To Offer Or Not?

Tomorrow represents the first real day of the hot stove league, as teams are required to make arbitration decisions on their respective free agents. Once teams understand who will and who will not require draft pick compensation to sign, the process will accelerate, as teams will be able to more accurately assess the cost of signing a particular player.

For some players, the decision to offer arbitration or not is an easy one. The Angels will certainly be offering it to John Lackey and Chone Figgins, while the White Sox will not be offering it to Jermaine Dye. It doesn’t take much in the way of analysis to reach those conclusions.

However, there is a large pool of players for which the decision is not so cut-and-dried. Should the Dodgers offer Orlando Hudson arbitration, even though they don’t really want him back, in order to secure the compensation he would bring as a Type A free agent? How about Mike Cameron, who has already been replaced in Milwaukee and been told that he is not in their plans, but has the type of skillset not likely to be correctly valued in arbitration? Injury prone pitchers such as Rich Harden and Erik Bedard also present dilemmas to the Cubs and Mariners respectively.

For many of these players, teams will decide that the risk of an arbitration offer being accepted is too high, cutting ties with a player they either don’t want or don’t believe they can afford. However, in many of these cases, I believe that teams may be incorrectly valuing the actual cost of the offer.

The marginal cost of the arbitration offer is not the full value of the player’s potential 2010 salary. It is not even the dollars beyond that which a team would be happy to pay the player. It is only the dollars beyond what any one team in baseball would be happy to pay for that player that are actually being risked.

Let’s use Adrian Beltre and the Mariners as an example. Based on some back-of-the-envelope calculations, I’m presuming that the Mariners have approximately $25 million to spend this winter as they shop to fill various needs. That is one of the main reasons why Beltre probably won’t be back in Seattle next year, as he would eat up a significant chunk of that budget, limiting the team’s options when pursuing other positions of need. In reality, Beltre would probably make at least $10 million if he accepted arbitration, and likely closer to the $13 million he earned in 2009.

However, the Mariners aren’t risking $10 to $13 million by offering Beltre arbitration. His market value is significantly north of $0, and on a one year deal, it’s probably somewhere between $8 and $12 million, I’d imagine. So, in reality, the Mariners would be risking something like $4 million, as that would be the potential difference between the arbitration award and his free market value. Remember, a team is free to trade a player who accepts arbitration, so it wouldn’t be particularly hard for the Mariners to then ship Beltre to, say, Philadelphia along with some cash to cover the difference between what Philly wants to pay him and what he may get in arbitration.

So, if the risk if ~$4 million, what is the actual cost of assuming that risk? That requires a probability calculation of how likely the player is to accept the offer. In many of these borderline cases, I’d assume the actual probability is probably around 50 percent, plus or minus 10 percent or so. That’s why they are borderline cases – it isn’t easy to figure out how the player would react to an arbitration offer.

With a probability of around 50 percent, that cuts the total risk in half. In the Beltre example, that would lower the cost of assuming that particular risk to $2 million, once the potential that he wouldn’t accept is factored in.

Is a supplemental pick in the #35-#45 range worth $2 million to the Mariners? Most of the research done on the subject would say yes, and that given these numbers, Seattle is better off taking the risk of Beltre accepting their offer to receive the potential reward of the compensation.

This is the calculation that teams should be doing – figuring the cost of a potential arbitration award over the market value of the player, adjusting for probability that he accepts the offer, and comparing the cost of that risk to the benefit of the compensation pick.

If a team is assessing their actual risk as the full potential salary that they would have to pay out if a player accepts, they’ll be overstating their own liability and miscalculating the costs and benefits of an arbitration offer. I would suspect we will see multiple teams do just this tomorrow, leaving value on the table by being overly risk averse.