Final Exam Sports analytics

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(8, 7, 6, 9, 10) Field Goals Attempted: c(15, 12, 18, 14, 13)

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

# Define the vectors representing the field goals made and attempted 
field_goals_made <- c(8, 7, 6, 9, 10)
field_goals_attempted <- c(15, 12, 18, 14, 13)

# Calculate the field goal percentage for each game
field_goals_percentage <- field_goals_made / field_goals_attempted * 100
#Print the average field goal percentage per game
field_goals_percentage

[1] 53.33333 58.33333 33.33333 64.28571 76.92308

Answer a)

We can see that the field goal percentage for each game respectively is

Game 1: 53.33%, Game 2: 58.33%, Game 3: 33.33%, Game 4: 64.29%, Game 5: 76.92%

# Calculate the average field goal percentage of all games combined
average_field_goals_percentage <- mean(field_goals_percentage)
#Print the average field goal percentage of all games 
average_field_goals_percentage

[1] 57.24176

Answer b)

We can see that the average field goal percentage of all 5 games combined is 57.24%

57.24%

Question 6

Consider the following vectors representing the number of three-pointers made and attempted by a basketball player in five games:

Three-Pointers Made: c(4, 5, 3, 6, 7) Three-Pointers Attempted: c(9, 10, 8, 11, 12)

Calculate the three-point shooting percentage for each game and select the correct average three-point shooting percentage for the five games.

# Define the vectors representing three-pointers made and attempted
three_pointers_made <- c(4, 5, 3, 6, 7)
three_pointers_attempted <- c(9, 10, 8, 11, 12)

# Calculate the three-point shooting percentage for each game
three_point_percentage <- (three_pointers_made / three_pointers_attempted) * 100
three_point_percentage

[1] 44.44444 50.00000 37.50000 54.54545 58.33333

Answer a)

We can see that the three-point shooting percentage for each game respectively is

Game 1: 44.44%, Game 2: 50%, Game 3: 37.5%, Game 4: 54.55%, Game 5: 58.33%

# Calculate the average three-point shooting percentage for the five games
average_three_point_percentage <- mean(three_point_percentage)
average_three_point_percentage

[1] 48.96465

Answer b)

We can see that the average three-point shooting percentage of all 5 games combined is 48.97%

48.97%

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             120       400           15          40     80

2             140       450           12          50     75

3             110       380            8            30    60

4             160       500           20          60     90

5             130       420           10          45     70

Compute the on-base percentage (OBP) for each player and select the player with the highest OBP.

1. Player 1 b) Player 2 c) Player 3 d) Player 4 e) Player 5

To calculate OBP, you can use the following formula:

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

data <- data.frame(
  PlayerID = 1:5,
  Hits = c(120, 140, 110, 160, 130),
  At_Bats = c(400, 450, 380, 500, 420),
  HR = c(15, 12, 8, 20, 10),
  BB = c(40, 50, 30, 60, 45),
  SO = c(80, 75, 60, 90, 70)
)

data

data$OBP <- (data$Hits + data$BB) / (data$At_Bats + data$BB)
data$OBP

[1] 0.3636364 0.3800000 0.3414634 0.3928571 0.3763441

Answer a)

We can see that the on-base percentage (OBP) for each player respectively is

a)Player 1: 0.364, b)Player 2: 0.38, c)Player 3: 0.342%, d)Player 4: 0.393, e)Player 5: 0.376

# find the player with the highest 
player_with_highest_ <- data$PlayerID[which.max(data$OBP)]

# print player with the highest
player_with_highest_

[1] 4

We can see the player with the highest OBP is number 4

Player ID 4