Valuing Players

Baseball analysts often toss around dollar values of players, accompanied by an assessment of whether a team overpaid or underpaid to sign a player or acquire him in a trade. The commentary can be confusing for several reasons, including the uncertainty over which definition of value the analysts are using. To take a step back, let’s talk about the various definitions of the dollar value of a player. It seems that when the above references of “overpaid/underpaid” are made, they often refer to market value of a player. Even the definition of market value can be confusing, so we’ll come back to that later. Another way to define player value is to analyze his value to a specific team, basing it on the team’s unique circumstances, such as their revenue opportunity from improving their win total, which is driven by their market size, excess seating capacity, location on the win-curve (i.e., are they contending for a postseason berth), etc.

A third definition of value is to estimate a player’s asset value to his team. This is often a way to assess the fairness of a trade. A player’s asset value refers to the value of a team having control of the player and includes a calculation using the player’s salary, relative to some value estimate (e.g., either of the two value definitions referenced above), over the number of years he is under team control. For a simplified example, let’s say a team acquires a player making $5 million per year for two more years, but his “value” to the team is $8 million. His asset value would be 2 years X $3 million per year for $6 million (not counting the time value of money or amending his value for any risk factors). It might be considered a fair trade if the team gave up a player whose salary is $4 million per year for one year, but his “value” to the team is $10 million per year. In this simplistic example, the team would be acquiring a player and giving up a player with approximately the same value—$6 million.

Asset values can get very interesting when a player is being paid “at the market” or even above market value, as is the case with Cliff Lee. The Phillies lefty is owed a minimum of $87.5 for pitching the next 3 seasons ($25m per year + a $12.5m buyout of 2016 option). However, if Lee’s $27.5 million option vests, then a team would be obligated to pay Lee $102.5m over the next 4 seasons. There are only a limited number of circumstances in which Lee would have a positive asset value to a team. The team would need to believe that Lee was the last piece of the puzzle and the difference between possibly missing the playoffs versus a deep run into the postseason. Furthermore, they would need to believe they would be competitive over the four year span of Lee’s contract. Just reaching the postseason once, with Lee being a difference maker, would likely not foot the bill. On top of that, a team would likely need to give up a player in order to get Lee. I happen to love Cliff Lee as a player. My Starting Pitcher Ranking system has him in the top 10 of all starting pitchers this year—a year in which he’s won only 4 games! Despite my accolades for Lee, an example of a fair trade may be the Phillies giving up Cliff Lee and Domonic Brown, a disappointing, highly touted prospect with a couple of years of control remaining at pre-arbitration rates, in exchange for a low-level minor league prospect. In other words, trading Lee and a player with a low asset value (Brown), in exchange for another player with a low asset value. When assessing a player’s asset value, even the top players in the game can get “upside down” with respect to value versus salary.

Regarding the market value of players, I’ve statistically modeled the last ten years of free agent signings in order to develop a framework as to how teams value various attributes of a player, such as his age, position, handedness, recent past performance, along with several other factors. But think of this as a generic valuation, not a team-specific valuation. For example, in last year’s free agent market, my model valued Michael Cuddyer at $11 million per year for 3 years. As it turned out, Cuddyer signed a contract with Colorado for $10.5 million X 3 years. In this instance, my estimate of the market rate turned out to be very close to his actual contract value. However, if the Yankees were in the market for Cuddyer, they possibly could have valued him at a higher dollar amount, based on their unique revenue opportunities.

It’s interesting to look back at how the free agent market valued position players and pitchers over the last several years. Keep in mind there is a difference between what teams expect to pay for performance versus what they actually pay for performance, since the pay is set before the performance is delivered. I tallied all one-year free agent deals for the last eight years, capturing the player’s one-year compensation and their wins above replacement (WAR from FanGraphs). The results are listed below. It’s interesting to see the high water mark in terms of cost per WAR was 2008. Teams spent nearly $8 million per win for pitching free agents and $5.6 million per win in the position player free agent market in 2008.

A few closing thoughts on a player’s value to a specific team. This can be estimated by analyzing their revenues in the context of their on-field performance. I want to emphasize that statistical models of a team’s win-curve (whether from actual team financial data or estimated financials from publicly available information) is just one input into understanding a complex question: how do revenues respond to on-field performance? In much the same way statistical analysis of a player’s performance must be integrated with scouting reports, a medical assessment, an evaluation of the player’s makeup and other factors, before a complete picture can be created, the same applies to the estimation of how winning will impact revenues. Revenues are the result of consumer behavior—fans’ unique response to changes in team performance. The items that need to be considered when creating a more complete picture of a team’s win-curve are fans expectations of team performance, their motivations, and the time lag between performance and fan actions, among others.


Two thoughts:

Team specific value is less of an issue than you imply since the offseason player market works much like an auction, so a team which values a player highly only has to compensate that player more than his next best opportunity. In most cases (that is, assuming the player doesn’t have non-monetary reasons to prefer another team), that means paying a bit more than the 2nd highest team specific valuation, which is often a lot less than the highest team specific valuation. So, even if Cuddyer was worth $17m/year to the Yankees (over a three year contract), they probably could have had him for $11m to $12m ($10,500,001 seems too precise given the uncertainties of a negotiation). Now if he was worth $15m/year to the Dodgers in addition to being worth $17m/year to the Yankees….

If you’re comparing player WAR values in the season of their one year contract to their cost (which is what it looked like, but I wasn’t positive that you weren’t using a projection), then the differences between player WAR value and salary might reflect trends in the quality of team WAR projections for those free agents rather than the value they placed on each WAR. It’s hard to distinguish between those two cases, but it might be worthwhile to take a quick look for a strong effect by seeing if there is any correlation between projected WAR (using, say, Marcel)/actual WAR and salary/actual WAR. That said, I suspect that projection quality isn’t the main cause of the $/WAR value, since the peak just before the 2008-9 recession suggests a financial cause.

The chart above is not based on any projections. It reflects the salary paid relative to the actual performance delivered for the season in question. For example, player signs a one-year deal at $4 million and then delivers 0.8 WAR for the season, for a cost per WAR of $5 million. I have looked at this issue using projection and there is a huge variation on a case-by-case basis between projected cost/WAR vs. actual cost/WAR.

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