THE BOOK--Playing The Percentages In Baseball

Wednesday, December 15, 2010

Pablo Sandoval and WAR

Here’s a “fun” WAR thread at Primer.  I probably most align myself with Ron J/19 in that thread. 

Anyway, there was an interesting point discussing Sandoval’s WAR, with the two competing WAR implementations, from Fangraphs (fWAR) and Baseball-Reference/Rally (rWAR).  Here is how it breaks down, with fWAR listed first and rWAR second (note that B-R.com rounds to nearest integer, so keep that in mind):
Offense: -3.5, -4… a match

Fielding: +0.3, -6… 6 run difference, which is pretty typical, as you’ll get plenty of players off by 5-10 runs… just the nature of the beast

Playing Time: +20.5, +17… 3.5 run difference, which is also standard, except it’s more or less fixed… this is because the Fangraphs replacement level is lower than the B-R.com replacement level… where Fangraphs has close to 1100 WAR in the league, B-R.com has close to 900 WAR… that’s a 200 WAR difference, or about 6 or 7 per team, or about 4 for the 6000 PA for the non-pitchers on a team, or about 0.4 wins per 600 PA… which is 4 runs.... got all that?… that means +20.5 and +17 is a match… they would HAVE to be, since the ONLY variable that goes into it is the player’s PA…

Position: +1.4, +1… also a match

If you add it up, you get +1.9 wins for fWAR and +0.8 for rWAR.  All of a suddenly, we have a 1.1 win difference, when really, the mild disagreement is only in fielding.

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You will also see that if you use 4.5MM$ per win from fWAR, you will get about 5 billion dollars (4.5 x 1100).  In order to get that same 5 billion dollars from rWAR, then each wins from rWAR has to be valued at 5.5MM$ (5.5 x 900 = 5 billion).  Sandoval’s 1.9 WAR x 4.5 comes in at 8.5MM$, while his rWAR of 0.8 comes in at 4.4MM$.  That difference is 4.1MM$.  That’s the only common currency between rWAR and fWAR, because a win in rWAR is not the same as a win in fWAR.

The main difference, the 6.7 runs in fielding+position, accounts for close to 3.5MM$ in the difference.  As you can see, with such a huge uncertainty around the fielding metric, it really impacts the overall value.

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For what it’s worth, BPro has his WARP at 2.0.  BPro has an even lower replacement level.  They probably have closer to 1200 or 1300 wins per year-league.  Starting again with the 5 billion$, that would mean about 4MM$ per win.  That would mean his value is 8MM$.

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Also, someone is surely asking, how can you value all players at 5 billion$, if MLB payroll totals 90MM$ per team, or about 2.7 billion dollars?  This is because of the player development cost that is not carried in the payroll, but is carried in players’ values that we see in free agency.  Suppose that all the player development costs comes in at 40MM$ per team.  So, that’s another 1.2 billion dollars.  You subtract out the salaries for minor leaguers and you have another say 0.8 billion dollars of value (that doesn’t appear in salaries).  This only brings us up to 3.5 billion$. 

We may be able to say there’s an inefficiency of some 1.5 billion$ in the free agent market.  For those who wish to say that there is a circular logic in valuing a win at 4.5MM$ or 5.5MM$ because that’s what the free agent market is bearing, then you definitely have a point.  A win should be valued closer to say 3.0MM$ - 3.5MM$ (which is close to what you get from one year deals).  It’s possible that the extra 1MM$ to 2MM$ per win being paid out is because the market is inefficient, or the market thinks that those wins are worth more for their particular team (i.e., playoff sweetspot).  Or, teams are paying for the greater certainty of being able to value the true talent level of someone with 3000 MLB PA.

If for example all players were signed to one year deals and were free agents every year, it’s almost certain that the $ per win would be 2.7 billion dollars divided by total league WAR (900 for rWAR, 1100 for fWAR, 1200-1300 for WARP).  So, say about 2.5MM$ per win, give or take.

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Once you understand how the sausage is made, you’ll see that you can enjoy an italian sausage just as much as you can enjoy a kielbasa.