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Probability and Cumulative Dice Sums

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Who Controls the Pace in Basketball, Offense or Defense?

During a recent chat with basketball analyst Seth Partnow, he mentioned a topic that came up during a discussion at the recent MIT Sloan Sports Analytics Conference. Who  controls the pace of a game more, the offense or defense? And what is the percentage of pace responsibility for each side? The analysts came up with a rough consensus opinion, but is there a way to answer this question analytically? I came up with one approach that examines the variations in possession times, but it suddenly occurred to me that this question could also be answered immediately by looking at the offense-defense asymmetry of the home court advantage.

As you can see in the R output of my NCAA team model code in one of my public basketball repositories, the offense at home scores points at a rate about \( e^{0.0302} = 1.031 \) times the rate on a neutral court, everything else the same. Likewise, the defense at home allows points at a rate about \( e^{-0.0165} = 0.984\) times the rate on a neutral court; in both cases the neutral court rate is the reference level. Notice the geometric asymmetry; \( 1.031\cdot 0.984 = 1.015 > 1\). The implication is that the offense is responsible for about the fraction \[ \frac{(1.031-1)}{(1.031-1)+(1-0.984)} = 0.66 \] of the scoring pace. That is, offensive controls 2/3 of the pace, defense 1/3 of the pace. The consensus opinion the analysts came up with at Sloan? It was 2/3 offense, 1/3 defense! It's nice when things work out, isn't it?

I've used NCAA basketball because there are plenty of neutral court games; to examine the NBA directly we'll have to use a more sophisticated (but perhaps less beautiful) approach involving the variation in possession times. I'll do that next, and I'll also show you how to apply this new information to make better game predictions. Finally, there's a nice connection to some recent work on inferring causality that I'll outline.

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