Getting Started with R: Concepts in Sports Analytics

Case Scenario 1 This is the fourth season of outfielder Luis Robert with the Chicago White Socks. If during the first three seasons he hit 11, 13, and 12 home runs, how many does he need on this season for his overall average to be at least 20?

#Home Runs so far
HR_Before<-c(11,13,12)
Wanted_Homeruns<-20
n_seasons<-4
#20=11+13+12+x/4
#80-36=x
x_4<-n_seasons*Wanted_Homeruns-sum(HR_Before)
x_4

[1] 44

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

[1] 20

# Find the 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)

[1] 11

We can also use the summary() function to find basic statistics, including the median!

summary(Robert_HRS)

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

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?

Soto_Walks<-c(79,108,41,145,135)
Wanted_Walks<-100
Number_Seasons<-6
#Needed walks on Season 6
walks_6<-Number_Seasons*Wanted_Walks-sum(Soto_Walks)
walks_6

[1] 92

Case Scenario 2

The average salary of 10 baseball players is 72,000 dollars a week and the average salary of 4 soccer players is 84,000. Find the mean salary of all 14 professional players.

n_1<-10
n_2<-4
y_1<-72000
y_2<-84000

#Mean Salary Overall
salary_ave<-(n_1*y_1+n_2*y_2)/(n_1+n_2)
salary_ave

[1] 75428.57

bp_1<-7
fp_1<-9
w_1<-102000
w_2<-91000

#Mean Salary overall
w_salary_ave<-(bp_1*w_1+fp_1*w_2)/(bp_1+fp_1)
w_salary_ave

[1] 95812.5

getwd()

[1] "/cloud/project"

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

contract_mean<-mean(contract_years)
contract_mean<-round(contract_mean,digits = 1)
contract_mean

[1] 3.5

#Median
contract_median<-median(contract_years)
contract_median

[1] 3

#find the number of observations
contract_n<-length(contract_years)

#find the standard deviation
contract_sd<-sd(contract_years)
contract_sd

[1] 1.695331

contract_w1sd<-sum((contract_years-contract_mean)/contract_sd<1) /contract_n

#Percentage of observations within one sd from the mean
contract_w1sd

[1] 0.842

#Difference from empirical
contract_w1sd-0.68

[1] 0.162

#within 2 sd
contract_w2sd <-sum((contract_years-contract_mean)/contract_sd<2)/contract_n
contract_w2sd

[1] 1

#difference from empirical
contract_w2sd-0.95

[1] 0.05

#within standard deviation 3
contract_w3sd<-sum((contract_years-contract_mean)/contract_sd<3)/contract_n
contract_w3sd

[1] 1

## Difference from empirical 
contract_w3sd - 0.9973

[1] 0.0027

5. Draw Histrgram

#Create a histogram hist()
#xlab = X Axis Title
#xlim = X Axis
#ylim = Y Axis
#break break points
hist(contract_years,xlab = "Years Left in Contract",col = "blue",border = "white",xlim = c(1,6),ylim = c(0,250),breaks = 3)

NA
NA
NA

# Making a box plot

boxplot(contract_years,main="Years in Contract",ylab="Years")

boxplot(contract_years,main="Years in Contract",ylab="Years",col = "lightblue",border = "blue",horizontal = FALSE)

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

doubles_hit_mean<-mean(doubles_hit)
doubles_hit_mean

[1] 23.55

doubles_hit_median<-median(doubles_hit)
doubles_hit_median

[1] 23.5

doubles_hit_n<-length(doubles_hit)
doubles_hit_sd<-sd(doubles_hit)

doubles_hit_w1sd<-sum((doubles_hit-doubles_hit_mean)/doubles_hit_sd<1)/doubles_hit_n
doubles_hit_w1sd

[1] 0.79

# Diffrence from empirical
doubles_hit_w1sd -0.68

[1] 0.11

doubles_hit_w2sd<-sum((doubles_hit-doubles_hit_mean)/doubles_hit_sd<2)/doubles_hit_n
doubles_hit_w2sd

[1] 1

# Diffrence from empirical
doubles_hit_w2sd -0.95

[1] 0.05

doubles_hit_w3sd<-sum((doubles_hit-doubles_hit_mean)/doubles_hit_sd<3)/doubles_hit_n
doubles_hit_w3sd

[1] 1

# Diffrence from empirical
doubles_hit_w3sd -0.9973

[1] 0.0027

# Building a histogram

hist(doubles_hit,xlab = "Number of Doubles", col = "blue",border = "lightblue",
     xlim = c(0,60),ylim = c(0,30),breaks = 7)

# Making a Box Plot
boxplot(doubles_hit,main="Boxplot of Doubles Hit by Player",ylab="Doubles",
                          col="blue",border="lightblue")