Getting Started

load("more/kobe.RData")
head(kobe)
##    vs game quarter time
## 1 ORL    1       1 9:47
## 2 ORL    1       1 9:07
## 3 ORL    1       1 8:11
## 4 ORL    1       1 7:41
## 5 ORL    1       1 7:03
## 6 ORL    1       1 6:01
##                                               description basket
## 1                 Kobe Bryant makes 4-foot two point shot      H
## 2                               Kobe Bryant misses jumper      M
## 3                        Kobe Bryant misses 7-foot jumper      M
## 4 Kobe Bryant makes 16-foot jumper (Derek Fisher assists)      H
## 5                         Kobe Bryant makes driving layup      H
## 6                               Kobe Bryant misses jumper      M
kobe$basket[1:9]
## [1] "H" "M" "M" "H" "H" "M" "M" "M" "M"
  1. What does a streak length of 1 mean, i.e. how many hits and misses are in a streak of 1? What about a streak length of 0?

Streak length of 1 meas that the player made one basket. Streak one has 1 basket and no misses.Streak 0 means player missed the basket.

kobe_streak <- calc_streak(kobe$basket)
table(kobe_streak)
## kobe_streak
##  0  1  2  3  4 
## 39 24  6  6  1
barplot(table(kobe_streak))

mean(kobe_streak)
## [1] 0.7631579
  1. Describe the distribution of Kobe’s streak lengths from the 2009 NBA finals. What was his typical streak length? How long was his longest streak of baskets?
table(kobe_streak)
## kobe_streak
##  0  1  2  3  4 
## 39 24  6  6  1
mean(kobe_streak)
## [1] 0.7631579

Most of his streak was of length 0 or 1. Occaccionaly he had a streak of 2 and 3. He also had one streak of 4. He Longest streak is 4. Mean is 0.76. Typical streak lenght is “1”

Simulations in R

outcomes <- c("heads", "tails")
sample(outcomes, size = 1, replace = TRUE)
## [1] "tails"
sim_fair_coin <- sample(outcomes, size = 100, replace = TRUE)

To view the results of this simulation, type the name of the object and then use table to count up the number of heads and tails.

table(sim_fair_coin)
## sim_fair_coin
## heads tails 
##    47    53
sim_unfair_coin <- sample(outcomes, size = 100, replace = TRUE, prob = c(0.2, 0.8))
  1. In your simulation of flipping the unfair coin 100 times, how many flips came up heads?

81, 80, 77 heads and 19,20, 23 tails. Heads will be about 80% of the time and 20% tails. If we run the simulation longer(like 100,000) then the numbers will get closer.

sim_unfair_coin <- sample(outcomes, size = 100, replace = TRUE, prob = c(0.2, 0.8))
table(sim_unfair_coin)
## sim_unfair_coin
## heads tails 
##    15    85
sim_unfair_coin <- sample(outcomes, size = 100, replace = TRUE, prob = c(0.2, 0.8))
table(sim_unfair_coin)
## sim_unfair_coin
## heads tails 
##    17    83

Simulating the Independent Shooter

outcomes <- c("H", "M")
sim_basket <- sample(outcomes, size = 1, replace = TRUE)

To make a valid comparison between Kobe and our simulated independent shooter, we need to align both their shooting percentage and the number of attempted shots.

  1. What change needs to be made to the sample function so that it reflects a shooting percentage of 45%? Make this adjustment, then run a simulation to sample 133 shots. Assign the output of this simulation to a new object called sim_basket.
outcomes <- c("H", "M")
sim_basket <- sample(outcomes, size = 133, replace = TRUE, c(0.45, 0.55))
table(sim_basket)
## sim_basket
##  H  M 
## 53 80
#kobe 
kobe$basket
##   [1] "H" "M" "M" "H" "H" "M" "M" "M" "M" "H" "H" "H" "M" "H" "H" "M" "M"
##  [18] "H" "H" "H" "M" "M" "H" "M" "H" "H" "H" "M" "M" "M" "M" "M" "M" "H"
##  [35] "M" "H" "M" "M" "H" "H" "H" "H" "M" "H" "M" "M" "H" "M" "M" "H" "M"
##  [52] "M" "H" "M" "H" "H" "M" "M" "H" "M" "H" "H" "M" "H" "M" "M" "M" "H"
##  [69] "M" "M" "M" "M" "H" "M" "H" "M" "M" "H" "M" "M" "H" "H" "M" "M" "M"
##  [86] "M" "H" "H" "H" "M" "M" "H" "M" "M" "H" "M" "H" "H" "M" "H" "M" "M"
## [103] "H" "M" "M" "M" "H" "M" "H" "H" "H" "M" "H" "H" "H" "M" "H" "M" "H"
## [120] "M" "M" "M" "M" "M" "M" "H" "M" "H" "M" "M" "M" "M" "H"
#Simulated shooter
sim_basket
##   [1] "M" "M" "H" "H" "M" "H" "M" "M" "M" "H" "M" "H" "M" "M" "M" "M" "H"
##  [18] "H" "M" "M" "M" "H" "M" "H" "H" "M" "M" "M" "M" "H" "M" "H" "M" "M"
##  [35] "M" "H" "M" "H" "H" "M" "H" "M" "H" "H" "H" "H" "H" "H" "M" "H" "M"
##  [52] "M" "M" "H" "H" "M" "H" "H" "M" "M" "H" "M" "H" "M" "M" "M" "H" "M"
##  [69] "M" "H" "M" "M" "H" "M" "M" "H" "M" "H" "M" "M" "M" "M" "H" "M" "M"
##  [86] "M" "M" "H" "M" "M" "M" "H" "M" "H" "H" "M" "M" "H" "M" "H" "M" "M"
## [103] "H" "M" "M" "M" "H" "H" "M" "M" "H" "M" "M" "M" "H" "M" "M" "M" "H"
## [120] "M" "M" "H" "H" "H" "M" "M" "H" "M" "M" "M" "H" "H" "M"
table(kobe$basket)
## 
##  H  M 
## 58 75
table(sim_basket)
## sim_basket
##  H  M 
## 53 80

On your own

Comparing Kobe Bryant to the Independent Shooter

Using calc_streak, compute the streak lengths of sim_basket.

  • Describe the distribution of streak lengths. What is the typical streak length for this simulated independent shooter with a 45% shooting percentage? How long is the player’s longest streak of baskets in 133 shots?

Streak is very similar to that of Kobe’s. Mostly had a streak of length 1 or 0. Occasional streak length of greater than 2 and one or two outliers. I have seen streak length of 6, this changes every time I run the r mark down.

sim_basket_streak <- calc_streak(sim_basket)
table(sim_basket_streak)
## sim_basket_streak
##  0  1  2  3  6 
## 44 26  9  1  1
mean(sim_basket_streak)
## [1] 0.654321
barplot(table(sim_basket_streak))

  • If you were to run the simulation of the independent shooter a second time, how would you expect its streak distribution to compare to the distribution from the question above? Exactly the same? Somewhat similar? Totally different? Explain your reasoning.

The streak distribution is similar with different streak lengths and frequency. Simulated player’s shooting percent is 45% so it will vary a bit each time we run the simulation. If we run the simulation longer(greater number of shots) it will be very similar each time we run it.

  • How does Kobe Bryant’s distribution of streak lengths compare to the distribution of streak lengths for the simulated shooter? Using this comparison, do you have evidence that the hot hand model fits Kobe’s shooting patterns? Explain.

Simulated players streak length is very similar to that of Kobe’s. Based on this, we could see that hot hand model doesnt fit kobe’s or simulated players shooting pattern. Each shot is indepenent of other shots so any player with similar shooting percentage will have similar pattern as Kobe. I play basketball at times, I could say that at times the shots will just go in and I attribute this to some sort of muscle memmory or something else.