The existence of one type of statistic does not preclude the determination of, and discussion about, another stat. Other sports have added to the list of stats many times.
Yes, traditionally, "balls per inning" was the reported stat. But, as other posters have noted, that stat gives quite a limited picture of what happened in the game. It's also a misnomer, because the numerator is points scored rather than balls pocketed. For example, a player may have made 175 balls to end up with 150 points.
Why not look at it in more than one way -- with and without counting safeties and intentional fouls in the denominator? When I reported stats for the Accu-Stats "Make-It-Happen" 14.1 Invitational 5 months ago, I calculated two scoring averages for each player for each game. Here's what I said in that thread:
"In the following stats, the term
Attempted Scoring Innings means the player's total number of innings for the game minus the number of innings that he played only a safety or an intentional foul (no attempt to score a point).
PPI is Points per Inning based on the total number of innings in the game for that player. [Note: I am calling this measure Points per Inning rather than Balls per Inning to be a bit more precise in the definition.]
PPASI is Points per Attempted Scoring Inning, i.e., points per inning based on the number of Attempted Scoring Innings in the game for that player."
Obviously, the two measures can produce quite different results. Here is that thread again:
http://forums.azbilliards.com/showthread.php?t=330023
[Note: A third measure is
Points per Scoring Inning, which would be total points divided by the number of innings in which points were scored. I preferred to also count innings that consisted simply of one missed shot, hence my
Points per Attempted Scoring Inning.]