The Baseball Economist: The Real Game Exposed (3 page)

The test of any theory is how well it conforms to the real world. The American League adopted the DH rule in 1973; therefore, if the law-of-demand explanation is correct, then hit batter rates should rise in the American League relative to the National League after 1972. The National League acts as a control group, because it lacks the rule the American League added.
Figure 1 shows the hit batters rates in both leagues from 1921 to 2005. This picture shows a startling, if not surprising, change. From 1921—the start of the modern baseball era of the home run and the end of the spitball—until 1972, the rate at which batters were hit in both leagues moved together from year to year, but no league had a consistently higher rate than the other. Following the introduction of the DH, the hit batter rate in the American League was higher than in the National League for the next twenty-one years. From 1973 to 2005, on average, the hit batter rate in the American League was 15 percent
higher than in the National League. This is pretty strong evidence that pitchers are responding to the price difference in hit batters in accordance with the law of demand.
However, this picture is a little more complicated than it appears. There are several excellent objections to be made to the argument that the difference in hit batter rates in the leagues is the product of a law-of-demand response by pitchers.
Retribution in the 1990s
The most obvious strike against the law-of-demand explanation is that in the 1990s, the interleague difference in hit batters shrinks. In 1994, the National League hit batter rate rose above the American League rate for the first time in twenty-one years. And for the next few seasons that followed, the rates were much closer than in the past, with the National League rate exceeding the American League rate three more times over the next decade. Is it possible that the twenty-one-year run of American League dominance in hit batters was just a run of luck? Of course it’s possible, but not very likely. There is about a one-in-one-thousand chance that the hit batter rates across the league would be equal; therefore it’s more probable that the shift in 1973 was a response to something real rather than a random fluctuation.
Do we have any reasons to expect the league differences in hit batter rates to change in the 1990s in the way that they did? In fact, we do. There were two significant changes that can explain the narrowing of hit batter rates; one of which lends further support to the law of demand.
The first results from the league expansion in the 1990s—two teams in 1993 and two teams in 1998. Expanding the league dilutes the quality of talent in the game by letting in, at the minimum, a hundred new players (four twenty-five-man rosters) who otherwise would not have been good enough to play in the league. These less skilled players included pitchers who were more likely to accidentally hit batters, and batters who were less able to get out of the way of inside pitches. This expansion was heavily concentrated in the National League, with the addition of the Rockies and Marlins in 1993 and the Diamondbacks in 1998. The Devil Rays joined the American League in 1998, with the Brewers switching from the American to the National League. In the first year of expansion (1993) the leagues’ difference in hit batsmen fell to 10 percent, while it had been nearly 20 percent over the previous twenty years.
However, the concentration of lower-quality talent in the National League has more to do with the way new talent was allocated than with the league the new teams joined. The rules for the expansion draft of the 1993 teams, from which the new teams stocked their rosters, favored the selection of talent from National League teams: American League teams were allowed to protect more of the talent on their rosters than National League teams. Some support for this explanation is that three of the four years in which the National League rate exceeded the American League rate occurred during the first five years of expansion. In the second round of expansion, neither league had an advantage in protecting its rosters in the expansion draft, and only once since that time did the National League rate exceed the American League rate.
The second explanation has to do with a rule change that directly affected the price of hitting batters. In 1994, major-league baseball adopted the “double-warning” rule for hitting batters, in hopes of halting plunking wars between teams. The double-warning rule requires the umpire to warn both teams if, in the umpire’s view, a pitcher throws at an opposing player intentionally. Once the umpire issues the warning, a future hit batter by either team results in the immediate expulsion of the offending pitcher and his manager, along with monetary fines and suspensions. While the intention behind the double-warning rule is good, it has the unfortunate side effect of reducing the retaliatory threat that kept pitchers in check in the first place. Unintended consequences of good intentions are a popular theme among economists, and this is a perfect example. The double-warning rule raises the price of retaliating against offending pitchers, and it is very likely that the high price of hitting batters in the National League deters pitchers from hitting batters. But with the rule change, pitchers in the National League now know that retaliation for plunking has become more expensive, and in accordance with the law of demand, teams ought to consume less retaliation. The code of
lex talionis
(law of retaliation) loses its teeth.
As a result, the double-warning rule actually gives protection to National League pitchers, because the opposing team would likely have to forfeit its own pitcher and manager if it chooses to retaliate. Retaliation now carries a pretty steep price, so it is no surprise that the National League hit batter rate has ticked a bit closer to the American League rate in recent years. The relative price of hitting batters decreased in the National League with the lower threat of retaliation, and therefore National League pitchers began to behave more like their brethren in the American League. It’s interesting to note that something similar occurred in Japanese professional baseball. The Nippon Professional Baseball League, which also has the DH in its Pacific League, experienced a similar convergence of hit batsmen— following several years of a higher hit batsmen rate in the DH league—after the implementation of new disciplinary measures for hit batters.
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But wait, maybe the change in price of retribution is not the whole answer. . . .
Ceteris Paribus
, Another Aspect of Demand
The law of demand makes perfect sense intuitively, but it can be confusing to identify in practice. The definition above is a little misleading. When we predict an inverse relationship between price and quantity we assume that nothing else about the product in question has changed. The Latin phrase
ceteris paribus
is attached to the definition— if not explicitly, it is always implied. The Latin translates as “all else being equal.” When looking at the difference in hit batters between leagues, even beyond the fact that pitchers don’t bat, all things are not equal.
The introduction of a designated hitter into American League lineups changes the pitcher’s costs and benefits in different ways. Perhaps most importantly the pitcher has to face another good batter—the DH—in the lineup, instead of the weak-hitting pitcher. Typically, pitchers are very poor hitters, as even most pitchers considered to be good hitters barely bat over .200. Due to his poor hitting, the pitcher at the plate represents an easy out for the pitcher on the mound. The last thing a pitcher on the mound wants to do is allow the batting pitcher, who will produce a near-certain out, to reach base. It is possible that pitchers feel that requiring them to bat has almost no effect on their decision to hit batters. The fact that putting the opposing team’s worst hitter on base is a bad strategy may cause the pitcher to assume that no team would attempt retaliation. If true, the price-change explanation cannot be correct. And we must remember that all the evidence regarding plunking as an effective retributive threat is anecdotal folklore, which is not the most rigorous evidence.
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Therefore, the increase in the quantity of hit batsmen in the American League following the introduction of the DH may not be a response to a change in the price, but rather a change in the benefit to hitting batters. This highlights an important distinction between the economic phrases
change in demand
and
change in quantity demanded
.
A change in quantity demanded describes a
behavioral response to a price change
, in accordance with the law of demand. For example, as the price goes up for a product, we can expect humans to consume less of the quantity of that product. Nothing about any particular person’s preference for a product has changed, only the price. Pitchers in the National League face a higher price for hitting batters than pitchers in the American League. But a change in demand refers to a change in someone’s willingness to consume a product
at the same price
. Something else about the consumer’s preference for the product has changed, which caused a change in consumption. Overall, pitchers are less willing to hit batters in the National League because there is always at least one very bad hitter in the lineup to whom they do not want to give a free pass to first base, which is not the case when the DH bats in place of the pitcher.
This adds up to an interleague difference in the willingness to hit batters that violates the “all else being equal” assumption that accompanies the law of demand. Rather than a price difference causing the quantity of hit batters demanded to differ, maybe a different degree of preference for hitting batters explains the greater number of hit batsmen in the American League. Note that pitchers in both leagues are still beholden to the law of demand. There is an inverse relationship between the price and quantity of hit batters for pitchers in both leagues; however, at the same price pitchers in the leagues have different preferences for the amount of batters they are willing to hit.
The difference in the demand schedules is produced by having the good-hitting designated hitter in the batting lineup in the American League. Even without a price change, we have a competing hypothesis that explains the hit batter differential without employing the law of demand.
A Solution
Just because we have two competing theories to predict the same phenomenon does not mean we have to throw up our hands in the air and guess which one is right. There is no need to let the confusion of a complex world get in the way of an economic analysis. Many statistical tools exist that allow us to isolate individual impacts among many overlapping relationships in the world. The problem with using some of the most basic tools to evaluate the hypotheses is that they don’t give us the power to distinguish between them. A particular problem in this case is the rarity with which hit batters occur. Even in an era where hit batters are at an all-time high, a hit batter occurs in about only 1 percent of all plate appearances. This means the totals can be heavily influenced by a few instances where hit batter totals are high or low based on game situations that induce pitchers to be extra careful or not so careful.
An altercation between the Houston Astros and Chicago Cubs in August 2004 reveals the importance of the conflicting strategic incentives within the game in regard to the decision to plunk a batter.
After giving up a home run to the previous batter, Roy Oswalt of the Astros plunked Michael Barrett of the Cubs in the back. Barrett took exception and walked toward the mound before order was restored. The umpire ejected Oswalt from the game, so retaliation wasn’t an option for the Cubs. But Barrett sent a message to Oswalt through the media: “I thought he was better than that. We’re going to see him again.” Five days later when the teams met again, the situation was tense, not just because of the animosity between Oswalt and Barrett, but because both teams were neck and neck in vying for a wild-card playoff berth. When Oswalt stepped to the plate in the second inning, he and Barrett argued, but Oswalt was not hit. The Astros led 4–2, and it was much too early for the Cubs to give the opposition a free runner, especially in such an important game. However, when Oswalt stepped to the plate in the sixth, the state of the game had changed quite a bit. With the Astros now leading 8–4, Cubs reliever Kent Mercker hit Oswalt in the thigh on his first pitch.
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All of the activity in this game was in response to a perceived intentional plunking the week before. When the lead was two runs, a relatively close game, the Cubs decided it was too costly to punish Oswalt; however, when the Astros extended their lead later in the game, the Cubs retaliated. The cost of putting Oswalt on base—Oswalt had a career .194 on-base percentage—was much lower at this point in the game since there was a high probability that the Cubs would lose the game.
The problem of controlling for all of the factors that might influence hit batters is what my friend, Doug Drinen, and I set out to solve. Doug is a math professor and a former colleague of mine at the University of the South. In addition to being an excellent mathematician and critical thinker, Doug is a former All-Conference college pitcher who brought a few personal insights to the issue. Doug and I decided we would have to use play-by-play and game-by-game data to control for the incentives faced by pitchers in any given situation. What is the importance of the configuration of runners on base? What is the score of the game? How good is the hitter? Is the pitcher coming to bat in the next inning? These are just a few of the things we looked at to determine the factors that impacted the likelihood that a batter would be hit. Once we “controlled for,” or held equal, all of these factors, we could then estimate how much influence the law of demand had over the frequency with which pitchers hit batters. Any difference in hit batters between leagues that persisted after we excluded the other competing possibilities would lend support to the law-of-demand explanation. If the difference disappeared because it was, in fact, the product of something that we could not see on the surface, then this would cast doubt on the law of demand explanation.

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