Baseball BeatNovember 30, 2010
What's a Free Agent Worth?
By Rich Lederer

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 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.



1. We don't want PAST WAR, but FUTURE WAR. That means regression, meaning a lower expected WAR in the future than what was observed in the past.

2. You must separate one year deals from multi-year deals.

We've done this analysis already for a few years now. You'll get somehting like 2.6 million future dollars for 1 future win for 1-yr deals, and 4.5MM future dollars for 1 future win for multi-year deals.

Great work as always Rich. On Holliday, I find it interesting that his contract reflects his value almost to a T, when comparing it to the league averages minus the RP's. For a contract that was widely panned last winter, it seems like in reality, it was really a very solid one. Fair to Holliday and to the Cards. My fear about it echos Tangotiger's comment about future WAR projections. Holliday will need to keep producing at a high level to justify the length of the contract. A 4 or 5 year deal would have made it easily to stomach.

Here's a thought for a future story: take the FA signings and their value in terms of $/WAR, and then rank the GM's. It would be interesting to see which GM's get the most value for their money.

Tango: The difference in our $/WAR has more to do with including or excluding relief pitchers than regression. By including relief pitchers, you artificially increase the average $/WAR for starting pitchers and position players. That was the point of my article.

You always make me think and improve my baseball knowledge. This was great stuff but why is it that the relievers are so overvalued and overpaid especially when you subscribe to Bill James theory on relief pitching?

Rich, I think Tango's point still stands. Holliday was signed for his age 30-36 seasons.

No one can assume he's going to average the same WAR in those seasons as he did in his age 27-29 seasons.

You're crediting him with too much WAR over the life of the contract, which obviously will reduce the $/WAR.

Of course there's also the assumed inflation over the life of the contract. As Holliday's expected WAR declines each year, the market value of a win will also be assumed to be increasing.

A reliever's WAR (at least in the Fangraphs model) is dependent upon his LI, and several of the relievers in your chart moved from setup or shared closer roles to full closer roles (at least that was the plan, prior to injuries and poor performance and the like)--Gonzalez, Wagner, Saito, Dotel, and Soriano all moved to teams that intended to use them in higher leverage situations than did their previous team. Since leverage is largely influenced by usage, it follows that FA relievers would be paid according to their maximum WAR given the leverage bidding teams would plan to give them rather than according to the level their previous team chose.

Re relief pitchers, yes, I believe they are generally overpaid as a group. Based on the number of innings pitched, even when adjusted for leverage, it is hard to justify the salaries of most relievers. However, that was not the essence of my article. Instead, it is my contention that relievers, irrespective of their usage, are not paid on the same $/WAR scale as starting pitchers and position players. As a result, I believe it is a mistake to include their salaries and WAR in the aggregate mix when trying to place a value on free agents. Doing so serves to artificially increase the dollars per WAR for all free agents.

Players are paid for future performance, not past performance. If we put 2010 WAR values into the chart, we get the following numbers ('7-'09 values in parentheses):

Total WAR: 75 (104)
Non-pitcher WAR: 44 (60)
Starting pitcher WAR: 19 (34)
Relief pitcher WAR: 12 (11)

Total $$/WAR: $4.2M ($3.0M)
Non-pitcher $$/WAR: $3.4M
Starting pitcher $$/WAR: $5.5MM
Relief pitcher WAR: $5.1MM

I covered this for several years--in the THT Annual and on our site. I used Win Shares Above Bench *in that year* divided by dollars paid *in that year.* Anything else is a guesstimate. Took me 40-50 hours and some inside contacts to make sure I had the info correct.

Here are my figures for 2007:

Since it takes three win shares above bench to make one win above bench, teams paid $5.3 above the minimum salary per actual win delivered in 2007 from free agents.

Here is a post that shows that WSAB and salaries above minimum matched extremely well (see comments for exact info):

Yes, there are difference between WAR and WSAB, but I don't believe they're significant enough to warrant a figure of half that $5.1 million.

I have felt that fangraphs' WAR is less effective in valuing relief pitchers. Leverage is given less emphasis than the Win Shares methodology (due to chaining). And FIP probably isn't the most accurate method of valuing relief pitcher performance. In any event, the results seem to indicate that teams place different values on leverage and perceptions of reliever performance than Fangraphs.

I think the economy had a negative impact on free agent salaries, beginning in the 2009 off-season and extending to last off-season. Players remained unsigned longer and many ended up signing for significantly less than expected. During the depth of the recession (prior to the 2009 season), many teams publicly stated that they were cutting their payrolls due to declining advertising.

Good work, Rich. Worth mentioning also is that WAR seems to be a more conservative estimate of marginal productivity than some alternatives, such as WARP; that'll inflate calculations about what the market is saying a win costs.

On Tango's point about contracts being forward-looking so we want future marginal product, that's true -- but it's not always true that regression to the mean implies lower forecast values. That will depend on recent observations (e.g., was last year's output a negative deviation from the mean, from which we might see a bounceback?), the age of the player, and the forecast horizon.

And noseeum's point should not be lost in the shuffle: long-deferred outlays (like Tulo's) could be reduced to present value in making these $/win calculations, and then combined with forecasts about output.

But your key finding -- that a team which assumes it ought to pay $4.5M per marginal win is likely to be disappointed in its return on investment -- seems eminently reasonable.

He's worth whatever he can get a GM to pay.