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May 17, 2007
Organized Common Sense
"[Economics] is a method rather than a doctrine, an apparatus of the mind, a technique of thinking which helps its possessor to draw correct conclusions."
The Victorian historian Thomas Carlyle once disparagingly referred to economics as "the dismal science." Its adherents prefer to think of it simply as organized common sense. Fortunately for baseball fans, two new books published this spring evince the latter more than the former: J.C. Bradbury's The Baseball Economist: The Real Game Exposed and Vince Gennaro's Diamond Dollars: The Economics of Winning in Baseball. Both books use economic concepts and methods in their attempt to enliven and deepen our understanding of the game.
Diamond Dollars deserved a review all its own, so this week we'll take a romp through The Baseball Economist to see how it stacks up.
Exposing the Game
An economist and professor at Kenesaw State University and the University of the South, Bradbury is the force behind the blog Sabernomics, where he mixes sabermetrics with economic assumptions about human behavior. Those familiar with the blog will no doubt feel right at home with the book, since many of the ideas for the chapters began as discussions and debates with his readers.
The book begins with on-field issues like hit batsmen and managers lobbying for balls and strikes, then moves on to "almost off-the-field" issues such as steroids and the evolution of baseball talent, and finally delves into front office strategies in player evaluation. He finishes by discussing issues relating to the structure of the game itself, focusing on baseball's monopoly power. The end features 75 pages of appendices that give a short overview of multiple regression, and a team-by-team accounting of the gross Marginal Revenue Product (MRP) measure that he develops earlier in the book.
The book has to walk a tightrope. On the one hand, it aims to explain economic concepts to baseball fans. At the same time, Bradbury shares the results of more hardcore sabermetric analyses related to those concepts. I found the discussions of the economic theories especially interesting as they relate to baseball. If you're just a little fuzzy on externalities, rent seeking, game theory, the Nash equilibrium, creative destruction, constrained maximization, and the difference between single and multi-price monopolies, then you're in the right place. Bradbury does a nice job of defining and explaining each idea while keeping the focus on baseball, avoiding the trap of falling into long-winded and technical explanations. Where he does diverge from baseball, he does so very briefly with the simplest of examples, in order to drive home a point. His discussion of game theory and the relationship of the Prisoner's Dilemma to performance-enhancing substances is but one of several cases that is well-handled. If only my Econ 101 professor had used baseball in his lectures, I might have actually retained something from the course.
There are a variety of sabermetric studies in the book, and are primarily concentrated in the first two sections and include the following:
With the more traditional sabermetric studies out of the way, Bradbury moves on to measuring the value of players using his Marginal Revenue Product (MRP) metric. He calculates this by first estimating the impact of runs on revenue using run differentials. This allows him to draw a non-linear curve not entirely dissimilar from the win-revenue curve that Nate Silver discusses in "Is Alex Rodriguez Overpaid?" from Baseball Between the Numbers .
Bradbury finds that the first run scored or prevented that puts a team above .500 is worth $127,000. It turns out that at a .500 win percentage Bradbury's figures are pretty close to what Silver found, where the 82nd win was worth about $1.2 million. Roughly ten runs equate to one win, so the first win above .500 would be worth around $1.3 million. However, in Silver's more sophisticated model, the wins from 83 to 90 bring in increasingly more revenue, with the 90th win worth $3.5 million. After 90, each additional win brings in less revenue because of its decreasing relevance in making the playoffs. In Bradbury's model, the curve is less steep, though additional revenue continues to accrue to around $175,000 per run as the run differential nears 200, equating to just over 100 wins.
Silver's general model is supported by Gennaro's analysis in Diamond Dollars, where his win-revenue curves look very similar. Gennaro takes the additional steps of customizing them per team, and augmenting the curves for additional postseason and World Championship revenue. But since Bradbury is using this analysis to get at the dollar value of players and not trying to predict the impact on revenues if a particular team adds a particular player, his more linear approach is better suited for his next steps.
Bradbury next calculates the number of runs a hitter would produce, and the number of runs a pitcher saves, if they were a team unto themselves. He uses formulas derived from regression equations, considering OBP and SLG for hitters, and strikeout, walk, and home run rates for pitchers (taking DIPs theory into account). These values are then park-adjusted and prorated by playing time to produce a Runs Scored Above Average for hitters (RSAA) and runs allowed below average (RABA) for pitchers.
Finally, these values are translated into revenue figures using the curve he created in step one, added to a baseline amount of revenue the average player would contribute given the same percentage of playing time (with "average player" defined as one who would produce an 81-81 record and thereby generate $54.5 million in revenue). The result is an MRP value for each player in 2005 and 2006: Derrek Lee took the top spot in 2005 at $19.18 million, and Albert Pujols lead with $20.58 million in 2006.
While this technique allows Bradbury to create a single list of players with a value attached to each, it overlooks the more complex reality that a Derrek Lee who produced 74.38 RSAA in 2005 is actually more valuable to a team who capitalizes on his additional run differential to move into the 90-win territory, thereby increasing revenue in non-linear way, as per the Silver and Gennaro win-revenue curves. In the market for free agents, players are often viewed in terms of the "last piece of the puzzle" in Gennaro's terms; teams are, or should be, willing to ante up commensurate with their predicted place on the win-revenue curve given that player's contribution(s). As a result, what a player is really worth depends in great deal on the teams that are interested in signing him.
Secondly, Bradbury's technique doesn't take into consideration the defensive value of a player, nor is it based on replacement value like Gennaro's system, which uses WARP.
These two problems compound one another, skewing the one-size-fits-all valuations of some players. Take Bradbury's example of Neifi Perez. In 2005 Perez consumed just under 10 percent of the Cubs' plate appearances; in this model, if he were an average hitter, he would have been valued at $5.45 million. Since he was in fact below average (-16 RSAA), he is valued at $3.54 million. Remember that this method is based only on offensive performance, and in defending it, Bradbury argues that the valuation is fair since Dusty Baker played Perez because "he brings something to the team other than his offense." In other words, Neifi's other contributions are rolled into the value as evidenced by his playing time. Perez's defense was exemplary in 2005, and rated a +20 in The Fielding Bible .
But Bradbury's system doesn't account for defense. The fact that Perez's overall performance (a 4.3 WARP) may be in the ballpark with his calculated MRP is really more of a coincidence. What if Perez had been an average defender along the lines of Felipe Lopez or David Eckstein, but Baker simply had no other choice but to play him? In that scenario, it would be clear that his value was nowhere near three and half million dollars, and was instead closer to the replacement level salary of $380,000. In fact this was precisely the case with Angel Berroa, who in 2005 had a -17.7 RSAA and registered a -26 in the Plus/Minus system, and yet is valued by Bradbury at $3.82 million. If Bradbury had used a replacement level baseline (and included defense) he could have still used his curve to assign player valuations (starting at a much lower baseline in terms of revenue for each additional run). The result would be much more realistic results for players like these.
The Big Picture
Despite the difficulties with MRP, Bradbury then explains how the valuations are related to actual salaries. Here he does a nice job of explicating the differences in player classes, and how those differences manifest themselves in value versus salary. He also discusses where the additional revenue not paid out in salaries is spent.
In the final section, Bradbury is clearly in his element, discussing major league baseball's monopoly power (and how it relates to other sports leagues), the shape that monopoly takes, and how market forces have acted on the league to bring "fans the baseball we deserve." His lucid descriptions of single- and multi-price monopolies--and his argument that baseball acts as the latter, thereby leading to more games at acceptable prices for fans--seem well-reasoned. He then couples this with an argument that baseball is a contestable market, as evidenced by the Federal League and the threat of the Central League that forced the industry through an "invisible hand" to keep expanding as the country grew. This section alone makes the book worth reading.
The wide-ranging subject matter and the connection of baseball to economic concepts far overshadow the minor quibbles I have with it. And since that was one of the primary goals Bradbury had in mind, I'd call the effort a success and recommend the book for those seeking a challenge.