14.17M), and Jason Bay ($11.79M). Figgins and Bay have three years left on their contracts and Wolf has two years to go. Due to injuries, Mike Cameron (-0.3 WAR), Nick Johnson (0.1), and Rich Harden (-0.7) didn't pan out as their new employers expected.
Let's check out how this year's free agents are doing:
I excluded RP Joaquin Benoit and Jose Contreras from this table. For consistency, I also excluded Geoff Blum, who signed a two-year contract for $2.7 million (which was less than the $3M minimum I required for the 2009-2010 free agents).
With seven precincts reporting, the sample size is small. Nevertheless, the results are as follows:
- Excluding relief pitchers, the arithmetic mean $/WAR was $3.41 million.
- Excluding relief pitchers, the weighted average $/WAR was $3.37 million.
- Excluding relief pitchers, the median $/WAR was $3.59 million.
While it may be too early to get a definitive read for this year's class, excluding relief pitchers, the average free agent has signed for about $3.4-$3.6M/WAR this offseason.
There are several big-name players who haven't signed yet. The crop is headlined by Cliff Lee (6.97 average WAR from 2008-2010), Carl Crawford (5.0), Jayson Werth (5.0), Beltre (4.53), and Derek Jeter (4.43). Rounding up last year's $/WAR to $3M and using the mid-point of $3.5M/WAR this year produces the following average annual salaries: Lee ($20.9M-$24.4M), Crawford and Werth ($15M-$17.5M), Beltre ($13.6M-$15.9M), and Jeter ($13.3M-$15.5M). Unless the Yankees cave in to their captain, I would be surprised if any of these players sign for an average annual salary outside of these ranges. If so, it would help confirm my belief that free agents (sans relievers) are worth about $3M-$3.5M per WAR rather than the $4.5M that seems to be universally accepted.
Of note, one can reach slightly different conclusions by using Baseball-Reference WAR instead of Fangraphs WAR. I'm not necessarily more partial to one over the other. One can also weight the WAR differently. I used a simple average of the past three years, tweaking a few players based on injuries and playing time. There might be merits in going with a weighted system, such as a 3-2-1, in certain situations. In reality, teams are trying to project WAR but most estimates are going to be heavily influenced by observed WAR.
Furthermore, there are many other factors that teams consider when making offers to free agents, including a player's age, his position, current health status and history of injuries, the consistency and arc of his career, the supply and demand for that type of player, the length of contract, and whether he is a Type A or B free agent. Put it all together and shake it up, and it is my contention that the going rate for starting pitchers and position players who are free agents is somewhere in the range of $3,000,000 to $3,500,000 per the three-year trailing average WAR.