Lab 3 Probability

library(tidyverse)
library(openintro)

Exercise 1

For a streak of length one, there was one hit shot and one miss shot. For a streak length that is zero, Kobe missed on his first basket.

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 2

Kobe’s shot distribution is right skewed. For the 2009 finals, he tend to had streaks of length zero and one. His longest streak was length four, as he had 3 hit shots in the streak.

kobe_streak <- calc_streak(kobe_basket$shot)
ggplot(data = kobe_streak, aes(x = length)) +geom_bar()

Execerise 3

Out of 100 flips, 18 heads were drawn from the sample.

coin_outcomes <- c("heads", "tails")
set.seed(100)
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 
##    18    82

Execerise 4

In order to reflect the 45% success rate of a hit shoot, we have to input .45 in the left and the miss rate of .55 in the right side.

shot_outcomes <- c("H", "M")
set.seed(133)
sim_basket <- sample(shot_outcomes, size = 133, replace = TRUE,prob = c(.45,.55))
table(sim_basket)

## sim_basket
##  H  M 
## 73 60

Excercise 5

Now, Lets calculate Kobe’s win streaks with the predictive data of his shooting probability.

sim_streak<-calc_streak(sim_basket)

Excerise 6

Looking at the data, Kobe had a higher percentage to score an 0-2 streak. Majority of his shots create a streak length of 1+, as 35 hits begin the streaks. Kobe could achieved a streak length of 6 in 133 total shots.

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

Execrise 7

I expect that the independent shooter results will be left skewed like Kobe’s but lack the interference that came with his results. The independent shooter results are not affected by outside forces like pressure, physical skill, and the opposing team. So, the sample will produced longer streak than the average basketball star might have on a good season!

ind_Shooter<-sample(shot_outcomes,size=133,replace=TRUE)
ind_streak<-calc_streak(ind_Shooter)
ggplot(data=ind_streak,aes(x=length))+geom_bar()

table(sim_streak)

## sim_streak
##  0  1  2  3  4  5  6 
## 25 16 12  3  2  2  1

table(ind_streak)

## ind_streak
##  0  1  2  3  4  5  6 10 
## 28 14 12  2  2  1  1  1

Execrise 8

Kobe’s predicted shot probability gave his sample a new weighted space, where he has a 45% percent chance of a hit. Kobe scorced more streaks of 0 than the independent shooter and had the range of 0-6 than 0-10. However, I believe Kobe has “Hot hands” from his frequency of streaks. Compared to the independent shooter, Kobe achieved more multiples of 1+ streaks. Although, the independent shooter achieved a 10L streak, its probability for a second time is less than Kobe scoring two 5L streaks.

table(sim_streak)

## sim_streak
##  0  1  2  3  4  5  6 
## 25 16 12  3  2  2  1

table(ind_streak)

## ind_streak
##  0  1  2  3  4  5  6 10 
## 28 14 12  2  2  1  1  1