[Roberton3]

Points per play isn't a good metric for an offense (or a defense).  Consider two different offensive styles: one that gains yards a few at a time, and one that relies on a few explosive plays.  Suppose each offense scores an average of exactly 4 points per possession, but the explosive-play offense averages 5 plays per drive and the a-few-at-a-time offense averages 15.  Is the explosive-play offense 3 times as good as the a-few-at-a-time offense?  Of course not.  Each offense is scoring the same number of points on average before giving the ball back to the opponent.  So they're roughly equally good (which is not to say that they're exactly equivalent -- for example, if you're behind late in the game, you'd rather have the explosive-play offense, and if you're ahead you'd rather have the a-few-at-a-time offense -- but they're roughly comparable).  Using points per play makes the explosive-play offense look artificially better than it really is.

Similarly, points per game isn't a good metric.  A hurry-up offense scores a lot of points per game, but also gives the opposing team a lot of possessions -- i.e., a lot of opportunities to score.  So using points per game makes a hurry-up offense look artificially good (and makes that team's defense look artificially bad).

If you want one points-related statistic, points per possession is the best single measure, because regardless of what style you play, for every possession your team gets, the other team gets a possession (with the exception of end-of-the-half drives).

[Roberton3]

Points per play isn't a good metric for an offense (or a defense).  Consider two different offensive styles: one that gains yards a few at a time, and one that relies on a few explosive plays.  Suppose each offense scores an average of exactly 4 points per possession, but the explosive-play offense averages 5 plays per drive and the a-few-at-a-time offense averages 15.  Is the explosive-play offense 3 times as good as the a-few-at-a-time offense?  Of course not.  Each offense is scoring the same number of points on average before giving the ball back to the opponent.  So they're roughly equally good (which is not to say that they're exactly equivalent -- for example, if you're behind late in the game, you'd rather have the explosive-play offense, and if you're ahead you'd rather have the a-few-at-a-time offense -- but they're roughly comparable).  Using points per play makes the explosive-play offense look artificially better than it really is.

Similarly, points per game isn't a good metric.  A hurry-up offense scores a lot of points per game, but also gives the opposing team a lot of possessions -- i.e., a lot of opportunities to score.  So using points per game makes a hurry-up offense look artificially good (and makes that team's defense look artificially bad).

If you want one points-related statistic, points per possession is the best single measure, because regardless of what style you play, for every possession your team gets, the other team gets a possession (with the exception of end-of-the-half drives).