Basic Question

[Ben Gibson]

I'm new to the world of advanced stats, or at least learning to do them myself. I currently write for 8 Points, 9 Seconds.

I'm working on a post about the Pacers trying to play faster next year. When I had a friend run their 2014-15 numbers through SPSS, he said that it looked like for every possession added for the Pacers, they're chances of winning went down almost 1%.

I'm still working on it with him, but is it common for teams to see a strong negative correlation with a faster pace?

[Nolan Goeken]

If the team is worse than the opponent, yes, as it creates more opportunities for the opponent to "prove" it is better.

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[Harrison Brown]

In more rigorous statistical terms: think of the number of points scored in a possession as a random variable. If these random variables are independent and identically distributed, then their sum -- i.e., the total number of points the Pacers score -- will follow an approximate normal distribution by the central limit theorem. Now, the expected value of total number of points will increase linearly -- it'll be the Pacers' offensive rating (divided by 100) times the number of possessions. But the standard deviation of the total number of points will increase like the square root of the number of possessions. In relative terms, the variation around the average gets smaller as you add more possessions. The same process goes for the opponent.

An intuitive way to think of it: If you flip a coin 10 times and get 7 heads, that's not really surprising. If you flip a coin 1000 times and get 700 heads, there's probably something wrong with your coin. 

Now, in practice, the random variables possession_1, possession_2, etc., are neither independent nor identically distributed. But they're close enough that the logic more or less goes through; the standard deviation of the Pacers' and their opponents' expected score will grow more slowly than the difference between the expected scores, and it becomes harder and harder for the worse team to win.

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[Ben Gibson]

I guess I meant to add that the negative correlation was with their offensive rating more than anything else. As the game gets faster, the Pacers offense gets worse (Offensive Rating), and as Nolan put it, that creates more chances for other teams to prove they are better.

[David Searle]

I ran a factorial regression using sigma-restricted coding, and it came out looking like this:

David Searle

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