Load Packages

library(tidyverse)
## -- Attaching packages --------------------------------------- tidyverse 1.3.2 --
## v ggplot2 3.3.6     v purrr   0.3.4
## v tibble  3.1.6     v dplyr   1.0.9
## v tidyr   1.2.0     v stringr 1.4.0
## v readr   2.1.2     v forcats 0.5.1
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(openintro)
## Loading required package: airports
## Loading required package: cherryblossom
## Loading required package: usdata

Data

Here we are taking a look into the kobe_basket dataset. We see that it’s organized by opponent, game, quarter, time, description, shot.

glimpse(kobe_basket)
## Rows: 133
## Columns: 6
## $ vs          <fct> ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL, ORL~
## $ game        <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1~
## $ quarter     <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3~
## $ time        <fct> 9:47, 9:07, 8:11, 7:41, 7:03, 6:01, 4:07, 0:52, 0:00, 6:35~
## $ description <fct> Kobe Bryant makes 4-foot two point shot, Kobe Bryant misse~
## $ shot        <chr> "H", "M", "M", "H", "H", "M", "M", "M", "M", "H", "H", "H"~

Exercise 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?

A streak length of 1 means that there was a shot made and a shot miss, for ex: (H,M)

A steak length of 0 means that there was a shot missed, for ex: (M)

Kobe Streak Dataset

The investigation involves looking at the length of Kobe Bryant’s make and miss streak. Below we assign the calc_streak function to kobe_streak to look at his make and misses and then graph it in a barplot.

kobe_streak <- calc_streak(kobe_basket$shot)

Exercise 2

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? Make sure to include the accompanying plot in your answer.

ggplot(data = kobe_streak, aes(x = length)) + geom_bar()

The distribution of Kobe’s streak length is right-skewed. The length of his typical shooting streak is 0. His longest streak of made baskets is 4.

Simulations in R

coin_outcomes <- c("heads", "tails")
sample(coin_outcomes, size = 1, replace = TRUE)
## [1] "heads"
sim_fair_coin <- sample(coin_outcomes, size = 100, replace = TRUE)
sim_fair_coin
##   [1] "tails" "tails" "heads" "tails" "heads" "tails" "tails" "heads" "heads"
##  [10] "tails" "heads" "heads" "heads" "tails" "tails" "heads" "heads" "tails"
##  [19] "tails" "tails" "tails" "heads" "tails" "tails" "tails" "tails" "tails"
##  [28] "heads" "heads" "tails" "heads" "tails" "tails" "heads" "heads" "tails"
##  [37] "heads" "tails" "tails" "heads" "heads" "tails" "tails" "heads" "tails"
##  [46] "heads" "tails" "heads" "tails" "heads" "tails" "heads" "heads" "heads"
##  [55] "tails" "heads" "heads" "tails" "tails" "tails" "tails" "heads" "heads"
##  [64] "tails" "tails" "heads" "heads" "heads" "heads" "tails" "tails" "tails"
##  [73] "heads" "tails" "heads" "heads" "tails" "tails" "tails" "tails" "heads"
##  [82] "heads" "heads" "heads" "tails" "tails" "heads" "tails" "tails" "heads"
##  [91] "tails" "heads" "tails" "heads" "tails" "heads" "heads" "tails" "heads"
## [100] "heads"
table(sim_fair_coin)
## sim_fair_coin
## heads tails 
##    48    52

Exercise 3

In your simulation of flipping the unfair coin 100 times, how many flips came up heads? Include the code for sampling the unfair coin in your response. Since the markdown file will run the code, and generate a new sample each time you Knit it, you should also “set a seed” before you sample. Read more about setting a seed below.

set.seed(629)
sim_unfair_coin <- sample(coin_outcomes, size = 100, replace = TRUE, prob = c(0.2,0.8))
table(sim_unfair_coin)
## sim_unfair_coin
## heads tails 
##    17    83

17 flips came up heads

Simulating the Independent Shooter

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

Exercise 4

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.

set.seed(62)
sim_basket <- sample(shot_outcomes, size = 133, replace = TRUE, prob = c(0.45,0.55))

In order for the sample function to reflect a shooting percentage of 45% we need add the prob function and design it so that it has a hit value of 45% and miss value of 55%

Exercise 5

Using calc_streak, compute the streak lengths of sim_basket, and save the results in a data frame called sim_streak

sim_streak <- calc_streak(sim_basket)

Exercise 6

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? Make sure to include a plot in your answer.

ggplot(data = sim_streak, aes(x = length)) +
geom_bar()

The distribution is right skewed. The typical streak length is 0. This player’s longest streak is 5.

Exercise 7

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.

I expect a second simulation of the independent shooter to generate a similar result, since we set their made shot percentage to be 45%. The distribution will still be right skewed, since the player would still be missing around 55% of the time.

Exercise 8

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.

The kobe_streak and sim_streak are both right skewed and have very similar distributions. If we were only use this comparison, we would not have the evidence to support the hot hand model. If there was evidence of a hot hand model, we would likely see a left skewed distribution.

The hot hand model assumes that a player is more likely like to make the next basket after consecutive makes. If that’s the case, in the bar graph we would see high makes after a consecutive streak. The higher the streak, the more makes make we expect to see. We don’t observe this pattern in our bar graphs.