Introduction to R for Sports Analytics #2

Question 1 Now, you must complete the problem below which represents a similar case scenario. You may use the steps that we executed in Case-scenario 1 as a template for your solution.

This is the sixth season of outfielder Juan Soto in the majors. If during the first five seasons he received 79, 108,41,145, and 135 walks, how many does he need on this season for his overall number of walks per season to be at least 100?

# Walks so far
walks_before <- c(79, 108, 41, 145, 135)
# Average walks per season wanted
wanted_walks <- 100
# Number of seasons
n_seasons <- 6
# Needed walks in season 6
x_6 <- n_seasons*wanted_walks - sum(walks_before)
x_6

[1] 92

Question 2 The average salary of 7 basketball players is 102,000 dollars a week and the average salary of 9 NFL players is 91,000. Find the mean salary of all 16 professional players.

n_1 <- 7
n_2 <- 9
x_1 <- 102000
x_2 <- 91000
salary_ave <- (n_1*x_1 + n_2*x_2)/(n_1+n_2)
salary_ave

[1] 95812.5

Case-scenario 3 The frequency distribution below lists the number of active players in the Barclays Premier League and the time left in their contract.

Find the mean,the median and the standard deviation.

What percentage of the data lies within one standard deviation of the mean?

What percentage of the data lies within two standard deviations of the mean?

What percent of the data lies within three standard deviations of the mean?

Draw a histogram to illustrate the data.

Solution The allcontracts.csv file contains all the players’ contracts length. We can read this file in R using the read.csv() function.

contract_length <- read.table("allcontracts.csv", header = TRUE, sep = ",")
contract_years <- contract_length$years

Make comments about the code we just ran above.

1. To find the mean and the standard deviation

# Mean 
contracts_mean  <- mean(contract_years)
contracts_mean

[1] 3.458918

# Median
contracts_median <- median(contract_years)
contracts_median

[1] 3

# Find number of observations
contracts_n <- length(contract_years)
# Find standard deviation
contracts_sd <- sd(contract_years)

2.What percentage of the data lies within one standard deviation of the mean?

contracts_w1sd <- sum((contract_years - contracts_mean)/contracts_sd < 1)/ contracts_n
# Percentage of observation within one standard deviation of the mean
contracts_w1sd

[1] 0.8416834

## Difference from empirical 
contracts_w1sd - 0.68

[1] 0.1616834

3.What percentage of the data lies within two standard deviations of the mean?

## Within 2 sd
contracts_w2sd <- sum((contract_years - contracts_mean)/ contracts_sd < 2)/contracts_n
contracts_w2sd

[1] 1

## Difference from empirical 
contracts_w2sd - 0.95

[1] 0.05

4.What percent of the data lies within three standard deviations of the mean?

## Within 3 sd 
contracts_w3sd <- sum((contract_years - contracts_mean)/ contracts_sd < 3)/contracts_n
contracts_w3sd

[1] 1

## Difference from empirical 
contracts_w3sd - 0.9973

[1] 0.0027

5.Draw a histogram

# Create histogram
hist(contract_years,xlab = "Years Left in Contract",col = "green",border = "red", xlim = c(0,8), ylim = c(0,225),
   breaks = 5)

Question 3 Use the skills learned in case scenario number 3 on one the following data sets. You may choose only one dataset. They are both available in Canvas.

doubles_hit.csv and triples_hit.csv

I will use the triples_hit.csv

hits <- read.csv("triples_hit.csv")

triples_hit <- hits$triples_hit  

# 1. Mean, median, standard deviation
mean(triples_hit)

[1] 4.96

median(triples_hit)

[1] 5

sd(triples_hit)

[1] 2.884721

# 2-4. Percentage of data within 1, 2, and 3 SD of the mean
m <- mean(triples_hit); s <- sd(triples_hit)
within_1sd <- mean(triples_hit > m - s & triples_hit < m + s) * 100
within_2sd <- mean(triples_hit > m - 2*s & triples_hit < m + 2*s) * 100
within_3sd <- mean(triples_hit > m - 3*s & triples_hit < m + 3*s) * 100
within_1sd; within_2sd; within_3sd

[1] 67
[1] 93
[1] 98

# 5. Histogram
hist(triples_hit, xlab = "Triples", col = "blue", border = "black")

getwd()

[1] "/Users/victorcuerdo/In Class Assigment #4"

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