Basketball IQ
In basketball, which shot should you take?
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.Common Core Standards
Content Standards
Mathematical Practices
Downloads
Shoutouts
NBA, Stephen Curry, Dwight Howard, Kobe Bryant, Paul Millsap
Related Lessons
Oh, Craps!
What is the likelihood of winning at craps? Students learn the rules of the popular casino game, and use probabilities to determine how likely players are to win big (or go broke).
Bracketology
What’s the best strategy for creating a March Madness bracket? Students use probability to discover that it’s basically impossible to correctly predict every game in the tournament. Nevertheless, that doesn’t stop people from trying.
Oddsballs
When is it worth buying a Powerball ticket? Students count combinations and apply basic rules of probability and expected value to determine when the Powerball jackpot is large enough to justify the cost of playing the game.
Driving Question
When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.
Going Once, Going Twice
How much should you bid in an auction? Students create polynomial functions to model the expected value of a given bid and determine the optimal amount someone should bid in any auction.
Happy Meal
How much would it cost to get all the toys in a Happy Meal? Students use trials, probabilities, and expected value to determine how many meals it takes to get a complete set of Happy Meal toys and debate whether McDonald’s should allow customers to pay a fee to choose their own figurine.
Bumpy Flight
Should airlines overbook their flights? Students use compound probability and expected value to determine the optimal number of tickets an airline should sell and discuss whether airlines should be allowed to overbook their flights.
Spin City
What’s the best way to play roulette? Students use probabilities and odds to analyze roulette payouts and debate the optimal strategy for winning the game (including not playing at all).
