Hi JustNum,
Cool to find another player interested in the analytical aspect of 14.1. I have developed a 14.1 scoreboard software that calculated a fair amount of statistics. You can see an example of it in action here:
https://www.facebook.com/sean.c.morgan/videos/2508176239221462/
For stats, look in between racks and at the end for the finals stats. The app is called 'Fourteen-One Engine'. While I was developing it I put a lot of thought into 14.1 stats, how to calculate them, which ones are relevant, what is getting measured, etc....
But first, to answer your questions: Asking for a rerack should definitely have no effect on the average balls per inning of player B. I cannot think of any arguments in favor of this being counted. Also this is how the app '14.1 scorer' does it.
But this is not too important because I consider the stat you call 'average balls per inning' a.k.a BPI (balls per inning) a.k.a PPI (points per innings) to be meaningless.
You give the example of a player having a BPI of 50 (extremely high). In this case, yes, you can deduce that the player did not play bad (a beginner cannot achieve a BPI of 50). But this is a very rare case. In the stats I have seen (mostly from AtLarge posts) BPI will usually be a number between 0 and 30 and it does not correlate at all with the level of the player of the quality of the performance in that match. You can see the same player having 5, 10 and then 20 for different matches.
Of course this is because safety battles will push BPI down quickly. In the example you give, let's say at the beginning there is a safety battle of 12 innings for each player. Now your BPI will be 10 instead of 50. But that safetly battle doesn't change the fact that the player ran 150 and played extremely well. How can one number of 1/5 of the other?
Which brings the question: what is BPI supposed to measure anyway? It obviously does an horrible job of measuring the quality of the offensive play of a player. It doesn't seem to say anything about the defensive play either. So yes, this is what I am getting to: BPI/PPI/'average balls per inning' does not measure anything of interest reliably and it is almost completely useless.
The stat PPASI (what you call average balls per run) is better because, at least, it focused on only one aspect: offensive play, it ignores safeties and intentional fouls. I do calculate it in my scoreboard software. But my experience with it so far is that, just like BPI, it fails to correlate well with the (offensive) performance of a player because small unimportant runs takes the number down quickly.
I think 'attempted scoring innings' is not the correct data to average over if you want to calculate a scalar that will be a measure the offensive performance of a player, mainly because the same importance is giving to small runs and big runs while this is not how we conceptualize offensive performance.
I feel the correct data to average over is the 'offensive shots taken'. The stat 'offensive play index' (the first line on the stats board of my scoreboard app) uses this strategy. 1.000 is perfection and 0.000 is a guy who misses every shot. I have scored about 25 matches with it so far and I can now say that it correlates extremely well with the offensive performance of a player. i see the same players scoring very similar OPI values values match after match.
(Note: The number between brackets is the number of offensive shots taken. This is to give an idea of how relevant the value is.)
Rough guideline for signification of values:
Beginner: 0.000 to 0.200
Amateur: 0.200 to 0.500
Good Amateur: 0.500 to 0.750
Pros: 0.750 to 0.900
Top Pros: 0.900 to 1.000
I will make a post soon describing in detail how to calculate it. I just want to have a little more data to be sure it works well. Would love to have exchanges with anyone interested in that kind of analytical stuff so comments/questions are welcome.