The Baseball Economist: The Real Game Exposed (47 page)

70.
The Bill James Baseball Abstract,
1987.

71. The nature of the data used to estimate the regression results creates some complicated problems. For those readers who are familiar with some advanced regression techniques: I estimated the model using random effects and corrected for first-order serial correlation. I used the pitcher’s team’s seasonal BABIP for all pitchers to proxy defense, assumed the impact of age on ERA to be U-shaped (quadratic), and used indicator variables equal to 1 or 0 to identify the league and year in which the pitcher’s stats were posted. I made a correction for the propensity of a pitcher’s home park to yield runs. So pitchers with an unfriendly home park (such as Coors Field in Denver) are not punished, and pitchers with friendly home parks are not rewarded. See my study article in
Journal of Sports Economics,
“Does the Baseball Labor Market Properly Value Pitchers?” (forthcoming). Also, you can find some similar findings in my article “Another Look At DIPS” in
The Hardball Times
, May 24, 2005.

72. For the remainder of the analysis I exclude hit batters, because they are such rare events that don’t strongly correlate from year to year.

73. Michael Lewis,
Moneyball,
p. 236.

74.
Principles of Economics
, p. 43.

75. “Pay and Performance in Major League Baseball,”
American Economic Review
, 1974.

76. The relationship between winning and revenue is a quadratic function, with increasing dollar value added for each win beyond seventy-one.

77. Total Revenue = (0.126 × Run Difference) + (0.000665 × Run Difference
²
) + (3.88 × MSA Population) + 109.022; Adj. R
²
= .52. All estimates are statistically significant at the 5 percent level. I use the 2004 season to estimate the impact of the run differential on revenue as reported in the 2005
Forbes Business of Baseball
report. Estimates using several seasons of data did not yield much different results. The model is simple, but more complicated specifications—including the interaction between wins and population and per capita income—performed no better. While other factors may have some slight importance, they should not bias the relationship between wins and revenue.

78. Runs Scored = (3012.54 × OBP) + (1688.17 × SLG) + (29.18 × AL) −966.04; Adj. R
²
= .93. All estimates are statistically significant at the 5 percent level.

79. Runs Allowed = (−25.83 × K9) + (60.65 × BB9) + (249.5 × HR9) − (4196.21 × Team Outs on Balls in Play percent) + (26.64 × AL) + 3419.59; Adj. R
²
= .91. All estimates are statistically significant at the 5 percent level. Reported estimates in this edition include a correction, and therefore differ slightly from estimates reported in the first edition.

80.
The Fielding Bible
by John Dewan presents an experimental new system for objectively evaluating defense. Dewan estimates that Perez made twenty more plays than the average shortstop in 2005, which translates to about 9.2 runs. Using our runs-to-dollars conversion, this translates to approximately $1.22 million, which is close to the amount Cedeno would have added with his bat, $1.85 million.

81. Berri, Schmidt, and Brook,
The Wages of Wins,
p. 189.

82. Helyar,
Lords of the Realm: The Real History of Baseball
.

83. All price data from
www.teammarketing.com
. Rodney Fort compiles the many years of this data on his Web site (
www.rodneyfort.com/SportsData/BizFrame.htm
).

84.
An Inquiry into the Nature and Causes of the Wealth of Nations
, Oxford University Press, 1976, pp. 26–27.

85. Figure 22 graphically demonstrates exactly how price discrimination eliminates deadweight loss. A single-price monopolist maximizes its profits by producing the output where the additional revenue of selling an additional unit—known as marginal revenue (MR)—equals the cost of producing an additional unit— known at the marginal cost (MC). Thus, the monopolist in this example produces Q
m
amount of output, while it sells each unit for the price of P
m
. The rectangle A measures the profits captured by the monopolist. Triangles B and C represent two untapped profit opportunities to the monopolist.

From zero to Q
m,
every consumers pays price P
m,
although according to the demand curve (D), which captures the consumer willingness-to-pay for the product at different prices, some consumers are willing to pay more and less. Triangle B represents that revenue lost to a seller charging P
m,
because some consumers would be willing to pay a higher price. Qm to Q* is the quantity of the product that consumers would be willing to purchase if the price were less than Pm and greater than P*. To the left of Q* the price that would be received by the seller exceeds the marginal cost of producing those units. If the monopolist could sell the goods to these customers at a price lower than P
m,
it would do so because the additional revenue would exceed the additional cost. Triangle C represents the uncaptured revenue from units the monopolist doesn’t sell. This area is equal to the deadweight loss.

Together, the areas of Triangle B and C equal the total uncaptured revenue available to the monopolist if it could charge different prices to different consumers using price discrimination. Triangle B differs from C because B represents revenue lost from individuals who consume the product. We are not concerned with these individuals, because they valued these units at least as much as the amount they paid for them. The loss of revenue in Triangle C is much worse than the loss reflected in Triangle B, because the lost revenue of Triangle C also means that some sellable products will not be sold.

86. Ticket price data from
www.teammarketing.com
.

87.
Capitalism, Socialism, and Democracy,
p. 99.

88. Anyone interested in doing serious research with multiple regression analysis would be wise to acquire software that is designed to handle some common problems the empirical researcher faces. I typically use the regression package Stata, but R, SPSS, Limdep, and SAS all work well.

89. This assumes the data are distributed in a certain manner. Different regression estimators are needed for different types of data to interpret the statistical significance of coefficient estimates.

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