THE BOOK--Playing The Percentages In Baseball

Monday, November 16, 2009

How much did the 2009 free agents sign for, per win?

I LOVE when others do all the heavy lifting.  Makes my life easy.  This time, Saber Rattling (great name) compiles all the data, including the most important value: expected WAR.  And, he provides the data in a perfect format.  Let’s see what we’ve got.

He’s got 53 players in his list who signed for 1 year, from Andy Pettitte’s expected 3.5 WAR to Tom Glavine’s 0.3.  In all, his players were expected to generate 63 WAR and they were paid $164.5 million dollars, for an average of only 2.6MM per win.

He’s got 21 players who signed for 2 years for a total of 222.5MM$.  His expected WAR for the first year was 29.3 wins.  Now, he really needs to show the WAR for the 2nd year as well.  If we use my standard of knocking out 0.5 wins per year, then we knock out 10.5 MM (actually, 10.4, because one guy had a 0.4 WAR), or a total of 18.9 WAR in year 2.  The total WAR is therefore 48.2.  That comes in at 4.6MM$ per win.

For the 9 guys who signed for 3 years for a total of 232.8MM$, his expected WAR in year 1 was 17.9.  That makes it 13.4 in year 2 and 9.0 in year 3 for a total 3-yr WAR of 40.2.  That makes the payout 5.8MM$ per win.

For the 5 guys who signed for 4+ years, they are being paid 535.5MM$.  And their total expected WAR is 93.4 wins.  That puts the rate at 5.7MM$ per win.

So, we see a clear divide between those guys who signed a 1 year deal, against those guys who signed multi-year deals.  If we add up all the 35 multi-year guys, they are being paid 991MM$ for 181.8 wins, or 5.45MM$ per win.  The single year guys as noted are being paid 2.6MM$ per win.

Now, there are two unresolved issues here:
1. Does the WAR model work?  If the replacement level is being set too low, then it looks like teams are paying little for alot of wins.  For example, if we set the replacement level higher by 0.5 wins for each player, then teams are buying 37 wins at a cost of $164.5MM for one-year deals, or 4.4MM$ per win.  For the multi-year players, it’s 133 wins for that billion dollars or 7.5MM$ per win.

Hmmm.. no, that’s not it.

2. Guys who signed a 1-yr deal were heavily discounted.  If we look at the guys with an expected WAR of at least 2.5 (guys who almost always get multi-year deals), 8 of them signed 1 year deals, totalling $44.55MM for 22.6 wins.  Mark Teixeira signed by himself for 8 years (as opposed to 8 guys at 1 year each) expecting to generate 22.2 wins (same as our 1-yr guys) but for 180MM$! For the 33 guys who were expected to have 1 WAR or less and signed for 1 year, that also gives us 22.6 wins, and it cost the teams $64.7MM.

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If we apply a 10% increase to the marginal dollar per win each year, then we get 4.7MM for the first year, and 10% higher after that, for the multi-year deals.  That’s pretty much what we expected, ignoring the economic collapse. 

I think it’s fair to say that we had two markets, one where the free agents got what they were supposed to get (4.7MM$ per win) if they signed multi-year deals, and another where they gave a 45% discount to their teams to sign a 1 year deal.