Question 10.6.4: Table 4 shows the career batting statistics for Jose Oquendo...
Table 4 shows the career batting statistics for Jose Oquendo, who played for the New York Mets and St. Louis Cardinals in the 1980s and 1990s. Compute his offensive earned run average.
| TABLE 4 Jose Oquendo Batting Statistics | ||||||
| Outs | Home Runs | Triples | Doubles | Singles | Hit Batsman | Walks |
| 2381 | 14 | 24 | 104 | 679 | 5 | 448 |
Construct the transition matrix from this data as described in Example 2, and then compute M and SM: The sum of the first column of M is 4.6052, so a team entirely composed of Jose Oquendos would come to bat an average of 4.6052 times per inning. That is, E[B] = 4.6052. The first column of SM is
\left[\begin{array}{l}.2844 \\.3161 \\.2725 \\.1270\end{array}\right].
so the expected number of runners left on base is
E[L]=0(.2844)+1(.3161)+2(.2725)+3(.1270)=1.2421.
From Equation (6), the expected number of earned runs is
E[R]=E[B]-E[L]-3 (6).
E[R]=E[B]-E[L]-3=4.6052-1.2421-3=.3631.
The offensive earned run average for Jose Oquendo is .3631 \times 9=3.2679. This compares with an offensive earned run average of about 10 for teams composed of the greatest hitters in baseball history. See the Exercises.