## The Value of a Compensation Draft Pick

If the magnitude of deals for free agents like Robinson Cano and Jacoby Ellsbury already seem too high to you, the market rate might be even higher than you see on the surface. Both Cano and Ellsbury were signed with draft pick compensation attached. If MLB teams are evaluating the draft picks accurately, the valuation of Cano and Ellsbury are even higher than just their contracts on surface. How much should the draft picks discount these contracts? To answer the question, we have to determine how much the draft picks are worth by themselves.

Numerous studies have been done on the value of draft picks. The methodology I follow most closely is Nate Silver's. I look at all the first round and supplemental round picks from 10 drafts from 1995 to 2004. This makes the sample a bit uneven, as there are 10 no.1 picks but only seven no. 40 picks in my sample. I did not apply any plate appearance or innings filter to determine the exact number of seasons the player is under team control. Instead, I consider each player's first seven season in the major league, regardless of their playing time. Some players, like Josh Hamilton, end up getting another year of service, while some who shuffle between the majors and minors would lose seasons under team control under this system. This is a graph of the WAR produced by each pick in their first seven seasons according to Baseball-Reference.

I fit a logarithmic regression of WAR produced in each season on the pick number to calculate the expected WAR of each pick in each of the first seven seasons. I assume that these picks in the 2014 draft would be making their major league debut in the 2017 season and remain under team control through 2023. Using a starting \$/WAR figure of 6 million in 2014 and an annual growth rate of 5%, the market value of each pick's production can be calculated. I assume that the salaries of a draft pick are as follow:

First season: \$250,000 (only in the major league for part of the season)

Second season: \$500,000

Third season: \$750,000

Fourth season: 20% of market value (comprise of those eligible for Super 2 arbitration and minimum contracts)

Fifth season: 40% of market value (1st year of arbitration)

Sixth season: 60% of market value (2nd year of arbitration)

Seventh season: 80% of market value (3rd year of arbitration)

The salaries are subtracted from the market value to determine the surplus in value of each pick. The surplus is further discounted at an annual rate of 5% to reflect the growth in salary and how much the surplus is worth during this offseason. The signing bonus of each pick also needs to be accounted. In the 2013 draft, the draft slot increased by 8.20% from 2012. I assume that the draft slot in 2014 grows by the same amount, and that each pick signs for exactly the amount as the draft slot. The total discounted surplus, minus the signing bonus, is the net value of each pick in this offseason.

The average value of picks 11-40, picks that would be given up when a new team signs a free agent with qualifying offer, is \$9,150,723. Even teams who re-sign their free agents are effectively abandoning a compensation pick in the 25-35 range, with an average value of \$6,984,245.

Using this evaluation, the Mariners should be valuing Cano at \$245 million over 10 years to pay him \$240 million, as they are giving up their second round pick (36) worth around 5 million dollars. The Yankees should be valuing Ellsbury at \$165 million over 7 years to give up their 18th pick worth about 12 million dollars. Similarly, the Mets' deal with Curtis Granderson is not strongly affected by the draft pick attached, as the Mets are only giving up their second round pick. These may not sound very different from their contracts on surface. However, if you focus on smaller deals, the value of the draft pick can change your perception of the contract drastically. For example, it might not be difficult to imagine Mike Napoli worth \$32 million over 2 years. However, once the draft pick is factored in, the Red Sox are essentially valuing him at \$39 million. The same applies to Carlos Beltran. Many writers have already regarded Beltran's \$45 million deal over 3 years as an overpay. It would be even harder to fathom the Yankees valuing at \$57 million. Hiroki Kuroda may be more of a special case, as he was rumored to be choosing between the Yankees and returning to Japan. If he were to leave the major league, the Yankees would not have received a compensation pick. Therefore, Kuroda's contract can be evaluated at face value without the consideration of the draft pick.

From the contracts of Beltran and Napoli, it seems fair to question if MLB teams are evaluating their lost draft picks properly. My study on the value of draft picks is hardly definitive. More drafts can be included and calculating the exact number of seasons under team control would improve the accuracy of the results too. Nonetheless, it should at least raise some questions about the recent free agent signings. Maybe the market rate for wins is even higher than we have seen on the surface. Or maybe this is still a market inefficiency that can be exploited by an analytically inclined team.

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