I get that FGA + (0.47)FTA + TO - OREB only measures FGA + (0.47)FTA + TO - OREB. But that equation is the core, the starting point, of all non +/- metrics. Every metric uses that number, as you said, to define offensive and defensive efficiency. But it also uses it to 'count' the actions within a possession, and to define what a possession is. My question why? Why that number? Does that actually measure a possession more effectively than FGA + (0.47)FTA + TO? IF we have counted possessions inaccurately, then ALL non +/- statistics are also inaccurate.
Basketball is different than many other sports. In hockey or soccer, we talk about possession time, not numbers of possessions. That makes sense, because a single team could theoretically control possession of the ball for the entire game. In basketball, though, every time you make a shot you give your opponent the ball. Basketball is more like football in that sense, in that it's about taking turns trying to score. You get the ball, and you're trying to score a bucket before the other team gets the ball. Those are the only two possible outcomes, except at the ends of quarters: either you score (after some number of dribbles, passes, shots, and defensive fouls), or the other team finds a way to take the ball away from you before you score (by stealing your dribble, picking off your pass, rebounding your missed shot, or getting you to commit an offensive foul or violation).
What I'm trying to explain to you is that possessions, as defined by FGA + (0.47)FTA + TO - OREB, is a statistic that only measures FGA + (0.47)FTA + TO - OREB. I've already explained why you use this definition of possession in offensive/defensive efficiency.
No, a missed shot is still a missed shot, and a rebound is still a rebound. They are measured in exactly the same way. They are valued differently. But how they are valued has nothing to do with what we're talking about. Both of those stats are individual measures, and the only time the definition FGA + (0.47)FTA + TO - OREB is used is when you are talking about team stats, not individual stats.