A Study Analyzed the Probability of Major League Baseball (MLB)players

question 34

Essay

A study analyzed the probability of Major League Baseball (MLB)players to "survive"
for another season, or, in other words, to play one more season.The researchers had a
sample of 4,728 hitters and 3,803 pitchers for the years 1901-1999.All explanatory
variables are standardized.The probit estimation yielded the results as shown in the
table: $$\begin{array} { | c | c | c | } \hline \text { Regression } & \text { (1) Hitters } & \text { (2) Pitchers } \\\hline \text { Regression model } & \text { probit } & \text { probit } \\\hline \text { constant } & 2.010 & 1.625 \\& ( 0.030 ) & ( 0.031 ) \\\hline \text { number of seasons } & - 0.058 & - 0.031 \\\text { played } & ( 0.004 ) & ( 0.005 ) \\\hline \text { performance } & 0.794 & 0.677 \\& ( 0.025 ) & ( 0.026 ) \\\hline \text { average performance } & 0.022 & 0.100 \\& ( 0.033 ) & ( 0.036 ) \\\hline\end{array}$$ where the limited dependent variable takes on a value of one if the player had one more
season (a minimum of 50 at bats or 25 innings pitched), number of seasons played is
measured in years, performance is the batting average for hitters and the earned run
average for pitchers, and average performance refers to performance over the career.
16
(a)Interpret the two probit equations and calculate survival probabilities for hitters and
pitchers at the sample mean.Why are these so high?

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Definitions:

Sedimentary Rock

Rock formed by the accumulation or deposition of mineral and organic particles at the Earth's surface, followed by compaction and cementation.

Iron Formation

A rock composed of millimeter- to centimeter-thick layers of iron-bearing minerals, especially iron oxide, commonly with quartz.

Gypsum Formation

A geological process leading to the creation of gypsum, a mineral used in building materials and fertilizers, through the evaporation of mineral-rich water.

Calcium Carbonate

A chemical compound (CaCO3) found in rocks as the minerals calcite and aragonite and is the main component of pearls, shells of marine organisms, snails, and eggs.