Below are correlation graphs illustration a significant (albeit slightly weak) correlation between how many points one team will score and how many points their opponents will score in a given game.
This isn’t anything novel, but rather an illustration and confirmation about what you might surmise about teams that play faster score more and their opponents in turn score more, because there are more possessions over the course of the game. The Pearson’s correlation coefficients are:
(The higher value means the game scores are more strongly correlated with each other. Typically .30 is a good correlation, less than that is rather weak.)
To contrast a sport that doesn’t exhibit this, here’s a break down of the Penguin’s season two years ago (the last full season). The trend line is virtually straight and the confident interval on the trend line dips negative, suggesting there is no statistically significant correlation between how many goals the Penguins score and the how many goals their opponent’s score in a given game.
The correlation coefficient for the Penguins is .0572, which is not statistically significant. We can conclude that hockey offenses opperate essentially independent of each other.
To further analyze basketball scoring, it would be good to eliminate overtime games, and to see if the team’s correlation to their schedule is related to how good or bad they are, since over the course of a season, a team plays a rather balanced scheduled. My thinking is mediocre teams will correlate better over a course of a season versus a good or bad team.