A great introductory probability and stats problem I saw from Christopher Long

Christopher Long has written a little bit about some old interview questions the Charlotte Hornets asked when they were looking for quantatative analyist:

Charlote Hornets’ interview question #1

Here’s the question:

Last year the Celtics finished with the 5th worst record in the NBA. Whether it’s two years from now or twenty years from now, what pick are the Celtics more likely to land first, the #1 pick or the #5 pick? Assume that the lottery odds and structure remain the same going forward. Further assume that the Celtics are likely to improve and every year the team will either:

Improve by 3 positions (e.g. they go from 5th worst to 8th worst) with a probability of 0.6
OR fall 2 positions (e.g. they go from 5th worst to 3rd worst) with a probability of 0.4.

The question itself isn’t what caught my eye as a good introductory question, but rather one piece that you have to do to get started.

Here’s the Wikipedia page describing how the NBA lottery works:

The NBA draft Lottery as described by Wikipedia

The page includes this chart showing the probability of a team getting a particular draft pick in the lottery based on their rank at the end of the season (being ranked #1 in this chart means you finished in last place, btw):

Screen Shot 2015-10-25 at 6.33.33 PM

So, the neat introductory probability and stats problem is this – based on the description of how the NBA draft lottery works in the Wikipedia article, recreate that chart!

There are a few different ways to do it, and all, I bet, will lead to some neat conversations about probability.

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