I don’t quite agree with your stats that a dry break should count as a missed shot. I think break statistics, as important as they obviously are, should still be kept separate from shotmaking stats after the break. For instance, what good is it to make 3 balls on the break if you have no shot, as opposed to making one ball on the break and having an ideal layout with a high percentage first shot?
For that matter, safety/defensive shots should also be kept separate. If anything, a poorly executed safety should count the same as a missed shot, and a 2-way shot which even if missed if it leads to a good safety, should not count as a missed shot. It takes a lot of work to compile such detailed stats, but there is certainly some subjectivity and debate involved in completely and accurately evaluating some shots.
About dry breaks being counted as a missed shot, I can completely understand the logic behind your concerns. Our reasoning is that a break shot is still, nevertheless, a shot. By our data, players make this shot roughly 73% of the time and if we count it as a made shot, then the converse should also be true. This is why we include the stat
Adjusted Shooting Percent, which can be calculated one of three ways. More on that later. To be short about it, this percentage doesn't count dry breaks as a missed shot in it's calculation, therefore adjusting it for people who share a similar concern as you (and we) do.
Safety/defensive shots
are kept separate and factor into the calculation of Shooting Percent and adjusted shooting percent. We wrote a paper about the Quasi-subjectivity of pool game data collection. Briefly, what seems subjective at first, is really an educated guess (scientific method?) and through data analysis we can adjust this "subjectivity" to become objective. That's the reason for us coining the term Quasi-subjectivity. If you want to know how effective a player's safety play is, we have a stat for that:
Defensive Success Rate (DSR)
http://poolst.at/dsr
Two-way shots are always calculated in favor of the player. That is, if he/she was attempting to pot a ball, but it is relatively clear by all parties that not making the pot will, most likely, leave an advantageous safety shot, the stat is recorded as such. We have documented all this in previous write-ups that you can find on our website.
I hope that may clear up some of your concerns as there are many to meditated on and we appreciate you asking these as it gives us food for thought.