Lab 1: Intro to R

Probability

Hot Hands Lab

Getting Started

library(tidyverse)
library(openintro)

Glimpse the data

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?

*Answer: A streak length of 1 means that Kobe shot one hit but missed the next few shots. A streak length of 0 means that Kobe made zero hits and kept making misses.

Counting streak lengths 

kobe_streak <- calc_streak(kobe_basket$shot)

Making a small graph of the distribution:

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

Exercise 2

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? Make sure to include the accompanying plot in your answer

*Answer: The distribution is skewed to the right as there is a tail on the right side. His typical streak length is 0 as it had the most counts. The longest streak length is 4 with less than 5 occurrences.

## Simulations In R


``` r
coin_outcomes <- c("heads", "tails")
sample(coin_outcomes, size = 1, replace = TRUE)
```

```
## [1] "heads"
```

### 100 times coin flips


``` r
sim_fair_coin <- sample(coin_outcomes, size = 100, replace = TRUE)
```

A simple table:

sim_fair_coin

##   [1] "tails" "heads" "tails" "heads" "heads" "tails" "tails" "heads" "tails"
##  [10] "tails" "heads" "heads" "heads" "heads" "tails" "heads" "tails" "tails"
##  [19] "heads" "tails" "heads" "heads" "heads" "heads" "heads" "heads" "heads"
##  [28] "tails" "tails" "heads" "tails" "tails" "heads" "heads" "tails" "tails"
##  [37] "heads" "tails" "tails" "heads" "tails" "heads" "tails" "tails" "heads"
##  [46] "heads" "heads" "tails" "heads" "tails" "heads" "tails" "tails" "tails"
##  [55] "heads" "heads" "heads" "heads" "tails" "tails" "tails" "tails" "tails"
##  [64] "tails" "heads" "tails" "tails" "heads" "heads" "heads" "heads" "tails"
##  [73] "tails" "heads" "heads" "tails" "heads" "heads" "tails" "heads" "tails"
##  [82] "tails" "heads" "tails" "tails" "tails" "tails" "tails" "heads" "tails"
##  [91] "tails" "tails" "heads" "heads" "tails" "tails" "tails" "heads" "heads"
## [100] "heads"

table(sim_fair_coin)

## sim_fair_coin
## heads tails 
##    49    51

Changing probability of the coin:

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 
##    13    87

set.seed(1211)

Exercise 3

1. 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.

*Answer: In my simulation, I got 14 heads and 86 tails.

Simulating the Independent Shooter

shot_outcomes <- c("H", "M")
sim_basket <- sample(shot_outcomes, size = 133, replace = TRUE, prob = c(0.46,0.65))

Exercise 4

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.

*Answer: For the code above of the sample function to represent 45% it was easy. All I had to do was change the prob to 0.46 and .65. Then to sample 133 shots I changed the size = to 133.

Exercise 5

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

   set.seed(1212)
   shot_outcomes <- c("H", "M")
   sim_basket2 <- sample(shot_outcomes, size = 133, replace = TRUE,prob=c(0.45,0.55))
   sim_streak2 <- calc_streak(sim_basket)

Exercise 6

1. 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.

*Answer: The distribution is yet again skewed to the right with the most at 0 streaks. The longest streak here is also four hits before any misses.

``` r
ggplot(data=sim_streak2,aes(x=length))+
  geom_bar()
```

<img src="Kobe-project_files/figure-html/unnamed-chunk-10-1.png" width="672" />

Exercise 7

1. 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.

*Answer: If I were to run this code for a second time the results would be super similar as it would follow a skewed right distribution. There may be more 0 hits because it has a huge lean towards misses than hits. The probability stays the same so the data will be similar if we change the probability then we will see a difference.

Exercise 8

1. 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.

*Answer: Kobe distribution and the independent distribution share the same skewed right distribution. There was more misses than hits and both models followed that the next big group was 1 hit. I will say that Kobe didn’t have hot hands because the graphs show that his hits didn’t always result in the next shot going in but most of the time ending the streaks. His most impressive streak is 4 and both models don’t go past that. He was a good player but never had the hot-hand theory due to the data in my eyes.