Reference no: EM132294108
Project - Hack a Shaq!
Assignment Description - "There were his usual clunkers off the rim, and several other tries actually were close to the mark, but spun in and out of the hoop. When it was over, Shaquille O'Neal had broken Wilt Chamberlain's record for free-throw futility in a single game. Eleven times, O'Neal furrowed his brow, remembered to bend his knees, and tried to arc the ball into [the] basket. None made it." (Ken Peters, Associated Press, December 9, 2000).
In the early 2000s, many teams around the NBA adopted a strategy to defend NBA legend Shaq by intentionally fouling him, because he was a notoriously bad free-point shooter. This strategy became known as "Hack a Shaq". In the early 2010s, a similar approach was taken with center Dwight Howard. Is this a good strategy? In this project, you will investigate the idea of streaks and 'shoot your own free throws', as well as determining if teams were smart in using "Hack a Shaq" with Howard.
Materials Needed:
Part 1: Free Throw Phenom?
Fill out the table below. Write the result (numbers 1 to 6) of rolling your dice in the "Result" box. In the "Made" box, put an X if you rolled an even number (2, 4, 6) or leave it blank if you rolled an odd number (1, 3, 5)
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Roll#
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1
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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17
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18
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19
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20
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Result
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Made
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Roll#
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21
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22
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23
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24
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25
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26
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27
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28
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29
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30
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31
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32
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33
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34
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35
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36
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37
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38
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39
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40
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Result
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Made
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Roll#
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41
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42
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43
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44
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45
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46
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47
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48
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49
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50
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51
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52
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53
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54
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55
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56
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57
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58
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59
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60
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Result
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Made
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Roll#
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61
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62
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63
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64
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65
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66
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67
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68
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69
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70
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71
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72
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73
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74
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75
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76
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77
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78
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79
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80
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Result
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Made
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Roll#
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81
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82
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83
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84
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85
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86
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87
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88
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89
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90
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91
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92
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93
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94
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95
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96
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97
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98
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99
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100
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Result
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Made
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Part 2: Result Summary
Look at your first box (rolls 0-20):
Total # of rolls: _______
# rolls of a 3: _______ Probability of rolling a 3: _______
# of even rolls: _______ Probability of rolling an even:______
Look at your first two boxes (rolls 0-40):
Total # of rolls: _______
# rolls of a 3: _______ Probability of rolling a 3: _______
# of even rolls: _______ Probability of rolling an even:______
Look at your first four boxes (rolls 0-80):
Total # of rolls: _______
# rolls of a 3: _______ Probability of rolling a 3: _______
# of even rolls: _______ Probability of rolling an even:______
Look at all the boxes (rolls 0-100):
Total # of rolls: _______
# rolls of a 3: _______ Probability of rolling a 3: _______
# of even rolls: _______ Probability of rolling an even:______
Longest streak of Made: ________ Longest streak of Misses: _______
Your Free Throw Percentage: _________
(Number of evens divided by total number of shots):
Part 3: Analysis
1) What type of probability (theoretical, empirical, subjective) are we doing above? Why?
2) What is the theoretical probability of rolling a 3? How does this compare to the probability you got above, for the first/second/fourth/all boxes?
3) What is the theoretical probability of rolling an even number? How does this compare to your above probabilities?
4) Compare your probabilities above, to the theoretical probabilities (for rolling a 3, and rolling an even). How do they compare as you include more and more data (from just 0-20, then 0-40, then 0-80, then 0-100)?
5) Assume that you throwing an even means you made the free-throw, and an odd means you missed. What was your longest streak of "missed" shots? Did you do better than Shaq's?
6) In his career, Shaq made 52.7% of his free throws, and 58.2% of his normal shots. How did this compare to your percentage?
Part 4 - Expected Value
We can use Expected Value to determine if it is better to foul a player (based on their free throw percentage) or let them shoot (their field goal percentage).
Expected Value for Field Goals= 2 pts* percentage made + 0 points * percentage missed
Shaq's Expected Value for Field Goals = He makes 58.2%, which means he misses 100% - 58.2% = 41.8%
2(0.582) + 0(0.418) = 1.164
Expected Value Free Throws - for a free throw, you get 2 shots. You can either make both shots (earn 2 points), make the first and miss the second (earn 1 point), miss the first and make the second (earn 1 point), or miss both (0 pts).
2 * (%made * %made) + 1 * (%made * %missed) + 1 * (%missed * %made) + 0 (%missed *%missed)
Shaq's Expected Value for Free Throws = He makes 52.7% which means he misses 100% - 52.7% = 47.3%
2*(0.527 * 0.527) + 1*( 0.527 * 0.473) + 1*(0.473 * 0.527) + 0*(0.473 * 0.473) = 1.054
Shaq has an Expected Value of +1.164 for making a field goal, versus +1.054 for making a free throw - so "Hack a Shaq" was a good strategy for him.
Dwight Howard made 57.7% of his Field Goals, and 57.6% of his Free Throws.
Calculate Dwight Howard's Expected Value Field Goals: 2(_____) + 0(______) = _______
Calculate Dwight Howard's Expected Value Free Throws: 2*(____ * ____) + 1*(_____ * ______) + 1*(_____ * _____) + 0*(____ * _____) =
Is "Hack a Shaq" a good strategy to use against Dwight? Why or why not?
Attachment:- Assignment File.rar