NBA Scouts

Imagine you are an NBA scout and you have been sent by your owner to find a basketball player that will make 90% of all the free throws he will shoot next season. Here is a table so you can see how many shots a player takes a year.

  • How many do you need to see them make “in-a-row” until you make an offer to the player?

OK, now you are competing against other scouts and need to make an offer before someone else beats you to the best shooter.

  • How many do you need to see them make “in-a-row” until you make an offer to the player? That is how few made shots in a row would you accept to make an offer?
  • What distribution could we use to model this?
  • What is the R function and inputs to the function?
  • What other statement should you make to the team owner once you find your player?
  • Make a graph of the probability of missing no shots after a x number of shots are taken.

Shooting Streaks

Most of us know that Shaq played in the NBA. In fact, if we know that he played in the NBA, we also know that he couldn’t hit free throws. They invented a game strategy called “Hack-a-Shaq” that is built on his poor free throw shooting. While Shaq isn’t the worst free throw shooter, he only made about 50% of his free throws. Let’s answer the following questions using our distributions;

  • The top free throw shooters shoot over 400 free throws a year. Assuming a 52.7% free trow success rate, what is the longest series of made shots that Shaq could make in 400 shots?
  • What is the longest series he could make in 11,252 shots?1
  • Looks like he has had longer series of made shots than what our binomial distribution returns. What could we do to modify our assumptions?

Attempts in a Game

Last season Kobe Bryant left the NBA with a 60 point game. However, it took 50 shots to get those 60 points. Assuming that the average number of shots per game for an NBA player that is the primary shooter for their team is 24 shots per game:

  • how rare was Kobe’s 50 shot performance?
  • The next highest number of shots per game was Russell Westbrook at 36, where does his performance sit?
  • Make a histogram (or density plot) of a Poisson distribution with a mean of 24. What do you notice about the distribution?

  1. If someone wants to compare shaq’s free throw makes play-by-play by ripping data from this website, they could do this for their project. 123↩