In-class Activity 14

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.

#Three-Pointers Made: 
three_made <- c(4, 5, 3, 6, 7) 

#Three-Pointers Attempted: 
three_attempted <- c(9, 10, 8, 11, 12)

three_made

[1] 4 5 3 6 7

three_attempted

[1]  9 10  8 11 12

avg_game <- round(three_made/three_attempted,3)
avg_game

[1] 0.444 0.500 0.375 0.545 0.583

overall_avg <- round(mean(avg_game),2)
overall_avg

[1] 0.49

avg_total <- round(sum(three_made)/sum(three_attempted),3)
avg_total

[1] 0.5

overall_avg represents the unweighted average of the per-game percentages. It treats a game with 8 attempts the same as a game with 12 attempts.

avg_total represents the true cumulative shooting percentage. It weights each attempt equally, making it the standard metric for sports analytics.

When you take the mean of the avg_game vector, you are treating every single game as an equal data point, completely ignoring the volume of attempts. Because the sample size (three-pointers attempted) changes from game to game, calculating an average of these percentages skews the result. For example, if a player goes 1 for 1 in Game A (100%) and 2 for 10 in Game B (20%), this unweighted calculation suggests their performance is 60%. It disproportionately rewards low-volume, high-efficiency outliers.

By summing all the makes and dividing by the sum of all attempts, you are calculating a weighted average. This treats every single shot attempt as an equal event, regardless of which game it happened in. Using the same extreme example above, 3 total makes on 11 total attempts results in a 27.2% true shooting percentage. This reflects the reality of the player’s total efficiency.