When the Atlanta Braves data from Example 2 is used to construct the transition matrix (not shown here), it turns out that the sum of the first column of the fundamental matrix M is 4:5048, and the first column of the matrix SM is [ .3520 .3309 .2365 .0805 ] Compute the number of earned runs the

Question

When the Atlanta Braves data from Example 2 is used to construct the transition matrix (not shown here), it turns out that the sum of the first column of the fundamental matrix M is 4.5048, and the first column of the matrix SM is

[latex]\left[\begin{array}{l}.3520 \.3309 \.2365 \.0805\end{array} ight][/latex].

Compute the number of earned runs the Braves can expect to score per inning based on their performance in 2002. How many earned runs does the model predict for the entire season, if the Braves play 1443 [latex]\frac{2}{3}[/latex] innings, as they did in 2002?

Accepted Answer

The first column of SM shows that, for example, the probability that the Braves left no runners on base is .3520. The expected number of runners left on base is

[latex]E[L]=0(.3520)+1(.3309)+2(.2365)+3(.0805)=1.0454[/latex].

The expected number of batters is E[B] = 4.5048, the sum of the first column of M: From Equation (6), the expected number of earned runs E[R] is

[latex]E[R]=E[B]-E[L]-3[/latex] (6).

[latex]E[R]=E[B]-E[L]-3=4.5048-1.0454-3=.4594[/latex].

The Markov chain model predicts that the Braves should average .4594 earned run per inning. In 1443 [latex]\frac{2}{3}[/latex] innings, the total number of earned runs expected is

[latex].4594 imes 1443.67=663.22[/latex].

The actual number of earned runs for the Braves in 2002 was 636, so the model’s error is 27.22 runs, or about 4.3%.

Question 10.6.3: When the Atlanta Braves data from Example 2 is used to const...

Related Answered Questions

Let A be the matrix just before Example 1. Explain why entry (3, 6) is zero. ...

Verified Answer:

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. ...

Verified Answer:

a. Justify the transition probabilities for the initial state “no bases occupied.” b. Justify the transition probabilities for the initial state “second base occupied.” ...

Verified Answer:

Batting statistics are often displayed as in Table 3. Use the data in Table 3 to obtain the transition probabilities for the 2002 Atlanta Braves. ...

Verified Answer:

Explain why entry (6, 3) of A is .5p1. ...

Verified Answer:

Verified Answer:

Verified Answer:

Consider a simple random walk on the graph in Figure 1. What is the probability that a walker starting at state 1 visits state 4 before visiting state 7? ...

Verified Answer:

Consider the unbiased random walk on {1, 2, 3, 4, 5} with absorbing boundaries studied in Example 1. Find the probability that the chain is absorbed into state 1 given that the chain starts at state 4. ...

Verified Answer:

Consider an unbiased random walk on {1, 2, 3, 4, 5} with reflecting boundaries. Find the expected number of steps tj 4 required to get to state 4 starting at any state j ≠ 4 of the chain. ...

Verified Answer: