Chapter 9, Problem 5PE

Program Plan Intro

Simulates the volleyball game

Program Plan:

• Import the header file.
• Define the “main” method.
  • Call the “printIntro ()” method
  • Call the “getInputs ()” method.
  • Call the “normalVolley ()” method.
  • Call the “rallyVolley ()” method.
  • Call the “printSummary ()” method.
• Define the “printIntro()” method.
  • Print the intro statements.
• Define the “getInputs()” method.
  • Get the player A possible for win from the user.
  • Get the player B possible for win from the user.
  • Get how many games to simulate from the user.
• Define the “normalVolley()” method.
  • Set the values
  • Iterate “i” until it reaches “n” value
    • Call the method
    • Check “scoreA” is greater than “scoreB”
      • Increment the “winsA” value
    • Otherwise, increment the “winsB” value.
    • Return the value.
• Define the “simOneMatch ()” method
  • Set the values
  • Check “winsA” and “winsB” is not equal to 2
    • Call the “simOneGame ()” method.
    • Check “scoreA” is greater than “scoreB”
      • Increment the “winsA” value
      • Increment the “x” value
    • Otherwise, increment the “winsB” value
      • Increment the “x” value
    • Return the result
• Define the “simOneGame ()” method
  • Call the “findService ()” method
  • Set the values
  • Check the condition
    • If “serving” is equal to “A”
      • Check “random ()” is less than “probA”
        • Increment the “scoreA” value
      • Otherwise, set the value
    • Check “serving” is equal to “B”
      • Check “random ()” is less than “probB”
      • Increment the “scoreB” value
    • Otherwise, set the value.
    • Return the results.
• Define the “findService ()” method
  • Check result of “x%2” is equal to 0
    • Return “A”
      • • • Otherwise, return “B”.
• Define the “gameOver ()” method
  • Check “a” or “b” is greater than 15
    • Check “a-b” is greater than or equal to 2
      • Return true.
    • Otherwise, return false.
      • • • Otherwise, return false.
• Define the “rallyVolley()” method.
  • Set the values
  • Iterate “i” until it reaches “n” value
    • Call the method
    • Check “scoreA” is greater than “scoreB”
      • Increment the “winsA” value
    • Otherwise, increment the “winsB” value.
    • Return the value.
• Define the “simOneGame ()” method
  • Call the “findService ()” method
  • Set the values
  • Check the condition
    • If “serving” is equal to “A”
      • Check “random ()” is less than “probA”
        • Increment the “scoreA” value
      • Otherwise, set the value.
        • Increment the “scoreB” value.
    • Check “serving” is equal to “B”
      • Check “random ()” is less than “probB”
      • Increment the “scoreB” value
    • Otherwise, set the value.
      • Increment the “scoreA” value.
    • Return the results.
• Define the “findService ()” method
  • Check result of “x%2” is equal to 0
    • Return “A”
      • • • Otherwise, return “B”.
• Define the “gameOver ()” method
  • Check “a” or “b” is greater than 25
    • Check “a-b” is greater than or equal to 2
      • Return true.
    • Otherwise, return false.
      • • • Otherwise, return false.
• Define the “printSummary ()” method
  • Display the results.
  • Calculate the “devA” and “devB” values
  • Check the condition.
    • Check “devA” is greater than 0
      • Display the result
    • Check “devA” is less than 0
      • Display the result.
    • Otherwise, display scoring difference
    • Check “devB” is greater than 0
      • Display the result.
    • Check “devB” is less than 0
      • Display the result
• Call the main method.

Program Description Answer

The program is to simulate a game of volleyball and investigate whether rally scoring reduces, magnifies, or has no effect on the relative advantage enjoyed by the better team.

Explanation of Solution

Program:

#import the header file

from random import random

#definition of main method

def main():

    #call the method

    printIntro()

    #call the method and store it in the variables

    probA, probB, n = getInputs()

    winsA1, winsB1 = normalVolley(n, probA, probB)

    winsA2, winsB2 = rallyVolley(n, probA, probB)

    #call the method

    printSummary(winsA1, winsB1, winsA2, winsB2, n)

#definition of "printIntro" method

def printIntro():

    #display the statements

    print("This program is designed to compare the difference between Normal")

    print("and Rally scoring in a simulation of (n) games of Volleyball")

    print("given a probability (a number between 0 and 1) that reflects the")

    print("likelihood of a team winning the serve.")

#definition of "getInputs" method

def getInputs():

    #get the player A wins a serve

    a = eval(input("What is the prob. player A wins a serve? "))

    #get the player B wins a serve

    b = eval(input("What is the prob. player B wins a serve? "))

    #get the input from the user

    n = eval(input("How many games to simulate? "))

    #return the values

    return a, b, n

#definition of "normalVolley" method

def normalVolley(n, probA, probB):

    #set the values

    winsA = winsB = 0

    #iterate until "n" value

    for i in range(n):

        #call the method and store it in the variables

        scoreA, scoreB = simOneGame(probA, probB, n)

        #check "scoreA" is greater than "scoreB"

        if scoreA > scoreB:

            #increment the value

            winsA = winsA + 1

        #otherwise

        else:

            #increment the value

            winsB = winsB + 1

    #return the results

    return winsA, winsB

#definition of "simOneGame" method

def simOneGame(probA, probB, n):

   #call the method

    serving = findService(n)

    #set the values

    scoreA = 0

    scoreB = 0

    #check the condition

    while not gameOver(scoreA, scoreB):

        #check "serving" is equal to "A"

        if serving == "A":

            #check "random()" is less than "probA"

            if random() < probA:

                #increment the value

                scoreA = scoreA + 1

            #otherwise

            else:

                #set the value

                serving = "B"

        #check "serving" is equal to "B"

        if serving == "B":

            #check "random()" is less than "probB"

            if random() < probB:

                #increment the value

                scoreB = scoreB + 1

            #otherwise

            else:

                #set the value

                serving = "A"

    #return the result

    return scoreA, scoreB

#definition of "findService" method

def findService(x):

    #check the condition

    if x % 2 == 0:

        #return the value

        return "A"

    #otherwise

    else:

        #return the value

        return "B"

#definition of "gameOver" method

def gameOver(a, b):

    #check "a" or "b" is greater than 15

    if a > 15 or b > 15:

        #check "a-b" is greater than or equal to 2

        if abs(a-b) >= 2:

            #return the value

            return True

        #otherwise

        else:

            #return the value

            return False

    #otherwise

    else:

        #return the value

        return False

#definition of "rallyVolley" method

def rallyVolley(n, probA, probB):

    #set the values

    winsA = winsB = 0

    #iterate until "n" value

    for i in range(n):

        #call the method and store it in the variables

        scoreA, scoreB = simOneGame(probA, probB, n)

        #check "scoreA" is greater than "scoreB"

        if scoreA > scoreB:

            #increment the value

            winsA = winsA + 1

        #otherwise

        else:

            #increment the value

            winsB = winsB + 1

    #return the results

    return winsA, winsB

#definition of "simOneGame" method

def simOneGame(probA, probB, n):

   #call the method

    serving = findService(n)

    #set the values

    scoreA = 0

    scoreB = 0

    #check the condition

    while not gameOver(scoreA, scoreB):

        #check "serving" is equal to "A"

        if serving == "A":

            #check "random()" is less than "probA"

            if random() < probA:

                #increment the value

                scoreA = scoreA + 1

            #otherwise

            else:

                #set the value

                serving = "B"

                #increment the value

                scoreB = scoreB + 1

        #check "serving" is equal to "B"

        if serving == "B":

            #check "random()" is less than "probB"

            if random() < probB:

                #increment the value

                scoreB = scoreB + 1

            #otherwise

            else:

                #set the value

                serving = "A"

                #increment the value

                scoreA = scoreA + 1

    #return the result

    return scoreA, scoreB

#definition of "findService" method

def findService(x):

    #check the condition

    if x % 2 == 0:

        #return the value

        return "A"

    #otherwise

    else:

        #return the value

        return "B"

#definition of "gameOver" method

def gameOver(a, b):

    #check "a" or "b" is greater than 15

    if a > 25 or b > 25:

        #check "a-b" is greater than or equal to 2

        if abs(a-b) >= 2:

            #return the value

            return True

        #otherwise

        else:

            #return the value

            return False

    #otherwise

    else:

        #return the value

        return False

#definition of "printSummary" method

def printSummary(winsA1, winsB1, winsA2, winsB2, n):

    #display the results

    print("\nGames simulated: ", n)

    print("Results for Normal Volleyball to 15, score on own serve.")

    print("Wins for A: {0} ({1:0.1%})".format(winsA1, winsA1/n))

    print("Wins for B: {0} ({1:0.1%})".format(winsB1, winsB1/n))

    print()

    print("Results for Rally Volleyball to 25, score on any serve.")

    print("Wins for A: {0} ({1:0.1%})".format(winsA2, winsA2/n))

    print("Wins for B: {0} ({1:0.1%})".format(winsB2, winsB2/n))

    print()

    #calculate the "devA" value

    devA = (winsA2/n - winsA1/n)

    #calculate the "devB" value

    devB = (winsB2/n - winsB1/n)

    #check the condition

    if (winsA1 > winsB1) and (winsA2 > winsB2):

        #check "devA" greater than 0

        if devA > 0:

            #display the result

            print("Team A's advantage was magnified {0:0.1%} in their favor".format(devA))

            print("during the rally scoring match.")

        #check "devA" less than 0

        elif devA < 0:

             #display the result

            print("Team A's advantage was reduced {0:0.1%} in their favor".format(abs(devA)))

            print("during the rally scoring match.")

        #otherwise

        else:

             #display the result

            print("The scoring differences were not statistically significant.")

    #check the condition

    elif (winsB1 > winsA1) and (winsB2 > winsA2):

        #check "devB" greater than 0

        if devB > 0:

             #display the result

            print("Team B's advantage was magnified {0:0.1%} in their favor".format(devB))

            print("during the rally scoring match.")

        #check "devB" less than 0

        elif devB < 0:

             #display the result

            print("Team B's advantage was reduced {0:0.1%} in their favor".format(abs(devB)))

            print("during the rally scoring match.")

        #otherwise

        else:

             #display the result

            print("The scoring differences were not statistically significant.")

    #otherwise

    else:

         #display the results

        print("Neither team's advantage was statistically significant.")

        print("If the initial probabilities were near equal, it is impossible to")

        print("derive significance from the data.")

        print("Try a larger sample size.")

if __name__ == '__main__': main()

Sample Output

Output:

This program is designed to compare the difference between Normal

and Rally scoring in a simulation of (n) games of Volleyball

given a probability (a number between 0 and 1) that reflects the

likelihood of a team winning the serve.

What is the prob. player A wins a serve? 0.65

What is the prob. player B wins a serve? 0.6

How many games to simulate? 5000

Games simulated:  5000

Results for Normal Volleyball to 15, score on own serve.

Wins for A: 3312 (66.2%)

Wins for B: 1688 (33.8%)

Results for Rally Volleyball to 25, score on any serve.

Wins for A: 3325 (66.5%)

Wins for B: 1675 (33.5%)

Team A's advantage was magnified 0.3% in their favor

during the rally scoring match.