Tommy "Blogger on a Mission" Rancel has already done a nice write-up of the Soriano trade, but I wanted to look back at the decision that started the chain of events leading to the trade. The Braves decided to offer arbitration to both of their Type A free agent relievers: Mike Gonzalez and Rafael Soriano. Before either player decided whether or not to accept, the Braves signed free agents Billy Wagner and Takashi Saito for a combined $10 million plus the compensation pick they will surrender to the Red Sox. 

Mike Gonzalez declined the Braves' offer of arbitration, meaning the Braves are likely to recoup at least one draft pick. But Soriano surprised the Braves--and many fans--by accepting the Braves' offer. Some went so far as to say that the decision to offer arbitration to their departing free agents had blown up in their faces. Many see the return the Braves got on Soriano from the Rays (N*SYNC member reliever Jesse Chavez, acquired earlier this offseason from the Pirates for Akinori Iwamura) as evidence that the Braves were over a barrel and had to trade Soriano for pennies on the dollar. 

The relevant question isn't whether the Braves got pennies on the dollar. It's whether they'd rather have pennies or nothing.

Last week, I formulated my theory of the arbitration offer. Here's the relevant bit:

[A] team should offer arbitration if the probability a player accepts arbitration times the expected surplus he offers (which can be negative) plus the probability the player does not accept (assuming he does not retire) times the value of the draft picks received is greater than zero.

I'm sure the Braves thought the probability of Soriano accepting arbitration was very low (I certainly did). And they likely thought, given their history of success in scouting and player development, the value of the draft picks received would be high. But here's the thing: even if the draft picks were basically worthless and Soriano was a near-lock to accept their offer, it would still have been a good decision to offer him arbitration. 

To see why, we have to ask what the expected surplus was if Soriano were to accept. We have some evidence of that now, in the form of Jesse Chavez. The value Chavez represents is slightly different from the expected surplus the Braves could have expected from the ex ante perspective, but it is a good estimate. 

CHONE projects Chavez as a one run pitcher, which is about as close as you can come to replacement level without actually hitting it (which is important if you're playing by Price is Right rules). Bill James has him pegged for a 4.29 FIP in 72 IP, which is probably closer to two runs above replacement. After checking my calculations, I can confirm that neither valuation is less than or equal to zero runs.

So let's balance the arbitration equation. On the one hand, the Braves could have offered arbitration to Soriano, which in the worst case scenario, would have netted them a run or two, and in the best case scenario would have scored them two top-50 draft picks in the 2010 draft. Or, they could decline to offer him arbitration and get bupkis. This is the kind of decision that is so mind-numbingly simple that it's easy to forget that teams mess it up all the time. 

Now, I'm not entirely sure Soriano did the wrong thing by accepting. There's an argument to be made that, because of his Type A status, he would have gotten less money (and certainly a lower AAV) on the open market than he did by accepting arbitration (the Rays will pay him $7MM next year). But it should be very plain that not all decisions are zero sum. That Soriano accepted arbitration didn't hurt the Braves in any way except in relation to the world in which he declined and signed with another team. It certainly didn't hurt them relative to the world where they failed to offer him arbitration at all.