James defined sabermetrics as “the search for objective knowledge about baseball.” Though sabermetricians often use mathematical and statistical tools, it is the methodological approach that differentiates sabermetrics from the traditional approach to understanding baseball. Erroneously, sabermetrics has been labeled the application of statistics or computers to baseball. Statistics and computers are common tools of the sabermetrician, but these tools are utterly useless without critical thinking. However, sabermetrics does not quite describe my approach.
I apply a wide range of economic principles to baseball, so I think of what I do as
sabernomics
. Sabermetrics involves analytical and statistical methods, but the analysis is often narrow and is not based on economic assumptions about human behavior. For example, sabermetricians have studied whether or not the on-deck batter can protect a star slugger. I’m interested in this, but I’m also concerned about how the man on deck might influence the opposing pitcher, and how this effect applies to all hitters in the lineup. Baseball and economics are to sabernomics what peanut butter and chocolate are to a Reese’s Peanut Butter Cup. While both subjects can stand alone, they are quite good consumed together. I hope to demonstrate that economics has a lot to say about not just baseball, but all human behavior. Yes, economists do talk about boring, even dismal, subjects such as cash flows, deficits, inflation, and taxes; but, it’s the economic way of thinking that inspired me, and most of my colleagues, to follow economics as a vocation.
Broadly, we start with economic decisions on the field, then progress to off-the-field choices. The issues are interrelated, and therefore to build a successful baseball team, a general manager, or fantasy baseball player, must understand both. By the way, I expect the dominant team for years to come will not be the mega-market New York Yankees, but the smaller-market Florida Marlins. The reasons will become clear in the later sections of the book.
One of the more complicated tools that I use,
multiple regression analysis
, merits an appendix in which its genius is explained. In short, multiple regression analysis isolates the individual impacts of many factors on a single event. It can quantify the impacts of latitude, altitude, and proximity to water on the snowfall in towns in the United States. While all of these factors are important, multiple regression analysis can give each factor a specific value, taking into account the potential influence of all of the factors, based on the historical record. In understanding individual contributions in team sports, this analytical tool is invaluable. Also included is an appendix listing all major-league players by team, along with a calculation of each player’s dollar value to his team. Turns out, some players have negative values, and they too are listed.
Writing on my blog,
Sabernomics
, led me to this book. Many of the ideas in the chapters that follow were debated by readers of my site. I thank them for tempering my thoughts. What started out as a few questions about puzzles in baseball has turned into an obsession. As most economists find out, working with a universal theory of human action often leads to close examination of previously unexamined corners of our daily lives. I’ve been hooked by sabernomics. Baseball is a fantastic game, full of unsolved puzzles, and I find myself thinking of little else on many days. I hope you’ll find the discussion as consuming as I have.
Part One
ON THE FIELD
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Accidents Happen... but More So in the American League
Are you seriously going to throw at somebody when you’re facing Randy Johnson?
—CURT SCHILLING
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ONE WARM SATURDAY AFTERNOON in New York City, Roger Clemens hit Mike Piazza in the head during an interleague matchup between the crosstown rivals Mets and Yankees. The Mets felt that the fastball that gave their star slugger a concussion was intentional, and wanted payback. But the game was played (on July 8, 2000) at Yankee Stadium, an American League ballpark, where a designated hitter (DH) bats for the pitcher. Clemens was safe, but the Mets would not forget. Nearly two years later, on June 15, 2002, Clemens came back to New York to pitch at Shea Stadium where the game was played by National League rules—no DH. Like a child pulling a snowball from the freezer in the middle of summer, Piazza crouched behind the plate and called the pitch. The pitcher, Shawn Estes—who wasn’t even on the Mets when the first incident occurred— reared back and aimed some payback right at Clemens’s backside . . . and just missed.
There is no concept more sacred to economists than the
law of demand
. Though the study of economics began without it, its discovery yielded a vital tool for social scientists studying human behavior. The law of demand states that there is an inverse relationship between the price of a product and the amount of a product consumed. If the price of a product goes up, expect the consumption of the product to fall. If the price falls, expect the consumption to go up. It sounds pretty simple, right? Maybe that’s why Alfred Marshall believed economics to be nothing more than the organized analysis of common sense.
Economists have traditionally illustrated the law of demand in a retail context. Shelf prices in stores move up and down, and customers adjust their purchases of goods based on the price. It’s a useful way to learn the concept, but the law of demand has much broader application. Prices aren’t only paid in dollars; a price can be just something a person gives up in order to get something else—an “opportunity cost,” as economists refer to it.
On the baseball field, managers and players are constantly making decisions based on the “prices” of their actions even though there is no money involved. For example, the price to the manager of pinch-hitting for his ace starter is to lose his skills in preventing runs for the rest of the game; because, once a player leaves the game, he cannot return. When a starting pitcher takes his turn at bat in the early innings, and his arm is still fresh, the manager loses a lot by replacing him with a superior hitter. But in the eighth inning, when the pitcher might be running out of gas, forgoing his services for the rest of the game is cheaper than it was earlier in the game. According to the law of demand, we expect managers to pinch-hit for their pitchers later in the game (when the price is low) more often than early in the game (when the price is high). Again, this just seems like common sense, because that is exactly what we do observe.
To examine players’ behavior where large differences in prices suggest obvious choices is a bit boring. What is interesting is that the law of demand is a powerful force that influences seemingly trivial areas of human behavior. We often view a pitch that hits a batter as an inadvertent event: a hiccup in a pitcher’s performance. However, hitting a batter has a price to the pitcher and his team. So even though it might not seem to make a difference to who wins the game, as the price changes for hitting batters, we should expect pitchers to change the frequency with which they plunk opposing hitters. It just so happens that the adoption of the designated hitter rule in the American League had an interesting effect on hit batsmen. It lowered the price of hitting batters, which yields an obvious prediction from the law of demand. The designated hitter rule demonstrates how sensitive humans can be to even the tiniest of price changes.
The Price of Hitting Batters
In 2004, when Major League Baseball adopted the policy of assigning home-field advantage in the World Series to the league winning the All-Star Game, FOX television advertised the game with a montage of clips of hit batters while the voice-over boomed, “This time, it counts!” It’s funny that a major network sought to promote a baseball game using an event that happens barely more than once per hundred times that a batter steps to the plate. And when a batter gets hit, it normally results in about as much excitement as a base-on-balls, with the hitter trotting down to first base.
The bloodlust provoked by a pitcher hitting a batter can be quite exciting. Of course, batters don’t like being hit by a ninety-mile-an-hour hardball. Most batters don’t think the free trip to first base is sufficient compensation for the inflicted damage. And even if it’s something the pitcher didn’t mean to do, the victimized batter surely doesn’t appreciate the pitcher’s lack of care and doesn’t know for sure that the blow wasn’t intentional. Sometimes the batter will stare or yell, or maybe even charge the mound to brawl, which gets fans to their feet, makes for good television, and sells advertising. Turning a game children play into a blood sport, played by men of honor who don’t shy from taking the law into their own hands, boosts ratings.
However, even when a batter feels he’s been wronged by a pitcher, he rarely responds with immediate violence. The punishment for fighting is quite severe, with most participants receiving multi-game suspensions, fines, and not to mention a few extra bruises. Instead, teams are said to employ Hammurabi’s code of retributive justice. Hammurabi ruled Babylon nearly four thousand years ago and became famous for his laws, some of the first ever written, which pronounced punishments equivalent to the damage the crime caused. Plunking pitchers are sometimes reminded of the discomfort of being plunked when they take their turn in the batting order. It’s this punishment according to an unwritten “eye for an eye” code that is thought to deter pitchers from being careless.
If plunking pitchers are criminals negligently inflicting harm on fellow players, a useful framework for analyzing the phenomenon is an economic model of crime. After all, negligence is a legal term that describes the failure of a party to take proper care in protecting other people or property. Developed by Nobel Prize–winning economist Gary Becker in the 1960s, the economic approach to crime begins with treating criminals as rational human actors who base their choices regarding illegal activity on the potential benefits and costs. Simply stated, the greater the expected benefits—based on the likelihood of success and the size of reward—and the lower expected costs— determined by the probability of getting caught and the severity of the punishment—the more likely it is for a criminal to commit a crime.
Becker’s model is a fascinating application of the law of demand. The higher the price of committing a crime, the fewer people we expect to see engaging in criminal activity. The price may be due to a new law or a private response of potential victims. For example, to reduce auto theft the government could increase the length of prison sentences for stealing cars, or car owners could purchase alarm systems. Both of these activities raise the cost of committing a crime, and correspondingly ought to lower the “consumption,” that is, auto theft.
The written official rules of baseball dictate that the price for hitting a batter is that the plunked hitter goes to first base. Given this punishment, pitchers will hit batters at a rate commensurate with costs of putting men on base. Though pitchers don’t want to hit batters, the optimal number of batters hit isn’t zero. Why not? Because, avoiding hitting batters at all costs can have some pretty disastrous consequences. To ensure that the ball doesn’t hit a batter, the pitcher will have to throw softer and err on the side of leaving the ball over the plate, which results in the increased likelihood of the batter depositing the ball in the outfield bleachers. Therefore, the pitcher must make a trade-off between batter safety and pitching success.
When a batting team feels the opposing pitcher is neglecting batter safety too much, one response is to raise the price. It’s impossible for a team to rewrite the rule book, awarding the batter two bases instead of one or sentencing the pitcher to forty lashes. Instead, according to the unwritten retributive justice code of baseball, the team will plunk the offending pitcher when the time is right—an eye for an eye. How is punishing a person for a past indiscretion supposed to stop him from misbehaving in the first place? Certainly, he can’t go back in time and undo his misdeed, but he, along with any other pitcher who takes the mound against that team, expects this justice will be served. By establishing a reputation for punishing plunking pitchers, the retaliating team will credibly raise the price to future offenders in order to deter them from negligent pitching.
From the pitching team’s perspective, hitting a batter on the opposing team is a pretty poor deal. Giving the other team a man on base isn’t the best way to prevent runs. That’s why most hit batsmen are legitimately accidental. But losing a player to injury from being hit by a pitch is also costly to a team, possibly more costly than the benefits of the compensation of a free base. This is why teams often feel retaliation is not only justified, but necessary to protect the interests of the team. The Mets didn’t mind putting Roger Clemens on first if it sent a message to opposing pitchers that the Mets would be exacting revenge against those who plunked their star slugger.
How effective is this long-standing unwritten code if hitting batters is largely unintentional? While it’s clear that rarely does a pitcher intentionally hit a batter, not all accidents in life are random, and therefore they don’t render a guilty party faultless. For example, the motorist who drives sixty miles per hour through a dense fog is much more likely to crash than the motorist who slows down. While neither driver intentionally wants to crash, the slower driver is being more careful in trying to avoid a collision. Certainly, the fast driver bears more culpability for his actions than the slow driver. A pitcher who isn’t being as careful as he should has to know he will be punished, and with this in mind, he might take a little more care in keeping his inside pitches away from the batter. As Cy Young Award–winning pitcher Randy Johnson describes it, when a pitcher doesn’t have to bat, “you may have a tendency to throw inside a little bit more knowing when that ninth hole comes up, you won’t be hitting.”
4
A Price Change
If the threat of retaliation really does raise the price of hitting batters, then this yields a prediction that we can easily test. In the American League, where a designated hitter bats in place of the pitcher and the pitcher faces no threat, pitchers ought to hit batters at a higher rate than in the National League. The lower the price for hitting a batter, the greater number of batters a pitcher will hit. Veteran NL manager Dusty Baker states the theory more bluntly: “You can be bold in [the American] League and get away with [hitting batters]. It’s different in our league where you have to hit.”
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