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.




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Dave is a co-founder of USSMariner.com and contributes to the Wall Street Journal.


35 Responses to “To Offer Or Not?”

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  1. JoeR43 says:

    “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.

    I’m not a Kenny Williams hater or out to bash you, but have you seen his track record on outfielder defense?

    (yes this is mostly meant in the sarcastic sense, but I honestly would not put it past KW).

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  2. Michael says:

    That’s a great point, Dave. I hadn’t really thought of it that way, but it makes perfect sense. Provided these trades give back little in return (PTBNL’s come to mind), there’s little incentive not to offer arbitration to all but the most vastly overpriced players.

    Makes me sad that the Marlins won’t offer to Type B’s like Calero and Nick Johnson because they fear they’ll be stuck with the salary, even though they could easily turn around and deal them away if the worst case scenario occurs.

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  3. Jimbo says:

    Beltre is a great example.

    I’m curious what sort of case could be made against offering him arbitration. If there’s a chance he doesn’t take it, but worst-case is trading him…what’s the downside? That he wins a favorable arbitration number, accepts it, and can’t be dealt without a lot of cash included? Even if they get nothing of value in return there doesn’t seem to be much risk.

    I guess if a team expects market-based salaries to fall, but arbitration to lag that trend…then there’s risk of his pricetag being too high for a supply and demand free agent market.

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    • Matt Walsh says:

      The risk is that Beltre accepts, and then is awarded a favorable $13-14 million and no one will take him on for anything more than $8. Not saying the chance of this is high, but certainly not negligible either.

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  4. notdissertating says:

    You may have overstated the importance of the probability of a player accepting an arbitration offer. The probability of accepting is likely highly positively correlated with the magnitude of the offer. So there is a great deal more weight on the “bad” outcomes for the team then there is on the “good” outcomes. Just using a flat 50% rate as in the Beltre example will understate the true cost (because he is really, say 75% likely to take a high offer and 25% likely to take a low offer). This also highlights the importance of coming up with some sort of probability distribution over potential arbitration figures.

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    • Dave Cameron says:

      They don’t offer specific numbers. They only have to decide whether to offer him arbitration or not. The figure is submitted later.

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      • notdissertating says:

        Maybe I wasn’t clear. You wrote:

        “With a probability of around 50 percent, that cuts the total risk in half.”

        Not really, because a player is more likely to accept a large figure than a small figure.

        From the perspective of a team both the actual figure and whether the player will accept the figure are uncertain. So when calculating expected cost/value the team needs to come up with both a probability distribution of the arbitration figure (you implicitly assume a uniform distribution between $10 and $13M), and the probability of a player’s accepting, conditional on each possible realization of the arbitration figure. Then the team would need to sum up the probability of each event occurring, where an event is the realization of an arbitration figure and whether the player accepts or not. Each even has a probability of occurring and a value. Sum up each probability*value across events and you have the true expected cost to the team. This will be different from what you present because the probability of accepting is not independent of the arbitration figure.

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      • notdissertating says:

        never mind. players, like teams, have to decide before knowing the figure, whether to accept. perhaps this is what you were trying to tell me. ah well.

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      • ajs340 says:

        notdissertating sort of didn’t understand your point, Dave, but I think he brings up a larger point that you skip over. Which is: The chance of any particular player agreeing to arbitration isn’t really that close to 50-50.

        I think a lot of these borderline cases are borderline for the teams, but not the players. Take a guy like Beltre, who had a down season and is widely regarded as something of a one-year-wonder. Do you think he will turn down arbitration? He’s probably thinking he will get a much higher arbitration award than whatever contract he would end up with in the free agent market (simply because arbitration tends to lag the market, not predict it).

        If that’s the case, the Mariners would be stuck with him because they’d have to throw in too much money to make any other team take him.

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      • ajs340 says:

        Also so many of the “Type A” guys are not truly franchise players. For example: Bengie Molina, Octavio Dotel, Darren Oliver. When you’re considering those guys, yes, the reward in terms of draft picks may be high, but they’re not going to turn down arbitration when it’s fairly likely their services won’t nearly be valued enough by other teams to make them worth giving up the draft pick to sign.

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  5. Ronald says:

    Awesome. I have nothing to add.

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  6. Mark says:

    Billy Wagner in Boston won’t get the arbitration offer – way too much for a set up guy coming off of TJ in his late 30s. Marco Scutaro undoubtedly will get it though because if the Blue Jays thought he would accept they never would have signed AGon.

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    • Judy says:

      The Red Sox are absolutely going to offer Billy Wagner arbitration.

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    • The Hit Dog says:

      Yup, Wagner will be offered arb. He has stated publicly that he wants to be somewhere where he can close, thus severely limiting the risk that he will accept a 1-year deal as a set-up man.

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  7. Ron says:

    If you are factoring in the probability of the FA accepting the arbitration, shouldn’t you also factor in the probability of getting the supplemental pick? In the Beltre example, there is a 50% chance he will accept the arbitration (in which case the Mariners are down $4M and do not get a compensation pick) and a 50% chance he will decline (in which case the Mariners don’t lose any money + get the comp pick). So, essentially, you need to compare $2M (50% of the $4M) to 50% the value of the comp pick (or the $4M to the comp pick), and not $M to the comp pick, as you did. Am I missing something here?

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    • Ron says:

      Woops, typo – l dropped the amount in the last line. Last line should read: “… and not $4M to the comp pick, as you did” ……

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    • james says:

      yeah… i don’t think you’re factoring in the value in trade they’d get for assuming the difference in his market value and what he got in arbitration… which would go up the more of the difference they take on. It might not be the same value as a 25-35 pick, could be more or less, but there is still value there.

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  8. WallyBall says:

    Dave

    Thoughtful and thought-provoking. A few questions (and maybe a comment or two). Staying with your Beltre example, when you say ‘Is a supplemental pick in the #35-#45 range worth $2 million to the Mariners?’, are you fully accounting for the cost? In other words, do you mean ‘is a prospect drafted between 35-45 worth $2m’? or just the right to draft him? If the latter, don’t you have to include another $1m or so to sign him, making the fully loaded cost of the decision equal to $3m? Also, when you make analyses based on market value (even ignoring a likely shifting market place), don’t you have to factor in transactions within the relatively small marketplace affecting value? In other words, most market trader/quant types want their trades to be so small that their actions, by themselves, don’t move the market. With only 30 MLB teams, let alone subdividing by position and/or availability within those positions, wouldn’t a decision like the Mariners v. Beltre affect the market value of available 3rd basemen? Especially if the Mariners budget process is such that they are not allowed to ‘spend’ the money that they are assumed to be saving by ultimately trading him until he actually clears their books, isn’t that a fairly obvious market signal that other teams can read, ultimately leading to reduced value?

    Lastly, and conversely, even if teams value it the ‘old fashoned way’ (ie it is a $13m decision), can’t they cut arbitration guys before the end of spring training and only be liable for 1/6 of the salary?

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    • Steve says:

      Yes, they can cut the player. But I believe the player has to exhibit an “erosion of skills”, or something like that. In other words, this avenue is not so easy, and would probably come with a grievance from the union. It’s happened a handful of times, but it’s not common.

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      • james says:

        seems like it’s easier these days with all the ways we can convert a player’s value into $ value and replacement value and all that other junk. If a player asks for and gets a ridiculous amount in arbitration because he can only take so much of a paycut, and that number is way above his market value… there’s an erosion in there somewhere.

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    • TCQ says:

      I’m certainly no expert, but it’d seem that the cost of signing the prospect would be factored into the studies that Cameron referenced – since that research really is meant to ascertain the *surplus* value of a draft pick in the first place.

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  9. Mike Green says:

    Yes. It’s tough to get a handle on the value of type A compensation because it depends on who is likely to sign the player and what other players that team is likely to sign.

    If a team is stuck with a salary it does not want, the risk might be somewhat higher than stated here because there may be a “forced sale” element to it, with the result that the club gets significantly less than market value.

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  10. rwperu34 says:

    Does Beltre lose his 10 and 5 rights if he accepts arbitration?

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  11. philosofool says:

    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

    Is this right? I mean, would most teams rationally pay $2M for the option to sign a player, given that the cost of signing the player isn’t factored into the cost of the option to sign him? This basically adds $2M to the cost of your draft for the season.

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    • Steve says:

      also overlooked is the value of simply plowing that $2M into your draft budget instead of taking the risk. talent in the draft is distributed in such a way that you can probably get a 2nd round talent-type player who slides down the board b/c of bonus demands if you are willing to use that $$ to overpay later in the draft.

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  12. Al Dimond says:

    A couple comments.

    1. If you’re dividing the $4 mil risk in half because there’s a 50% chance the player declines you have to multiply the expected value of the supplemental draft pick in half also because there’s only a 50% chance you’ll get the pick. If there’s a 60% chance the player accepts arb you have to multiply the risk by 60% and the reward by 40%.

    2. You’re assuming that you can find a trading partner when you go to sell. That’s like planning bunt strategy on the assumption that your team will execute the bunt. There will likely only be a couple buyers at the position.

    3. A GM that pulled this “arb-and-trade” scheme and had to eat money to make the trade happen would get killed in the press for it, even if his reasoning was pretty sound. A GM that took the risk and had it pay off wouldn’t get much credit because the player signed wouldn’t be around for a few years, if ever. I’m sure these things are considered, fairly or not.

    4. I don’t think agents make a career out of deluding themselves and their clients when it comes to free-agent and arb values. While there is some uncertainty involved for everyone in both, if public information indicates that it’s likely that the arb value is higher than the market value the player should be pretty likely to accept arb, right?

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    • james says:

      if you ascertain his market value to be nil and his potential arbitration award to be immense, you definitely don’t offer him arbitration… because then it becomes much closer to 100% risk of him accepting.

      Only a douchebag of a GM would avoid this process because of the disparity of positive versus negative credit for the move… which is probably why most of the teams in baseball get this wrong.

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  13. DM says:

    Interesting thought, but I think your logic may be flawed. Wouldn’t the Mariners be more concerned with the potential difference between the arbitration award and either A) The amount they are willing to spend at third base, or B) The amount they value Beltre at?

    Beltre’s free market value is fairly irrelevant, isn’t it? To the Mariners, it doesn’t matter what the market is willing to pay. It matters what they are willing to pay. You allude to this when you state that the Mariners have approximately $25 million to spend this season, but then completely disregard such budget constraints in your equation.

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    • james says:

      You’re right in that they would have to move Beltre before they can look towards their own solutions at third base… or anywhere else for that matter since the ridiculous arbitration award he’ll get will eat in to what they can do at first base and at pitcher. They had to make a Beltre and Bedard decision before they moved on to other decisions. For them the risk of being “stuck” with Beltre for a year wasn’t as bad as losing out on draft-pick compensation.

      His market value is only important because if he has no market value you wouldn’t offer him arbitration at all… and you have to know what you’ll have to ship to a team to make up for the difference in his perceived market value and his arbitration award… and also what to ask for in return.

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  14. mydquin says:

    DM is right. Dave’s model is misspecified. The real risk is the weighted difference between the arby settlement and the cost of obtaining Beltre’s expected WAR on the OPEN FA market. At this point Scutaro’s expected WAR is probably just as high as Beltre’s. F. Lopez and J. Uribe are in that ball park too. If Scutaro can be signed for $4MM/yr, then the real risk to the Ms is roughly $4MM = ($12MM – $4MM) * 50%.

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  15. What I didn’t get was what Al Dimond also mentioned. If the cost of Beltre accepting arbitration ($4M) is divided by two because there’s a 50-50 chance he’ll accept it, then why isn’t the reward of the draft pick ($2) also divided by two (same 50-50 chance)? Could you briefly explain this Dave?

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