Using Markov chains for basketball
The NBA hackathon application process asked a fun question that I got excited about:
Given that the Warriors win a game with probability 0.800, what’s the probability that they play an entire 82-game season without consecutive losses?
I modeled the season as a Markov chain. There are 3 states:
W transitions to itself with and
L with .
L transitions to
W with and
2L with .
2L transitions to itself with . This results in the following transition matrix: where the columns represent the “source” states and the rows are the “destination” states. We start off with of being in state
W, of being in state
L, and of being in state
2L, so and we need to solve for .
Therefore, the probability of the Warriors never losing consecutive games is .
If you loosen the assumption and tried to model their season as a function of their opponents, their rest schedule, etc. that would be much more difficult. You would need to use some more involved ML techniques.