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How much a shot is worth on the basketball court depends on the shooter’s location and whether or not he’s drawn a foul. But is the number of points a shot is worth the best way for a player to decide which type of shot to make?

In this lesson, students use probability and expected value to determine how much 3-point and 2-point shots are “worth” to different NBA players. They also model foul shots as independent events, and identify players for whom the best option is a trip to the free throw line.

### Students will

• Use NBA statistics to calculate the probability of making a 3- and 2-point shot for different players
• Calculate the expected value of 3- and 2-point shots for different players
• Calculate the expected value of drawing a foul when attempting a 2-point shot
• Compare expected values to identify a best option when shooting for different NBA players

### Before you begin

Students should be familiar with the concept of probability as a ratio of successes to trials (e.g. if a player made 272 3-pointers in 600 attempts, his probability of making a 3-pointer is 272 ÷ 600 = 45.3%.) Familiarity with expected value will also be helpful. Finally, students should know what it means for events to be independent and be able to calculate the compound probability of independent events. For example, if a player makes 90% of his free throws, the probability of him making two free throws in a row is 0.902 = 0.81.