Tuesday, July 2, 2013

Keys to win a basketball game

This is a famous quote about basketball,

Offence sells tickets, defences wins games, rebounding wins championships - Pat Summitt

In fact, if we try to translate the game of basketball into mathematics (very naively) we have the following equation.

\( \begin{align} \text{Score advantage}_x &= \text{Possession}_x \times \text{Probability of Scoring}_x - \text{Possession}_y \times \text{Probability of Scoring}_y\\ &= [\text{out of bounds}_x + \text{rebound}_x] \times \text{Probability of Scoring}_x\\ &- [\text{out of bounds}_y + \text{rebound}_y] \times \text{Probability of Scoring}_y\\ &= [\text{out of bounds}_x + \text{rebound}_x] \times \text{Probability of Scoring}_x\\ &- [\text{out of bounds}_y + (\text{total rebound} - \text{rebound}_x)] \times \text{Probability of Scoring}_y \end{align} \)

From the equation we can see that a good scoring team has a high probability to score, while a good defensive team reduces the opponents ability and probability to score. Yet, we can see that the rebound appears on both end where a rebound for team x is one less rebound for team y. Which modifies the number of possession giving more chance to attack and a potentially larger score advantage!

Of course, rebounds can be offensive and defensive and they are a function of your and your opponents scoring ability. The events are inter-connected and should be modelled as a chained event. Maybe I'll do that when I recover from my hang-over.

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