Basketball Probability Problem

Introduction

You are the head coach to the Massachusetts Manatees - a youth basketball team that is playing for the state championship. 

Task

Throughout the season, your team shoots 33% from three and 47% from two. In order to best optimize our score, would we rather shoot all 3s or all 2s?

Process

Find the expected value of shooting 100 shots:

For 3 points at 33% per 100 possessions - they would make 33 shots

33 * 3 points = 99 expected points

 

For 2 pointers at 47% per 100 possessions - they would make 47 shots

47 * 2 points = 94 expected points 

Evaluation

Showing work for 3 pointers - 1 point 

Showing work for 2 pointers - 1 point

Correct EV for 3 - 1 point

Correct EV for 2 - 1 point

 

4 total Points 

Conclusion

In a bubble - this team has a better expected value when they shoot from 3 and would have their best chance to win the game if they shoot 3s.

 

Though prompt - why don't NBA teams that shoot a high percentage from 3 only shoot 3's all game?

Credits