The Cost of WAR

As most of you know there has been quite a bit of discussion here about valuing free agents, with most of the discussion being tied to wins above replacement (WAR).  The really smart guys will tell you that the cost of a win above replacement on the free market is somewhere between $4.5-5M .  I don't know what they might say about the potential long-term impact of this season's free agent contracts on the future market value of a win.  The common thread at VEB has been, "let's sign player X for $9-10M because he is a 2 WAR player".  I wondered why our front office never really seemed to be making "market" offers based on this valuation method, so I started to do a little research. 

I used free agent salary data from espn's free agent tracker  and WAR data from fangraphs.  Since the espn site only has data for the past three off-seasons, I have only attempted to draw conclusions based on the 2006-2008 timeframe.  Obviously, data for the current off-season is still incomplete, but the picture is somewhat clear. 

I doubt that any of this information comes from a large enough sample set to actually "prove" anything, but I think it is sufficiently valuable to stimulate some conversation nonetheless.  What I have done is simply take the average annual value of each free agent contract without regard to any incentives, deferred money, or back loading and divided each player's WAR for the season completed immediately prior to signing the contract in order to obtain a cost per WAR for each free agent.  Then I have compared the costs for each WAR range and also compared the cost to the succeeding season's performance. 

According to this admittedly simplistic look at the data, 2006-07 free agents were paid an average of $4.2M per WAR which is pretty close to what you would expect.  For 2007-08 that number drops to just under $3.8M and currently sits at just over $3.3M for 2008-09.  If you dig a little deeper it gets more interesting.  It is extremely difficult to value certain classes of low WAR players like relief pitchers, aging players, and near-replacment bench types. 

When the data are separated into two buckets and you look at the <1 WAR players separately it is stunning to see the effect.  For example, in 2006-07 there were 78 free agents signed with a 2006 WAR below 1.  In fact, there were 28 players signed who posted 2006 WARs that were negative - indicating they were below replacement level.  The bulk of these were relief pitchers and players coming off injuries.  These players signed free agent contracts totaling over $200M in annual value despite a cumulate 2006 WAR rating of 9.2, making for a cost per WAR of nearly $22M!  That certainly skews the cost per WAR for the players who actually have significant value. 

There were 55 players in 2006-2007 who signed free agent contracts worth a total of over $400M in annualized value.  These players 2006 WARs totaled 135.6 for a cost per WAR of just under $3M.  A similar, but not quite so dramatic, difference can be seen in the numbers for the succeeding seasons.

During the 2007-08 off-season there were 50 contracts signed by free agents with 2007 WAR values below 1 for a total of over $130M.  There cumulative WAR total was 14.2 resulting in a cost per WAR of over $9M.  In the same period the 36 >=1 WAR players signed contracts totaling almost $266M for a cost per WAR of just over 2.9M - nearly identical to the 2006-07 class.  During the current off-season, 51 players with 2008 WAR <1 have signed for a total of over $95M resulting in a cost per WAR of just under $7.9M.  The >=1 WAR group has seen a modest decrease in pay with an average price of just under $2.8M per WAR.   

There are a couple of interesting conclusions here:

  1. If you are a marginal player, or a relief pitcher, or any other near-replacement type then your value is dropping precipitously.  The <1 WAR group has seen its value plummet by nearly 65%. 
  2. When we talk about the value of significant free agents, $4.5M per WAR is much more than the market seems to have been paying.  In 2008 only two players out of 20 with 2008 WARs above 2 signed contracts worth more than $4.5M per WAR.  They were Kerry Wood at about $4.7M and Raul Ibanez at $4.56M.  Other than those two players, the highest cost per WAR was one Brian Fuentes at $3.5M.  CC Sabathia was at a cool $2.99M.  The numbers aren't much different for 2006-07 and 2007-08.

I have posted the complete data if you care to look at the details.

Some explanations of the column headings: 

  • The column headings with years (i.e. 2008-09) represent the value per win based on the preceding season's WAR.
  • The column headings with "Actual" in the heading indicate the cost per WAR of the players in the year they actually earned the money.
  • "% Incr" is how much more (or less) the given group cost than the value assigned at the time of contract signing. 

I would be curious to hear whether the community thinks that WAR undervalues bench players and relief pitchers or whether "baseball men" put too much value on situational context.  


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