Not sure how to answer. You begin by saying that success runs much deeper than batting averages, but if you are successful, then you should be able to quantify it in some way. OPS is my favorite offense stat. Then probably slugging pct.
But then again, stats are relative and dependent on the level of competition. Your daughter is a much better pitcher today than she was five years ago, but her college stats are probably not as good as her high school/travel stats. So another way to quantify success on the field is to measure the level of competition against which you are competent. I coached DD's travel teams for four years, and my goal was to go around .500 each season, but to measure success based on the level at which we went .500. Year One was basically entry-level, all-star+ travel ball. Year Four we played entirely A-ball. If you reach a point where ou're willing to travel far and wide and there aren't enough good teams to keep you at .500, I guess you've become pretty successful.
Absolutely. But to your point you don't go into a game trying to hit .400 or generate other quantifiable stats. So what do you as a coach use to focus your players on the specific task at hand?
BTW - You are dead on about my DD. Stats are not transitive! Although she is a much better pitcher after only 1 college season the stats took a dip. Her K's per game went from 14+ in HS and 10+ in TB to 8.5 in college. It is a very different world when 1 - 9 can hit rockets and you throw upwards of 200 innings in just 4 months.