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Should the Yankees have offered Johnny Damon arbitration?

Yesterday the Yankees decided to cut ties with free agent LF Johnny Damon by not offering him arbitration.

The general feeling is that the team was worried he might accept and earn around a one year / $15 million deal in arbitration.

Was it a good move for the team to forego the possibility of draft picks and let Damon walk for nothing?

Damon was a type A free agent according to the Elias rankings.  That means he would command either a first or second round pick depending on which team signed him, as well as a supplemental pick between the first and second rounds.  For more information on how draft pick compensation works, see this primer at MLB Trade Rumors.

Let's say that the Yankees did offer Damon arbitration and he signed with another team.  Without analyzing the fit with each of the teams, let's assume that there's a 50% chance the team has a protected pick.  That means that the Yankees have a 50% chance of getting a first round pick, and a 50% chance of getting a second round pick (they're guaranteed the sandwich pick).

Victor Wang has calculated the average surplus value for a draft pick in each of the three tiers: the second half of the first round, the supplemental round, and the first half of the second round.

He found that draft picks in each tier were worth the following amounts on average:

Tier 1 Surplus Value: $5.23 million
Tier 2 Surplus Value: $2.63 million
Tier 3 Surplus Value: $0.76 million

Based on our assumption that there's a 50% probability of getting a Tier 1 and Tier 2 pick, and a 50% probability of getting a Tier 1 and a Tier 3 pick, we can project the value of the draft picks as:

.5 x 5.23 + .5 x .76 + 2.63 = $5.63 million

That's the value the Yankees can expect if Damon declines arbitration.

What's the cost if Damon accepts?

As mentioned above, the number being tossed about in Twitter is a $15 million dollar deal for one season.  The fans over at Fangraphs currently project Damon as being worth $11.4 million next season (although the Yankee fans project him lower).

Based on those values, Damon would provide a surplus value of $-3.6 million next season.

The final piece of the puzzle is the likelihood that Damon would accept arbitration.  If we assume a 50% chance of him accepting, then the Yankees expected value calculation would be:

.5 x 5.63 + .5 x -3.6 = $1.015 million

So with a 50% chance of Damon accepting arbitration, the Yankees actually come out on top by offering arbitration to the tune of $1 million.

In order for offering arbitration to be a bad deal for the Yankees, assuming all our projected monetary values, they would have to assume Damon is more than 61% likely to accept.

Considering Scott Boras, Damon's agent, is talking about a multi-year deal, I'd have to assume the odds of him accepting are substantially lower.

Of course there are an awful lot of assumptions in this analysis.  The Yankees may know a lot that we don't. 

They may have surveyed the landscape and decided that the Mets or some other team with a protected pick are the most likely team to sign Damon - which would drive down the expected value of the draft picks. 

Or they may be more pessimistic than the fans about Damon's prospects for next season and may expect a larger negative surplus.

And I'm sure Brian Cashman has a better idea of the Yankees finances than we do, but it doesn't seem likely that a one year deal for $15 million will cripple the team or stop them from going after a free agent.  Unless, of course, that free agent plays the same position as Damon (Matt Holliday, or Jason Bay, anyone?)

The Yankees have both LF and DH slots open next season, although they likely will want to slot Jorge Posada into the DH role more frequently.  If Damon were to move from a full time LF to a full time DH, it would likely only cost the team a few runs on the season.  There are other, potentially cheaper, DH options on the market though, from Russell Branyan to Rick Ankiel to Vladimir Guerrero, which may change things.

So why didn't the Yankees offer Damon arbitration?  The numbers suggest they'd come out ahead based on the likelihood of Damon accepting the offer. 

Perhaps the Yankees' financial situation is more dire than we expect, or perhaps this is a harbinger to pursuit of Matt Holliday or Jason Bay.