You can use R for basic computations you would perform in a calculator
2-3
2/3
2^3
sqrt(2)
log(2)
#Question_1: Compute the log base 5 of 10 and the log of 10.
log(10,base = 5)## [1] 1.430677log(10,base= 10)## [1] 1Computing some offensive metrics in Baseball
#Batting Average=(No. of Hits)/(No. of At Bats) #What is the batting average of a player that bats 29 hits in 112 at bats? BA=(29)/(112) BA
Batting_Average=round(BA,digits = 3) Batting_Average
#Question_2:What is the batting average of a player that bats 42 hits in 212 at bats?
BA= (42)/(212)
Batting_Average2=round(BA, digits = 3)
Batting_Average2## [1] 0.198#On Base Percentage #OBP=(H+BB+HBP)/(At Bats+H+BB+HBP+SF) #Let us compute the OBP for a player with the following general stats #AB=515,H=172,BB=84,HBP=5,SF=6 OBP=(172+84+5)/(515+172+84+5+6) OBP
On_Base_Percentage=round(OBP,digits = 3) On_Base_Percentage
#Question_3:Compute the OBP for a player with the following general stats: #AB=565,H=156,BB=65,HBP=3,SF=7
OBP=(156+65+3)/(565+156+65+3+7)
OBP=round(OBP, digits = 3)
OBP## [1] 0.281Often you will want to test whether something is less than, greater than or equal to something.
3 == 8# Does 3 equals 8?
3 != 8# Is 3 different from 8?
3 <= 8# Is 3 less than or equal to 8?
The logical operators are & for logical AND, | for logical OR, and ! for NOT. These are some examples:
FALSE | FALSE # False OR False
TRUE & FALSE #True AND False
2 < 3 | 1 == 5 # 2<3 is True, 1==5 is False, True OR False is True
Assigning Values to Variables
In R, you create a variable and assign it a value using <- as follows
Total_Bases <- 6 + 5 Total_Bases*3
To see the variables that are currently defined, use ls (as in “list”)
ls()
To delete a variable, use rm (as in “remove”)
rm(Total_Bases)
Either <- or = can be used to assign a value to a variable, but I prefer <- because is less likely to be confused with the logical operator == Vectors
The basic type of object in R is a vector, which is an ordered list of values of the same type. You can create a vector using the c() function (as in “concatenate”).
pitches_by_innings <- c(12, 15, 10, 20, 10) pitches_by_innings
strikes_by_innings <- c(9, 12, 6, 14, 9) strikes_by_innings
#Question_4: Define two vectors,runs_per_9innings and hits_per_9innings, each with five elements.
runs_per_9innings <- c(9,15,6,14,9)
runs_per_9innings## [1] 9 15 6 14 9hits_per_9innings <- c(9,12,12,7,2)
hits_per_9innings## [1] 9 12 12 7 2There are also some functions that will create vectors with regular patterns, like repeated elements.
rep(2, 5)
1:5
seq(1, 10, by=2)
Many functions and operators like + or - will work on all elements of the vector.
pitches_by_innings+strikes_by_innings
pitches_by_innings == strikes_by_innings
length(pitches_by_innings)
min(pitches_by_innings)
mean(pitches_by_innings)
You can access parts of a vector by using [. Recall what the value is of the vector pitches_by_innings.
pitches_by_innings
pitches_by_innings[1]
#Question_5: Get the first element of hits_per_9innings.
hits_per_9innings[1]## [1] 9If you want to get the last element of pitches_by_innings without explicitly typing the number of elements of pitches_by_innings, make use of the length function, which calculates the length of a vector:
pitches_by_innings[length(pitches_by_innings)]
#Question_6: Get the last element of hits_per_9innings.
hits_per_9innings[length(hits_per_9innings)]## [1] 2You can also extract multiple values from a vector. For instance to get the 2nd through 4th values use
pitches_by_innings[c(2, 3, 4)]
Vectors can also be strings or logical values
player_positions <- c(“catcher”, “pitcher”, “infielders”, “outfielders”)
Data Frames
In statistical applications, data is often stored as a data frame, which is like a spreadsheet, with rows as observations and columns as variables.
To manually create a data frame, use the data.frame() function.
data.frame(bonus = c(2, 3, 1),#in millions active_roster = c(“yes”, “no”, “yes”), salary = c(1.5, 2.5, 1))#in millions
bonus
active_roster
salary
Most often you will be using data frames loaded from a file. For example, load the results of a fan’s survey. The function load or read.table can be used for this. How to Make a Random Sample
To randomly select a sample use the function sample(). The following code selects 5 numbers between 1 and 10 at random (without duplication)
sample(1:10, size=5)
The first argument gives the vector of data to select elements from.
The second argument (size=) gives the size of the sample to select.Taking a simple random sample from a data frame is only slightly more complicated, having two steps:
Use sample() to select a sample of size n from a vector of the row numbers of the data frame.
Use the index operator [ to select those rows from the data frame.Consider the following example with fake data. First, make up a data frame with two columns. (LETTERS is a character vector of length 26 with capital letters âAâ to âZâ; LETTERS is automatically defined and pre-loaded in R)
bar <- data.frame(var1 = LETTERS[1:10], var2 = 1:10) # Check data frame bar
var1
var2
Suppose you want to select a random sample of size 5. First, define a variable n with the size of the sample, i.e. 5
n <- 5
Now, select a sample of size 5 from the vector with 1 to 10 (the number of rows in bar). Use the function nrow() to find the number of rows in bar instead of manually entering that number.
Use : to create a vector with all the integers between 1 and the number of rows in bar.
samplerows <- sample(1:nrow(bar), size=n) # print sample rows samplerows
The variable samplerows contains the rows of bar which make a random sample from all the rows in bar. Extract those rows from bar with
barsample <- bar[samplerows, ] # print sample print(barsample)
The code above creates a new data frame called barsample with a random sample of rows from bar.
In a single line of code:
bar[sample(1:nrow(bar), n), ]
var1
var2
The table() command allows us to look at tables. Its simplest usage looks like table(x) where x is a categorical variable.
For example, a survey asks people if they support the home team or not. The data is
Yes, No, No, Yes, Yes
We can enter this into R with the c() command, and summarize with the table() command as follows
x <- c(“Yes”,“No”,“No”,“Yes”,“Yes”) table(x)
Numerical measures of center and spread
Suppose, MLB Teams’ CEOs yearly compensations are sampled and the following are found (in millions)
12 .4 5 2 50 8 3 1 4 0.25
sals <- c(12, .4, 5, 2, 50, 8, 3, 1, 4, 0.25) # the average mean(sals)
var(sals)
sd(sals)
median(sals)
fivenum(sals)
summary(sals)
How about the mode?
In R we can write our own functions, and a first example of a function is shown below in order to compute the mode of a vector of observations x
getMode <- function(x) { ux <- unique(x) ux[which.max(tabulate(match(x, ux)))] }
As an example, we can use the function defined above to find the most frequent value of the number of pitches_by_innings
getMode(pitches_by_innings)
#Question_7: Find the most frequent value of hits_per_9innings.
#getMode(hits_per_9innings)#Question_8: Summarize the following survey with the
table() command: #What is your favorite day of the week to
watch baseball? A total of 10 fans submitted this survey. #Saturday,
Saturday, Sunday, Monday, Saturday,Tuesday, Sunday, Friday, Friday,
Monday
game_day <-c("Saturday", "Saturday", "Sunday", "Monday", "Saturday","Tuesday", "Sunday", "Friday", "Friday", "Monday")game_day## [1] "Saturday" "Saturday" "Sunday" "Monday" "Saturday" "Tuesday"
## [7] "Sunday" "Friday" "Friday" "Monday"table(game_day)## game_day
## Friday Monday Saturday Sunday Tuesday
## 2 2 3 2 1#Question_9: What is the most frequent answer recorded in the survey? Use the getMode function to compute results.
#getMode(game_day)