Unless stated otherwise in the exercise, use software to find the exact Poisson.

Question 5.56

5.56 Baseball runs scored.

We found in Example 5.20 (pages 271–272) that, in soccer, goal scoring is well described by the Poisson model. It will be interesting to investigate if that phenomenon carries over to other sports. Consider data on the number of runs scored per game by the Washington Nationals for the 2013 season. Parts (a) through (e) can be done with any software.

washnat

  1. Produce a histogram of the runs. Describe the distribution.
  2. What is the mean number of runs scored by the Nationals? What is the sample variance of the runs scored?
  3. What do your answers from part (b) tell you about the applicability of the Poisson model for these data?
  4. If you were to use the Poisson model, how many games in a 162-game season would you expect the Nationals not to score in?
  5. Sort the runs scored column and count the actual number of games that the Nationals did not score in. Compare this count with part (d) and respond.
  6. JMP users only: Provide output of Poisson fit superimposed on the histogram of runs. To do this, first create a histogram using the Distribution platform and then pick the Poisson option found in the Discrete Fit option. Discuss what you see.