Question

The Grizzlies are a basketball team. Collectively, the team makes 36% for 3-point shots, and 50% from long 2-point shots. They currently take as many long-range 2-point shots as 3-point shots in each game. One of the coaches has been arguing that the team should take more 3-pointers, given these percentages. Assume that if they take more or less 3’s or 2’s, the percentage they make will not change. Apply the concept of expected value to this example and to settle the dispute among the coaches. Your answer should explain what expected value is and explain whether the team would be more successful – would they score more points in a game – if they took more or less threes.

Answer 1

Here, the expected value is the expected number of point that they would score while attempting a shot, be it a 3-point or a long 2-point. Now, we will calculate the expected value by multiplying the value of the shot and their respective probabilities and then adding up. Hence, the expected value = (0.36 * 3) + (0.50 * 2) = 2.08 points.
Since the expected value is 2.08 points, this means that, on average, the team would score 2.08 points while attempting a shot. This also means that the team have to take more 3's, so that the expected value of each shot that they attempt becomes closer to 3. This will help to achieve higher scores per match, hence, enabling them to win more matches and ultimately the tournament.