In-class activity #5: Introduction to R for Sports Analytics, Part 2

Question 1

# Home-runs so far
HR_before <- c(11, 13, 12)
# Average Number of Home-runs per season wanted
wanted_HR <- 20
# Number of seasons
n_seasons <- 4
# Needed Home-runs on season 4
x_4 <- n_seasons*wanted_HR - sum(HR_before)
# Minimum number of Home-runs needed by Robert
x_4

[1] 44

According to the calculations above, Robert must hit 44 home-runs or better on this season to get an average number of home-runs per season of at least 20.

# Robert's performance
Robert_HRs <- c(11, 13, 12,44)
# Find mean
mean(Robert_HRs)

[1] 20

# Find standard deviation
sd(Robert_HRs)

[1] 16.02082

# Find the maximum number of home-runs during the four seasons period
max(Robert_HRs)

[1] 44

# Find the minimum number of home-runs during the four seasons period
min(Robert_HRs)

summary(Robert_HRs)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  11.00   11.75   12.50   20.00   20.75   44.00 

Question 2

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

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

doubles <- read.table("doubles_hit.csv", header = TRUE, sep = ",")
doublesnumber <- doubles$doubles_hit

1. To find the mean and the standard deviation

# Mean 
doublesnumber_mean  <- mean(doublesnumber)
doublesnumber_mean

[1] 23.55

# Median
doublesnumber_median <- median(doublesnumber)
doublesnumber_median

[1] 23.5

# Find number of observations
players_n <- length(doublesnumber)
# Find standard deviation
players_sd <- sd(doublesnumber)

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

doublesnumber_w1sd <- sum((doublesnumber - doublesnumber_mean)/players_sd < 1)/ players_n
# Percentage of observation within one standard deviation of the mean
doublesnumber_w1sd

[1] 0.79

## Difference from empirical 
doublesnumber_w1sd - 0.68

[1] 0.11

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

doublesnumber_w1sd <- sum((doublesnumber - doublesnumber_mean)/players_sd < 2)/ players_n
doublesnumber_w1sd

[1] 1

doublesnumber_w1sd - 0.95

[1] 0.05

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

doublesnumber_w1sd <- sum((doublesnumber - doublesnumber_mean)/players_sd < 3)/ players_n
doublesnumber_w1sd

[1] 1

doublesnumber_w1sd - 0.9973

[1] 0.0027

# Create histogram
hist(doublesnumber,xlab = "Number of Doubles",col = "green",border = "red", xlim = c(0,40), ylim = c(0,70), breaks = 5)