The Baseball Economist: The Real Game Exposed (26 page)

GOOD THINGS tend to be scarce, thanks to the finite nature of our world, which means we must make trade-offs when consuming resources. Economists refer to the process of getting the most out of what you have as
constrained maximization
, and managing a baseball team is an exercise in precisely this process. Imagine that just this instant you are hired as the GM of your favorite baseball team. It is now your job to take all that you have—your players, staff, facilities, etc.—to earn as much money as possible for the owner. It’s not your fault that the previous GM raided the farm system and signed washed-up veterans to hefty long-term contracts, but it is your job to take your lot and win as many games as possible. To improve, how should you best rearrange what you already have? Should you hire or fire coaches, trade away players, or sign free agents? Constrained maximization is what it is all about.

This is not a simple task, which makes it fun. In fact, millions of rotisserie league fans simulate the act of baseball general managers— choosing players on a limited budget—every year. While money is involved in the exercise, it is primarily useful as a tool to measure value. To properly allocate resources, you need to value the trade-offs of resources, and money makes the task simpler.

Economists operate on the assumption that humans prefer more money to less. And since owners are human beings, it’s probably not a bad assumption to make when evaluating team decisions. There are plenty of goals other than wealth that motivate owners—public relations, ego, and altruism are a few—but there is no doubt that money plays a large part. Even though most owners don’t have a direct hand in baseball decisions, a GM seeking something other than financial reward for the owner cannot expect to keep his or her job for too long. Therefore, in order to value players, I’m going to assume that owners are profit maximizers.

However, if owners only care about profits, this might take the fun out of evaluating players. Attempting to value their ability to give rich men more money is about as fun as trying to find an additional product endorsement for Donald Trump. Luckily, this is not going to be a problem. The fans who spend their incomes on baseball tend to value wins; hence, the financial success of a team is directly linked to its success on the field. Certainly, there are other factors involved, but owners concerned about maximizing profits can do so through winning; therefore, we are justified in valuing players according to their abilities to generate wins.

In order to win baseball games, you have to build an organization that is equipped for the job, and the things that lead to wins vary in price. A general manager needs to purchase many inputs—facilities, equipment, coaches, and, most importantly, players—to put a winning team on the field. Subpar inputs can lead to bad outcomes, so a GM is always going to want to buy the best. The cheaper you can purchase any one factor, the more financial resources will be available to purchase other items that contribute to winning.

Unfortunately for any one GM, but fortunate for players, twenty-nine other GMs want to purchase the same inputs, forcing GMs to bid against one another for available resources. Some factors, like bats, helmets, and medical equipment, are not auctioned; one team purchasing a video camera to record performances doesn’t prevent another team from purchasing another camera just like it. But some players, managers, coaches, scouts, and trainers are better than others, and hiring one of these people prevents another team from getting that individual. Better personnel will earn higher salaries than inferior personnel because teams will bid higher wages for people who contribute more to winning. Underbidding for a potentially valuable employee will generally cause the individual to move to a new team. Leo Mazzone’s excellent performance as a pitching coach eventually caused him to leave the Atlanta Braves for the Baltimore Orioles, who were willing to nearly double his annual salary.

Evaluating off-the-field inputs such as coaching are difficult, because we do not have a good idea of what all these people do to help/hinder winning. Players are much easier to value, because we can directly observe their contribution. The two biggest contributors to winning are hitting and pitching. Using factors that predict how many runs hitters and pitchers generate, we can measure individual player contributions in dollars.

The basic method for converting player performance into dollar values was developed by economist Gerald Scully in 1974.
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At the time Scully wrote his landmark paper, the organization of MLB, with respect to paying players, was much different. All players were bound by the “reserve clause,” which gave teams exclusive rights to their players, and thus prevented players from seeking employment on other teams. Consequently, team owners didn’t feel any pressure to pay players much more than a fraction of their monetary contributions to winning, because players could play for the team that held their reserve rights or not at all.

Economists value an input into production according to its marginal revenue product (MRP). The MRP of any input is the added dollar value that the input brings to generating output. Thus, the MRP of a player is the value he adds to a team’s revenue through his individual contributions. In a free market for labor, which professional baseball lacked when Scully conducted his study, players ought to earn wages equal to their MRPs. This occurs because teams bidding against one another for talent are willing to pay a player up to the revenue value he generates for the team. For example, a player who is expected to produce an additional $2 million for a team could not be hired for less than $2 million. Why not? There is still profit generated by hiring the player at a wage of less than his MRP. Just as a pedestrian is willing to expend the effort to bend over and pick up a $100 bill blowing down the sidewalk, any team would certainly be willing to pay a player a wage below his production value. But if one team offers a player less than his MRP, other teams will be willing to offer higher bids to capture the added value that the player brings. But once a player receives an offer equal to his MRP, the bidding should stop, because no team wants to pay a player more than he brings to the team.

Because the reserve clause did not allow a competitive bidding process to take place, it was unlikely that players earned their MRPs. Scully wanted to know how much of their value players earned under the reserve system. To find out, he developed a three-step method for estimating a player’s MRP to compare to player wages.

Step 1: Estimate the dollar value of a win to a team.

Step 2: Estimate the contribution of a player to winning, accounting for the quality and quantity of play.

Step 3: Convert the player contribution to wins from Step 2 into dollars using the estimates from Step 1, which should approximate a player’s MRP.

Scully found that reserved players earned between 80 and 90 percent less than their MRP values, which meant major-league owners were extracting excess value from their players. In 1976, soon after Scully’s study, the right of “free agency” was added to the collective bargaining agreement (CBA) between players and owners. While the rules are a bit complicated, and have changed some over time, the CBA now permits a player with six years of major-league service to become a free agent and sign with any team willing to offer him a contract. Interestingly, free agent players’ wages rose to levels similar to the MRP estimates of Scully soon after free agency came to baseball.

While Scully’s method is useful as a policy tool, it can also help the armchair general manager. Using Scully’s method as a guide, we can build a similar model to estimate player values in the present era. We are going to have to change a few things, but the overall process is the same.

Estimating the value of a win requires connecting a few pieces of information. First, we need to know the revenues of all MLB clubs. By looking at how team revenues differ according to relevant factors, we can weight each factor’s impact on revenue. Wins and the size of the local fan base are obviously important determinants of revenue. Winning teams generate more fan interest than losing teams, which results in more dollars to the team. Bigger cities benefit from a larger population of potential fans who are likely to spend their incomes on the local baseball club.

There is not much that any owner can do about the size of the city in which he hosts the team; thus, the GM need not worry much about this. However, because city size does influence revenue, it is important to take its influence into account to ensure that the estimated impact of wins on revenue is not picking up any biases from city size. It turns out that every person in a city is worth about $3.88 to team revenue. For example, the city of Atlanta, with approximately 4.1 million people, generates approximately $15.9 million to the Braves (4.1 × $3.88 = $15.9). While controlling for city size, a win for a .500 team is worth about $1.34 million.
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A slight modification to the Scully method is necessary. For Step 2, we are going to need to know how much each player contributes to winning. The things that pitchers and hitters contribute to winning are independent of each other. If we were to estimate the impact of the
sum total of pitcher and hitter performances on winning, rather than preventing and producing runs independently, the estimates could be biased. For example, if a few teams have excellent pitching and horrible hitting, or vice versa, the estimated individual impact of player contributions to winning may be distorted. What we would like is know how much
runs
are worth to teams as they produce wins, since both pitchers and hitters affect runs.

Not surprisingly, there is a very strong relationship between the runs-scored-versus-runs-allowed difference and winning. Bill James even developed a technique, which he dubbed the Pythagorean method, for estimating wins from a team’s difference in runs scored and runs allowed. Figure 16 shows the tight relationship between a team’s run differential and winning [from 1998–2005], with the run differential explaining more than 90 percent of the difference in wins across teams. Therefore, instead of estimating the impact of wins on revenue, we can use the difference between runs scored and runs allowed. This enables us to use the estimates of individual player contributions to run production and prevention to value their individual impact on revenue.

Figure 17 maps the relationship between the run differential and
revenue in 2004. The relationship is positive and nonlinear, with each run scored or prevented adding a little more to revenue than the previous run. It turns out that the first run scored or prevented that pushes a team’s record above .500 adds approximately $127,000 to team revenue. However, additional runs beyond .500 are worth a little more. What does this mean? Being a little above average brings in more fans, but being a good bit better than average draws in increasingly more fans.
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A few teams earned far more (e.g., Yankees, Mets, and Mariners) and far less (e.g., Expos, Marlins, and Twins) than the amount estimated by run differential. That is to be expected, considering that other factors may determine revenue. For example, we expect some of these divergences because of differences in market size. But recall that the estimate of the run differential on revenue takes into account differences in city size, so New York teams don’t get extra credit for winning just because of their larger population base. While other factors besides winning and population may influence revenue, there are no obvious factors that should bias the estimate of the impact of the run differential on winning.

The next step requires measuring how the things that players do on the field contribute to winning, by determining how many runs hitters produce and pitchers prevent. Chapter 12 reveals some simple but good metrics we can use for estimating players’ contributions to run production and prevention. The on-base percentage (OBP) and slugging percentage (SLG) do an excellent job of measuring the run production of hitters. Strikeouts, walks, and home runs are factors that pitchers control and that measure their contributions to run prevention. Using these factors, we can estimate how many runs a player contributed— scored or allowed—based on his on-field performance and playing time. To get a recent but large sample, I use four seasons of team data (2002–2005) to estimate the impact of the performance metrics on runs.