Click here to view the qualifying offer valuation model and play with the assumptions and variables discussed in this article.
In sports, “free agency” is generally a fallacy. While free agent professional athletes ultimately select their future employers, collectively bargained salary cap structures and other related rules – designed to enhance competitive balance – restrict their freedom. Among a variety of complex rules, the NBA’s Collective Bargaining Agreement caps their stars’ earning potential at a maximum percentage of the salary cap, while also enabling a player’s previous employer the ability to offer a higher percentage than any other team. The NFL offers a different obstacle restricting player movement by allowing teams to designate one of their free agents as their “franchise player,” forcing the player to either come to terms on a long term deal or accept a one-year tender with that franchise. Salary caps and other collectively bargained rules prevent free market opportunities.
Baseball remains the lone major American professional sports league immune from the restrictions of a salary cap. After six years in the MLB, players are free to sign with the highest bidder for their services and teams may spend as much as they want to assemble their MLB rosters.
Despite this freedom, the 2011 MLB Collective Bargaining Agreement provides for other measures to foster competitive balance. Instead of players primarily bearing this burden like in the NBA, NFL, or NHL (ignoring the sums major market franchises sacrifice in revenue sharing), the MLB has promulgated spending rules with significant financial and organizational penalties for transgressions. For teams that spend over the league’s designated “competitive balance tax” threshold ($189MM in 2016), for example, teams must surrender accelerating sums for each consecutive year spending in excess.
The CBA also equips teams with the option to offer their free agents a one year “qualifying offer” tender valued at the average salary of the top 125 players in the league. If accepted by the player, the team retains the player at a relatively high salary ($15.8 million last offseason). If rejected, the player becomes a free agent and the team receives a sandwich pick in the subsequent MLB draft. The eventual signing team, however, must surrender their first round pick if it falls outside the top ten selections (or their second round pick if the team owns a top ten pick).
While the previous CBA also required surrendering draft picks to sign premier free agents, teams without their first or second round selections could elect to overspend recommended signing bonuses later in the draft to acquire premium prospects that fell due to exceptional demands. Now, however, teams also face significant penalties for exceeding their bonus pools, including the loss of future draft picks if egregious. Organizations face similar restrictions for exceeding international bonus pools and may not be able to sign elite international free agents in the next or multiple signing periods.
Since the 2011 MLB CBA restricted draft and international free agent spending, teams now have finite opportunities to add young talent to their organizations. Given these severe restrictions, surrendering one of the few avenues to acquire talent is costly; with fewer quality prospects to supplement the Major League roster, franchises must spend greater resources on the free agent market to piece together a quality team. Since homegrown products provide their organizations with cheap labor, each draft pick maintains a certain amount of surplus value. Teams that express a willingness to sign free agents who turned down qualifying offers must also include this figure when considering the overall cost to the organization. This article seeks to quantify that cost.
- Draft Pick Productivity: Average WAR Under Team Control
In order to properly value draft picks, we must first determine the performance (in terms of Wins Above Replacement) that players at each draft selection provide their franchises while under team control. Given the significant amount of time it would take to catalog the production of decades of draft classes, I elected to defer to outside sources to provide a formula of the average WAR produced by players at each draft choice through the first six years of their Major League career (before they hit free agency) to isolate the typical value provided to the drafting franchise.
After presented with several alternatives, I proceeded with a formula determined by the Hardball Times’ Matthew Murphy, who calculated the average WAR provided by the 1991-2005 draft classes. While his sample remains limited to 15 years, it operates under the assumption (analyzed by Chris Cwik on Sports on Earth) that the most recent draft classes provide a better predictive measure into future draft classes than earlier years given the influx of greater resources devoted to identifying amateur talent. Compared to older classes, improved information has made the draft more efficient in funneling the best players to the top of the draft. Future draft classes should only further demonstrate such efficiency since new draft restrictions limit the ability for top prospects to fall in the draft due to signability concerns. While ordering previous draft classes by signing bonuses may prove a more effective measure, such an undertaking would be more difficult to compile and the draft likely serves as a strong proxy for such regardless.
An alternative formula developed by Sky Andrecheck analyzes a greater sample of draft classes, which ultimately provides lower expected WAR values for top selections. As Murphy discusses, however, Andrecheck’s model, while limited in describing the value by top picks, is actually more accurate in predicting the actual WAR of picks toward the end of the first round. The following graph provides the actual WAR generated by each draft position (blue) with Murphy’s model (green) and Andrecheck’s model (red) superimposed.
An important caveat to this analysis remains the potentially false assumption that “average” represents the best measure of draft pick value. While it requires further research, the average WAR of each draft position is significantly higher than the median; most draft picks do not reach the Majors, while stars serve as outliers raising the average. The median WAR may therefore serve as a better predictive measure. For the purposes of this study, however, I elected to proceed with Murphy’s approach as the most accurate third party representation of draft pick value.
- Present Value of Draft Pick WAR
While we have a model providing for the expected total future WAR of each draft pick while under team control, utilizing such as our tool for calculating its monetary worth ignores time-value concepts (i.e., a dollar today is worth more than a dollar in the future, assuming normal inflation). A team may receive 14 WAR from the first pick, but they do not receive that benefit for several years, which is likely spread over the six-year period a player remains under team control. For the purposes of this analysis, I assumed that players typically require three years in the minor leagues before reaching the Majors to start to realize their worth to the team; however, the assumption may be manipulated on the attached spreadsheet. Further, I assumed a 5% discount rate on future seasons, as advocated by FiveThirtyEight’s Nate Silver while writing for Baseball Prospectus in 2005. This value, too, may be altered to produce different results in the spreadsheet; for example, a rebuilding team may not value present wins as significantly as future wins, while others seeking to compete in 2016 may value them more.
The present value formula must also consider when a player will produce WAR for the team; it would likely be wrong to conclude that the average rookie and average five-year veteran provide the same performance to a team. In analyzing the value that top prospects provide their franchises (a similar type of analysis as the one conducted here), Kevin Creagh and Steve DiMiceli of Point of Pittsburgh discovered that most players produce about 2/3 of their team control WAR during their final three years before reaching free agency (while proceeding through arbitration). For this reason, I allocated 1/9 of the total average WAR to each of the first three years of a player’s career, and 2/9 to each of the player’s latter three years (1/3 total to the first three years, 2/3 total for the last three). These percentages of total WAR may be changed in the spreadsheet if a better study exists.
- WAR Valuation
A now-common measure in evaluating the value in a free agent signing remains a comparison of the cost of the signing with the WAR the player is expected to produce over the term of his contract. Retroactive analyses of the WAR received in contracts (e.g., Matt Swartz) as well as forward-looking models based on projection tools (e.g., Dave Cameron) have generated a variety of valuations that inflate each season. As part of the 2013 Diamond Dollars competition, I calculated a “$/WAR” value of slightly north of $7 million with a 5.5% growth rate (and closer to $8 million for players tied to draft pick compensation). With a variety of valuation techniques, the $/WAR figure may be changed in the spreadsheet as seen fit, but I assumed Dave Cameron’s $8 million 2016 assumption.
The $/WAR figure demonstrates the amount of money teams pay for wins on the open market, their only unrestricted access to talent. Theoretically, if the team knew they would receive exactly 2 WAR for one season from a rookie or veteran free agent, all else held equal, they would not discriminate in who they would seek to sign. Thus, we can use the free agent $/WAR figure as a proxy to determine the value a player under team control provides the team. By multiplying the present-value net WAR described above, we can determine the average value a player selected at each pick will provide its team (“Gross Val. WAR” in the spreadsheet).
While I utilized a flat $/WAR figure for this analysis, future models may include a $/WAR growth factor to account for $/WAR inflation. Assuming a player reaches the Majors in three years, the $/WAR of a hypothetical 2 WAR season in his rookie season may be valued higher in the future. Assuming teams continue to spend more per win each season, the value of a draft pick may actually be greater than the current model suggests.
- Cost of a Player While Under Team Control
Although we have determined the value a team provides his team over his six years under team control, we must also account for the costs to employ the player. There are four basic costs paid to the player that must be added together to provide the net total cost: (a) the signing bonus paid upon signing, (b) pre-arbitration salary (generally paid the first three years in the Majors), (c) arbitration salary (paid in the fourth, fifth, and six seasons after reaching the Majors), and (d) minor league salary prior to reaching the Majors.
- Signing Bonus
While teams often pay different bonuses than the recommended “slot” figures, given the aforementioned strict penalties on exceeding draft bonus pools, the slot value assigned to each draft pick serves as an adequate proxy for this figure.
- Pre-Arbitration Salaries
For the first three years of a Major League player’s career, he makes close to the league minimum salary of $500,000 (estimated at $500,000, $510,000, and $525,000, respectively, in the spreadsheet). While Matthew Murphy’s valuation dismisses these costs since all players must earn this salary while on a Major League roster anyway, I have elected to include it since the minimum figure is not discounted in most (if not all) $/WAR valuations. Although a theoretical replacement level player assumes a league minimum salary, the salary remains a cost of employing the player and receiving the value of his services.
Given that WAR production has been discounted (and thus discounting the player’s value provided to the team in the model), the costs must also be discounted. Since the discounted WAR valuation is part of the formula for calculating arbitration costs (see below), such costs have already been discounted. The signing bonus, however, does not need to be altered since it is presumably paid immediately upon acquiring the player. Alternatively, the pre-arbitration salaries must be reduced since they are paid four, five, and six years following the player’s signing (assuming the player takes three years to reach the Majors and start receiving such figures).
- Arbitration Salaries
After three years, a player normally enters arbitration where he starts to earn salaries closer to what he would earn on the free agent market for the last three years he remains under team control. Matthew Murphy’s analysis revealed that players in their first year of arbitration on average earn 28% of their market value, 37% of their market value in their second year, and 62% of their market value in their final year of arbitration. Creagh and DiMiceli alternatively propose 40%, 60%, 80%, respectively. While I elected to incorporate the latter’s structure into the spreadsheet, those figures may be manipulated.
To determine the total arbitration cost, we first take the net “Gross Val. WAR” and multiply it by the percentage of WAR accumulated during arbitration (may be manipulated as mentioned above, but default at 2/3) to isolate the value generated to the team during the player’s arbitration years. Since the player earns less than his market value during arbitration, however, we must then multiply the arbitration value by the net percent of market value between the three years. To appropriately align a player’s performance with his salary, the model actually multiplies the percentage of WAR accumulated in a particular season (i.e., 2/9) with the respective year’s salary market rate percentage. Given that the default model attributes equal WAR percentages among the three arbitration years, it has the same result as simply adding the percentages together and multiplying by the average arbitration market rate. Should the team elect to distribute different WAR percentages to each season, it may affect the draft pick values.
- Minor League Salaries
Minor league salaries are not irrelevant, but they are miniscule compared to other costs. The spreadsheet agrees with Murphy’s model in ignoring minor league salaries in the cost calculation.
- Surplus Value: Worth of a Draft Pick/Qualifying Offer
To complete the analysis, we simply subtract the net costs found in the above Section 4 from the WAR valuation in Section 3, which provides the net surplus of each draft pick – the average value of a draft pick. Depending on where the team selects in the following June’s draft, a franchise can adequately consider the additional cost in signing a high end free agent. A deal that appears to represent a bargain based on a simple $/WAR calculation may actually represent a below market deal given the value of the surrendered pick. Lesser tier free agents attached to qualifying offers may see their markets dramatically reduced.
- Additional Important Consideration: Draft as a Zero Sum Game
While we have focused on the direct cost of surrendering a draft pick, it also enriches other franchises. When a team relinquishes their pick, the team losing the free agent gains a selection between the first and second rounds. Further, each selection between the location of the original pick and the new added selection increases in value equivalent to the difference between its new spot in the order one pick higher and its previous selection. For example, if a team loses the 20th pick for signing a free agent attached to a qualifying offer, every team below them and above the new selection moves up one position in the draft. Another team originally picking 27th would now pick 26th, and would thus obtain approximately $150,000 in additional value because of the higher selection.
Ultimately, the new draft pick compensation system resembles a zero sum game. Regardless of who owns each selection, the number of selections remains constant; thus, for a team to lose value, at least one team must gain that value. While I have been wrestling with how to value this reciprocal gain – considering whether to simply double the value – it ultimately depends on other, more difficult to quantify, circumstances, specifically the teams set to gain from the pick changing hands and incremental selection modifications. For example, signing a free agent away from a division rival may provide an obvious significant benefit for the signing team, but the rival gains the value of the draft pick – surely a team would prefer a team in the opposite league to obtain the selection instead. While the signing team would merely dismiss this as the cost of business of acquiring a key player from a rival, it nevertheless provides their rival a potentially significant benefit.
Conclusion: How Much is a Qualifying Offer Worth?
Given the aforementioned parameters and assumptions, the model provides for the following first round pick values:
The major takeaway? Depending on where a team is projected to pick in the first round, it must consider the opportunity cost of signing a player who turned down a qualifying offer when determining an appropriate offer for the player. For example, a team picking 14th overall should recognize that a $40 million offer effectively costs them $50 million in value.
Likewise, free agents facing a qualifying offer must scrutinize their position in the free agent market. While top tier free agents will not see their markets suffer, the average free agent should reconsider turning down a qualifying offer if their salary demands plus the the opportunity cost to signing them exceeds their projected $/WAR performance.
Ultimately, teams and players can both make better informed decisions by understanding the economic significance of qualifying offers.
Click here to view the qualifying offer valuation model and play with the assumptions and variables discussed in this article.
 Teams that exceed the threshold must pay a 17.5% tax on each dollar over the limit. If they eclipse that figure two years in a row, they must pay a 30% tax; three years in a row, 40%; and four years and above, 50%. See http://www.fangraphs.com/library/business/luxury-tax/.
 Formula: y = 14.055x-.481 See http://www.hardballtimes.com/how-much-is-a-draft-pick-worth-in-2014/
 Analyzing the correlation between draft position and signing bonus remains beyond the scope of this article, but it can be reasonably assumed that there is a strong correlation.
 Formula: y = 12.03x-.52 See http://baseballanalysts.com/archives/2009/06/draft_picks_and.php
 Stephen Drew, Kendrys Morales, and Nelson Cruz, among others, would agree.
 One such example: in order to sign Orlando Hudson in 2009, the Dodgers relinquished the pick used by the Diamondbacks to select A.J. Pollock.