Exam 2 - Questions 5,6,7

Question 5

Consider the following vectors representing the number of field goals made and attempted by a basketball player in five games:

Field Goals Made: c(18, 7, 6, 9, 10,13) Field Goals Attempted: c(36, 23, 12, 18, 24,22)

Calculate the field goal percentage for each game and select the correct average field goal percentage for the five games.

field_goals_made <- c(18, 7, 6, 9, 10,13)
field_goals_attempted <- c(36, 23, 12, 18, 24,22)

# Calculate the field goal percentage
fg_percentage <- (field_goals_made / field_goals_attempted) * 100
round(fg_percentage, 2)

[1] 50.00 30.43 50.00 50.00 41.67 59.09

#Average field goal percentage for the all six games
mean(fg_percentage)

[1] 46.86539

#Restrict to the first five games
fgm_five <- field_goals_made[1:5]
fga_five <- field_goals_attempted[1:5]

# Field goal percentage for each of the five games
fg_percentage_five <- (fgm_five / fga_five) * 100
round(fg_percentage_five, 2)

[1] 50.00 30.43 50.00 50.00 41.67

# Average field goal percentage for the five games
mean(fg_percentage_five)

[1] 44.42029

Results: Note that there are six games given not five. All six games - Average field goal percentage: 46.87% First five games - Average field goal percentage: 44.42%

Question 6

Consider the following vectors in R representing the number of three-pointers made (3PM) and attempted (3PA) by a basketball player over a seven-game span:

Three-Pointers Made: c(3, 5, 10, 6, 3, 7, 1)

Three-Pointers Attempted: c(9, 10, 18, 12, 11, 12, 11)

Calculate both the average of the individual per-game three-point percentages and the overall (cumulative) three-point shooting percentage across all seven games. Submit your code and knitted R HTML file or RPubs link as instructed.

#Three-Pointers Made: 
three_made<-c(3, 5, 10, 6, 3, 7, 1) 
#Three-Pointers Attempted: 
three_attempted<-c(9, 10, 18, 12, 11, 12, 11)

#Per-game 3PM percentage
pct_per_game <- (three_made / three_attempted) * 100
round(pct_per_game, 2)

[1] 33.33 50.00 55.56 50.00 27.27 58.33  9.09

#Average of individual per-game percentage
mean(pct_per_game)

[1] 40.51227

# Overall cumulative 3P percentage
sum(three_made)

[1] 35

sum(three_attempted)

[1] 83

(sum(three_made) / sum(three_attempted)) * 100

[1] 42.16867

Results: Average of Individual per-game percentages: 40.51 Total Made: 35 | Total attempted: 83 Overall (cumulative) percentage: 42.17%

Question 7

Consider the following dataset representing the performance of baseball players in a season. It includes the following variables: PlayerID, Hits, At-Bats, Home Runs (HR), Walks (BB), and Strikeouts (SO).

PlayerID Hits At-Bats HR BB SO

1             112       400           25          50     60

2             124       450           22          60     65

3             121       380           8            19     67

4             106       500           20         150     92

5             140       402           11          55     70

Compute the On-Base Percentage (OBP) for each player and select the player with the highest OBP. Submit your code and knitted R HTML file or RPubs link as instructed.

(Formula: OBP = (Hits + Walks) / (At-Bats + Walks))

# On-Base Percentage (OBP)

PlayerID <- c(1, 2, 3, 4, 5)
Hits     <- c(112, 124, 121, 106, 140)
AtBats   <- c(400, 450, 380, 500, 402)
HR       <- c(25, 22, 8, 20, 11)
BB       <- c(50, 60, 19, 150, 55)
SO       <- c(60, 65, 67, 92, 70)

baseball <- data.frame(PlayerID, Hits, AtBats, HR, BB, SO)

# OBP = (Hits + Walks) / (At-Bats + Walks)
baseball$OBP <- round((baseball$Hits + baseball$BB) / (baseball$AtBats + baseball$BB), 4)

# View the results
baseball[, c("PlayerID", "Hits", "AtBats", "BB", "OBP")]

# Player with the highest OBP
baseball$PlayerID[which.max(baseball$OBP)]

[1] 5

max(baseball$OBP)

[1] 0.4267

Results The player with the highest OBP is player 5 at 0.4267