MSU Economy of Sports and Conditional Probability Project

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Question Description

economy of sports project 5 : hot hand. compute conditional prob. requirements, example and my data are in the files.

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Project 5: Hot Hand Due date: June 26 1. Enter the data on a spreadsheet. Put your name in cell A1 and enter the 1’s and 0’s across the row from B1 to CW1. (You should have done this already in Project 1) 2. Find your shooting percentage. (Just sum the data and divide by 100). 3. Find the correlation coefficient. a) Paste the data to the second row from A2 to CV2. (Just the data, not your name.) b) (Type =CORREL(B1:CV1, B2:CV2) in an empty cell. 4. Find the conditional probabilities for a make following 3 misses, 2 misses, 1 miss, 1 make, 2 makes, 3 makes. You can use the program I provided. Just paste your data over mine in the top row. 5. Enter the statistics in the space provided. Note that this is the same data that is in the table on the Philadelphia 76ers in the hot hand article. 6. Interpret your results in the space provided. 7. Next, count the number of runs in your series. For example, the series 11001110 has 4 runs. 8. Go to http://www.quantitativeskills.com/sisa/statistics/ordinal.htm a. Enter the data and do the WW runs test. b. Find the expected number of runs and the z-statistic. The z-statistic is the number of standard deviations that your outcome lies from the mean of the distribution of runs. 9. Show where your runs number falls on the normal distribution provided. 10. Enter the statistics in the space provided. 11. Interpret your results in the space provided. Name: Assignment Sheet Assignment #5 Hot Hand 1. Fill in the following: p(hit | 3 misses) p(hit | 2 misses) p(hit | 1 miss) p(hit) p(hit | 1 hit) p(hit | 2 hit) p(hit | 3 hit) ρ 2. Do your conditional probabilities show evidence of the hot hand? Explain. 3. Does your correlation coefficient ρ show evidence of the hot hand? Explain. 4. Fill in the following. hits misses runs 5. Show where your runs number falls on the distribution. 6. Is this evidence of the hot hand? Explain. expected runs z-statistic DATA (# of hits in a row prior to shot) (# of misses in a row prior to shot) 1 0 1 1 1 0 # of shots following 1 make #of shots made following 1 make 0 0 1 1 conditional probability given 1 make # of shots following 2 makes # of shots made following 2 makes conditional probability given 2 makes # of shots following 3 makes # of shots made following 3 makes conditional probability given 3 makes # of shots following a miss # of shots made following a miss 0 0.470588235 0 0 0.5 0 0 1 1 0.583333333 # of shots following 2 misses # of shots made following 2 misses 0 0 # of shots following 3 misses # of shots made following 3 misses conditional probability given 3 misses 0 0 0.5 conditional probability given 1 miss conditional probability given 2 misses 0 0 1 1 0 0 0.7 0 0 0.833333333 0 0 0 2 0 1 0 1 0 1 0 0 0 1 0 0 2 1 0 3 0 1 0 0 0 1 0 0 2 2 1 2 1 3 1 3 1 3 1 3 1 4 1 4 1 4 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 2 2 2 2 3 2 4 2 5 3 5 3 6 3 7 3 0 0 0 0 0 0 0 0 1 0 2 1 2 1 2 1 3 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 3 1 1 0 0 2 0 0 0 1 1 0 2 0 1 0 1 0 1 0 1 0 1 0 1 4 1 5 2 6 2 6 2 6 2 7 2 7 2 8 2 8 2 1 0 1 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 4 8 4 8 4 9 4 10 5 10 5 11 6 11 6 12 7 4 2 4 2 4 2 4 2 5 3 5 3 5 3 5 3 5 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 1 0 0 0 1 1 0 2 0 1 0 0 0 1 0 0 2 1 0 3 1 1 0 1 2 0 9 2 9 2 9 2 10 2 10 2 10 2 10 2 11 3 12 4 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 7 13 7 14 8 14 8 15 8 16 8 17 9 17 9 17 9 5 3 5 3 6 4 6 4 6 4 7 4 8 5 8 5 8 5 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 1 3 0 0 4 0 0 0 1 1 0 2 1 1 0 0 2 0 1 0 1 1 1 0 1 2 0 13 5 14 5 14 5 14 5 15 6 16 6 16 6 17 7 18 8 4 2 5 2 5 2 5 2 5 2 6 2 6 2 6 2 7 3 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 17 9 17 9 18 9 19 10 19 10 19 10 20 11 20 11 20 11 8 5 8 5 8 5 9 6 9 6 9 6 9 6 9 6 9 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 3 0 1 4 0 1 5 0 0 6 0 1 0 1 1 1 0 0 2 0 1 0 1 1 1 0 19 9 20 10 21 11 22 11 22 11 23 12 24 12 24 12 25 13 8 4 9 5 10 6 11 6 11 6 11 6 12 6 12 6 12 6 3 2 4 3 5 4 6 4 6 4 6 4 6 4 6 4 6 4 20 11 20 11 20 11 20 11 21 12 21 12 21 12 22 13 22 13 9 6 9 6 9 6 9 6 9 6 9 6 9 6 9 6 9 6 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 2 0 0 3 0 0 0 1 1 0 2 0 1 0 1 0 1 1 1 0 0 2 0 1 0 1 26 14 27 14 27 14 27 14 28 14 28 14 29 15 30 15 30 15 13 7 14 7 14 7 14 7 14 7 14 7 14 7 15 7 15 7 6 4 7 4 7 4 7 4 7 4 7 4 7 4 7 4 7 4 22 13 22 13 23 13 24 14 24 14 25 15 25 15 25 15 26 16 9 6 9 6 9 6 10 7 10 7 10 7 10 7 10 7 10 7 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0 1 0 0 0 1 1 0 2 0 1 0 1 0 1 1 1 0 1 2 0 1 3 0 0 4 0 31 15 31 15 31 15 32 15 32 15 33 16 34 17 35 18 36 18 15 7 15 7 15 7 15 7 15 7 15 7 16 8 17 9 18 9 7 4 7 4 7 4 7 4 7 4 7 4 7 4 8 5 9 5 26 16 27 16 28 17 28 17 29 18 29 18 29 18 29 18 29 18 10 7 10 7 11 8 11 8 11 8 11 8 11 8 11 8 11 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 0 1 0 1 0 0 0 1 1 0 2 0 1 0 0 0 1 0 0 2 0 0 3 1 0 4 36 18 37 18 37 18 37 18 38 18 38 18 38 18 38 18 38 18 18 9 18 9 18 9 18 9 18 9 18 9 18 9 18 9 18 9 9 5 9 5 9 5 9 5 9 5 9 5 9 5 9 5 9 5 30 19 30 19 31 19 32 20 32 20 33 20 34 20 35 20 36 21 11 8 11 8 11 8 12 9 12 9 12 9 13 9 14 9 15 10 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 5 4 0 1 0 1 0 1 0 1 0 0 0 1 1 0 2 1 1 0 0 2 0 1 0 1 0 1 0 39 18 39 18 40 18 40 18 40 18 41 19 42 19 42 19 43 19 18 9 18 9 18 9 18 9 18 9 18 9 19 9 19 9 19 9 9 5 9 5 9 5 9 5 9 5 9 5 9 5 9 5 9 5 36 21 37 22 37 22 38 22 39 23 39 23 39 23 40 24 40 24 15 10 15 10 15 10 15 10 16 11 16 11 16 11 16 11 16 11 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 0 0 1 0 0 2 1 0 3 1 1 0 1 2 0 1 3 0 0 4 0 1 0 1 1 1 0 43 19 43 19 43 19 44 20 45 21 46 22 47 22 47 22 48 23 19 9 19 9 19 9 19 9 20 10 21 11 22 11 22 11 22 11 9 5 9 5 9 5 9 5 9 5 10 6 11 6 11 6 11 6 41 24 42 24 43 25 43 25 43 25 43 25 43 25 44 26 44 26 16 11 17 11 18 12 18 12 18 12 18 12 18 12 18 12 18 12 5 4 5 4 6 5 6 5 6 5 6 5 6 5 6 5 6 5 1 2 0 0 3 0 0 0 1 1 0 2 0 1 0 0 0 1 1 0 2 49 24 50 24 50 24 50 24 51 24 51 24 51 24 23 12 24 12 24 12 24 12 24 12 24 12 24 12 11 6 12 6 12 6 12 6 12 6 12 6 12 6 44 26 44 26 45 26 46 27 46 27 47 27 48 28 18 12 18 12 18 12 19 13 19 13 19 13 20 14 6 5 6 5 6 5 6 5 6 5 6 5 6 5 52 Eva 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 0 ...
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Tutor Answer

SelfiexWriter
School: Carnegie Mellon University

Attached.

Question 1

p(hit | 3 misses) = 0

p(hit | 2 misses) =

p(hit | 1 miss) =

p(hit) =

0.297297

0.301887

0.47

p(hit | 1 hit) =

p(hit | 2 hit) =

p(hit | 3 hit) =

Ρ=

0.673913

0.666667

0.684211

0.371569

Question 2
Yes. It is because the hit probability that is given to a person who made three hits is higher than
the standard probability of hitting. That is, the three hits probability is 0.684211 and the standard
probability is 0.47.

Question 3
The correlation for the first two rows is 0.371569. it means that if a person is successful in the
last game, he or she has more chances of succeeding the game. This is because, with a 0.371569, it
shows that there is a lower correlation among the points gained in games that are played.
Question 4

hits
47

misses
53

runs
42

expected runs
43

z-statistic
1.645

Question 5

Question 6
Yes. It is because the runs come below the z-statistic which is 1.645 and it is equivalent to p =
0.1


EVA
0
Shooting Percentage
Correlation Coefficient

(# of hits in a row prior to shot)
(# of misses in a row prior to shot)

# of shots following 1 make
#of shots made following 1 make
conditional probability given 1 make
# of shots following 2 makes
# of shots made following 2 makes
con...

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