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Directions for the following two questions: Answer the questions based on the following information.
The batting average (BA) of a Test batsman is computed from runs scored and innings played — completed innings and incomplete innings (not out) in the following manner:
$$r_1 =$$ Number of runs scored in completed innings
$$n_1 =$$ Number of completed innings
$$r_2 =$$ Number of runs scored in incomplete innings
$$n_2 =$$ Number of incomplete innings
$$BA=\frac{r_1+r_2}{n_1}$$
To better assess a batsman’s accomplishments, the ICC is considering two other measures $$MBA_1$$ and $$MBA_2$$ defined as follows:
$$MBA_1 = \frac{r_1}{n_1} + \frac{n_2}{n_1}*max[0,(\frac{r_2}{n_2}-\frac{r_1}{n_1})]$$
$$MBA_2 = \frac{r_1 + r_2}{n_1 + n_2}$$
An experienced cricketer with no incomplete innings has BA of 50. The next time he bats, the innings is incomplete and he scores 45 runs. It can be inferred that
With no incomplete innings and $$BA$$ of 50 , lets assume $$r_1 = 50$$ and $$n_1 = 1$$.
Now we have $$BA = MBA_2 = 50$$
So we have $$r_2 = 45$$ and $$n_2 = 1$$ .
We have $$BA = 95$$ and $$MBA_2 = \frac{95}{2} < 50$$.
Hence $$MBA_2$$ decreases.
So $$BA$$ will increase and $${MBA}_2$$ will decrease.
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