Calculating Economic Values

Posted on March 18, 2007 by


The Baseball Economist has now been on the market for three days. Surprisingly, some people have not bought this book. To further advance its cause, I thought I would spend part of my Sunday commenting on this book again.

The Scully Model

In Chapter 13 Bradbury asks “What is a Baseball Player Worth?” His answer builds upon the work of Gerald Scully. Scully, in 1974, published the first empirical paper on the subject of sports and economics. Appearing in the American Economic Review (the top journal in economics), Scully’s study examined the impact the reserve clause had on the salaries of Major League Baseball players. Because the reserve clause prevented baseball players from selling their services on a free market, economic theory would predict that baseball players would be paid less than the revenue the players generated for their respective teams.

To test this hypothesis, Scully had to determine the value of a baseball player. Scully’s method began by determining how many wins each player produces – which is what economists would call the player’s marginal product. With the number of wins determined, Scully created a model of team revenue that allowed him to determine the dollars each win generated. This is what economists would call marginal revenue. When you put marginal product (or wins), together with marginal revenue (the revenue created by wins), you have each player’s marginal revenue product (MRP) – or the amount of revenue each player creates. With each player’s MRP estimated, Scully then compared these estimates to the wages paid. The results indicated, as theory predicted, that baseball players – prior to the institution of free agency – were underpaid. This means that great players like Mickey Mantle, Willie Mays, Henry Aaron, Jackie Robinson, Stan Musial, Joe DiMaggio, Ted Williams, Babe Ruth, etc… were exploited (or paid wages less than the revenue they generated for their respective teams).

Updating Scully

JC Bradbury has utilized the basic Scully approach to measuring the MRP of baseball players in 2005. Bradbury does update the Scully model with a bit more sophisticated approach to the measurement of productivity from pitchers and hitters. It is important to remember that Scully was writing in the early 1970s before the advent of much of what we call the Sabermetric movement. Consequently it should not surprise readers to find Bradbury’s approach to be somewhat different (although the essence of his approach is the same as Scully).

The actual differences I will let people see in the book. I do want to comment briefly on the results. Bradbury finds – consistent with economic theory – that players who sell their labor on a free market earn a wage quite close to Bradbury’s estimate of MRP. Players who only had access to arbitration or who were completely reserved by teams (these would be players with less than six years of Major League experience) were paid a wage far less than the estimate of their MRP. In sum, if the market is free you tend to be paid what you are worth. If the market is restricted, you tend to be paid less than what you are worth.

Bradbury does note – an observation echoed in the work of fellow sports economist Tony Krautmann (who has an alternative to the Scully method that I might need to post on sometime) – that part of the reason non-free agents are paid less than their MRP is because baseball teams spend money training players. Unlike the NBA or NFL, Major League Baseball does not rely upon the NCAA to develop its talent. The players drafted by baseball teams almost always start their career in the minor leagues where the player is trained for the Major League. Because baseball pays for this training, economists tend to believe that part of the difference between the wage paid and revenue generated for non-free agents is simply teams re-gaining the cost of training. Of course, although training is part of the difference, the inability of young players to bargain surely contributes to this difference as well.

Some Results

Yesterday Bradbury was interviewed by a Boston radio station. To introduce his work to the Boston market, Bradbury posted his MRP estimates for Boston players in 2006. The results indicate that David Ortiz was worth $17.09 million and Manny Ramirez produced $14.44 million. For pitchers, Curt Schilling led Boston, producing $12.06 million.

What would be interesting to see are the results for all players from last season. This is not reported in The Baseball Economist, but it would be nice to see it at Sabernomics sometime in the near future. It’s not that I want to add to JC’s workload, but I would love to see MRP estimates for all baseball players (or maybe just for my team, the Detroit Tigers).

– DJ

Update: As JC Bradbury has indicated at Sabernomics, the Baseball Economist does report the values of every player in baseball for both the 2005 and 2006 season.  My review copy of the book, though, did not.  Of course, JC says I get a copy of the final version of the book (which is very nice of him).


Posted in: Baseball Stories