For this assignment, you will modify the VolleyBallSimulator class and perform numerous experiments using the simulation.

1. Download the files VolleyBallSimulator.java and Die.java and build a working project. If you specify equal rankings, are the scores of games relatively close? Should they be? Explain your answer and provide the scores for several games to support it.

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

2. As it is currently written, the winningPercentage method simulates multiple games by repeatedly calling playGame. Unfortunately, this means that all of the individual points in a game are displayed (by playGame), cluttering up the screen and greatly slowing down the simulation. Make the following modifications to the class so that the winningPercentage method can turn off output and so speed up the simulation.
   • Modify the VolleyBallSimulator class so that it has another field, a boolean value named SHOW_POINTS, which initially is true.
     
     
   • The playGame method should be modified to check the value of this field -- if it is true, then the results of each rally should be displayed as before. If this field is false, however, then playGame should output nothing.
     
     
   • Finally, modify the winningPercentage method so that it sets the field to false before performing the simulations, and then resets it to true when done.

   
   
   

3. Assuming team 1 has a ranking of 50 and team 2 has a ranking of 55 (10% better), perform three different sets of simulations for each of the following game lengths. Report the winning percentages of team 1 in the table below:

   	SIMULATION 1	SIMULATION 2	SIMULATION 3
   1,000 games to 25
   10,000 games to 25
   100,000 games to 25
   1,000 games to 30
   10,000 games to 30
   100,000 games to 30

   
   
   

4. Does the consistency of the results improve when the number of games simulated increases? That is, are the three percentages obtained from 10,000 games closer together than the three percentages obtained from 1,000 games? Likewise, are the percentages obtained from 100,000 games closer together than those obtained from 10,000 games? Should they be? Explain.

   
   
   
   
   
   
   
   
   

5. Are the winning percentages affected by the game length? That is, if the game is longer, does this positively or negatively affect the chances of team 1 winning? If your data suggests this, run several more simulations with different game lengths to confirm the pattern. Would this affect (if any) be more pronounced if the teams were less evenly matched, say 50 vs. 80?

   
   
   
   
   
   
   
   
   
   

6. Next, we want to compare the two different scoring schemes, rally and sideout scoring. A simple approach would be to define another method, named playGameSideoutScoring, which simulates a game using the sideout scoring system. This new method would be almost identical to the existing playGame method that uses rally scoring, except that it would keep track of who is serving and award a point only if the server wins the rally. In software development, however, duplicating large blocks of code can lead to bad consequences. If any part of the simulation were to change, then it would have to consistently change in both methods. A better solution is to have a single method that works for either scoring scheme.
   • Modify the playGame method to have an additional boolean parameter named sideout. If this parameter is true, then the game simulation should use sideout scoring. Otherwise, it should use rally scoring. Make this modified method private, so that it can't be called directly by the user. To balance out the fact that sideout scoring gives a slight advantage to the team who serves first, have the initial serve randomly assigned to one of the teams.
     
     
   • Define the following method, which calls the playGame method to simulate a game using rally scoring. /** * Simulates an entire game using the rally scoring system. * @param winningPoints the number of points needed to win the game (winningPoints > 0) * @return the winner of the game (either "team 1" or "team 2") */ public String playGameRallyScoring(int winningPoints) { return playGame(winningPoints, false); }
   • Similarly, define a method playGameSideoutScoring that simulates a game using sideout scoring.
     
     
   • Finally, modify the winningPercentage method so that it performs repeated experiments using both scoring schemes and displays both winning percentages. There should be an additional parameter, allowing the user to specify different game lengths for each of the scoring schemes. For example, the output of the method should look like: Out of 10000 games, team 1 (50-55) won: 36.58% using rally scoring to 25 33.09% using sideout scoring to 30

   
   
   
   
   
   
   
   
   
   
   
   
   

7. Assuming team 1 has a ranking of 50 and team 2 has a ranking of 60 (20% better), perform three different sets of simulations for each of the following game lengths. Report the winning percentages of team 1 using both rally and sideout scoring in the table below:

   	SIMULATION 1 (rally/sideout)	SIMULATION 2 (rally/sideout)	SIMULATION 3 (rally/sideout)
   1,000 games to 25
   10,000 games to 25
   100,000 games to 25
   1,000 games to 30
   10,000 games to 30
   100,000 games to 30

   
   
   

8. As we saw in class, rally scoring accentuates differences in talent. That is, if team 1 is 10% better than team 2, the likelihood of them winning a game is actually much more than 10% better than for team 2. Which of the two scoring schemes accentuates differences more? Provide statistics to justify your claim.

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

9. Suppose you were a member of the committee deciding on a switch from sideout to rally scoring. Recall that women's college volleyball previously used sideout scoring, with games played to 15. Perform experiments to determine the equivalent game length for rally scoring that would preserve competitive balance. That is, the winning percentage of team 1 using rally scoring should be roughly the same sa the winning percentage using sideout scoring to 15. This relationship should hold for a wide range of team strengths. Provide statistics to justify your answer.

   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

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